So, we wrote down n equations and the moment we have n equations, we think that we can solve all those equations and get n estimates of the parameters. But I told you that even though we perform n experiments, the number of regression parameters or regression coefficients we estimate is smaller than n. Essentially that means we are not solving those n equations in n unknowns, right. It makes no sense also to have a huge number of parameters in our regression model. We are having such a large number that they equal to the number of experimental observations. We need only a small set of parameters. So, we do not solve those equations simultaneously, we adopt some other method. You can solve n equations in n unknowns using the matrix method. But we are going to use another method also involving matrices to get good estimates of the parameters beta hat, beta 0, beta 1 hat, beta 2 hat so on to beta k hat. So, we have totally p parameters to estimate, p is equal to k plus 1. The k regression coefficients associated with the k regressor variables plus the intercept beta 0 hat which makes it k plus 1, we call p is equal to k plus 1. All these things are very clear. The method we are going to adopt is the least squares estimation technique for the parameter set given by the beta column vector. So, what we do is we define a function L which is defined as sigma i is equal to 1 to n epsilon i squared. In matrix notation, epsilon i squared may be written as epsilon prime epsilon. This is very simple. I will explain this. Epsilon was given by epsilon 1, epsilon 2 so on to epsilon n. When you take transpose, that is what is given by epsilon prime, you get epsilon 1, epsilon 2 so on to epsilon n. So, this is n rows one column. This is one row n column. You cannot do epsilon, epsilon prime because then you will get n by 1 into 1 by n, n rows one column, one row n column. And when you do that, you will get n by n. How is that possible? Okay, epsilon 1 squared and then you will get epsilon 1, 2. So, this is not what we want. We want epsilon which is 1 by n into n by 1. Then these two will get cancelled out and then you get 1 by 1. What is epsilon prime epsilon? You have epsilon 1, epsilon 2 so on to epsilon n and then you have epsilon 1, epsilon 2 so on to epsilon n and here you get epsilon 1 squared plus epsilon 2 squared plus so on to plus epsilon n squared. So, what is happening is epsilon 1 is multiplied with epsilon 1 here plus epsilon 2 is multiplied with epsilon 2 here. So, on to epsilon n is multiplied with epsilon n here so that we get sigma epsilon i squared i running from 1 to n. So, what we want to do is we want to identify the parameters beta such that dou L by dou beta is equal to 0. We want to minimize L. What is L? L is the sum of the square of the errors and what is error? That is very simple. What is error? This is very important. Error is y minus beta x. We wrote the model y is equal to beta x plus epsilon. So the error term is equal to y minus beta x. Sometimes you may have positive errors, sometimes you may have negative errors and to account for the error in an impartial manner we do not want to add the positive errors and the negative error and then show us net small error or 0 error. We square the errors so that irrespective of whether the error is positive or negative you are squaring all the errors so that all of them become positive and we get a complete total error. So we have sigma epsilon i squared and that may be written in matrix notation as epsilon prime epsilon. Now we have the sum of the square of the deviations and we want to minimize that. This is the good old least squares principle. You might have done that in maybe higher secondary or in the second year of your engineering program but the main idea is the same. In matrix notation we have dou L by dou beta is equal to 0. epsilon prime epsilon is also scalar and so you have after the dust has settled down x prime x beta hat is equal to x prime y or beta hat is equal to x prime x inverse x prime y. This is a very famous equation. You can predict the parameters for your regression model by multiplying x prime y matrix with x prime x inverse. To find beta hat we pre-multiply x prime y with x prime x inverse. So this is going to directly give us the set of parameters. I am not giving you the proof and this follows from this relation. So to find beta hat we pre-multiply x prime y with the inverse of x prime x inverse. So if I put x prime x inverse on both sides x prime x inverse x prime x will become the identity matrix and then you have this matrix inverse multiplying with x prime y that will give you directly beta hat. You do not have to do these calculations by hand. Sometimes for large matrices finding the inverses may become cumbersome and error prone. You can use the aid of mathematical software like MATLAB for instance to do the matrix manipulations. So let us look at the dimensions of these matrices. We are having x prime x beta hat is equal to x prime y, beta hat is equal to x prime x inverse into x prime y. So are the dimensions consistent? It is a good time to summarize the dimensions of the different matrices involved. X matrix is having n rows and p columns, n experimental observations and p regression coefficients or the parameters beta not so on to beta k which would be k plus 1 parameters. X prime x transpose of x multiplying with x, so if x is n by p transpose of x would be p by n. When I am saying transpose I am interchanging the rows and columns. So suppose I have a matrix with a certain number of rows and certain number of columns when I take the transpose of that matrix I am converting rows into columns and columns into rows. So if I am having n by p for x matrix the transpose of the x matrix would have dimensions of p by n. You had n rows and p columns originally in the x matrix. In the x prime matrix you have p rows and n columns because the rows and columns have interchanged. So when I multiply these 2 the n by n will cancel out and then we have p cross p. X prime y would be p cross n as we saw here and y is a column vector of n observations. So it will be n by 1. So x prime y would be p cross 1 and beta hat would be p cross 1. It is a column vector comprising of p parameters and 1 column. The p parameters are arranged row wise and this should be capital Y which is the vector of responses n rows and 1 column. I will just make it as capital Y. So the fitted regression model is given by y predicted is equal to x beta hat. The difference between the actual height observation and the predicted value given above is called as a residual and may be expressed in matrix notation as E is equal to y-y hat. So we have been using epsilon and now I am using E. There is a reason for this change. Epsilon represents the true error, the random component of the experiments reflected in the form of epsilon, the random experimental error. But I am using E. I am saying that E is a residual and that residual may be only due to the random error or it may also be including the unexplained effects in the experiment because of inadequate modeling, okay. If my model is not fully able to explain the variations in the experimental response then that discrepancy cannot be dismissed as random error. So my residual contains possibly unexplained variability and also the experimental error. So I am using E here. If all the possible variability has been accounted for in the model then the residuals would be a true reflection on the random error component. So first we will calculate the error sum of squares. The moment we see the term sum of squares we can guess that some analysis of variance is involved. So you have y-y hat is equal to E which is the residual. E prime will become y prime-y hat prime and then we have y prime x beta hat is equal to beta prime x prime y but both are the same. Both are the same because both of them are scalars. It can be easily shown that y prime x beta hat is a scalar. It has dimensions of 1 by 1. That calculation is shown here and then you also have beta prime x prime y which is again a scalar and that dimensions are also shown in this calculation. The n's will cancel out nicely leaving 1 by 1, right. Now we can show elegantly that the sum of squares of the error is given by y prime y-beta hat prime x prime y. This is very interesting. Let us see the proof. John, board and then do the derivation directly so that people who are not familiar with these can follow the steps. So we have y-x beta hat prime into y-x beta hat. So I take the prime inside and we know that when you take a of b prime this becomes b prime a prime. So using that there is no problem with y it becomes y prime x beta hat whole prime becomes beta hat prime into x prime into y-x beta prime. So this becomes y prime y-y prime x beta hat minus beta prime x prime y plus beta prime x prime x beta hat. So I am just multiplying the last two terms here. So this will be beta hat prime x prime x beta hat. So we saw that from the previous slide that y prime x beta hat is equal to beta prime x prime y. So you also have minus beta prime x prime y plus you have this term. So these two can be written as minus 2 beta hat prime x prime y so we get y prime y minus 2 beta hat prime x prime y plus beta hat prime x prime x beta hat and we also know by definition that x prime x beta hat is equal to x prime y. You may recollect that we found the parameters beta hat by taking x prime x inverse x prime y. So this is the equation which I can use here and that becomes beta hat x prime y. You have minus 2 beta hat x prime y so you get y prime y minus beta hat x prime y. So this completes the derivation. It is always good to go to the board and do the derivations. Power points also have their own charm and make teaching more convenient. On the other hand writing on the board you make mistakes, you correct the mistakes and learn in the process. I hope that you would also feel interested to do the derivations independently on a paper and see whether your results are matching with the final expected results. Now we are going to talk about a very important property of linear regression analysis. It is the variance covariance matrix. So obviously we are going to talk about the matrix and we have found the parameters beta 0, beta 1 so on to beta k. We want to know how precise these parameter estimates are. So to have an idea about that we can use the variance covariance matrix. So let me just introduce the matrix to you and then we will talk about how to apply it in real regression problems. So the variance of the least square estimators are the elements of x prime x inverse matrix multiplied by the error variance sigma squared. Where did we see sigma squared previously? I showed a figure where we had the true relationship line and we showed the experimental data scattered around this line. We said that the scatter was described by a probability distribution which was a normal distribution. The mean of that distribution was given by the equation but the data was not exactly aligning with that value given by the equation or the data was not present exactly at the mean value but it was present somewhere else because of random effect. This probability distribution was having a variance sigma squared. All the data points which were scattered around the true line had the same variance sigma squared. Let me go to that figure again. So here we have this particular figure.  The scatter is described in terms of probability distributions and these are normal distributions most conveniently and the mean of these distributions are given by the equation. This mean would be different from this mean because this x value is different from this x value. Here you have one x value, here you have another x value. Then you have the data points which are scattered around this and the probability distribution is having a mean given by beta 0 plus beta 1x and changes with x but it has a constant variance sigma squared. This is the sigma squared we are going to use in the variance covariance matrix. So now coming back to the variance covariance matrix, we have x prime x inverse multiplied by sigma squared and that sigma squared was the constant error variance. But unfortunately we do not know sigma squared. We need to estimate the parameters beta 0, beta 1 so on to beta k. We also need to estimate the error variance sigma squared. We are having a variance covariance matrix. That term implies that matrix contains both variances as well as covariances which are the variances and which are the covariances. The diagonal terms in this matrix x prime x inverse sigma squared matrix represents the variances. The diagonal terms means first row first column and the second row second column the element corresponding to third row third column and so on. So if you look at the matrix, the main diagonal will comprise of the variances of the estimated parameters. The off diagonal elements of the variance covariance matrix will represent the covariances between the parameters. So just now we are introducing the variance covariance matrix. It is important and enough at this point if you understand that the variances are given by the diagonal terms and the covariances are given by the off diagonal terms. And it is also important to note that the variance covariance matrix is symmetric. What is a symmetric matrix? A symmetric matrix is one whose appearance is unchanged when you change rows into columns and columns into rows. So you can have a symmetric matrix and when you interchange the columns and rows it appears to be just as the same. It is also important to note that the variance covariance matrix or simply called as the covariance matrix. Sometimes people call it as a variance matrix also. So the covariance matrix dimensions are p cross p. Do not get confused if sometimes you see variance covariance matrix or another times you see covariance matrix both are the same. Basically we have come to the form of the variance covariance matrix or simply the covariance matrix that is represented by C. It is bold. It is bold because it indicates a matrix and not a scalar and here we have x prime x inverse sigma squared. Let us represent the columns of x prime x inverse as C naught naught, C naught 1, C naught 2, C 1 0, C 1 1, C 1 2, C 2 0, C 2 1, C 2 2. So this represents the diagonal of the matrix. So C naught naught, C 1 1 and C 2 2 are the diagonal elements of this matrix and the off diagonal elements are given by those entities which are not along the diagonal. So all elements other than C naught naught, C 1 1 and C 2 2 are off diagonal elements. So you have sigma squared outside. You may as well take sigma squared inside and multiply all these terms with sigma squared. So this is a symmetric matrix. What is a symmetric matrix? If I change rows into columns and columns into rows, the matrix appearance is unchanged. That means C naught 1 will be equal to C 1 0, C naught 2 will be equal to C 2 0. If C naught 1 is equal to C 1 naught, then it will appear as if there is no change. Similarly C naught 2 will be equal to C 2 0 and here also C 2 1 will be equal to C 1 2 and C 2 0 will be equal to C 0 2. So then you have a symmetric matrix and that is what I have represented here. C 1 0 is equal to C naught 1, C 2 0 is equal to C 0 2 and C 2 1 is equal to C 1 2 and this is a x prime x inverse matrix. It is a symmetric matrix and the variance of the estimated parameters beta hat are given by the diagonal term sigma squared C jj where j is equal to 1 or 0 or 2 and the covariance between 2 different parameters beta i and beta j are given by the off diagonal terms. So there is obviously a typo here which I will correct. So that is what you have here. The covariance between 2 different parameters beta i hat and beta j hat will be sigma squared C ij where i is not equal to j. As I said earlier, we do not know the value of sigma squared and hence we need to have an estimate for the error variance and we also have to make sure that this estimate is the true error variance and not have any systematic influences. So we want to replace sigma squared by an estimate of sigma squared. We call it as sigma hat squared. In the true regression model, we had y is equal to x beta plus error. That beta is the column vector of true parameters describing the experimental phenomena or rather the phenomena investigated by the experiments. Since we do the parameter estimation based on the available experimental data, the influence of errors are also there and hence our model is not accounting for the random phenomena, it is only accounting for the systematic phenomena and hence we are only getting estimates of beta and that is given by beta hat. Even though we would like beta hat to be as close as possible to beta, we may not be able to achieve the aim because the data is subject to experimental uncertainty which is not included in our regression model. It is accounted for separately as the error term. Similarly, when you want to use sigma squared, since the true value of sigma squared is not known, we need an estimate of sigma squared which we use in our calculations and we call that sigma squared as sigma hat squared. How to find it out? We will see shortly and then once you are able to find the sigma hat squared, the square root of the estimated variance of the jth regression coefficient is called as the estimated standard error of the least squares estimator beta hat j. Now we do not use the term standard deviation here, we are again taking the square root of the estimated variance of the jth regression coefficient and we call it as estimated standard error, it is not called as standard deviation. So the estimated standard error of the least squares estimator is given by Se, Se stands for standard error for beta hat j and that is given by square root of sigma hat squared Cjj. So this j here is matching with the j's given here and this is an estimated value and we are using the variance, covariance, diagonal element multiplying it with the estimated error variance and when we take the square root, we get the standard error of the estimated beta hat j. How did we get the beta j hat or beta hat j? It is the least square method we adopted to find this parameter and hence it is called as the least square estimator of beta j and it is represented by beta hat j. The standard errors are a measure of the precision of the estimation for the regression coefficients. Small standard errors imply good precision. So it is a measure of the fuzziness associated with the estimated regression coefficients. If the fuzziness is too much, then there is a big spread around the estimated beta hat. But if the spread given by the standard error is quite narrow, then we have estimated betas or the beta hats with good precision or reasonable precision. For analysis of variance purposes, the estimation of the residual error is required. In order to also get an estimate of sigma squared, we need the estimation of residual error. The residual should ideally reflect the difference due to random factors and not systematic discrepancies created by using an inadequate model. And the residual error is also an unbiased estimator of sigma squared. So we define the error variance in the following manner. We have sigma hat squared is equal to sigma is equal to 1 to n EI squared divided by n minus p and that is given by sum of square of the error divided by n minus p. It is the difference between the actual experimental value and the predicted value. The error in a column vector form as y minus y hat experimental vector and this is the model predicted vector. Each entity we may represent it as EI, I running from 1 to n. So it will be yI minus y hat I for the residual I or the ith residual. Sum of square of the error is actually given here itself. I is equal to 1 to n yI minus y hat I whole squared and that is summed to give the sum of square of the error. So if you look at Kutner et al 2004 reference, we can define the covariance matrix or the variance covariance matrix as the expected value of beta hat minus expected value of beta hat. That is multiplied by again transpose of beta hat minus expected value of beta hat. So you have this and we have to expand it and express it in matrix form. So we have expected value of beta naught minus beta naught beta 1 hat minus beta 1 beta 2 hat minus beta 2. So we have that matrix multiplying with this matrix compressing of only 1 row and 3 columns. So we have transpose of this written here, transpose I am converting rows into columns. So I am having 1 column here with 3 rows. I am converting it into a matrix with 1 row and 3 columns. So this becomes beta naught minus beta hat minus beta naught and then this goes to the row element beta 1 hat minus beta 1 then it goes to the next row element beta 2 hat minus beta 2. So this is what we have. I can first multiply this and then find the expected value as given by E and also an important thing to realize is the expected value of beta hat is that parameter beta itself. So this is an unbiased estimator beta hat. Now when we first multiply this it becomes symmetric matrix and the expected value of the diagonal terms will become the variances and the expected value of the off diagonal terms will become the covariances. So let us do the multiplication we can beta naught minus beta naught into beta naught hat minus beta naught that is what you have here, beta naught hat minus beta naught into beta 1 hat minus beta 1 and that is what you have here. You may want to do the calculations on your own to see whether you get this particular form.  So the matrix is symmetric. We can show it for other terms also. What other term we can show? So you have 3 2 will be equal to 2 3, third row and second column element is this that should be equal to the second row and third column element and that is what these two are matching. So we can conclude that the matrix presents inside the argument is symmetric then we apply the expectation to all these elements in the matrix and we know that the expected value of beta naught hat minus beta naught squared is nothing but the variance of beta naught hat okay. So that becomes quite straightforward and the off diagonal terms will become expected value of beta naught hat minus beta naught into beta 1 hat minus beta 1 and that would relate to the covariance beta naught hat and beta 1 hat. So to find the sigma hat squared we have sigma is equal to 1 to n EI squared divided by n minus p that is sum of square of error divided by n minus p. So this is how we are finding an estimate of sigma squared the error variance and since we are finding an estimate we denote it as sigma hat squared and sigma is equal to 1 to n EI squared divided by n minus p equal to sum of square of error by n minus p. So that is accounted for. And then what we do is we have that value sigma hat squared and then we can multiply all these elements with that sigma hat squared and then we can find the different variances and covariances of the parameters and their combinations. So when I multiply this, this would become the variance of beta naught hat and this would be the variance of beta 1 hat and so on. Now we are going to talk about regression sum of squares and error sum of squares. So what we do here is we express the deviation between an actual response and the predicted response in terms of two deviations, deviation of actual response from mean response and deviation of predicted response from mean response. So rather than putting it in the words, let us see in symbols. So first we are expressing the deviation of a particular response from the average value of the observations. You are conducting all the n experiments and you take the average value of the response. This is yi minus y bar and that may be written as yi minus y hat i plus y hat i minus y bar. This will cancel out with this. So you will be finally getting yi minus y bar or we can write this equation involving the deviation of the actual experimental data point from the predicted value y hat i as y minus y bar, yi minus y bar minus yi hat minus y bar. So we are defining the residual as the sum of two or as the difference of two entities, deviation of the experimental observation from the mean value, deviation of the predicted value from the mean value. This is very interesting. Directly writing yi minus y hat i, you are writing it as yi minus y bar minus yi hat or y hat i minus y bar. So you are adding and subtracting and adding y bar in this expression. So the residual which is the discrepancy between the actual experimental value and the predicted value is expressed as the difference between yi minus y bar and yi hat minus y bar. So what is the discrepancy of yi with respect to the mean value that I will subtract with the discrepancy between the predicted value and the average value y bar. So that can be shown graphically in a nice fashion. This is the actual experimental data point and that is slightly off from the prediction value. This is yi and then you have y hat i and this is the average value based on all the experimental data points. So we want to find the deviation between these two, the residual that may be expressed as the deviation of yi with respect to y bar minus the deviation of y hat i with respect to y bar. Next we go to hypothesis testing and linear regression. So we are going to start a new phase in the regression analysis and it is also interesting to note that whatever we studied in the first part of statistics for experimentalists are coming into play in the second part as well or in the second phase as well. So now you will be able to appreciate with your background and inferential statistics on what we are going to do with linear regression. When we apply those to linear regression things will become very clear and you also will understand why we are doing these kinds of tests. So the hypothesis test is what we are going to study in detail in the next lecture. I request you to not only brush up your fundamentals in linear algebra but also look at the concepts we covered in hypothesis testing. Find out what is meant by level of significance, the p value, the region of acceptance, region of rejection, the confidence intervals. Please refresh your concepts on these topics and if and if and once you have done so whatever we are going to discuss next will become very simple. Thank you for your attention.


So, we derived an expression for the Fourier transform of the occupancy probability in a d dimensional space. So, in principle the problem has been solved, but it is in the conjugate space. So, we just recapitulate we showed that the Fourier transform defined as the Fourier series on the discrete lattice points of finding the probability at the nth step can be written in terms of the conjugate variables k 1, k 2, if there is a d dimensional space there will be d conjugate variables and that was given as 1 by d sigma i equal to 1 to d cos k i whole to the power n. So, this is the general solution to the symmetric random walk problem in dimensional space. The general solution to the problem now given the Fourier transform one can always obtain the occupancy probability in the real space by d dimensional Fourier inversion. So, that is we can obtain W n let us say these integers of the lattice points are denoted by m 1, m 2 etcetera in the various directions. There are d such directions and this will come as 1 by 2 pi it will be 2 pi to the power d and there will be d fold integrals minus pi to pi minus pi to pi over all k i. So, it will be d k 1 etcetera d k d then the Fourier transform will be i into k 1 m 1 plus etcetera k d m d multiplied by by definition W n tilde k 1 to k. So, this formally closes the problem, but the real insight comes only when we actually carry out this inversion for that we can quickly see that in a hypersphere or in a hyperspace the components k 1 k 2 k d etcetera can be represented as components of a vector k. So, if we define k is a vector which has components k 1 etcetera up to k d and similarly r is a vector which has components on the lattice points all integer components m 1 m d along the various dimensions. Then we can write in a compact form W n m W n r nth step the probability of being at a vector point r which merely designates all these coordinates will be 1 by 2 pi to the power d and there will be d fold integrals basically one could write d k d that is just illustrate that there will be d such integrals of e to the power minus then you can write i k dot r and W n tilde vector k just let us remember it is a k fold integral to explain the left hand side is the occupancy probability of the particle at a lattice point denoted by a vector r with the components m 1 m 2 m d up to m d at the nth step that is given as a Fourier inversion of the Fourier transformed or characteristic function we can call it of the occupancy probability in the k space. Inversion being carried out through d integrals each of them varying from minus pi to pi y minus pi to pi we saw that there is a completeness and orthogonality of d to the power k or cos k sin k functions in this space for periodic lattice problems. So, in a general hyper lattice like this. So, we are at some vector point r and we have started from some origin here 0 0 d dimensional origin. So, we random walker has executed a path possibly landing here this is one of the paths. So, we are asking for the occupancy probability at the point r via which is a superposition of several such paths with the proper weighting. Now, the we introduced the concept of the probability of return to the origin. We can ask a question if a random walker starts from the origin spans the entire hyperspace what is the probability that he could arrive at the origin at some point in time during his path. It is possible that he will arrive infinitely many times over because if he arrives once then it allows you to imagine or restart the process from that point in time and then he has to arrive once again. So, in other words we therefore, can ask a legitimate question what is the probability of return for the first time to the origin. It is somewhat closely connected to the absorber problem that we mentioned which refer to the probability of contact at a on an absorber placed at a point other than the point of starting. So, here there is no absorber. So, it is only a point of revisitation that we are looking for. Hence, we can postulate a probability probability that a random walker visits the starting point in this case origin in for the first time in k steps. For example, for in a one dimensional walk the probability that he visits in the first step is 0, but in the second step there is a probability that he would come back because in the first step he would have gone to sites minus 1 or plus 1 and. So, any side you would have a probability if it is he has gone to the plus 1 then there is a probability again of half of him visiting back to the origin from the plus 1 side and half from the minus 1 side. So, one has therefore, a finite probability of visiting the origin infinite number of steps. We denote this probability as denote by a notation f k. We have thus two concepts one there are two concepts which we should distinguish. One occupancy probability at the origin that is w let us say n 0. This merely gives the probability of finding the random walker at the nth step at origin and that finding could be a result of several returns that has happened before the nth step, but it is actually it is more like the mass or weight you associate with that point origin. So, this is a different concept and the probability of return for the first time say in n or k steps it is a k steps. These two are different concepts and to illustrate we it is useful to discuss first the concept of occupancy probability a little more with the whatever we have understand understood so far then return to the concept of the return probability in k steps. So, let us delineate a few aspects of the occupancy probability occupancy probability let us say w n 0. If we go back to the formula we have a very general expression for the occupancy probability at any site r denoted by vector r which can be obtained as a Fourier inversion of the Fourier transform of it for which we have already developed a closed form expression in terms of the sum 1 by d i equal to 1 to d cos k i to the power n. If we consider just one dimension for example, we have already a closed form solution we even obtained a closed form solution even in two dimensions. So, in general w n at the origin can be computed by just putting r equal to 0 in this expression. So, in which case it just becomes w n 0 is going to be in a d dimensional system 2 pi to the power d and there will be d fold integrals minus pi to pi d k say d fold integral then e to the power i k dot r become 0 1 because r is 0 e to the power 0 is 1. So, that will be multiplied by 1 and then w n tilde vector k in d dimensional space. So, this quantity can be understood a little better by studying the case of 1 d. For example, in 1 dimensional system we have the most general result that w n say let us say w 2 m even steps in 1 d 0 is given by 1 by 2 to the power 2 m 2 m c m. How does it come? Recall w n 1 d at m equal to 1 by 2 to the power n n c n plus m by 2 formula and since we knew that it exists only for n plus m even then only it exists and not otherwise. Now, in our case we are talking of specifically at the origin. So, we put n m equal to 0 and then it becomes 1 by 2 to the power n n c n by 2. Now, we know that since m equal to 0 n also has to be even because m is even. So, hence if put n equal to 2 m then it will be 1 by 2 to the power 2 m 2 m c m as we showed here. So, this is our starting formula from which we can derive it. We can show in fact, we had shown earlier in while discussing the properties of 1 dimensional random walk that for large m by performing a symptotic approximation to factorials using Sterling's formula w 2 m in 1 d at 0 it will go as 1 by root m. I am I am not including some of the pre factors, but as a functional behavior it has a probability will decrease very slowly in this as a square root of m. So, this is a very important property to note. And as you can understand the probability at m equal to 1 for example, w 2 in 2 steps 1 d of being in origin can put m equal to 1. So, you will have it will be 2 square and here it is 2 c 1, 2 c 1 is 2 factorial divided by 1 factorial. So, it is 2 by 4 which is half. So, in the after the first after the second step there is a probability half of the random walker being at the origin. So, we can delineate what we are saying in the asymptotics is that after sufficiently large number of steps the probabilities decrease rather slowly. We also solved similarly we also developed a solution for the occupancy probability in 2 d and if you apply that formula it actually included involved with sum it was something like n factorial divided by 4 to the power n it included a sum r equal to 0 to n. Now, if you put m equal to 0 or m 1 and m 2 both the site indices being 0 then it will be r by 2 factorial and again there will be a r by 2 factorial. So, it will be r by 2 factorial square and similarly here it will be n minus r by 2 factorial square. This follows substituting say m 1 comma m 2 equal to 0 in the expression for the solution to 2 d random walk problem. Since even in 2 dimensional case the possibility of coming back to the origin exists only in even steps for symmetric random walk we can then this whole W n equal to 2 m if we put now m here refers to steps of coming back to origin that will be it will be you can actually write it as 2 m factorial divided by 4 to the power 2 m. Now r r by 2 can be changed by replacing r equal to 2 k and then k equal to 0 to m it will be then it will be 1 by k factorial square into 1 by m minus k factorial square.  In fact, these kind of results are available in many handbooks and software such as Mathematica automatically sum this series and give you the results. So, this can be for example, summed in Mathematica. So, there is a closed form expression for the probability of return to the origin in a 2 dimensionals case after 2 m steps. Again we can do the asymptotics and we can see that ok we can note for example, we can assign values of m equal to 0 1 2 etcetera and we can see that w 1 0 0 that is 2 steps will become 1 4th and the next probability w 4 0 0 will turn out to be 0.141 etcetera can assign values and then obtain this. Asymptotically m tends to infinity we can use the sterling approximation for the gamma functions which are factorials we merely present the result here which says that w 2 m 2 d it will vary as 1 by m some pre factors are there I am ignoring the pre factors as m tends to infinity. So, now we have 2 results in 1 d the occupancy probability w 2 m 1 d at 0 varies as 1 by root m in 2 d same thing w 2 m 2 d 0 0 varies as 1 by m. So, let us say if m is 100 it will be varying as 1 by 100 or if we increase 100 to 400 it will become 1 4th 4 times less it was 1 by 100 and it has become 1 by 400 which is 1 by 20. So, basically it has become twice 1 by 4 or 4 times less whereas, here when m was 100 this is 1 by 10 and where m is 400 is 1 by 20. So, it is only twice less. So, the decay in one dimensional case is much slower in other words in two dimensional case there is a far more rapid dispersal tendency to disperse away from the origin is much more stronger than in one dimensional case. In other words the dimensionality of the space now has a role to play in terms of the speed of the process. One can actually plot this behavior as a function of m for 1 d and 2 d. So, if 1 d decreases like this 2 d will decrease this is for 1 d this is w 2 m at the origin and this is for 2 d there will be far more rapid decay of the probabilities of of finding the particle at the starting point at the origin in 1 d and 2 d. In fact, these probabilities will decay even faster at higher dimensions. So, with this picture of the occupancy probability we now move over to the general question of asking what is the probability of return which is a slightly different concept and what is the probability of ultimate return and in doing so we link the two concepts by a logical argument and if you know one you can calculate the other. So, they get related, but in the process we get an answer to a very important question of the what will be the probability in a general dimension or in lower dimensions is it possible to escape at all origin at all with certainty. This is called the Polytheorem which says that in 1 and 2 dimensions a random walker cannot escape revisiting the origin at some point in time he will revisit. So, if you revisit at some point in time you can restart the process and he will revisit again. So, in other words the process becomes infinitely recurrent from the property of its total time translational possibility. Thank you.


I was surprised to see in this popular infographic that there was evidently promising evidence that coconut oil could help with obesity. Well, if you pump the stomachs of rats with purified, medium-chain fatty acids, one component of coconut oil, they end up eating less food, but you don't know if there's any relevance to humans until you put it to the test. Researchers compared breakfast with the same amount of dairy fat, coconut oil fat, or tallow beef fat, and no effect on hunger, fullness, satisfaction, or how much they then went on to eat at lunchtime. So where did this whole idea that coconut fat was somehow different come from? Well, six years ago, an open-label pilot study was published. They asked 20 men and women to eat two tablespoons of coconut oil a day for a month, and the men appeared to lose about an inch off their waist. Now, open-label means that the participants knew what they were eating. There wasn't like some placebo control. In fact, there was no control group at all, so you don't know if the effects would have just happened anyway without the coconut oil. There's a well-recognized effect in dietary studies, where just being in a dietary study under observation tends to lead to a reduction in caloric intake, because you know they're going to weigh you and looking over your shoulder. But there had never been a controlled study of coconut oil and waistlines in men and women until 2015. About 100 men and women were given about a tablespoon of coconut oil a day for three months and lost nearly an inch off their waist after three months compared to control. What did the control group get instead? Nothing. There was no placebo, and so they were comparing doing something with doing nothing. And when one does that, there's often a placebo effect, regardless of the true efficacy of the treatment. And they also suggested that coconut oil group may want to take their dose with fruit, and if they did end up eating more fruit, that in and of itself may help, as despite its sugar content, fruit consumption tends to be associated with anti-obesity effects. What we need to see if coconut oil has some special effect is to give people a spoonful of coconut oil versus some other oil and see if there's any difference. And when you do that, two tablespoons of coconut oil a day versus two tablespoons of soybean oil a day, no significant difference in waistlines. But what did happen was a significant increase in insulin resistance in the coconut oil group, which is what eventually causes type 2 diabetes, despite being told to increase fruits and vegetables, cut down on sugars and animal fat, and despite an exercise program of walking 50 minutes a day, four days a week. The only other placebo-controlled study of coconut oil and waistlines was published in 2017, and no significant changes in weight or waist or hip measurements, total fat, belly fat, nor butt fat. No benefit to coconut oil for obesity over placebo shown in any study to date. So how can coconut oil proponents get away with saying otherwise? Well, they like to talk about studies like this, showing that Pacific Islanders who eat more traditional coconut-based diets are slimmer than those eating more modern diets with fewer coconut products. But guess what they were eating instead? The modernized dietary pattern was primarily characterized by high intakes of sausage eggs and processed foods.


And welcome back. We're here live at the Cosmopolitan Hotel in rainy Las Vegas. Doesn't rain often, but here it is. When we show up it starts to rain. I don't know what that's all about. We're here at .com 2012, Splunk's annual user conference. I'm Jeff Kelly from Wikibon. I'm joined by Jeff Brick, SiliconANGLE, my co-host. Hey Jeff, we're really excited to be here. The day's going fantastic. It's not only raining, it's huge thunder lightning, so we must be touching on some interesting topics or getting into some great places. But we're really excited to have our next guest, David Caruso with us. As he said, he's the third employee of Splunk. I know a lot of you out there have been at startups. I know a lot of you have been the third employee or the fifth employee or the startup guy. And it's not often that you get a company that's successful and makes it all the way out. Builds a successful product, has as many happy customers as we've talked to already, and then even gets the IPO, which is kind of another process on the journey. It's not an endpoint as all my venture capital friends are happy to remind me. But not only that, but David literally wrote the book on Splunk. And there just aren't that many guys that have written the book on a subject. So we're really excited to have you, David. Thank you very much. And welcome to theCUBE. Hopefully we'll get you back to theCUBE as a frequent visitor. Thank you very much.  Seven years ago, seven and a half years ago? Yeah, yeah. You know, what was it? Where did you come from? Who are these crazy guys that you decided to join? Why did you think maybe this might be the one? So when I interviewed, it was just a few guys in essentially a cubby of the venture capitalist office. So we didn't even have our own office. And when I started in February 2005, we had a very small space. We were actually renting a part of Six Apart's office space. And it was just six of us. And we were building a product and we were having a lot of fun doing it. And it was a small team, but a very good team. It had a lot of interesting qualities. The founders are very much a part of the success of the company in the sense that one was very concerned about the appearance and the coolness of the factor. One was very open and honest, and one was very brilliant technically in the sense that there was this combo, this perfect storm that made things really come together nicely. What inspired them? Were they working in a job and there was a challenge that they couldn't overcome because there was no tool? Yeah, so they struggled. They spent two years basically unemployed intentionally looking around for what problems there were in the IT space. And they interviewed company after company and basically found a niche that was glaringly untapped and they went after it. And that's why having the right niche is critical obviously to the success of your company. And they found a very good niche that was just completely untapped. When you talk to system administrators years ago, there really was no good tool for this kind of analytics. You have thousands of machines or even hundreds of machines and you have a problem on any one of them. There were no tools to diagnose things. You would have to connect into that box, look around on the logs. You could ref, which basically just do a tech search. And it was very primitive and people would spend hours doing these things. And there was just this real untapped need that Splunk filled. And with a lot of creativity and hard work, we made it faster and faster and better and better. And it's a really good scalable tool that is useful to people outside of the IT department now. Yeah, and when I first interviewed, by the way, it's interesting to say that I didn't want to take the call because logs sound boring. But once they described the problem, it was anything but boring because there's so many easy problems are not interesting, but hard problems are interesting. And these were all these hard problems that you have to deal with from AI, artificial intelligence to just good engineering and scalability and understanding your data. There's just a lot of really hard, interesting problems here. And that's what drew me to it. Tell us a little bit about your role. We've seen your title sometimes as principal scientist. I've heard Chief Mind. So I want to fill this in a little bit about what the Chief Mind does. Sure. Right now I'm in the office of the CTO. So Eric Swan is the CTO. And we have a team that basically does special projects. And that's a relatively new department. Previous to that, I was in engineering and basically building a lot of the core part of the data coming in. I wrote the search language and just sort of a lead engineer working on things. And in the office of the CTO, I'm working on special projects like the book. And different things. Building apps to make Splunk more useful. So there's a whole team of brilliant people building the product, but on top of the product, you can build apps that just make it more useful. And there's a whole world of things that you can do. Just like a database is a great thing, but there's a world of other things you can put on top of it to make it more useful. Let's dig into that. Kind of the apps. We've been covering the big data space for a while at Wikibon. And one of the things we're not seeing is a proliferation of big data applications at this point. A lot of work and the plumbing layer, you might say. The infrastructure. But really kind of that last mile is the application to bring it to the end user. So tell us about some of the applications you guys are working on. What are you excited to do? What interests me personally are things like predictive analytics and sentiment analysis. So predicting values in your data, understanding how users feel about your data, cleaning your data. There's anything to do to automate things. Finding anomalies automatically. So our core product has a search language, but out of the box, finding anomalies is a little bit of an artwork. But to build an app to help you find anomalies and things like that are great. I think part of the problem with apps and big data is monetizing it and making it the right place for modernization and just the right marketplace. And it's not quite there. We're working on it. But it's growing. It's definitely growing. We're building apps. Outside companies are building apps. It's growing. You'd love this massive exponential growth and I'd love to tell you that there are ten times more next year. They are growing. And not everybody, people build apps for their own corporation. They don't necessarily have an interest in, if I work in a corporation, what's my motivation to make it public and to help other companies? In the big data world, there's some of that community, but there's also some of that, you know, part of what we're using these tools and technologies for, for competitive advantage. So you don't necessarily have to share some of that on paper. Big data is a big advantage. A few percent between you and your competitor, a couple years you're out gunning them by far. These big data can add, these small percentages really add up and it's just critical to companies to use it. You've got gold in your data and it's being ignored. I'd like to say that if it's plugged in and it's not a coffee pot, it's spitting out data. And maybe even coffee pots nowadays. Coffee is the second most traded commodity in the world after oil. Actually, I think you need to start tapping in more coffee pots. There you go.  You know, key card data and data from your phones and data from every computer, server, cloud, just all over the place. And they're being ignored and there's really useful stuff in them. My kids were late. They had a school trip flying, believe it or not. My kids flew from Vegas back to the Bay Area. They had a trip. It was actually to Zion National Park. But they were late. And you know what I did? I splunked all the FAA data of every flight in the last 30 years. I just stuck it into splunk. Every little flight, how it was delayed, where it went, everything. I go, you know what? You should have known that flight's going to be delayed. That flight from LA to San Francisco is historically really, really late. How funny. And I knew it. You know, and it was just, there's so much interesting stuff out there. So I'm sure whoever the competitive airlines would have liked to have known that when they put their ticket on Expedia. Yeah, and you can see like over winter which airports slow down because of the snow and just amazing, amazing stuff in there. So I want to ship gears a lot. There's so many places we could go and again, I hope we get you back on the queue. But we talked before we started a little bit about the culture. We talked about, from a startup perspective, so many startups in the valley and so many of them unfortunately just don't make it for a whole host of reasons. But you guys did. And you mentioned very specifically about the culture of the company and the leadership of the company. And we've heard from some other people about tremendous things about the leaders, Godfrey and his leadership style. And of course he came in halfway through this journey from the beginning. So if you could expound on that a little bit, what makes those guys special? How do they lead and how has that really contributed to the success of the company and what you guys have going on? We can see it all in the little preview videos of the camera walking through the offices and it's like they're having a good time. So I guess I like to say that just like your product and your niche is critical and not an afterthought to your company and your patents and your strategy are not afterthoughts, the culture of your company shouldn't be an afterthought.   Your friends should be at work. You should want to be there. You'll be more productive. You'll have more fun. You'll be more open. You can criticize your friends. You can't criticize people that you're sort of cold and professional with. And so constructive criticism is really how you evolve. It's how your product gets better. It's how features get better. That constructive criticism allows things to improve. And if you have this cold professional environment, you don't. So Splunk is a very funny environment. Humor is just a good metric for intelligence as any job interview test. So I really encourage companies to have a good time while they're making money. They're not exclusive. It's not a coincidence. They go hand in hand. So human, they're pretty much from the beginning. Developing that kind of culture when you're a really small six person organization is one thing. But how do you scale that? It's an excellent question. We've actually, believe it or not, paid attention to it from almost day one. Every year we have a company meeting and we've had quarterly meetings and sales kickoffs and things like that. And we actually have a session about how do we keep the culture alive. We love working here. How do we keep it like this?  We like the beer. We like the ping-pong tables. We like this. We like that. How do we keep it fun? How do we not hire people that will take away our toys? And we've been pretty successful. I wouldn't say 100% successful. But we've been pretty good about maintaining that culture because we've been aware of it. And we've known that this is a precious commodity that we wanted to hold on to. So I think you have to spend some time thinking about the culture you want. And not from a top-down thing. It's a bottom-up. Where do you want to spend your working hours? It's an interesting twist. Intel is famous for their constructive criticism. In fact, they teach classes on constructive criticism so you can get in somebody's grill in the meeting and nobody takes offense because we all took the class last week in HR. You don't need a class if they're your friends. Yeah. But you've got disruptive as one of your core company values. But it's disruptive with fun. As he said, it's a different way to look at it when you can be disruptive with a real friend because you can tell them what you want to tell them because you're not worried about whether they're going to take it the wrong way if they're not going to take it really as a constructive when you're both working together to get to a better place. Absolutely. That's a great testament on the company. But of course there was the IPO and that can change things for some companies and not always for the better in terms of culturally. There was an IPO? I believe there was an IPO. Okay. Sorry. I missed that. Sometime in the spring. So has that put any, you know, when you're dealing with investors on a quarterly basis, can you put some pressure on the type of culture your company has built? Right, right. Have you found that to be the case and how have you guys dealt with that? A little bit. Not much. A little bit. There's a little bit of a tightening about what you can say, what you should, you know, what you can publicly say and what you, just being a little more careful in terms of your public face. So I wouldn't put on Facebook, you know, necessarily a really glowing spin on certain things. I would be a little more cautious on certain, but within the company I think we're all good. Yeah. Yeah. So I don't think it's put a damper on the fund. That's good to hear. The brew is still flowing. Very nice. So looking forward, what are some of the exciting things you plan to do in the next six, 12 months? What's your priority list look like? You know, next year at this conference, when you come join us at theCUBE, what will we be talking about? Sure. Well, I'm really excited by a lot of the improvements that engineering is doing. Not necessarily me. I'll be doing good stuff, but they're going to be doing great stuff. The speed and the improvements to the product are really, really amazing. I've been cautioned not to talk too much about the future, but it will be impressive. Yeah. And, you know, for my part, I'm going to be building out some more interesting apps and we'll be extending the book. The nice thing about this new world of print-on-demand is that you can basically send a new PDF and do a version two of the book. So the book is available on Amazon.com right now. But I also mentioned that it's actually free online. Oh, okay. The PDF, Kindle, and iPad version are free. Okay. We sell software. That's how we make our money. We don't make money on books. So we have no interest in having, you know, we want people to be educated about Splunk. So this is not how we make our money. So the book is free online. It costs money to buy it at Amazon purely because of the paper and the transport. Right. But if you go to splunkbook.com. Splunkbook.com. Yeah. You can find it. And so the book is divided half into basically an introduction to Splunk, how to see the world through the Splunk way of thinking. Great. And the second half is a cookbook, sort of recipes are the most common sort of problems and solutions and how to do them. So it should appeal to the very beginner as well as the intermediate person. Yeah. And hopefully over the year I'll be expanding the cookbook. Great. We look forward to that. Yeah, the predictive analytics is interesting because we just had Marquis on before you came on. Right. And he talked about the amazing event of typing in some search and key phrases and coming back with stuff that he wasn't anticipating. Right. It was far more interesting than that which he was looking for in the first place and going off down a whole other track of value. Right, right. So it looks like the pixie dust is right there. You just got to have it kick out in the first place without him having to put it into the search algorithm. I have a talk tomorrow on data mining in Splunk. Okay. And one of the things I emphasize is that people tend to look at Splunk or as any of these products is you build a dashboard of things you know you want to see, you know, the events per time or how many web pages I serve per time. But I would encourage people not to limit themselves to that, to really explore your data. Use Splunk as an exploratory engine to go and go, well, what about, you know, language versus IPs versus time versus, how does that compare to last week? There's a whole host of dimensions that you're ignoring because you sort of have this a priori belief in what's important. Right. But you know what? You're missing these outages. So we were once spending an interesting amount of our advertising budget on countries that didn't speak English. And data saved us some money. The people who weren't speaking English weren't buying the products surprisingly because our website was in English. And so there's a lot of gold in that data. Sure. And you got to pay attention to it. And you need to explore. Yeah, you need some kind of, I feel lucky button. And just, you know, keep hitting the button and it keeps spinning the dials here we are in Vegas. We don't have the other. It comes back, oh, here's the relationship I had. Absolutely no clue that these four factors correlated in some interesting way. Yeah, yeah, yeah. We don't have it to that level yet, but that would be very nice. Fantastic. Well, we're here live at .conf, Splunk's annual user conference in Las Vegas. We've been speaking with David Caruso, principal scientist, chief mind, just all around good guy. That's black. Thanks so much for joining us. Thank you very much. Thanks again. We really do appreciate it. And we'll be right back with our next guest.


Hi guys, this is Rich here on behalf of Rich TV Live We are 11 days 15 hours 54 minutes and 27 seconds away from history And if you want to learn about all the top news just go to www.richtvlive.com hover over news everything you need to know is right there cannabis news global news Canadian news American news Everything you want to learn about stocks and use all the tools I use all right there absolutely free and If you want to follow us you can follow our secret stop picks group our group chat and our discord chat Absolutely free and get picks 24 hours a day seven days a week and we got some more breaking news Livewell Canada Re-aligns its leadership to position company for global growth in health and wellness This is big news from Livewell LVWL on the TSX Venture Exchange LXLLF in America This is the news the company is pleased to announce that the health care leader mr. David Randy Monty in addition to his role as president will also assume responsibilities as chief executive officer effective Immediately the move is part of Livewell's vision to become a world leader and health and wellness through quality outcomes and Strategic partnerships love this company Livewell is an innovative Canadian hemp and cannabis company focused on advanced research on CBD three letters I love I'm in the CBD business live. Well, you guys should hold it at your boy I got the best CBD's in the world and 32 million dollars worth of isolate it's true and Other cannabinoids as well as developing and distributing prescription and consumer health products Supported by data discovery science and technology Sean Poli co-founder chief executive officer and director of Livewell Becomes a special advisor to the company in his new role mr. Poli will continue his focus on capital market efforts Including communication Communicating with dealers brokers and other market participants Mr. Poli will also continue to undertake searching for strategic partnerships and acquisitions a community outreach program coordinating relationships with various entities including the city of Ottawa other municipalities national and international organizations and Charities Tim McCunn Chairman of Livewell Canada stated as a fellow co-founder Sean has been instrumental in creating an organization with a significant asset-based and Strategic partners he will continue to focus on these areas and further value creation opportunities for live Well Sean Poli commented David has a consistent track record of building high performance teams and top brands that are both best in class and Industry his performance has been consistently delivered through highly creative strategic tactical and financial plans as well as Exceptional leadership and flawless execution. We welcome to an expanded role with live. Well Risk mr. Randy Monty is a health care leader with 30 year track record of building the number one brands Including senior roles at some of the world's most prominent organizations such as Johnson's and Johnson's Pfizer and Merck Impressive mr. Randy Monty drove innovation within the biotech and women's health markets in Canada and has extensive Experience in global health and wellness markets his pioneering spirit pursuit of innovation and background in capital markets Makes him ideally suited to optimize the company's growth trajectory in the fast developing cannabis and help based Health and wellness markets worldwide in his role as president in Chica's chief executive officer Mr. Randy Monty will continue to focus on Executing the company's global health and wellness vision including strategic partnerships investments and developing live wells prescription and consumer health products supported by data discovery science and Technology about live. Well guys. This is a dollar stock live. Well, Canada ink LVWL in Canada LX LLF in America is focused on improving health one person at a time Utilizing innovation supported by data discovery science and technology the cannabis and help company is conducting advanced research on CBD holler at your boy and other cannabinoids holler at your boy as well as developing and distributing Prescription and consumer health and wellness products love this company guys live Well is conducting major research on CBD has completed a white paper on CBD from industrial hemp and Is also investing in technologies for the extraction and isolation of CBD oh, I got extraction machines guys holler at your boy and other cannabinoids for use in Prescription and consumer health products the company has secured major supply agreements for industrial hemp biomass as More than 1.5 million square feet of greenhouse under construction in Ontario and Quebec I say pardon and is also supported by business partners such as can it be growth? What and can it be rivers? Okay, that's enough. I need to buy me some live Well, they need to get on my watch list. They need to get on your radar now Remember risk TV live is strictly for education entertainment purposes Do your due diligence do your research before you invest in anything that we talk about here on rich TV live Go to the company website read their news read their financials Understand their share structure get to know these companies guys If you really want to grow in this industry if you want to be a success you need to learn to do the due diligence You need to learn to do the research. I love live. Well, I think this is a company that can be a huge success Let me know what you guys think if you like this video smash the like button share it everywhere Subscribe and hit that bell for notifications. So every time we got a winner you get it first. It's true Live well if you're not winning you're not watching all we do is bring you winners and we bring them to you first This is your boy rich No, no only 11 days 15 hours 48 minutes and 19 seconds away from history Live well. What do you think? big winner Comment down below our Mission we are innovative Canadian company driven to be a global leader in health and well-being by creating health products that match The actual needs of the population our mission focuses on advanced research on cannabinoidial CBD and other cannabinoids as well as developing and distributing prescription and consumer health products based on Predictability safety control and quality experience with more than 1.5 million square feet of greenhouses under construction Located in Ontario, Quebec and a world-class research and innovative Centre in Litchfield, Quebec the company is supported by renowned academic and business partners What do you think guys? I think it's a winner. You can book it Peace


$4,000 at the restaurant and $1,000 if you could buy it straight from the source. This is my very first time in a wine shop, no cap. All right, I'm not going to lie. A nice bottle of wine always felt inaccessible to me. I imagine it was for people like this and this, but with LeBron James promoting it as part of a healthy lifestyle, how can we not look into it? So we sit down with wine expert David Choi from Magna Carta Sellers and we'll talk about everything from cheap versus expensive, red versus white, discuss why wine is the future and also how Asians can be respected in an industry rooted in Europe. If you like wine or want to learn something about it, then hit that like button right now. Let's go. All right, we are sitting down with the winery owner from Magna Carta Sellers, David Choi. Today, you are going to be explaining to us why Asians should drink more wine. You're going to be breaking down everything about wine, which is great because I'm not going to lie. My knowledge base is like a zero out of 10. Well, I'm taking you guys from high school straight to the pros. You're going to be in the NBA once we finish today. We have two different types of cuisines here. We have Korean food from Boca right here, which is going to be your more pungent, more flavorful, little bit spicier foods. And then on our left side, we got Joe's Ginger, Shanghai Knees food, which is obviously a lot lighter. We're going to make sure everything complements each other. We're looking for the perfect pairing between wine and food, between the flavors, savory, sweet, richness, opulence. We're going to see it all. So we are going to learn why Asians should drink more wine. We're going to be able to break down what are different wines and we're going to learn how wines pair with different foods. And we're going to do it in a way that it's not too technical. It's in everyday terms what we live in in this world. Yo, I've been wanting to get into wine because I know that a lot of NBA players, LeBron, Chris Paul, Carmelo, they're super duper into wine, like 10 out of 10 level. So I figure if they're out of 10 out of 10, I could at least be at a three. All right, you guys, before we get into some pairings, I got some super basic questions for you, David. What is wine? Wine is a fermented grape that is processed through, that turns into alcohol that you can drink and consume. Okay, but these grapes are not the grapes from the grocery store or are they? They are similar to those ones that you purchase and you want the same flavors, but they're different grapes. These are wine making grapes. When it comes to being Asian and we have like rice wines and stuff, is that truly wine or does it have to have grapes? So you could call it a wine, but it's called a rice wine, right? So wine is generally produced out of grapes and what we have here is red wines, white wines, sparkling wines, but broken down a little bit more. You guys probably know grape types, Cabernet, Chardonnay, Sauvignon Blanc, but what we have is the regions where they're from. We have Champagne. Grapes have to be from Champagne, France for it to be called Champagne or it's called sparkling wine. Burgundy, simplest term, Burgundy. Red Burgundy is Pinot Noir grapes. White Burgundy is going to be Chardonnay. And correct me if I'm wrong. Burgundy is a place.  Okay. So then we have Saint-Saire. So broken down, Saint-Saire produces Sauvignon Blanc grapes. Okay, it's starting to get over my head, but let's power through it. We got to taste it. We got to do our preparing. We do have a Grand Cru Champagne from Jacques Delos, one of the great producers. I think he's the Lebron James of Champagne right now, the greatest artist, seafood always goes well with Champagne and we have a chicken dumpling. You don't want anything that'll overpower what you're eating, right? So like if something's a little lighter like seafood doesn't have that full flavor, texture, fatness that you have like in a steak or beef. How does somebody that is Asian end up a master wine maker and wine expert? Typically we're thinking a European person for sure. Well, it does take a lot of years and you know there's a lot of education that goes behind it, but for me it's all started in a wine store. I was tasting hundreds of wines every week and really that defined my palate. I took a passion into Bordeaux and that's sort of by a background in wines and that's why Magna Carta is a you know left bank Bordeaux blend. It's been a lot of time in France. Six, seven times a year, every year visiting the vineyards, meeting the farmers, the winemakers, really learning the techniques and styles. We just had to let the people know your credentials, that's all. All right DC, so with the food and the wine pairing, do you drink it first or eat first and then drink? I would always say we got a toast first and celebrate life, right? Okay, right. Is there a word to say cheers? I just drink. I haven't drank a lot of champagne in my life, but that's the best champagne I've ever had. Wow. So as far as champagne, I don't have to swirl it like I see people do with red wine. You can't, I mean you can actually get into it. You don't really see a lot of wine you know in Korea anyway. Wine is super expensive just because of the taxes to bring in the wines, especially from America. There's no wine to be produced in Korea. Growing up, being Korean and obviously soju is like super, super popular now. Everybody's drinking it. Is there some sense when you see all your Korean friends drinking soju? You're like guys try the wine man. If you look at the different things that we have on the table, sake and soju just wouldn't pair with a lot of these things like as well as wine. Got some chicken dumplings here. I took a bite of the dumplings. I'm going to take a sip of the champagne. This is an expensive ball of champagne. This is not your $12 Andres from the grocery store. This is the highest. $650. Bro, that is more expensive than Asa Spades. We're talking about Jay-Z's wine. How do I describe how much better this is than Andres's Spamoni? So first thing off, it's not as sweet. Andres uses, it's a little bit sweeter in taste profile. This you get some apple notes for me. It's a you know a creamy texture that you would get. It goes really well with that chicken dumpling. It enhanced the flavor. It almost was like a salt of the mouth. Alright, moving on to our next pairing. We have our first red wine and it is your wine, Magna Carta. Magna Carta. Let's check it out man. Yeah. So Magna Carta is Cabernet based. You guys know Cabernet grapes? I do not know. Cabernet, by the way, is a breed of grape. It is. Broken down a little bit more technically for you guys. This has Cab Merlot, Cab Franck, and Petit Fredot in it. So it's a mix. Is that usual? That's a Bordeaux blend. So Bordeaux blends generally have five grapes including Malbec. This is for this year. We didn't use any Malbec in it. The grapes come from vineyards and partners that I work with in Napa Valley. And you did not name this after Magna Carta Jay-Z's album? I did not. But we can call it the Holy Grail. Most people know that like red wine kind of goes with beef or steak. Your wine pairs well with Korean Calbee. It does. The fatness in the short rib goes really well with the richness in the Cabernet. For this one we're gonna take a bite of the Calbee short rib prior to drinking your Magna Carta wine. Always give it a little spin, a little wrist action there. They're very nice. So generally you don't want anything with like Harvey that has super high tannins in it. Which means Cabernet has a lot of tannins, which is that dryness that you feel. You know, older the wines, the tannins definitely soften up which you know makes it a great pairing with Korean barbecue, you know, steaks. It's very versatile at this age. It's $100. I think this complements the flavor a lot better. First time you've seen this. We've eaten a lot of Chinese food but we've never had wine with it. What can people expect man? So rich. I mean you guys just taste it right? Dark fruit flavors. I felt the fruit. The fruit is in there deep. Why do you think all these athletes are drinking wine now? The art form behind this really to see like a Duane Wade create his own wine. You know once you get into wine it's addicting. You guys are into sneakers right? Art is another one of those because it's a it's a limited supply. You know once you drink it that comes off the market. All right so for our next pairing we have a white wine with our pork dumplings. We have Shaolongbaos and then we have the Shenzhen Baos. Why the sans-sair? It always goes well with pork. It's a great filling. The acidity in the sans-sair, samyang blanc always goes well with that. I'm a little bit of a fan of like maybe wetting the mouth with the wine prior. Coating? Yes. That's hey man I'm already developing my wine styles. Little minerality. You know that's the profile of a sans-sair. Yeah I did totally like wash that my palate down right there. It kind of helped break down the fat. Especially with the Shaolongbaos because that gelatin is pretty caloric. This is the first time I'm doing these pairings as well. So it's always a learning process in wine and you're always trying to you know find that great pairing. This is a Shenzhen Bao. This is a more pan-fried Bao with a similar juice in the middle. I mean for me I thought the other pairing was a little bit better. I thought possibly this could actually pair with a red one. You know it has a little bit more richness to it. If you're eating Shaolongbaos, XLB's, soup dumplings, get the sans-sair. All right we got the spam kimchi fried rice from Boca and we're gonna be pairing this with the Chardonnay. Chardonnay is very good with savory foods right? So it actually does wash it down and pairs really well with spam. For our fifth wine on this Asian food pairing we've got a very trendy wine in the past five years, rosé. Rosé is basically you know you leave the grape skins in you know when you're pressing leaves it in a little bit gives it that that hint of pinkish color in there and then those grape skins are taken out. It's basically a white wine with some red wine in it. Rosé. And you're saying we're pairing this with the Korean fried chicken drumsticks and wings. Paya city which cuts through a lot of the fat. Rosé and Korean fried chicken. The popularity and rosé has grown over the last you know 10 years. It's great to have on a summer day chill it's great with food as well. I remember Jay-Z talking about rosé 10 years ago. No he sets trends so you know whatever he says. He made us all wear button-ups. I wore a button-up back then. The rosé that your heaven doesn't overtake the chicken doesn't even know there's a lot of fat skin there's layers in it. It cuts through clean. All right you guys our sixth and final wine for our Asian food pairing. The one and only Chateau Mutant Rosé Child. Is it from the Rosé Child family? It's the Rosé Child family. Yo! Shout out to Jay Electronica. The Illuminati. Yo this is the most expensive wine $1,000 at the restaurant. Oh at a restaurant? Oh this would be about $4,000. $4,000 at the restaurant and $1,000 if you could buy it straight from the source. What can we expect from this? This is a Bordeaux blend. So they use predominantly calf. There's a ton of cob frog and merlot in this as well. Why is it important to get air in there? Is it to mix it up? What does it do? Because you want to get the aromatics and you want to be able to get that flavor to open up in the wine. I'm not going to like pretend like I can break it down to the most technical level but I can tell you I can tell you it was very smooth. That's all I can say. A lot of layers. This right here is you know 15 years plus of age.  This is a pairing right here. $1,000 bottle of wine with some LA Calbee. It works. It works. The most expensive wine I may ever drink in my entire life. What would you say to Asian people who are like they're so used to having that rice wine that hard cut with no fruit and they're like dude I'm not going to eat like something made from grapes. I mean I think that's being sort of closed-minded right? Like you really want to open your mind up to try new things. All right you guys before we close out this section and we move on to our next location what was your favorite pairing today? I think I go back to the first one. The chicken dumpling and the jokselos. All right so my favorite pairing actually was your Magna Carta Bordeaux with the Calbee. Man that was like that was hitting man. Just let you know hey I didn't pay him to say that. Nah you didn't pay him to say that. All right just doing this video so far I gotta ask the question why should Asians drink more wine? I mean I think a lot of the benefits between wine culturally even especially being here wine is accepted at all you know sort of classes. Now I understand that wine obviously you know it's pretty much mostly a European thing. Being Asian-American like did you feel at all as an outsider while trying to get into wine? I mean you definitely feel it. There's nobody else that looks like us that's in the wine industry that you know in the past you know decade plus that I've been in it. You know we got to keep growing as a culture. It's going to open you up and just have so many different things for you to talk about and I realize now that it's a really fun technical world to get into with a lot of depth. Now we're headed to Astro Wine over in East Village for a very very helpful segment for you to describe what you should look for when walking into a wine shop because I'm not gonna lie I haven't walked into that many wine shops and I need to know the basics. We'll break it down on an easy basis on an every night basis on how to choose a bottle of wine. Man it's almost like walking to do a sneaker store. Hey just get grown. Alright you guys we are outside of Astro Wines. One of the best wine shops here in New York City we're gonna check it out. So we're gonna talk about different wines for different occasions what to expect when walking into a wine store. When we walk by a wine store we typically do not walk in. No but now after this video I'll bet you I will. This is my very first time in a wine shop okay. Alright Detroit we are at one of the biggest wine shops in New York City. This is one of my favorite and the best one that I come to every time in New York City. The layout is it's done by region so you need to know where your wine is coming from. Right because I see this sign over there and it says Italy Sparkles three hours ago Italy Sparkles would have made no sense to me. Now I get it I can read it. Alright DC what's the first thing somebody should examine when they enter an expansive wine store like this? I would think you would want to know what's your the game plan behind the wine. Are you having it for dinner with your girl date night. So the occasion is I'm this Asian guy who's trying to get my Asian friends in a wine normally we're drinking Heineken Hennessy we want to get passed out in something else what are we doing? I would look for quality wine that had great value spending a ton over your budget is not going to really be in play there. Hey the first place I would take you to looking for value looking for you know a hangout but having your you know educating your friends would be the Rhone Valley that's in France. The quality of the wines that you're going to get for the money is always going to be the best here and it's always great. They've been a great producer behind European sellers for me is a great importer of French wine so I know that this has you know value in it already even without ever tasting the wine myself. You believe in who imported it. Exactly I believe in their vision of who they work with. I just saw this label it looked kind of cool it has a mermaid on it should I get it. Not just the label the labels uh yeah with the pretty mermaid. Well that is how oftentimes a very rookie makes a read right they're like picking the wine off the label. I think 95 percent you go in it's either the price or it's the label that uh someone chooses a wine from. Should we do that or don't do that? I would not but if you don't know anything about the wine obviously you have to go off something the two things I would look for I would look for where it's coming from does say Rhone. The other thing bolder the importer is a good importer of wine so I would take a chance on this. Everybody likes Prosecco what is that? It's a sparkling wine from Italy. What should we be looking for when it comes to Prosecco? For me I would look for this right here DOCG uh Superior just means it's a higher profile higher vineyard what you got there extra dry superior you know and you know it may be a little bit sweeter. All right that's Prosecco all right the next situation that I have uh concocted in my mind that I think a lot of people would find useful is like you want to get a present for your boss. Burgundy is a great place for that. What you have there you chose uh Marceau phenomenal region for white burgundies uh I mean I don't know anything about the import or anything like that but I know Marceau is a great area for Burgundy it would be something I'd give a chance. I chose this this is something we actually had earlier they knew anything about wines they would know the producer just off hand and that's a red burgundy. How much is this running us? Uh this is 55. RDC we thought of a different situation this one you're trying to meet your fiance's parents. We're at Astor's wine cellar where only the limited really allocated wines are through so for me if you're really trying to impress them I would look at this linchpodge portos here I think that would be well the price point 300 bucks. All right immediately me being the noob that I am my eyes went to something with the coolest packaging. These are natural wines really right now it's a hot trend uh getting natural wines you want to drink them fresher because they don't last as long but they're gonna be unfiltered so it's gonna taste a little bit crisper fresher like a fresh juice. So how do they make it differently? If that be impressed with additional sulfur it's one of the main differences and it's all organic grapes. All right next scenario I just turned 24 I'm literally buying my first bottle of wine but I got a party of friends we want to have a wine party but we don't know anything about wine what are we getting? You know I would go to Spain great bang for your buck um you get a lot of great wines for under ten dollars you have a couple of them here you know uh Tempore Nio Chardonnay very fresh your friends are gonna love it we'll pair great with foods as well there's always the vintage behind where so this is a 2018 so that's from 2019. I think after looking into wines I realized that this whole world has very very many many many different layers to it. What are some good resources if you can shout them out for looking up what's a good wine? There's Seller Tracker there's regular reviewers of normal everyday wine drinkers that you know taste these wines and every vintage of it. You've been able to increase my IQ very quickly what is a path that other people can take? A high level wine store that has a lot of expertise choose a few bottles if there's something a style that you like I would speak to one of these wine associates here try a few different kinds and then try one that's not in your comfort zone. Yo DC man shout out to you this has been very fascinating eye opening I'm not gonna lie this was a world that I had heard a lot about but it felt very inaccessible to me and you just made it way more accessible. Yo I hope you enjoyed it hope you got a little educated I know it was a lot to take in you know one afternoon. You got something very special for the audience that you want to tell them about. I'm giving away 10 bottles of my Magna Carta Sellers to the first 10 people that leaves feedback to us. Here's how you're going to win the Magna Carta Sellers giveaway you have to be 21 years and older leave in the comments down below a story about you getting into wine what you learned or how you got introduced to it and then also leave your Instagram so they can contact you. Alright you guys that brings us to the end of our wine 101 video huge shout out to DC man where they can they find out more about Magna Carta Sellers. Yeah you can see us on instagram Magna Carta Sellers or see us at MagnaCartaSellers.com we paired it with Asian food we had different types of wines and we even had like maybe the most expensive wine I'll be drinking for a while now. Alright guys thank you so much for watching that video remember the giveaway we got more details in the description down below shout out to David Troy from Magna Carta and until next time we out peace


This is stock number 20T93. We are here at Summit Automotive in Fond du Lac, Wisconsin. You're new and used light duty truck and RAM headquarters. Today we are checking out this brand new 2020 RAM 1500 Crew Cab 5' 7 inch short box. This is a Rebel level 2 with the black appearance group. It also has the Rebel 12 package which gives you the 12 inch radio and the Harbin Carton sound system. This one has the safety and convenience group as well. We're just going to do a walk around here. Diamond black pearl, this one has the 5.7 liter V8 Hemi motor with MDS which gives you 21 highways, 17 average and 15 city. We shoot all of our videos in 1080p 60 frames per second so if you have HD capabilities on your computer, tablet or smartphone device, turn them on right now because it's like you're right here looking at the truck with me. And if you want to check out all the photos in the upper right hand part of your screen is a link right to our website, click that and check us out there. Go to your Wrangler DuraTrak tires LT27570R18s with a mud terrain package or tread pattern on there. This one does have the four corner air suspension. You get the painted 18 inch alloy rims. This one has the LED headlamps, the LED running lights as well as the LED fog lamps and tail lamps, front bumper parking sensors. Has the black RAM stamped logo, the cowl hood, you get the 1500 and Hemi badge all blacked out as well, part of that black appearance group. Toe hooks are all blacked out, the RAM logo is all blacked out. These side steps are an option on here, in fact we're going to take a look at the original window sticker here so that you can see all the options. Feel free to pause at any point. I'm not going to go through exactly everything but basically on your left is all your standard features until it says optional and then your optional features include the safety and convenience group which gives you the adaptive cruise brake assist, the lane keep and high beam headlamp control. The black appearance group, the Rebel 12 group which gives you the 12 inch radio as well as the Harman Kardon sound system. The Rebel level 2 group, you can see all that stuff that that gives you. The Hemi, the dual pane panoramic sunroof, black side steps, 33 gallon fuel tank, air suspension, blind spot and cross path detection, trailer brake and spring and bed liner for a total MSRP of 64815 and if you want to check out all the pricing and discounts and incentives on this truck in the upper right hand part of the screen is a link right to this VDP where you can check out the pricing on it. Has 21 highway, 15 city for an average of 17, your safety rating is very good, 5 and 4 stars up and down the board. Now we're going to continue with our walk around here. Four wheel disc brakes, get the fender flares on here, all of the rams come with the bed rail covers, notice you have the LED tail lamps, the blacked out kind of like a chrome black chrome on the tail pipes there, full towing package which includes a receiver hitch four pin and seven pin wiring, the ram stamped tailgate, this one does have the spray and bed liner, that's really nice spray and bed liner and you can always tow its trucks, have the air suspension because they put a little sticker on the back window to let you know that it has the air suspension, backup parking sensors and I am going to show you how that air suspension works because right now we're in normal mode, you got off-road mode one and off-road mode two, you have normal and then you have entry exit mode as well so I'm going to press that and you'll watch the truck actually lower, goes down in the front first and then the back goes down, makes it easier to get in and out of the truck kind of neat, it'll also lower on the highway to get you a better fuel mileage has the enter and go system, this one also has a remote start, inside the Rebel level 2 package gives you the black all leather, well leather and it's kind of got a vinyl insert on the bolsters there, you do get the rebel stitched into the side there, really a good design on there, you have the all-weather floor mats throughout, power windows, power locks, power mirrors, kind of got this diamond plated finish on the doors and I think it's on the dash too, but you got the power folding mirrors, you got blind spot monitoring, heated mirrors, blind spot mirrors and directional signals in the side, they power fold in and out, auto headlamps, power pedals, tilt and telescopic steering wheel and as you hop inside here you can see that this one has the 7-inch LCD display, digital speedometer, the custom rebel instrument cluster there, the heated leather wrapped steering wheel, there's your adaptive cruise, your normal cruise and then your gear selectors, Bluetooth audio and information center controls and then there are audio controls in the back of the steering wheel, there's that diamond plated finish up top and then this is the 12-inch radio, part of the rebel 12 group and you get AM FM and Sirius XM radio capabilities on here, it also gives you a 4G LTE Wi-Fi hotspot capability, Sirius Guardian for a year, Sirius Traffic and Sirius Travel Link plus on here as well and of course the factory navigation, AM FM and Sirius XM radio capabilities, you can do your controls for your heated seats and heated steering wheel right there, you can also check out your backup camera, what I like about this backup camera is HD capability or HD quality I should say and those are dynamic guidelines being that they're going to turn as you turn the steering wheel, one thing to note if you press this little plus sign right here, it'll go right down over your hitch so that you can see just how close you are to lining up your receiver hitch on whatever you're pulling there, pretty cool system, so you got that, you also have your lane departure up here, if you're wondering what that was, there's your factory brake controller, your four corner air suspension, you can put that back to normal right now and when it goes it'll blink, it'll say that it's raising, you can actually see that the truck is going up right now and then it'll tell you when you've reached your normal ride height, down here you have two USBs, two USB C's and AUX jack, you do get the cell phone holder, 115 volt 400 watt plug-in, the dual glove box, you do get the panoramic sunroof in here, so it's dual pane and then that front piece does slide open, up here you have the SOS and assist buttons, all your sunroof and shade controls, then you do get homelink buttons up there as well, you can always tell it has the Harman Kardon by the little badge right there if you didn't see the window sticker, we'll take a quick look at the back seats and then we'll do one more final walk around on this truck, really like that diamond black crystal, also these trucks all now come with the Capless Feel Fill, which is a really nice feature, back seats, a lot of room back here, you do get the latch child safety system, take note that there are three spots to attach a car seat back here, they got one in the middle on the crew cabs which is pretty nice, power slide and rear window with the built-in rear defrost, you get the speakers and the ceiling and then these seats do fold up for extra storage, you do get a collapsible load floor or a storage compartment right here, also the flat floor which is nice if you're a hunter or a fisherman, you can put your poles or your shotguns back here on a nice flat surface, they're not going to teeter on the hump, also you got pets, they got a nice flat place to lay as well, 115 volt 400 watt plug-in, two more USBs and USB C's and finally you do get your in-floor storage bins like you always had, these come out for easy cleaning, you can put ice and drinks in there, it's like you got too many coolers or you can just store stuff in there or whatever, back doors are similarly trimmed to the fronts and you do have the child safety locks back here, I like these seats don't have any locks, they just go up and down kind of easily, they lock into place but anyways, we'll do one more final walk around here, I would personally like to thank you for checking out the video today and hopefully from this HD video you'll have learned a little bit about the Rebel level 2 group, the 12 inch radio, the black appearance look and feel to this truck and learn just a little bit about the new Ram for 2020 or the new body style I should say it's not new for 2020 but the new body style from last year and to see more pictures of this truck or one of our other 450 new and used cars, trucks, SUVs, minivans, Wranglers, half tons, three quarter tons, one tons, you name it we got it go to our website www.summitauto.com, full pictures and descriptions of every single vehicle from two locations all at summitauto.com and if you'd like to check out more HD videos you can go to youtube.com slash summit auto, remember to like subscribe and share on this video and all the videos that you see there in fact in a second you will see a link to subscribe to our YouTube channel on your left it links more half-ton truck videos like this one on your right if you've not been to our website on the bottom link to this vehicle on our website click those checks out and we really look forward to helping you with this 2020 Ram 1500 Rebel level 2