This is basically a lecture on support vector machines though you would see on the screen the title statistical learning theory. Let me tell you a bit of history, there were two statisticians named Wapnick and Chervonenkis they are the main persons who created this subject statistical learning theory, they are statisticians from Russia, you know there was a cold war period between America and Russia and these people have done their work basically during the cold war period and after the cold war was over after then there were communication between Russia and America they became normal. These people they went to United States and they presented the statistical learning theory in a conference in computer science, in a computer science conference they presented this one the basic problem that they attempted to solve here is when you design a classifier you have a training set using the training set you design the classifier then using the test set somehow you measure its performance and then if the performance on the test set is also satisfactory then you say that fine everything is fine with the classifier but is it really fine with the classifier even if it does well on the test set how do you say that your classifier is generalizable the performance of the classifier that you have somehow got how do you say that it has generalization capability is there any mathematical way of expressing it and if you express it mathematically is there any way of obtaining it and if you also obtain it then for the different classifiers that we are using is there any way in which you can calculate the generalizability of this classifier. So this is the basic question that they attempted to solve there since they are statisticians and they attempted to solve the whole thing using statistical language so they coined the term statistical learning theory support vector machines which probably you have heard from many people is sort of a byproduct of statistical learning theory sort of a byproduct of statistical learning theory this is the basic history and you will find a book by Wapnick on statistical learning theory which is basically a book on statistics and you will find support vector machines being considered a part of neural networks you will find them to be considered a part of machine learning and data mining and of course since we are talking about classifiers and their performance you will consider them to be a part of pattern recognition. So you will find support vector machines almost in all these fields you will find support vector machines in all these fields and the generalization of support vector machines like kernel machines etc this is sort of the basic little bit of history now let me try to explain the basic terminology you look at your screens first one is you are given points in capital N dimensional space okay you are given small n points x1 x2 xn you see the very first step you are given small n points x1 x2 xn they are in capital N dimensional space ?i denotes the label of the class label of the point xi I am assuming that you have two classes only and the class labels are given as – 1 and 1 and px ? small px ? this is a probability distribution on the data that means there is some probability distribution this is the small p is the density function and capital P that is the actual capital P of a is equal to integral of small p integral over a of small p small p is the density function and capital P is the actual probability now these points are x1 x2 xn and the corresponding ? is they are assuming they are assumed to come from the distribution px ? where px ? is not known and here it is written they are IID independent and identical distributed now in classification what exactly is the problem the problem is you are given n points small n points and you have a corresponding class labels somehow you need to find the function from xi to ?i are you understanding it somehow you need to find the function if you find the functional form which for every xi if it gives you if you find you find the functional form where for every xi the function gives the value ?i then you are done you need to find the corresponding functional form that is the basic problem of classification these f's you can call them as you can have many names for it okay and some f's when for one class it will give you plus one another class they are going to give you minus one and at some place they will get the value 0 if when the value is 0 then you call it as the separation between the class 1 and class minus 1 right when the value is given as 0 then you call it as separation between the class plus one and between the class plus one and minus now what is it that we are given we are given a set of functions script f that is the functions are small f xs are the input a a is the parameter set a bar it is written it is the vector form so all these alphas are adjustable parameters and f is a function actually let me just try to explain it to you I hope all of you know what multi-layer perceptron is you have an input layer and you have some hidden layers you have an output layer when you are going from input layer to hidden layer you have several connections and you have connection weights you start with some initial connection weights from input layer to hidden layer one hidden layer one if you assume two hidden layer and hidden layer one to hidden layer two then hidden layer two to output layer at between every two such layers you have many connections and you have connection weights put all the connection weights together and write it as a vector form that vector you take it as alpha that vector you take it as alpha okay and xs are your input okay given an x and given an given an x given an x and given an alpha and you have the usual neural network which is feed forward neural network it will give you an output the output is this f okay given the set of in given the given the set of input x1 x2 xn input vectors given alpha the adjustable parameters then if you apply your neural network methodology the output is f okay these are the adjustable parameters and f is a function now if you change is the alphas if you change is alphas the corresponding f is going to I mean the values are going to be changed if you change your network architecture then f is itself is going to be changed so for a given input x and choice of alpha f of x alpha will always give the same output if you have a function f and if you have specified your alpha f of x alpha will always do the same output a particular choice of alpha generates a train mission why this particular choice when you are training a neural network you start with some some choice and you go on changing it till by the end of your I mean you have given some rule for termination and when it terminates you assume that you have got a nice I mean values for alpha so you are training the machine to get nice value for this alpha in neural network with a fixed architecture course with alpha corresponding to the weights and biases is a learning machine now when you have a function f when you fix alpha what is the exact risk that you are taking the risk is it is observed is f of x alpha expected is the actual one is ? take the difference take the difference modulus and dpx ? do the integration over all these excess that will give you sort of error or risk what is it that we are calculating what we are calculating is ?i for the ith point for an alpha ?i is the targeted output f of xi alpha is your observed output the difference i is equal to 1 to n and 1 by 2 n this is empirical risk this is what actually we are calculating what we are supposed to calculate is this here I need to tell you one thing I need to tell you one thing all these things are explained here using the sign modulus and the similar results actually you will get when you take the square terms when you take the square terms which in neural network when you try to minimize the error you take the square terms and then you take the double summation you use some gradient descent and then you do that try to do the minimization okay there you take the square term for the error okay any of the results are similar okay so here everything is explained using the sign modulus this is one thing that I am telling you there is another one you will get them all this material from a famous lecture notes or I do not want to call it lecture notes it is tutorial it is written by Christopher Burgess it is available on internet okay a tutorial on support vector machine whatever I am going to tell you about the support vector machines most of it you will find you will get from that particular tutorial okay now so this is the risk that we are calculating and the actual risk that we are supposed to calculate is RF alpha now choose eta so that 0 less than or equal to eta less than or equal to 1 here I am sorry this less than or equal to sign should not be there it should be strictly less than 1 okay in fact I would prefer that the other less other equality also should not be there 0 than eta strictly less than 1 this equality signs should not be there okay then what was proved by Wapnick was the actual risk that we are supposed to calculate it is less than or equal to the empirical risk plus square root there is an h here log 2n n is the number of points divided by h plus 1 minus log eta by 4 by n with probability 1 minus eta that means this relationship holds with probability 1 minus eta this was what was shown by Wapnick this was I think in the year 1983-84 or is it 93-94 I am not exactly sure 83-84 or 93-94 this thing was shown okay now if you look at this expression note that in neural networks we are trying to minimize this empirical risk we are trying to minimize this empirical risk but what we are supposed to be doing is we are supposed to be minimizing the actual risk okay actual risk if we minimize it actual risk if we minimize it then that is the thing that we want to do it but by minimizing the empirical risk are we actually able to minimize the actual risk the problem is that after minimizing the empirical risk still this much term is there still this much term is there and the actual risk is less than or equal to this plus this this relationship is holding with probability 1 minus eta now if we want this relationship to hold then probably we need to take the value of eta to be very very small suppose we take it to be 0.05 then RF alpha less than or equal to empirical risk plus this that will happen with probability 0.95 so usually people take the value of eta to be either 0.05 or some 0.01 some very very small value now there is an unknown term here the term is H n is the number of points eta is this parameter 0.05 or I mean point yeah point 0.05 or 0.01 n is the number of points and there is this H what is this H H is a non-negative integer this is called VC dimension Vapnik VC for Vapnik Chervon in case this is a non-negative integer H is called VC dimension it has to be always an integer it cannot take fractional values this H provides what is known as capacity we will come to what this H is slightly later eta is a small value say 0.05 now let us denote this term this one square root of H log to n by H this whole term let us denote it by Xi okay this Xi is independent of the distribution P so in this one in this Xi eta is a constant that we have already fixed n is the number of points so the only term is H this H is a non-negative integer in fact H is independent of distribution what is this VC dimension we will define define it slightly later this is something independent of this is independent of the distribution of the points. So the whole Xi is independent of the distribution P Xi is called VC conference now if we know H we can compute now learning machine is another name for a family of functions f we take that the machine which minimizes the right hand side of one this is the right we actually we minimize this this is something independent of that independent of the independent of the distribution and we minimize this and by minimizing this we hope that RF alpha and empirical alpha they are somehow very close now let us see what the VC dimension is VC dimension it is actually a nice quantity Xi theta i they are the given points they belong to Xi they belong to Rn and you have n number of points theta is they take values – R1 and these are the family of functions under consideration now if you have small n points in how many different ways you can label them to power in different ways do you agree to that if you have small n points you can label them in two power in different ways that is all the points you put it in class 1 that is one way one point you put it in class 1 the rest and my sorry one point you put it in class – 1 rest n – 1 you put it in one point all the points you put it in class 1 that is one way n – 1 points you put it in class 1 1 point you put it in class 2 then n – 2 points you put it in class 1 1 point you put it in class 2 if you do like this you have 2 power n different ways in which you can label n points. Now a set of functions tau is set to shatter n points a collection of n points if for every labeling of these n points we can get a function f which provides that labeling is this clear to you let me try to explain you you have you have a set of functions you have a set of n points this set of n points can be labeled in 2 power n ways for every labeling you need to get a function note that when I started this lecture I asked you what is our aim from the set of points you need to get a function to ?i the corresponding labels once we get a function then we are through our aim is just to get that function okay. Now you have got 2 power n different labeling is possible okay for each labeling if you have a function which gives that labeling then we say that this set of functions is set to shatter n points I will explain it to you slightly more in a more detail after a few minutes. Now VC dimension for a set of functions is defined as the maximum number of points that can be shattered by this VC dimension is the maximum number of point that can be shattered by suppose the maximum number of points is 10 that means a set of 10 points if it is shattered by the collection of functions and no set of 11 points 11 points or 12 points or 13 points or 14 points no set of 11 points or 12 points or 13 points or 14 points can be shattered by the set of functions then the VC dimension then the VC dimension of the set of functions is that value 10 VC dimension for a set of functions is defined as is defined as the maximum number of points that can be shattered by ? VC dimension is H implies there exists one set of H points that can be shattered by ? but it does not mean that every set of H points can be shattered by it it does not mean that every set of H points can be shattered by it I will explain all these things by using an example now I can do the example on the board I will do the example on the board okay I can do it on the board suppose you take set of straight lines suppose you take set of straight lines and you take two points your function ? your set ? is all possible straight lines all possible straight lines okay and let us say we are in two dimensional space let us say we are in two dimensional space now you take two points how many labelling are possible you have four labelling okay now you take one straight line here and this arrow denotes they are the given the sign positive sign that means all these both the points they are in the class plus one this is the straight line that is giving you this now the second one for the same two point this is another straight line that is putting this point in class one this point in class minus one for the same two points we have a straight line which puts this point in class one this point in class minus one and you have the fourth one both the points are in class minus 1 and this side is class plus 1 is this clear. So two points they can be shattered by the set of straight lines I have taken these two points like this I could have taken them like this I could have taken these two points in this way I could have taken these two points in this way I could have taken these two points in this way in any way I take okay every set of two points it can be shattered by set of straight lines am I correct every set of two points now what I will do is that instead of two I will take three I will take three this is one two three five eight here first I will put all of them in class one all the three of them in class one then I will start putting two points these two points are in class one these two points are in class one and then these two points are in class one okay now I will put one point in class one this is in class one this is in class one this is in class one then I will put no point in class one for this one no point in class one so here I have taken a set of three points this is one set of three points this is shattered by all the lines this is shattered by the set of possible lines is this clear now let us see whether every set of three points can be shattered the answer is no the answer is no you take three points on a single line let us say this point goes to minus one these two points are plus one can you get a single straight line which gives you this result no okay so now here you have a set of three points that can be shattered by straight lines now you take any set of four points take any set of four points no set of four points can be shattered by straight line no set of four points can be shattered by straight line you have this famous example you remember this example Now you are seeing the connection between this one and neural networks many persons when they introduce support vector machines they I mean they into when I introduce this one they first tell this example and then they go to all the shattering and other things in fact this can be proved mathematically that no set of four points can be shattered by straight line so in R2 for the set of straight lines the VC dimension for the set of straight lines is 3 let me repeat in R2 the VC dimension for the set of straight lines is 3 because there exists a set of three points that can be shattered by the set of straight lines a set of three points okay and no set of four points are anything more than four can be shattered by set of straight lines okay so VC dimension for the set of straight lines is 3 this is the one so in two dimensions how consists of all straight lines this is the example VC dimension of straight lines is greater than or equal to 3 then note that VC dimension of straight lines is not four because no set of four points can be shattered by this one so VC dimension is 3 now it can be proved that VC dimension of hyper planes in Rn is n plus 1 VC dimension of hyper planes in Rn is n plus 1 that means if you are looking at Rn and if you are looking at all possible hyper planes then you will be able to get a set of n plus 1 points which can be shattered by these hyper planes and no set of n plus 2 or n plus 3 or n plus 4 points can be shattered by it why this shattering is important the shattering is important because note that in MLP we assume an architecture okay we assume an architecture and then we make it learn now the moment you assume an architecture you have assumed certain functional form right you have assumed certain functional form now with that functional form by varying all those alphas the given set of x1 x2 xn that for the given set of points if you are not able to forget about given set of points if you can if you are in a position to shatter at least a set of n points then probably we can think about getting the classification properly for the given set of n points let me repeat if the with the function under consideration if you are able to shatter at least a set of n points say you are given smaller number of points then we can think of whether we can shatter the given set of n points the given set of n points it has two classes some labeling is there and you are assuming a functional form by assuming an architecture you are assuming a functional form by assuming an architecture you are assuming a functional form whether this functional form whether it at all can it shatter at least a set of n points if it is not able to shatter it whatever you do I mean it is not going to I mean if the VC dimension is less than that then you have a problem are you understanding me if the VC dimension is less than the value small n then you do have a problem now there are some comments it is not necessarily true that learning machines with more parameters will have a high VC dimension and learning machines with less parameters will have low VC dimension examples exist in literature the second one is that a family of classifiers will have infinite VC dimension if they can shatter a set of n points however large n may be okay now examples exist in literature where a set of functions has infinite VC dimension but they are not able to shatter a set of four points here I wrote set of finitely point finitely many point the example that was given there was for four points it has infinite VC dimension but on the other hand a finite point set having just four points it is not able to shatter why the problem is that if you have a set of n points that can be shattered by the given function set then the VC dimension is at least equal to that value smaller a set of n point we are not saying that every set of n points is to be shattered so VC dimension by the very definition it is a very weak one I hope you are understanding this it is very weak because you are satisfied if it shatters a set of n points one set of n points if it shatters you are satisfied but then our given point set that also has n points but then one set it can shatter but this need may not be able to shatter then you have a difficulty here right then you have a difficulty here this is one of the problems that is actually I mean because VC dimension as per definition it is a very weak one yes if VC dimension is 10 means at least one set of 10 points it can shatter so if it is something 11 12 or 13 you know that you probably may not get the what is that you may not get the classification that is there but VC dimension 10 means 8 9 8 7 6 whether you can get the classification of this 8 7 6 point that is not clear something more you know that you cannot get it but something less than that you do not have an idea that is the basic difficulty with VC dimension that is the place where theory needs to be developed it should be something more strong than that that a set of points can be shattered these I do not want to delve into these things theory connecting SVM to structural risk minimization principle is not dealt here so I do not want to deal with these are extremely extremely highly mathematical subjects these are highly mathematical subjects and I do not want to go into all those mathematics at least now now maximum margin classifier so I do not want to go into the connections between the VC dimension theory and SVM I am directly coming to SVM so you have x i is ? i is equal to 1 to n ? i belongs to – 1 to plus 1 x i is r in Rn now I am assuming that data is linearly separable that means there exists a hyperplane which gives you on one side of the hyperplane you will get the positive points plus one point and on the other side of the hyperplane you will get negative point that is – 1 point now there is a basic theorem here if the given data set is linearly separable the given data set is linearly separable if and only if the convex hulls of those things do not intersect I hope you know this result okay I will repeat it the data is linearly separable that means the plus one point set and the – one point set they are linearly separable that there exists a hyperplane where on the positive side of a hyperplane you get all the plus one point on the negative side of hyperplane you get all the – one point this is possible if and only if you take all the positive points can construct its convex hull take all the negative point construct its convex hull then this convex hulls they do not intersect this is if and only if that is if the convex hulls do not intersect then you get a hyperplane and if you get a hyperplane then the convex hulls do not intersect both these things are satisfied so data is linearly separable so there exists a hyperplane W okay so W' XI greater than 0 for all I for which ? is equal to 1 less than 0 for all I for which ? is equal to – 1 or you multiply by ? I then ? I times these W' XI is greater than 0 for all I for when ? I is equal to 1 1 times W' XI that is greater than 0 when it is – 1 – 1 times this is also going to become greater than 0 so if there exists one such vector W for which this is greater than 0 this place this I and this I they should be replaced by prime transpose then there are infinitely many such vectors how does one choose one optimal classifier I hope this is known to all of you if you have one hyperplane then you are going to have infinitely many hyperplanes you are going to have infinitely many hyperplanes if you look at the basic the hard limiting simple perceptron okay simple perceptron then in the convergence theorem in the simple perceptron you assume the linear separability of the classes and you assume a hyperplane and you go on changing it till you go on changing it and then you can prove that as the number of iterations increases the error actually I mean it goes to actually 0 that can be shown mathematically that is called perceptron convergence theorem and so and you have too many hyperplanes it will go to one of the hyperplanes now here the question is how does one choose an optimal classifier optimal from the point of view of what now if there exists W such that ? I x W' XI is greater than 0 for all I then you take any ? x any ? then ? W also satisfies this condition okay then what we can do is that what we can do is that we shall set the margin that is minimum distance of hyperplane to the positive point same as minimum distance hyperplane to the negative point that is positive points and negative points we shall set the margin as one and achieve it with minimal weight now let us see the meaning of that let us see the meaning of that now you please look at it here you have two classes in this class 1 2 3 4 5 6 points in this class 1 2 3 4 5 6 7 points two classes now this is one hyperplane with respect to this plane this hyperplane you take the distance of this hyperplane with everyone of the point find out the one that has the minimal distance the minimal distance is this again with respect to this hyperplane find out the distance of this hyperplane with everyone of the point find out the one that has the minimal distance the minimum distance is this okay now you can choose this hyperplane in such a way that this is the shift is 1 and this shift is 1 okay this shift is 1 and this shift is 1 so that this totally it becomes 2 and the distance is actually 2 by norm of the weight weight norm of the vector okay it is 2 by norm of the vector now basically if you take this this distance is some value but then you look at this hyperplane this hyperplane when you take the distance of this hyperplane with everyone of these points the one that has the minimum distance is this and for this hyperplane again you do the same thing here the one that has the minimum distance is this now this is more than this this distance is more than this so basically what we would like to do is that we would like to choose a hyperplane in such a way that for that hyperplane with the same shift that you get a negative point and the same shift then you should get this positive point so that then basically you are going the distance between these two is 2 by actually norm of F norm of W where W is the W gives you the equation for this hyperplane that W prime X okay W gives you the equation for this hyperplane similarly in this case also W gives the equation for this hyperplane okay now you are what we would like to do is we would like to maximize this or another way of putting it is norm of W is same as W prime W and you take the square root then you will get the norm so you like to maximize this because you want to take the distance to be same a distance to be the maximum its maximization of this is same as minimization of this you want to maximize the margin maximize the distance between this and this the distance between this and this is taken as the margin and this classifier there is another name for it that name is maximum margin classifier the word margin is used as the distance between this hyperplane and this hyperplane the distance between this hyperplane and this hyperplane here if you take the distance between this and this hyperplane this will give you some margin here and this will give you another margin this margin it is maximum of all the possible margins that we can have so this is maximum margin classifier so a way of saying it is you get the margin you maximize it or you minimize this or you minimize this if you write a half here it does not matter because half is a constant you minimize this or you maximize this so minimization of half of W prime W where ? prime ? I into W prime Xi is greater than 1 for all i is equal to 1 to n now this is a what is known as QP problem quadratic programming problem many results in fact there is quite a bit of literature on convex optimization there is quite a bit of literature on convex optimization the functions under consideration here they are all they are mostly convex function in fact W prime W that is a convex function do you know the meaning of a convex function a function is said to be convex a function is said to be convex a function is said to be convex F is said to be convex if for every x and y these are vectors f of ? x 1- ? y is less than or equal to ? x 1- ? x f of y as an example you please look at this please look at this say this is your x this point is x say this point is y okay and this is your function now ? x 1- ? y is a point here ? x 1- ? into y this is a point in between now this is f of x this is f of y right ? x 1- ? x f y this is if you vary ? over all 0 to 1 this is for all ? belonging to 0 to 1 if you vary ? in the interval 0 to 1 then you will basically get this line segment now you consider every value of the function in this interval that value is less than the corresponding value here so this is convex is this clear you take any value of the function here and this is less than this value ? x 1- ? y so this is a convex function there is quite a bit of literature on convex optimization and this quadratic programming problem of how to get these W's that is basically solved by using many results that are available in convex optimization many results that are available in convex optimization as you can see the main problem here is a quadratic programming problem I hope all of you know what linear programming linear programming means you have constraints linear and the function that is to be optimized that is also linear then the problem is called linear programming problem in quadratic programming problem the function to be optimized that is quadratic as you can see W'W that is quadratic that is why actually it is called quadratic programming problem QP problem and so we have assumed that the data is not is linearly separable now if it is not linearly separable then what people would do is ? I times W' XI is greater than or equal to ? 1- ? or you can take this ? to be dependent on I you can take this ? to be dependent on I that also you can have it either you can have something fixed usually if you look at the literature you have this thing ? as dependent on I 1- ? I so minimum of again W'W subject to these constraints now this is going to be an extremely I mean in fact it is an extremely complicated problem to solve and this is when the classes are not linearly separable then we make what is known as a soft formulation of the problem now though it is quadratic programming problem that is true but then when people try to solve this thing quadratic programming is coming slightly later okay and you see the optimization function that is under consideration is half of W'W- ? I times W'XI-1 where this is are the Lagrange multipliers use Lagrange multiplier the basic problem is quadratic programming problem because the constraints that is the function to be maximized is quadratic that is half of W'W now you when you want to solve it one of the ways of that you do it is by using Lagrange multiplier this is are Lagrange multipliers now you do differentiation partial differentiation so you get you get this as one so you take this thing to be equal to 0 that gives your W as this now with a dual formulation the minimization can be achieved that is true but it is quite intensive in programming minimization can be achieved which is true but then the programming part of that thing is not actually a simple one is not actually a simple one so when this is generalized this is generalized to a case where the data sets the two class problem is not linearly separable which we had discussed in the previous slide then you take 1- ? or 1- ? I the second one is that suppose you have more than two classes suppose you have 3 4 5 classes then the problem becomes more complicated there are two ways in which people have tried to solve it one is one against the rest belongs to class 1 and not belonging to class 1 belongs to class 2 and not belonging to class 2 class 3 and not belonging to class 3 so one against the rest that is one way and the second way is you take every pair 1 2 1 3 1 4 1 5 and for each pair you try to get the linear boundary or the soft boundary for each pair you try to get either the linear one or the soft one now the problem formulation in all these cases it becomes the solution of the problem becomes extremely complicated extremely complicated and this has given raise to another class of problems which are known as support vector regression problems you see in this one this is the actual decision boundary this is the one that is giving you the maximum margin now this decision and this one it is passing through this point which is a data point this one it is passing through this data point what is the support vector in fact these two points are actually known as support vectors these two points are actually known as support vectors because this is the actual decision boundary and then if you give – 1 it is coming here if you give plus 1 it is coming here and the plus 1 line is passing through this one the – 1 line is passing through this now these are known as support vectors now what is the usual regression problem the usual regression problem is I will do it here the usual regression problem is you have a data set suppose you are looking at linear regression then you are you would like to approximate this data set by a line like this now you have a line draw two parallel lines with the same distance in such a way that on this side there are no points and on this side there are no points all the points are lying in between these two lines now getting hold of this line amounts to getting hold of these three lines and which amounts to the problem of support vector machines where in support vector machines that problem formulation the points are lying either on this side of the line or on this side of the line two classes here all the points are lying in between are you understanding me it is basically the complementary one here all the points are lying in between so when you have all the points lying in between when you get this slide this is basically your regression line which best approximates this so it gives it has given rise to what is known as support vector regression and regression has too many applications any forecasting problem is basically a regression problem or let me say most of the forecasting problems are regression problems for the past 20 days the price of this stock is so and so tomorrow what is the price so what line approximates this what curve approximates this is regression so and regression has too many applications even classification has too many application regression has too many application and quite many people are working on support vector regression there is one another comment that I would like to say I have been talking about linear boundary when linear boundary is non existing then what I am seeing is that I have put a margin there soft margin now there is an extension of this one to non-linear boundaries where people actually consider kernels people consider quadratic kernels or some other kernels for getting for obtaining boundaries non-linear boundaries you will find several topics or several subjects name say one subject is kernel machines you might have found a book titled kernel machines it is basically extension of SVM to non-linear when you have non-linear boundary then you basically use kernels to obtain them to at least try to obtain the non-linear boundaries. So this is another extension from support vector machines one is linear but not exactly error 0 and another one that is soft margin another one is non-linear where you consider kernels and another one is support vector regression so lot of work is going on in all these fields and the work on these fields nowadays is termed as machine learning so with this I stop the lecture.


In a static multiple-issue processor, we essentially collect a series of instructions and package them into one large instruction. Then, the large instruction has a series of issue slots where each issue slot can run one instruction. Depending on your architecture, those issue slots may be generic so that they can be used for any type of instruction, or we might have a special purpose one, where perhaps we have one issue slot for arithmetic instructions and one issue slot for memory instructions. In this case, if I have an arithmetic instruction, I can place that in the arithmetic issue slot, but I can't place it into the memory issue slot. If I have a memory instruction that I'd like to run it about the same time, then I can place that into the memory issue slot. This type of architecture will work well when you have lots of both types of instructions to run. In order to get good performance out of this type of architecture, you have to make sure all of your issue slots are being used. If you have some issue slots that aren't getting used because say you don't have enough memory instructions, then your performance isn't really improved over just having a single issue processor. There's also another issue that arises here. If we're going to issue several instructions in one cycle, we also have to make sure that there aren't any dependencies between them. We won't really be able to do forwarding in this case because all of these instructions will try to reach say the ALU at the same point. So in this case, we have to structure our macro instructions in such a way that they don't contain any dependencies or any other potential hazards. Static multiple issue processors then rely very heavily on the compiler to produce good high performance code. We want to be able to package as many instructions into one instruction word as we possibly can. This means the compiler may have to try to find instructions that aren't necessarily related to the other instructions that are running just to keep the pipeline full. In the extreme case, we end up with what's called a very long instruction word architecture where we have lots of instructions that are being passed in in every cycle. There are four different types of static issue processors that we can consider. We've already looked at what a single instruction single data processor is. Each cycle we issue one instruction. It has one set of data that it works with. It performs that operation on the one piece of data that it has and completes. The type of static issue processor that we've just looked at would be multiple instruction, multiple data architecture. In this case, we have multiple instructions and they're each using their own different pieces of data. This is not the most common architecture but it is one that we still build. A much more common variation is the single instruction multiple data architectures where we have one instruction and we give it a whole lot of data to apply that instruction to. GPUs are a good example of this type of architecture. We may want to apply one operation to all of the pixels on our screen so we have lots of data but only one operation that we're actually performing. We could potentially have a multiple instruction single data architecture as well and these are going to be less common in such a format but in a way you can consider some of the very complex instructions that we add to say the x86 architecture to be this type of instruction. Some of the modern x86 instructions are actually kind of a composite of a lot of other simpler operations that we used to do before. We might have a very complex task that we want to do like multimedia processing, encryption or processing an artificial neural network and previously that would take lots and lots of instructions, dozens or hundreds of instructions to process one meaningful operation. However, recent x86 processors have added instructions to do just those things. Now we get one instruction that does a whole lot of computation for us. In a way it's performing multiple instructions for us but with only one piece of data. We've got this one piece of data that's just moving through a very, very complex pipeline where lots of operations are happening to this one piece of data.


Freedom Studios and MGM Studios has our first original production. In the GTA experience, we took two YouTubers, were they you, and let them experience the most exciting moments of Grand Theft Auto 5 in real life. Shooting a gun, walking down Venice Beach. This is the video I promised you 24 hours ago. Let's experience it together. Roll it! My name is George, CEO and founder of Freedom and responsible for our gaming community MGM. That was just the teaser. Click that eye to see the full video, the full GTA experience with subtitles in seven languages. And tell us down there in the comments below what you think of it. Are you doing original productions? Do you want to get involved in Freedom Studios or MGM Studios? Tell us in the comments below as well and send links to your work so we can see what you've done. Original productions are on our 2017 roadmap. We have many more things to announce to help you grow Freedom Family. Did you know we already have the music factory? Click that eye to check out Ben Messonnet's introduction to composers creating custom music for you, the music factory. And we have a game development division of Freedom. Click that eye to see the latest update from Mike about our first game, Age. If you want to get involved in productions like these, we do look for one thing. Healthy people! That's one reason we're doing the George Challenge. Let's get fit together. Keep sending me links down there in the comments below to videos of you doing exercise so we can motivate each other. Here's my contribution for today. Roll it! 35. Here we are. Back on the stairs once again. Today's ritual, which I want all of you to be doing and filming. Let's go! 37. 38. 39. Last one. Push it! Push it! And stop. Today's ritual is not over. My name is George and I still have to do push-ups. That's in addition to the stairs. I just complete it. How many can I do? Let's go! Okay, so we won't count for too long. One, two, three, four, 15, 16, make it 20. So what is this? 17 and a half, 18, 19 and a half, 20. Pretty sad, but it will improve. And I want you to do the same freedom family. I want to see if you can do only two push-ups. I don't care. Do two until you can do three. For me, I did how many? 16. So I need to be able to do 20, 25, 30. How soon before I can do 100? Well, not too soon. There are limits to what a human body. Can do when you're starting with this body one day. And someday my wife will be very happy. There's the thumbs up from her, my camera woman. All right, freedom family. Keep doing your daily rituals. Keep filling them. Send us links down there in the comments below to your videos so we can feature them on the official The George Challenge playlist on Freedom Central. Let's get fit together. Ooh. I've added push-ups to my daily ritual. Are there other exercises you suggest I do? Tell me in the comments below. And anything not too crazy, I am willing to try. Who am I? I am George Sunpai, Papa George, and many other names you, the beautiful freedom family has given me. I am George, CEO and founder of Freedom. For freedom and the freedom family.  I am George and you've been watching. Click that I to partner with freedom and join the freedom family so we can all grow together. You get many perks like position music. You also get epidemic sound, a lot of other access to royalty free videos, sponsorships and many things to help you grow. Just click the links down there in the description below to get involved in our community, our forums, our Discord chat servers, meet our graphics team, meet our community team, all of that on Discord and the forums. What are you waiting for? Get started. And we will grow together as a family because this is the freedom family. You are part of it. We are all part of it. And we're all growing together.


Well a unique art challenge has brought works of art from around the world to Brainerd. For this week's in focus our Sarah Winkleman takes us to the Crossing Arts Alliance for a sneak peek of the new quilt challenge exhibit. Work is underway at the Crossing Arts Alliance as they prepare for the upcoming exhibit. It's like Christmas when you love art and you get to unpack all of these different art pieces and go oh look at this one look at that one that it's just a very fun day. It's very exciting. The Van Gogh quilt art challenge from Cherrywood fabrics in Baxter has led to submissions from artists all around the world. I wanted to come up with a platform where people could showcase their art, push themselves creatively, try a different technique and keep it small. As the challenge began all of the artists started off with the exact same color palette and had to use all four of these pieces of fabric. Just an amazing blue display. It really like walking into a world of Van Gogh's artwork and his life. Some of these quilts speak to his mental disorder. Some speak to his journey. Some speak to his actual artwork and the brushwork quilts from Japan, France and Australia can be found in the exhibit along with one local artist from Baxter. It's unbelievable. I can't believe how much it's grown and what doors have opened. Not just for me and Cherrywood, but for other people. All of the artwork from the challenge has also been published in a book. There's such a following of these quilts and these challenges. We're already anticipating record crowds here to come see it, which is very great for downtown Brainerd. With a challenge that started in Baxter went on exhibit in Canada and Australia will now be back in Brainerd for the community to enjoy. Quilts aren't just what we have perception of grandma making little quilts. It's moved beyond that into art and this is artwork. It's just using fabric instead of paint. Even with all of the quilts being the same size, fabric, color and theme, each piece is different and more unique than the last. To see a traditional art form like quilting be taken in this artistic direction is so fun. For this week's in focus in Brainerd, Sarah Winkleman, Lakeland News. The Van Gogh Quilt Challenge exhibit will open on Tuesday and will run until June 9th at the Crossing Arts Alliance in downtown Brainerd. If you enjoyed this segment of Lakeland News, please consider making a tax-deductible contribution to Lakeland PBS.


Do you have brown leaf tips like this? Don't worry, I've got you. Soft plants prefer the soil to dry out in between waterings, but sometimes we let it go too dry, especially for plants like the calacia, the alucacia, and some ferns that really prefer that we keep the soil moist at all times. So we let it dry, but not completely. So I always say that it's good to know the specific requirements for your plant. You may be letting the soil dry out too much in between waterings. Another common cause is lack of humidity. This is again, especially with the calatheas or prayer plants, which need lots of high humidity. I can tell you, with my calatheas, I have to put them in a room with a humidifier and keep the humidity levels at about 50 to 60% humidity. This is because these plants come from the tropics. And as you may know, these are very humid regions in the world. You may notice brown edges or brown tips on the leaves, especially during the winter when we turn on our heating systems. Because we turn them on, the air in our homes becomes really dry. And this may be too dry for our plants. So try to keep them away from heating vents and raise the humidity around them. This will help your plants thrive and will help you prevent brown edges or brown tips on the leaves. Another common cause for brown edges or brown tips on the leaves is too much fertilizer. As you can see, the edges of this fern are brown. We also have some tips that are brown here. And this was because I was fertilizing this fern every week. We have a very diluted organic fertilizer, but it proved to be too much for this plant. So again, I would recommend that you research the specific requirements for your plant. And when you're fertilizing, make sure that this is a diluted fertilizer and always observe your plant. If you think too much fertilizer is the cause for the brown tips on the leaves of your plant, just cut back on fertilizer and observe her and see how she reacts. Remember, most of the houseplants that we have at home come from tropical areas, which tend to have warmer temperatures. So try to keep your plants away from cold windows or windows that are gonna be opening and closing and will let in cold drafts. This may be too cold for your plant. And if that's the case, this may cause brown edges on the leaves. So if this is the case with you, just try to move your plant to a warmer space and keep observing her. Another common cause for brown edges is tap water. Some plants are very sensitive to the chemicals that we have in our tap water, especially fluoride, for example. And a very good example for this is the dracina compacta. This one seems to be fine, but it is because we filter the water before we water her. But it is a very sensitive plant when it comes to tap water. So make sure that you use the stilt water, filter water, or even rain water. You can also place the water in a bucket for 48 hours before you use it to water your plant. This will make sure that some of the chemicals will be released and there won't be in the water. Specifically to the dracina compacta, there may be other reasons why your plant is browning or yellowing. But I have a video just on that, so if you're having problems with this plant, I recommend you check it out. Let me know if any of these causes seem to be the problem with your plant. Or if you have found any other causes for the browning of the leaves, make sure to comment below. I can assure you that the community will really appreciate it. And as always, I will see you in the next one. Okay, ciao.


Okay, cool Adam E sixers Alex C Hawks Angelo Pacers Anthony C with the Warriors Chad B Nuggets Chris B bucks Chun Wei Mavericks Grizzlies T Wolves David a Nets Felix and jazz Frank C with the Hornets and calves hung why Lakers Marcy has the magic Mizushima with the Pelicans Nori bulls Rafi Clippers Randy with the Thunder Ryan M Rockets Ryan L sons sugar Nori Pistons Thomas are with the Kings Raptors and Wizards Nick's Kings Raptors and Wizards. Sorry town Thomas Tim D Celtics Vinny S Blazers Yife Spurs John with the heat. Good luck. Yeah, everybody. Here we go Yeah, pretty recent tanker. Good luck y'all Ejilla tell orange Ricky for the pelicans Pelicans kind of sneaky in this year's products Bison downs the Aussie spellbound orange Zion Edwards full-throttle T Wolves I'll try to keep the glare off these cards guys. Well, these is really tough Steph Curry Clarity Steph Clurry Clarity Which is how Charles Barkley would say it Loravia rookie for the Grizzlies Orange Lamello for the Hornets Edward spellbound T Wolves now Looking for our first two autos First one is a Carlos boozer for the jazz last spot mojo there 33 of 49 on the auto Carlos boozer All right jazz pretty neat hit there It was a beast With the jazz right he was with the he was best at the jazz. I think star status John Moran Who's the bulls and calves to Zion spell bounce? What's that? Because it was him like memado core I remember on the jazz Orange full-throttle Trey young for the Hawks and like tie law. No, not tie Lawson, right? Andre Miller. I think was there Yeah, yeah downhill with the bulls Star status Anthony Davis 13 of its key title waves so break number 35 is filling up faster than 34 everybody There are still nine teams left on number 34 like a handful of teams came in for the one after you're gonna eight to go now Eight to go on 34 rookie Tyree smarten for the Hawks Yeah, Chad, there's not an order you can find them on the schedule and you can find them on the live breaks page Spellbound Steph Curry Warriors, they're not in order because Shopify Corrupted like a bunch of product pages. We had to relist them. So there's not an order You'd find them on the schedule though LeBron James power formulas And we're dropping links in chat for you The bull were the bulls really that excited about getting d-weight I think Chicago was kid cutting in power formulas. I was gonna say he's he's a Chicago boy Orange will be topping Knicks. Oh, I didn't switch over to a Real deal here. We grew up. There you go blazer shade on sharp to a 49 a rookie yearbook auto Nice shade on he's a good one man pretty good autos in the first box Red will pardon wizards to 95 Spellbound LeBron James Yeah, I guess the fans raised from Chicago Yeah Butler was still up there at that time with the bulls right orange spellbounding to be Everett Steve Wolves It was like Butler Wade and Who's even on like because they weren't like bad I'm trying to think of who else is there yokich power formulas Well dang Lakers of the wall dang. There's another LeBron spellbounds rondo Man, it's yeah, okay now when you now you me say fever dream of on now I'm starting to feel it and you start talking about rondo on the bulls rookie Bochamp for the Grizzlies LeBron James spellbound Lakers orange Josh Hart Blazers I say Bochamp Grizzlies Well, he's a buck pen pals Jalen Doran one of 49 rookie auto for the pistons you go pistons very nice hit there All autos number to 49 so far interesting interesting. Maybe that's the lottery number. We need to go for Dust is killing.  Yeah, I sounded a couple of power formulas for the Bucks Colonel's Maybe come the spurs or he's a spur from that's a b.a. Is that from like KFC? Just bringing up like LeBron James and super teams and talking about All this MJ LeBron stuff Things that are not related to like the current topic really purple Levina 49 bulls Orange Kenneth Lofton junior rookie for the Grizzlies Orange John Morant spellbound for the Grizzlies Anthony Edwards T-Wolves Yeah, that that conversations over that happened like a couple hours ago Clint Capella glass cleaners Red Kyle Larry to 99 for the heat Star status Kyrie Irving the mellow orange power formulas for the Hornets now So one more auto in this box so one more auto or no still two out of this box Yeah, I'm on the third box now step curry Don't even see one of the baby They're pretty rare like most of time the 3d's that we hit are like the the rookie ones I feel like definitely tough to hit the title list or rare for what we've seen so far siacum on the Title waves, maybe we'll pull it up the title list tonight. I'm not sure. I mean it's it's an SSP and it's honest It's it's at least the three-figure card. I just don't know how high that goes with something like that for me lead Kenny Martin jr. Orange for the Rockets I'm not sure how sought after like that style of card is there's just not a whole lot of them out there and most products Trey young spellbound for the for the Hawks It's a pretty cool. It's a pretty cool-looking card that especially the honest with the uh him holding the two trophies Jabari Walker rookie for the Blazers He got bucks at 35 Orange Seth Curry Nets There he is rookie your book auto gold is a tarry eason 7 out of 10. How you doing? What's going on? There you go tarry eason gold at 10 Okay Oh, hey, what's going on?  You're also here. Yeah, I'm gonna be leaving in a minute Oh No, he's taking over Orange d-book sons dude. I would love to pull the chat. I'm trying. I'm trying to pull a chat auto We have some nice auto so far gold uh Gold uh What am I trying to say? Why can't I say his name right now tarry eason tarry eason? Thank you Gold tarry eason is very nice Pull a chat all for lane. Yeah, I'm here. There's gonna be a chat. There's gonna be a chat Yeah, give it give it like give it like give it the next box. Yeah, Darius garland orange We still have another auto this box Give it the next box and watch don't we chat Jabari walker rookie new breed auto for the blazers I'm just gonna say or just one of the other like six. Okay. See rookies. Yeah, there's a there's a cheddar a j dub in this uh In this box right here because land is here Stop dolla. Okay. It's not like 10 though. So But we were like behind our land when just Get to the b-ball I say I'm oblique calves rookie. Oh, we also got every state of the club. Yeah Orange broke down of his house Check out both of the bowman breaks actually Yeah, it should be the two down there John moran spell bounce I have the same card Nice, that's awesome. And you gotta check the next break too orange nethmas neth smith paesers Pretty good boxes Turn of the century auto j cross over for the clippers jamal crawford It's a cool one for the clips nice hit on a cheap team of j cross over Jalen green the 99 blue for the rock hard wise or real life wise. Oh, man Probably volty the garland power formulas I think the jayson hype is just like orange full throttle tyree coming back If he dominates the minors how he ended last season in the minors. He dominated spring Yeah, but I'm talking like he dominated spring last year and then had a really slow start to the minors And then the second half of his minor league season Lights out if he starts the minors this year the same way he ended last year I'd be afraid of what his market turns into I won't bring up bonds I mean bonds should be in the hall of fame I don't think that there's anyone outside of the writers that Say otherwise Yeah, the script writers star stat is lillard. I'll be scripting. I'll be script writers It is they will be hall of fame script writers to be fair. I'd rip it all to be honest travis Steph curry on the elite deck Travis as a yeah as a personal as a personal I would probably recommend contenders Red Malik monk the 99 kings also the most expensive of those boxes contenders thick I mean It's just gonna sound really like a lame answer. But if you like it rip it, I mean stadium club chrome is pretty sick Spellbound the brawn blue there to 99.  So that's pretty cool It's not a red sock orange spellbound trey young no red socks If you like like you got to check out the checklist at all of it, you know what I mean You could get an andy reed auto though and contenders. So So uh plan that accordingly also bret, uh, brock birdie is a sticker auto in contenders So you can hit like a big on-card and a brock birdie in the same box I do and I don't you'll get you clarity true Like I like it in the sense that like there's added values to the box But I don't like it because now like five ten years down the line brock birdies contenders auto Yeah, that's true I wonder why they did that Yeah, party's value is skyrocketing because the Niners came out and said brock birdies earned the right to be the starting quarterback As long as he's healthy Niners said that yesterday Yeah Ride the roller coaster the brock birdie wave full throttle step curry I mean, hey, I don't necessarily disagree with them. No, I don't either prove his value They didn't say buy to trey lans orange josh are on his rookie deal Yeah, trey lans go nowhere both of them combined are so way cheaper than like any other That's why they got rid of jimmy g And there he is jazz last spot mojo rookie auto. Oh shag bhaji. They got a Carlos. Is it oh shay? Oh shay bhaji oh shay berset Nice agh bhaji for the jazz jazz hit a boozer and agh bhaji. That's awesome last spot So good at kansas. He's been turning up lately in the NBA too. He was so good I hated playing against him. All right recap. We have the agh bhaji Jamal Crawford for the Clippers Jabari Walker a tari eason a 10 very nice hit for the Rockets This has been happening on my lane, uh this uh louis dampere colonel spurs auto Uh jaylen torn rookie out of the one to 49 pen pals durin. That's awesome, too This is a really good four boxer shade on sharp to 49 as well The blazers and the boozer to 49 for the jazz I don't know if they beat the eagles even if purdy didn't get it. Thanks again everybody on to the next one


her green desmond ridder this one is four of 25 that is jersey number there you go at lanta shaun s congrats shaun there you go buddy sky more awesome rider a couple of raiders coming around jersey number rider tonio gibson throw this up there chase there's fire and ice jailen hurts 250 red tj hawkinson to 175 contours randy moss rpa nice that is alec pierce on the ball rising rookie rpa very nice congrats colts going to matthew bu congrats mathew down to eight to go now guys thank you macaulay and mathew down to eight spots to go orange elijah more to 75 and hot routes staphon digs drop guys link again just 35 a spot on this one more break left to go today there's eight to go and eight to go here we go last box of this break very nice let's flame throwers herbert fire and ice robinson jr again that's the third one uh 22 of 50 we pulled 350 it's in the print run thanks shod penny the corner in the market from ryan robinson jr vnx h2 fire and ice parallels it's pretty wild if you ask me orange christian mcaffery for the Niners 275 hot routes cup red zack wilson to 175 matt ryan red uh jordan davis 150 and indra booth silver hot routes chrysolave orange sam williams 275 lamar jackson rookie rising garret wilson purple alan robinson 299 thai chandler rookie purple jonathan taylor 299 my home's contours do a quick recap here guys we've got reds jordan davis majai sanders damien pierce david bell uh kevan tibodeau brian asamoa purples uh sam williams wandale robinson chrysolave kyle schakir tyler algear oranges sam williams danie gray christian watson drake london uh fire nices andrew booth brian robinson brian robinson greens are desmond ridder and desmond ridder one of those is jersey numbered and alec pierce rpi uh for the colts then we also had black garret wilson numbered six of ten that'll do it for the break guys thanks again for the fill next up number three seven six six to go everybody thanks again for grabbing up some spots i do appreciate that very much six to go there we are underway and completed ram's planning to release a Leonard floyd blackster fire blackster fire and that one it's kind of like uh in basketball with the uh black velocity mm-hmm yep like those yep yeah those are those are some of the nicest parallels the black velocities yeah i love i'm i need to start getting some like magic ones that'd be cool that'd be cool let's go and get a ball out get a fronds that'd be tough on my bank oh yeah same here my friend maybe chase after apollo when it comes out just want to talk about her at your bank down to four to go now thank you there nicholas z took eight spots or down to four appreciate you guys four let's go there take this random in chris taking a spot as well thank chris l down to three to go now three to go everybody last group break uh spots of the morning here xandros s seven times one alvin s five times nope nope nope nope s albert g alexandros alvin one two three four five android t brad r brad w there and i'm there at the gary one two three four craig e trips of s shawn s William c you gotta soon you gotta soon perfect there's a random rockin and roll in here oh god what did wahoo's do two more i max uh we're sold out thank you there jesson uh brad appreciate you guys sold out on number four as well thank you guys do appreciate it yeah i saw both of you both of you are in time out your credit cards are putting you in time out don't worry p is right there with you guys to p i think bought three uh in the games as well names games uh let's get number three boom good luck here guys what's going on everyone sam here with late in sports games we are uh doing the random for 22 panini phoenix football each two hybrid five box break number three um random team style got a list of our 28 participants 28 teams and combos let's go ahead and roll the old dice going at nine times one two three four five six seven eight and nine alvin s down to gary h and nine times on your teams one two three four five six seven eight and nine jets down to chiefs alvin s jets joseph s seahawks alexandros colts titans broncos cardinals panthers raiders brad r bills gary h jags alexandros with the falcons alvin s ravens derrick d lions andruti bucks gary h commander shawna s with the stealers greg e patriots alvin s niners darren m dolphins william c vikings alvin s giants browns gary h texans albert g eagles alexandro saints yada sanar with the chargers alexandros cowboys yada sanar with the bangles alvin s packers brett w bears rams and gary h chiefs let me get the uh get these copied over guys we're gonna start in just a minute and break with sam button but unknown if it worked four fouls four fouls in 14 seconds ruckers just that's insanity that's like that's like impossible yeah it was just foul personal foul machine last night all right guys give me one sec i'll be all right to buck any picket 32 of 50 thrillers rookie auto congrats dealers you like that so sick that's nice congrats the war nice tiger let's go man cow is not expecting that that's so sick dude tiger purple pmg one of 75 wow wow wow that's awesome nice one there man we'll get yeah there's a meat market oh so we're out brock party rookie auto to 299 congrats 49ers in his professional uniform not a practice uniform this lonely box of spectra has been sitting out on the shelf out there wow for germany oh that's sick dude about sean alexander green shimmer auto going to derrick a and the seahawks congrats buddy that's nasty one of one madden legend fantasy football legend nice josh giddy face rated rookie auto going to the uh thunder congrats on that mohab a nice kitty giddy up baby we'll get that into a mac for you buddy on card windows into greatness a relic book card ronnie lecunia jr. 4-5 atlanta game use quad relic book there we go atlanta y'all see what i'm seeing y'all see what i'm seeing what do we have here daniel what do we have here one of one rakely this is disgusting shripple tag patch josh alan lamar jackson patrick moho's no way bro steven w with the one spot all right let's get going here here we go sam here with latent sports cards rippin 22 penini phoenix football h2 hybrid five box break number three random team style there's a look again at your random results as always you can find these on the website under the results tab as well as the link that's in chat it's good luck here everybody let's do it phoenix something out of ten or less massive auto all right let's see it let's see it flame thurge curt cousins can you pick it rookie dots in orange miles garret to 75 that's uh brissol laser rookie maybe not maybe though red tide chandler to 150 sake one barclays on the laser red is trayvon walker to 150 and randall conningham yeah me too tonight it's a solid little value product for sure purple dac prescott to uh 75 drake london hot routes cooper cup hot routes laser and contours matt corral rookie for the panthers purple jalen hertz nice one there to 75 or to 99 brand and i would be fleece rich and got josh jacob's sack wilson wait didn't you did you trade you traded for brand and i it so you got fleece yeah but look who wins the magic game true he was also true there's another black roquan smith for the ravens uh three of ten alvin i think now i think you may want to hit sam's line with that one yes alvin you may want to hit my line with this one for sure jalen hurts that's cool dude that's such a good one that's so bad i've pulled two of them now now there's only eight left he's a new yeah it's a sign right there red deandre hopkins to 175 and george kill you guys we got forest uh breaking at what time five uh dynasties first dynasties sold out let's see what else does he have mixer that's sold out okay perfect uh inception got inception random teams this is the next group break with spots right here 17 to go uh again that's forest ripping that starting that's probably at like six or so six uh p.m eastern time uh so normally check it out i know he'll appreciate that you guys get some more spots sold out james cook red justin ross for 150 jalen hurts purple romeo dobs erica's economy aj brown that changes tonight absolutely that changes tonight uh red jerry judy to 150 and a county gollanda forest will get you something nasty there's a fire nice the marvin leal for the steelers to 50 and treylon berks rookie rising uh purple charlie colar color match for the ravens to 99 kyer elan and cd lamb hot routes orange andrew booth that is to 75 jamar chase contours red staphon digs to 175 james cook flame throwers desmond ridder rookie the falcons contours mackerel rookie as well box number three green brian cook to 25 that is six of 25 technically a jersey number very nice congrats sheets contours erin rogers flame throwers ryan tannell jalen hurts fire nice to 50 for the eagles and russia wilson on your leaser bronco country let's rise flame throwers justin herbert got orange allen robinson to 75 for the rams and treylon berks hot routes rookie for the titans the rookie rising malik willis there's nico collins purple to 99 christian kirk leaser their car fire nice new saint uh this one obviously still for the raiders and snoop connor fireforge drew breeze they read davis mills to uh one no 175 brock lezner contours 125 oh is it 125 rookie uh to 99 dk matt calf and logan hall three is done and behind us on to the box number four these are going to be the other way around here you would think flame throwers josh allen there's a fire nice david montgomery to 50 for the bears patrick mahomes flame throwers there's an orange snoop connor nice one there for the jags to 75 and johan dotton laser room for the commanders montan it's another green coming up here it is marcus mariotta for the falcons that is seven of 25 it's the ante johnson falcons legend marcus mariotta marcus moriotto as roger gadel would say on draft night mariotto red cameron thomas the 150 tyler lockett people started making jerseys after that night that said moriotto on it can you pick it flame throwers jamis fireforge kurt warner it's like cheese dude look at you just one of the heisman how do you like yeah if you're the commissioner come on to 150 at justin ross for the cheap color match kind of picket rookie rising it'll be acceptable if it was like a you know like a late round yeah right right there's nico collins purple to uh 99 probably the top draft picket here yeah second overall with winston like it was winston mariotta it was like it was like who was going to go where obviously we should pick a mariotta purple bow melton to 99 adam feeling yeah not really actually not really gonna say really though say i'm kind of confident i mean they both are still like in the nfl which is good but i'd say winston had better stats yeah probably did they turn over the ball or did mariot turn over the ball as much as no i don't think anybody did that i think i probably turned over the ball as much as james winston did 30 30 that's insane no but i'm going to try that now admiral that sounds a fire is a rashad white laser really sounds really good dude i don't know what my heathers roommates got cinnamon toast crunch flavored like spread and it's the best thing i've ever had in my entire life ever it's it's a game changer is it like cheese or is it kind of like peanut butter-ish it's like butter okay butter there's uh christian mccaffrey red to 125 hot rocks cop it's it's so good dude i'm going to try that oh it's so good dude is it by nutella no maybe i don't know it's a 150 damian pierce pretty pebbles with marshmallows oh that sounds yeah and that is good that that is good i forgot there's they make pretty pebbles with marshmallows those are kind of fire i'm not a huge like fan of the pebbles like family there's a Elijah Moore to 75 roger stop it's not my favorite cereal of all time but those with the marshmallows are good flame throwers jared golf purple alan robinson to 99 little mac fire nice mica parson's to 50 for the cowboys johann dotton rice crispy treat yeah ricochet those are good i i can say i've had those before i'm not a huge cereal guy i don't really eat breakfast me either that's the thing dallas goddard uh to 125 right rookie rising skymore um what was i gonna say if i ever have cereal i always eat it dry i got always eat it dry me too i just like a little snack contours at patrick mahomes purple jonathan taylor to 99 and to a flame throwers do a quick recap here guys we had reds damian pierce justin ross cam thomas justin ross trevon walker ty chandler purples bow melton charlie colar romeo dobbs oranges snoop conor andrew booth uh fire nice the marvin leon green ryan cook and another black roquan smith very nice congrats on that everybody thanks again for getting this filled on up next up we got number four and fine thank you again guys for getting everything filled up today i do really appreciate that and guys we got forest uh breaking at five o'clock um he'll be doing a bunch of different py teas and random teams uh gonna be a fun night always is bananas on friday nights i do like what i said in the uh um i called uh i called him uh rainforest cafe so i called him subaru forest there amazon rainforest now rainforest cafe nice pretty hilarious if you ask me jake how do you say so myself all right it's best uh each two poll probably garret wilson black to ten rookie that was probably the biggest um and then uh what was the other one we pulled pull a couple rpa it's like an alex pierce rpa it was pretty solid i mean there was a few ridders yeah yeah two and two decimator ridder greens to 25 in the same break one was jersey numbered yes exactly this next oops random type some teams going in our later um py t don rusk breaks as well alexandros twice and an s andrew t arthur y brad r brad r c brett s chris l david b derek g dustin g dustin g darry w just g twice johnathan s joshua s and collie t matt b four time michael z richard h john m john s and william c perfect to go on the random that's awesome ricochet since everything felt oh rich oh yeah rich head's cool oh yeah what's up hazy yeah that burrow is sick i know which one you're talking about that one's nasty very awesome let's just want to start out not perfect let's do the random guys what's going on everybody sam here with lance sports cards rippin 22 uh phoenix our penini phoenix football each do hybrid five box break number four random team style got a list of our uh 28 participants as well as our 28 teams and combos let's go ahead and roll the dice see many times we're gonna go it's gonna be five times one two three four and five derek d down to shon m got five times on your teams one two three four and five lions down to colts derek d lions jesca g jags brad our jets nicklas z packers david b titans dustin g cowboys matt b eagles jonathan s uh falcons alexandre dolphins matt b buccaneers andrew t chargers jess g saints brad c steelers matt b ravens alexandre seahawks matt b chief scary w patriots joshua s broncos cardinals arthur y panthers raiders brad s giants browns brad r bears rams uh that is william c with the texans uh chris l bangles shon s vikings and then s with the bills richard h commanders mccawley t niners and shon m colts we got these copied over guys we got started in just a few minutes there you go as you guys the results get started in just a minute all right guys we'll get started in just two minutes here new york giants baseball i do not actually i do not wahooz i do not it's definitely one like all of like the they call them the cooperstown collection so it's like teams that it's like logos that aren't used anymore and hats that aren't used anymore uh they're always one that i'm looking at the ny which is pretty cool so auctions you could take anyone mic what would you say otani otani is a good bet otani should be the number one pick in every fantasy baseball you know who's the first one in ours but you're cool no he wasn't swear to god who it's illegals draft who took garrick cold number one overall i mean it's a little different i think the way that uh points are accrued that's why pictures go that high but yeah i took judge it too i was like all right let me judge it too i'll do it is otani a two way in your league no you can only play with the dh that's why otani went like second round okay yeah all right good luck here guys let's do it what's going on everyone sam here with late in sports cards rip in 22 panini phoenix football each two hybrid five box break number four random team style there's a look again at your random results as always you can find these on the website under the results tab as well as the link in chat thank you guys again for getting this filled up i really do appreciate it uh getting everything filled up today that was awesome um let me do one thing really quick hold on just one second thanks for the sub there andrew appreciate you buddy i have to do really quick all right good luck here we go sorry about that yeah otani's probably them the the guy to go to 101 shosh allen incoming gotta speak it into existence let's go let's go andan that's what we like to hear okay i'm thomas mike evans purple two at 99 person once it's future buccaneers starting quarterback person once y'all in kamara who's gonna start trash really another team that's not in on lamar now which is awesome there's flamethrowers lamar jaylen walle red jacoby meyers to 125 leo chanel it's like a green coming up here it is marcus mariotta second green mariotta this time at six of 25 person once laser drops kelsie red smear white nice one there to 150 christian watson rookie rising that's fire nice danie gray rookie to 50 for the niners and terian davis price for the niners rookies there but nice orange tom brady to 75 for the bucks 73 of 75 jaya alexander tj hawkinson to 125 you see the video of jaya alexander like talking smack about justin jefferson but he's got the big hat on no let me show you like uh alexander he gave an entire interview talking smack about justin jefferson with this hat on so funny or me i don't know if it was if that was the one where he was talking smack on justin jefferson but he was like talking trash in that video about something and he's just got the giant hat on i was breaking once i'm gonna buy a big hat and just wear it it's red leo chanel to 150 so ridiculous justin jefferson yeah like how do you take that seriously like if you're of a border like how are you taking that seriously i'd be like laughing me i'd be like is this dude serious there's rookie rising james and williams nice jama uh purple dak prescott to uh 99 kvon tibido owner of the kvon tibido chris olave a red brand nine to um 125 i want to say the wrong one contours tom brady i'm gonna i'm gonna have how i put that as my thumbnail tomorrow any picket no no the big hat direl xander machi harris that'd be great wouldn't that be awesome it should be you in the that'd be pretty funny josh jacob's um to uh 75 mac jones justin ross to 150 james and williams hot rod i feel like we pulled like five of those reds yeah cornering the market on that one again debon white debon white leaving the book in here's he's testing for you oh really yeah oh jeez purple javante williams to 99 or was it maybe it might have been david i think it was david yeah it was one of the two i mean david's good but like i'd rather have to wait yeah because he's younger or two there's a david montgomery orange to 75 i'm just gonna miss having both of them yeah because levante will probably get paid somewhere for like they'll get like a three-year like 40 million dollar deal app however old he's he's been away for what 11 years now he's 2012 i think he was a stud though talk about a great traffic for the box we always seem to drop good line back yes that is there is no shortage of good linebackers in tampa ever purple chrysalovay nice one there too um 99 desmond reader i know it's beautiful i i've had him before too where he's gotten hurt so frustrating speaking of david montgomery again to 75 treylon berks he plays 80 of the snaps yep yep 100 you know how it goes there's a red cam thomas to 150 nukobi deans stop earth from our chase contours playing throwers josh allen i will probably be staying away from david montgomery to be fair great running back just gets hurt dude always hurts like the bears running backs are always hurt george kittle fire nice to 50 and zack wilson it's going well earth are you doing buddy there's matt ryan to uh uh 75 john tate johnson red josh allen 125 that's one there and cd lamb this isn't right honestly but feels like there's rookie rising garret wilson on the velocity uh purple debon mccordy 275 and a sauce gardener bunch of nice lasers there hot routes aj brown laser can you pick it very nice orange jalen hurts to 75 contours randy moss close here there's a green mr brandon cooks to 25 for 25 nice one there taxes that's a guy who i would love the ravens to pick up at the gets caught it's like a cap casualty brandon cooks i really like brandon cooks i always have there's a red trayvon walker to 150 staphon digs again as long as it's not the answer to the wide receiver issue the glaring wide receiver issue in baltimore i would like brandon cooks it's like putting a bandaid on a bullet wound that's how i say with that there's purple miles garret to 75 to 99 can you pick it like when we signed to shan jackson mid season last year i'm like really that was a great pickup it was decent but it's like again it's like putting a bandaid like on a decapitated individual i'm saying oh that's all fixed there's john dotson it's like really it's like it's not 2015 like which time we were shot baby it's not a surgeon not a surgeon no too busy getting hurt to be a surgeon there's uh tyler alger tonight i'm so i'm ready right he's so good too when he's healthy dude that's like the issue like i love when he's out there but he's just never out there it's always like a foot injury his flame thrower is matt ryan matt jones fair that's very fair there's beautiful it's him and lamar overthrows him you can catch up to it fire nice charlie colar rookie to 50 for the ravens russia wilson we're gonna say an orthopedic he does he literally needs like an orthopedic dedicated to him milich jones red tyler alger or no tyler locket excuse me it's a one uh 25 chris godwin hot routes for the bucks last box of the day good luck here everybody purple erin rogers the 99 rising rookie candy picket fire forge kurt warner video which one of the gyro lexander green debauchery smith there you go eagles that is 17 of 25 so ridiculous i don't know i don't know what that was all about fire and ice garret wilson nice one there jets brad are 13 of 50 cam taylor britt i had james connor lacher when he was healthy he was really good but again he was like always questionable he was always like a game time decision and he was like should i start him should i not uh daniel jones to 125 and alvin kamara orange sauce gardener to 75 nice one there uh for the jets tyler murray jets doing very well here josh alan contours right exactly exactly playing throwers my homes red damien pierce to 150 and dallas goddard is a red damien pierce to 150 as well as a davante adams hot routes do a quick recap here everybody got damien pierce damien pierce uh four and ninety seven so nine of course uh travon walker the camera and thomas jesson haas leo chanel smear white purples tyler elgier chrysolave oranges sauce gardener fire and ice daniel gray charlie colar and garret wilson that will do it for the break guys thanks again for the fill next up uh we've got nothing last group break of the day thank you guys again for hanging out today do appreciate it uh we've got forest rainforest cafe starting in about two hours give or take little under two hours uh there is the break schedule he's got some uh f1 inception baseball uh he's got bowman's best he's got a six box nba mixer which is donress hobby prism draft uh hobby and choice three of each of those i believe uh donress basketball each two phoenix three box nfl mixers and then two full cases of imac and two full cases of impeccable so definitely a very heavy football night which is good i'm not doing any personals ricochet forest will be doing them after uh after his shift is over um so i will see you guys again tomorrow night have a good one everybody


Hi guys, welcome back to this channel. Remember it's mechs from the mechs creation. By the way, if you are new to this channel, consider subscribing and supporting this channel. Don't forget to click the notification bell for more videos. In today's video, we are going to talk about the latest development that is circulating around.  Don't forget to follow my tiktok account at mechscreationTV where I have the latest updates in Qatar. The latest updates in the Gulf countries for you to get informed. In today's video, I want us to look at what we call the new circulating information. Remember, this is all about the police clearance. Did you know that there is some requirement whereby if you need to change from the security job to a new job to another job, you need what you call a police clearance certificate? Yes, that is true. You will need what you call a police clearance certificate. For most of those people that have gone through the process that getting to change to those companies or that are aspiring or that have already presented in their document to change to new companies, I think you've been requested to what you call a police clearance. And remember, for you to access a police clearance, it's not just a matter of fact that it's not only, it's not a matter of fact for you to go to police and present your ID to get a police clearance. For you to get a police clearance here in Qatar, what you call the PCC, you need to get a police clearance from your country of origin. So you need to get that police clearance from your country of origin for you to have a police clearance certificate or to be cleared by police here in Qatar. Remember, we came as migrant workers, we came as workers, we are not born here. So meaning that they need to first check the criminal record from your country of origin before they can ascertain it or before they can give you a free criminal record report or certificate in this country. And how does it work? It means that for people who are in security, you must be on alert. You must be on alert for people, especially people working for security companies. If you are going to plan to change to a new job from the security company, you should be on alert because they will definitely, at one moment of time, they are going to require from you what you call a police clearance certificate. And for you to have a police clearance certificate, meaning that you need to have been cleared by your country of what you call a country of origin. So you need to get what you call a police clearance certificate from your country of origin. When you have it, it will be ascertained. When you ascertain it, that is when you present it to the Ministry of Interior at the government offices, they will verify it, they will stamp it and they will give you a police clearance here that is supposed to be used by the Qatar government. Remember, that is the latest development of Amhavi. So I'm letting you know you get prepared, prepared to have it. Be prepared such that that is another handbook of you to a paper to be by your pockets because when they need it and there's an opportunity for you to move on, definitely. It will be one opportunity that is going to deter you from moving to a new job that is going to come on your way. Hope I've tried to share up something for you. So if you have the opportunity to have it, have it, keep it, ascertain it stamped by the Ministry of Foreign Affairs in your country stamped by the Embassy, representing your country in Doha then definitely keep it for any further development that will come. In case you need it, then definitely you'll have to present it without delay. Thank you so much for coming back to this channel. Remember, it's Meks Arores. Keep on updating you. Thank you so much for the support, for the returning subscribers, for the new subscribers. Thank you so much. If you feel there's something that I need to talk about, if you think there's something that you need to know that you are not sure of, that you can share, drop a comment in the comment section. Arores will be more than happy to get back to you. Thank you so much. See you again in the next video.


Lignin is a complex polymer found in plant cell walls that can hinder the efficiency of biofuel production. Recently, nuclear magnetic resonance NMR has emerged as a powerful tool for studying the structure of lignin, providing valuable insight into how this material can be manipulated to improve biofuel production. This article was authored by Rundsong Sun, Jialong One, Bailean Xue, and others.


My work here on YouTube is supported by viewers. Please take a look at the link in the description below and visit my page at 50th Street where you can become a sponsor. Continuing with the theme of Victorian fiction, this time it's technically Edwardian, I guess. I recently read a study in Scarlet and the Sign of the Four, which turned out to be the first and second Sherlock Holmes novels consecutively, which I was not aware of. And my super short review is that I thought they were dumb. Yes, I said dumb. These aren't real detective stories. They don't have that satisfying feeling of real research and discovery of solutions. The stories revolve around Holmes' quirky personality and the solutions of the mysteries depend on that too. Which makes me just not really care. Plus the second half of each book is basically a separate novel which tells a tremendously detailed story of the life of the perpetrator, which again I don't care about. The third Sherlock Holmes novel was Hound of the Baskervilles, which I read in high school more than 30 years ago, and I had the same feeling about it back then. Thank you for watching. Please subscribe to my channel here on YouTube and please be sure to press that thumbs up button. That's how videos get recommended and seen and please take a look at the link in the description below and go to my 50th Street page where you can become a sponsor.


10. The peer administration introduced sweeping income tax reforms, personal income tax allowances increase from 18,000 to 25,000 dollars. People earning up to 25,000 dollars annually will pay no income tax and St. Lucian taxpayers will collectively save up to 14 million dollars every year. 9. The government of St. Lucia has secured more than EC 36.6 million dollars in funding from the European Investment Bank, EIB. At this loan, we'll assist us, not only strengthen our air systems, but also strengthen us in paying some of the commitments that we include during COVID. 8. Before, the only thing that you could have used as an asset was property. This bill will allow you to be able to use some assets as a security. The bill paves the way for entrepreneurs and the self-employed to secure the capital and funding needed to take their businesses to new heights. 7. The government needs to invest in the police. And this government, within our fiscal reality, is going to invest in the police. 8. The peer administration has initiated the largest infrastructure investment project for the island's police force. Prime Minister Hon. Philip J. Peer signed a bolt agreement with Nipro to commence construction of a new divisional police headquarters in Rosalind, estimated at 35 million dollars. 6. Travel advisors from St. Lucia's top global markets are being welcomed to the destination, along with leading publications Essence, Katy Keurig Media, Wedding and Honeymoons Digital Magazine and The Greal. The objective is for the participating travel trade to experience first-hand the full spectrum of the romantic offerings of the island to equip them in strongly recommending St. Lucia for marriage proposals, destination weddings, vow a renewal, romantic getaways or Honeymoons for which the destination is renowned. 5. St. Lucia Carnival 2023 is slated for the first to the 19th of July for next year. An early announcement of St. Lucia Carnival so that we could ensure that all the creative, the various artists would have been ahead of the coven terms of their preparation. 3 more schools are beneficiaries of multimedia classrooms, namely Granivier Secondary, Leon Hez Comprehensive and Babunow Secondary. The smart classrooms utilize large screen monitors, conferencing technology and a host of other software advancements aimed at enhancing instruction at the institutions. It is no longer acceptable in any school irrespective of the level, infant, primary or secondary, for lessons to be delivered with just chalk and talk or with marker and whiteboard. 3. Do not use these barriers to send on anything except food. And this is serious, this year's musical because several times other items were found in these barriers that are not food, that are not care packages, that are not toys. This idea of caring for the vulnerable has always been led by this Labour Party administration and we always like to be the one who champion caring and putting our people first. 2. The Ministry of Education extends a heartfelt thank you to everyone who supported our initiative present, proudly representing its school, exalting our nation's teachers. It was immensely heartwarming to see so many solutions from all walks of life, put on the uniforms of their alma mater and proudly represented its school while exalting our nation's teachers. 1. The retrofitting of 13 wellness centres around the island and two government health facilities. These facilities are now expected to provide comfort to patrons and staff while withstanding the forces of nature, the upgraded green facilities are already reporting reductions in daily operational costs.