R. Kelly is a former American singer, songwriter, actor and record producer. I say former not because he's passed on or anything but because, well, a federal grand jury has indicted Kelly on 13 counts, including child pornography, enticement of a minor and obstruction of justice. Yeah, that. Look, at some point R. Kelly was one of the most successful R&B producers in the music game and at his peak, his net worth would have been in the $100 million range. But over the years, his many, many legal problems made that nest egg take a hit, reducing it by tens of millions of dollars. These days, reports suggest that he owes more money than he can afford to pay back. But hey, R. Kelly has owned some gorgeous homes in his day, everywhere from Chicago to Atlanta, and we're gonna check them out. In these videos, we don't reveal any addresses and even though I've done a house tour of my own place, please do not show up at any private residences because it's not safe for anyone. Robert Sylvester Kelly, who we know as R. Kelly, has been credited with helping to redefine R&B and hip hop, earning him nicknames like the King of R&B, and leading him to release a ton of hit tracks like Ignition, The World's Greatest, and many more. But he's also been the subject of intense controversy since the 1990s, which I'm sure you already know all about. And in 2019, he was arrested on a long list of federal charges, 18 to be exact. Prior to this, in 2012, the IRS reported that R. Kelly owed as much as $5 million back in unpaid taxes, which would lead him to losing his gigantic mansion located in Chicago in an area known as Olympic Fields. Furthermore, he was evicted from two different homes that he owned in Atlanta, Georgia a few years later, after refusing to pay more than $30,000 in back rent and fees. With his real estate portfolio taking a massive hit, Kelly moved himself into Chicago's Trump Tower and battened down the hatches. Unfortunately for him, it didn't last long. Six months later, he was arrested and on his way to the Metropolis Correctional Center in downtown Chicago, which is where he calls home right now as he awaits his multiple trials. Hey guys, it's Kara and for today's House Tour, I'm reporting on a celebrity you guys requested. This time, we're taking a look at a few different homes of the infamous R. Kelly here for you on Famous Entertainment. Whether it's his music or his crimes that are well-documented in series like Surviving R. Kelly, people are fascinated by this man's story.  As you know, here we talk about celebrity houses, but have you ever wondered what David Dobrik spent on his Iron Man suit or about Conor McGregor's million dollar watches? We recently started a brand new channel, Famous Fashion, where myself and some other hosts are reporting on all things celebrity fashion. Join us and be one of the first to subscribe, you don't want to miss this. That's not even the only watch McGregor picked up during his recent shopping spree. He also bought another timepiece from Jacobs & Co. this time in a more X-rated flavor. Don't forget to follow me on Instagram and we can chat there. Alright, let's get into this video. In 1997, things were going great for R. Kelly. His hit song I Believe I Can Fly was still tearing up the airwaves getting tons of play and he was making enough cash to blow a whole bunch of it on this beautiful mansion located in Olympia Fields in Chicago for 3.5 million dollars. The community sits about 45 minutes away from the downtown area and Kelly had the home custom built to suit his tastes. The entire house features more than 14,000 square feet of space and fully landscaped acres situated behind an iron and stone gate with 12-foot-tall concrete encased fencing. Inside you'll find formal and informal lounging and entertainment areas as well as four fireplaces, six bedrooms, eight full-backs as well as six half-backs. It also features a colossal kitchen with a center island, high in commercial grade appliances and a super tall ceiling with heavy wood beams running across. Not too far away from there, the double height family room is adjoined to the home theater as well as a wood paneled room with a fireplace that most likely acts as a library. There's also a jungle themed indoor swimming pool which when R. Kelly was trying to move off of the home, he hyped up on the listing as a full on tropical experience, I don't know, that might be overselling it more than a little. Outside, the estate borders the Olympia Fields Country Club and includes a gated circular drive with a secondary motor court and acres of lawns with trees and outdoor tennis and basketball court, a private pond with fountains, a detached multi-car garage and whatever this thing is. Maybe I don't want to know. In 2011, it was reported that R. Kelly stopped making payments on his remaining $2.9 million mortgage for this home. At the time, people seemed to think it was a strategy on his part to get the lender to renegotiate the loan. It didn't work. Kelly lost the home to foreclosure and it was later sold at auction for a mere 587K. After losing his home in his native Chicago, R. Kelly moved south and took to renting two properties in the same neighborhood known as Johns Creek, located in Duluth, Georgia, just outside of Atlanta. One of the properties is a large mansion style estate, while the other is a smaller family style home. The larger home located on Old Homestead Trail was his primary residence. Kelly rented this property for $10,000 a month. Built in 2000, this 9000 square foot estate is built on the top of 2.5 acres and features extras like its own batting cage and a tenant's court that Kelly transformed into a basketball court. Inside the home, you'll find luxurious amenities like a home theater and a cigar bar. The majority of the ceilings around the home are over 12 feet high and the floors are made out of French limestone with elegant details featured in the living room, dining room and panel study. The kitchen has been updated to include stainless steel appliances as well as quartzite countertops. Further inside the home, the family room has one of the home's seven different fireplaces, as well as a rich beamed wood ceiling. The master suite is located on the main floor and has its very own spa bath along with his and her walk-in closets. And as much as I may want to, I'm gonna hold back for making any trapped-in-the-closet jokes. But needless to say, you could get lost in the size of these things. Upstairs are five more bedrooms each with their own private terrace. There's also an enormous den and home theater up here, which sits over top of the four-car garage. Moving on to the second smaller home, Kelly rented this far more unassuming place located on St. Devin Crossing. Built in 1992, this 2,348 square foot home sits in a cul-de-sac and has four bedrooms along with 2.5 bathrooms. According to records, Kelly was paying $3,000 a month for this property, which is just two miles away from the larger home. It features custom towel flooring, a renovated master bedroom and bath combo, alongside an upgraded kitchen with granite countertops and stainless steel appliances to go alongside the large Eden breakfast area. The family room offers plenty of space and windows to let in that gorgeous sunshine and there's an extra room located on the main floor that would be perfect for a home office. Meanwhile, out back is a private yard that's fenced off to keep out any unwanted attention. Speaking of unwanted attention, our Kelly's face is fair share of it while living in these two homes. First off, at the end of 2017, both of these homes were broken into and looted. Even worse, the culprit was a close personal friend of our Kelly's named Alfonso Walker, who ransacked the homes over that Thanksgiving weekend. According to reports, Walker hired movers to clean out both houses and then sold the contents at a price of $6,000 per room. The theft was discovered by a cleaning lady in late November and when Kelly finally got around to checking things out, he posted his findings to Instagram. Walker would turn himself into police only days later. If you ask me, it's more than a little curious that a man who is facing a whole ton of back taxes mysteriously had his homes broken into and stripped bare by a close personal friend when he wasn't home. But hey, I'm not a detective. Although it gets even weirder when you find out that after this incident happened, our Kelly simply stopped paying rent at both properties and left the homes behind. I guess he thinks that's how real estate works. When the property management company inspected the homes, they found extensive damage that was beyond normal wear and tear. After evaluating it, they asked Kelly for payment who refused to do so. That forced them to file a suit against Kelly looking for more than $200,000 in damages. Of course, if that was the worst thing that ever happened in these two homes, then I think we'd all be the happier for it. But we know that isn't the case. Both of these homes took center stage in the crimes that would be charged against the entertainer. Earlier that year, just before the homes were broken into, news of our Kelly's reported sex cult took the world by storm. It's all pretty depressing stuff, and it's the reason why our Kelly is now calling the Metropolitan Correctional Center in downtown Chicago home as he awaits his trials to begin in September of 2021. Opening in 1975, this prison features 20 stories and has a rooftop exercise yard. Each cell is designed with floor-to-ceiling slit windows, which are seven feet tall by five inches wide, which gives the building an extremely unique look, somewhat reminiscent of an old computer punch card. Because the windows are so narrow, they don't require bars, and the cells themselves were designed to resemble sailboat cabins with built-in hardwood beds and desks. I tell you all this simply to give you a taste of where I think our Kelly will probably be spending the rest of his natural-born life, but I guess we'll have to wait and see. Alright guys, I'm gonna bring this house tour to a wrap right here. What did you think of the different homes of our Kelly? If I'm being totally honest with you, considering what went on in those homes, I really don't want to live in any one of them. Too much bad juju. These days, his former homes in Georgia are looking all spiffy and new, but that Chicago mansion has fallen into a state of huge disrepair. It's super creepy to look at, and we'll have to wait and see if anyone ever bothers renovating it. In the meantime, don't forget to follow me on Instagram, and I'll see you guys soon in the next video. Bye!


All right, so let me thank the organizers for the invitation. So I'm going to talk about some large deviation problems for the spectrum of vigno-matrices. So as we know, many spectral asymptotics of vigno-matrices are universal, but much less is known about the large deviation behavior. And in particular, if there is a universality phenomenon also happening there. So in this talk, I will present different kinds of large deviation results for this model of random matrices. So we consider a vigno-matrix that is a random Hermitian matrix with independent coefficients up to the symmetry. We assume that the variance of the octagonal entries is normalized to be 1. We can define then the empirical aggregate distribution, which amounts for the global behavior of the spectrum. We know that if we normalize the spectrum by 1 over square root 10, then this random probability measure converges towards a deterministic measure, which is a semicircle low. So given this convergence, one may ask about the large deviation behavior. So one way to formalize this question goes through establishing a large deviation principle. So the goal is to compute at the logarithmic scale the probability that the empirical eigenvalue distribution is close to some fixed measure, which is different than the semicircle low. So the goal is to compute how fast this probability decreases to 0. So what is the speed of large deviation? And what is the constant, which is a function depending on the target measure here? So what is the rate function? So in this talk, we will focus on the question given that, I mean, for such results, how the speed and the rate function can depend on the distribution of the entries. So very few results are actually known for the large deviations of this statistics of the spectrum. So the first result was given for the classical Gaussian ensembles. So those are Vignum matrices, which have a low with density in exponential minus beta over 4 times the trace of h square, where beta equals 1 in the case of the GOE and beta equals 2 in the case of the GUE. So this beta over 4 is taken so that you have a variance equal to 1 for the diagonal entries. So what we saw in Alice Guiness Lectures is that the empirical angle value distribution of this model satisfies a large deviation principle, which is with speed n square, and with an explicit rate function, which is the following. So this rate function involves the so-called non-competitive entropy. So the point is that for this model, so the joint law of the eigenvalues is completely explicit. And this allows one to perform a Laplace method to obtain this kind of large deviation principle. But what is very crucial is to have this knowledge on the joint law of the spectrum. And it's very challenging to understand the large deviations of the spectrum in cases where this is not accessible. This said, there is actually a class of eigenmetrices where this is possible. And this class has been called the class of eigenmetrices without Gaussian tails. So those are eigenmetrices where the distribution of the entries have a tail distribution, which decreases in exponential minus some constant time t to the alpha with some alpha, which is strictly less than 2. So those are entries which have a tail distribution, which is strictly heavier than the Gaussian. So for these big matrices, Bordeneuve and Caputo proved a large deviation principle for the empirical eigenvalue distribution. They proved that the speed of large deviation actually depends on how fast the tail distribution decreases. So they showed that the speed is in n to the 1 plus alpha over 2. And they provided an explicit rate function, which is given in terms of complicated variational problem. This variational problem can actually be solved for specific target measures, which are free convolutions with the semicircular law by a symmetric probability measure. And for those measures, then the rate function is simply the alpha at the moment of nu. This rate function also has the surprising property that it is infinite for any measures which cannot be written as a free convolution by the semicircular law. So that any measures which are not of this form, actually, it's very unlikely to see such a deviation. So the reason why the speed of large deviation actually depends on the tail distribution is because of the following fact. So what they proved is that the large deviations of the empirical eigenvalue distribution is explained by deviations of order square with n of a number of entries which are of order n. So because of the behavior of the tail distribution, you get then this speed in n to the 1 plus alpha over 2. So in this large deviation regime, you have this network of entries which are making deviations of order square with n. And what happens is that the spectrum of the matrix with the rest of the entries sort of concentrate at the large deviation scale here. And therefore, the only possible deviations are around those free convolutions. Because somehow, in the large deviation scale, your matrix looks like a deformed Vigno matrix. So this strategy, however, seems to be very specific to this case of Vigno matrices. In particular, if you're looking at the case of bounded entries, you cannot possibly implement this kind of strategy. So what do we know in this case? So we have an idea of what is the speed of large deviation by just a concentration result, which is due to BNN Zetuni. So they prove that the probability that the empirical eigenvalue distribution is away from the semicircular, this decreases as exponential minus n square. But proving the existence of a large deviation principle is completely open for any example of Vigno matrices with bounded entries. But so motivated by this problem, I will consider a simpler problem, which is to understand the large deviations of the moment of the empirical eigenvalue distribution. So those are just the normalized traces of x over square root n to some power d, where x has centered and bounded entries. So we know that in this case, the normalized traces they converges to the moments of the semicircular in probability. And again, we can wonder about what is the large deviation behavior. And this will be the question I will address in this talk. Sorry. So first of all, in order to give you an intuition about the nature of the large deviations, I just want to give you an example of a simple lower bound. So assume that we are looking at an even power and that our Vigno matrix has only rademarrow variables. So sorry, what they are, rademarrow? Sorry? What it means, rademarrow? Right. So the entries are distributed with this distribution. So this is what I call rademarrow variable. So the existence of the rate function is not known. So I mean, you have those concentration results, which are very general. But computing, I mean, proving the actual existence of the limit is not known of this probability. You can always get lower bound by, you know, I mean, OK, so I don't know for general target measures, but you can probably build some strategies for certain deviations. You can build examples of lower bound. But the issue is to get matching, also, lower bound and upper bound. So let's assume we want to give a lower bound on the probability that the trace of x of a square root n to the power d is above some constant c times n. So one way to do that is to push the top eigenvalue to a level which is of order n to the power 1 over d, the top eigenvalue of x of a square root n. So if you have plus and minus 1 entries, one way to do that is to ask that you have a principal sub-matrix of a certain size, which has only once entries. And the size you have to take is of order n to the 1 over d plus 1 half.  So this lower bound indicates that the speed of large deviations for those traces actually will actually depend on the power of the moment. So what about upper bounds now? So we know by concentration results that we can get an upper bound on the probability that the trace of x of a square root n to the power d takes some unexpected value. So we have this result of Mekhes and Zarak, which show a two level deviation inequality. So you have here on the right-hand side competition between two kinds of behavior. So you have a sub-Gaussian behavior in n square t square and a behavior in t to the power 2 over d times the speed we saw before in n to the 1 plus 2 over d. So you see that if you take t, which is of order 1 over n, then it's the first Gaussian term, which will win. And you see that you obtain a concentration inequality, which is going to reflect the Gaussian fluctuations of the traces. On the other hand, if you take t, which is of order 1, then it's the other term, which will dominate in the minimum. And you obtain that the large deviation speed of the upper tail should be in n to the 1 plus 2 over d, since we saw before that we also have a matching lower bound in terms of order. So there is indeed in the case where d is event, there is a different behavior which happens below for the lower tail. So the deviations below the this moment of the semicircular. And the reason is, so if you look at the event where this moment of the empirical eigenvalue distribution is below the one of the semicircular minus something, this is an event which is a closed event for the weak topology. And therefore, if this happens, it means that this empirical eigenvalue distribution is away from the semicircular. And this we saw before that this event has a speed in exponential minus n squared. So you have two kinds of behavior in the case where the power d is even, whether you are above the limiting value or below. So in this talk, I will only consider the large deviation problem of the upper tail of those normalized traces, where the speed is in n to the 1 plus 2 over d. So I would like now to state the main result of this talk. So I need to introduce some notation. So I will denote, I will introduce, so the logarithmic Laplace transform of our vigno matrix, which I denote by lambda of h. And this is defined as the logarithm of the expectation of exponential the trace of x times h. Now we will also introduce its Legendre transform. And so our main result gives a description of the large deviation upper tail in terms of this function lambda star. So what we prove is the following. So we prove that the logarithmic scale, if you, the probability that the normalized trace of x over square root n to the power d is above this moment of the semicircular plus some positive t. This is in the leading order equal to minus some variational problem, which consists in optimizing this function lambda star of y, where y is a Hermitian matrix of size n, with the constraint that the normalized trace of y over square root n to the power d is above t. So note that this is not exactly a large deviation principle. But so indeed in this generality, I do not know if this variational problem actually has a limit. But we will see later that for a certain class of vigno matrices, we can actually give a large deviation principle. So here actually, so I wrote that I assume that the entries are bounded. But actually, I can also work with matrices which have the same concentration property as the one with bounded entries. So I need to know that convex lip sheets functionals of my matrix have sub-gaussian concentration. And in particular, so you can also allow entries which have a density, for example, in exponential minus x to the power alpha with some alpha bigger than 2. This will also work. So this main result is this description of the upper tail in terms of some variational problem. Yes? No? No, yeah, it's a everything. I mean, so this is of order n to the 1 plus 2 over d. This variational problem is also of that order. So it's just like an expansion of the. So I cannot pass the limit at that stage because I don't know if this variational problem has a limit. However, so we can actually go to the limit for a certain class of vigno matrices which have been introduced by Guyonet and Husson. And this class is called the class of vigno matrices with shops of gaussian tails. So those are vigno matrices where the logarithmic Laplace transform is point-wise bounded by the one of the GOE or the GUE, according to whether you are in the symmetric real case or the Hermitian complex case. So examples of vigno matrices which satisfy this condition are given by the one with entries which are rademars, so with this low, or which are uniformly sampled in some interval. So here I put square root 3 to get a variant which is equal to 1. So for this class of vigno matrices, so we can actually prove a full large division principle for the normalized traces with an explicit rate function. So this rate function is actually very simple. So it's this function beta over 4 times t to the power 2 over d. And what you can observe is that this rate function does not depend on the distribution of the entries. So you have some kind of universality result for the level of large deviation for this class of vigno matrices. So this universality phenomenon was already observed. By Alice Guionnet and Jonathan Husson, and they proved using different techniques that the top eigenvalue of those vigno matrices also have a universal large deviation behavior. So the speed and the rate function are universal and are the same as the GOE case or the GUE case. So our result complements theirs and complements this picture that in this class of vigno matrices, the moments of the empirical eigenvalue distribution also have a universal large deviation behavior. So this result kind of contrasts with what is expected for the empirical eigenvalue distribution where we don't really expect such universality to happen. However, what may happen is that certain deviations of the empirical eigenvalue distribution are universal, but this is again completely open. So during the rest of this talk, I would like to give you an interpretation of the variational problem which arises in this description of the large deviation upper tail of those traces. So what we will show is that this variational problem actually corresponds to say that certain changes of measures are actually optimal for this large deviation problem. And what we show is that the best large deviation strategy consists in those changes of measures. So if p is the law of your vigno matrix, you may consider now the family of all its tilts, which are probability measures with an affine log density. So the density is an exponential, the trace of some matrix h times x. You have to subtract the logarithmic Laplace transform to have something which is a probability measure. And what we will show is that those changes of measures are the optimal ones. So more concretely, so if you start from a vigno matrix which has rademarrow entries, then this family of probability measures is the set of the laws of vigno matrices where the entries are also rademarrow but with different parameters. So what do I mean by optimal strategies? So in the large deviation literature, there is this prevalent idea that one can obtain a large deviation lower bound by performing a change of measure which is going to transform a rare event into a typical one. So I would like to illustrate this kind of philosophy, which is very general. So I would like to justify it in a few lines. So if you take some function on the set of permission matrices and a potential change of measure q, which is absolutely continuous with respect to your initial probability measure p. And let's say we want to lower bound the probability of this rare event where f of x is above some level t. So what you can always write is you can always write this probability as an expectation under this new probability q. And now you can see that using Jensen inequality, you can get a lower bound on this probability, which involves the relative entropy of q with respect to p. And the probability of this event where f of x is above t, but this time under this new probability measure q. So the consequence that you can derive from this lower bound is the following philosophy that if you manage to find a change of measure, which is going to make typical your rare event, so the event where f of x is above t, then you obtain a lower bound, which is in exponential minus, roughly speaking, it's in exponential minus the relative entropy of q with respect to p. So the main part of the work is to find good changes of measures, which are going to give you a sharp lower bound. So for our example of the normalized traces of x or square root n to the power d, so what we claim is that a certain family of changes of measure are actually optimal. And so this family is this one, so the family of the tills, which I denoted by pH. What you can show is that the relative entropy of pH with respect to p only depends on the mean of x under this probability pH. And so it's just equal to this function lambda star of y, where y is the matrix of the mean. So remember the picture that I told you just before. So the idea is that if you find a change of measure, which makes your rare event typical, then you get large deviation lower bound, which is in exponential minus the relative entropy. So somehow it's very important to understand now what is the typical value of the normalized traces under this probability measure pH. So under this probability measure pH, now your matrix does not have centered entries. So what you can write is that you can see your matrix x under pH as a perturbation of a centered vector matrix. I can subtract the mean and add the mean. And so what you can show is that if the Hilbert-Schmidt norm of y is not too big, then essentially what you have is that this trace kind of split up into two parts. You have the trace of x minus y over square root n to the power d plus the normalized trace of y over square root n to the power d. So you can show that if the Hilbert-Schmidt norm of y is not too big, then all the mixed moments actually vanishes in the large n limit. And then so what you can also prove is that under this probability measure pH, so you move the entries of your Wigner matrix. But if you under this assumption that y is not too big, you did not change too much the variance profile. So that here the typical value of this recent Wigner matrix is still this moment of the semi-circular. So this means that under this change of measure pH, the typical value of our normalized trace is this sum of the displacement of the semi-circular plus the normalized trace of y over square root n to the power d. So now if we want to obtain a lower bound on the probability that the normalized trace of x over square root n to the power d is above the displacement of the semi-circular plus some t, then you can perform this change of measure pH with where the mean y under pH satisfy this condition. And you see that using this change of measure pH, now you transform this rare event into a typical one. And therefore, so using this kind of bound, you can show that therefore you have a bound in exponential minus lambda star of y. So this is true for any such y, which satisfy this condition and that condition. So you can now optimize on y. And you obtain a lower bound, which can be described in terms of some variational problem. So you can also show that this variational problem is actually achieved for matrices which satisfy this kind of condition so that you can remove it in the variational problem. So this variational problem is exactly the one that I claim to describe exactly the Taylor distribution. And the main point is that it corresponds to saying that this special family of tilts of your Vigno matrix are the optimal changes of measure. So it happens that many large deviation problems follow this strategy. And those have been put together under the name of nonlinear large deviations. So where the tilts of the background measure are the optimal changes of measures? So for example, for the large deviation of empirical means, of an IED sample, this is an example of a large deviation problem where those tilts are the optimal changes of measures. There's also the example of subgraph counts in Erdos-Renegraff's. So there is a huge literature on that subject. I'm only stating the first paper, which really shows a large deviation principle for subgraph count in the dense case. So an Erdos-Renegraff, maybe let me quickly remind you the definition. So an Erdos-Renegraff is defined as a graph on n vertices where for any pair of vertices, you put an edge with a fixed probability and independently for any pair of vertices. So when you have such a random graph, you may ask about what are the number of subgraphs which look like a given graph. For example, how many subgraphs there is which are triangles or which look like stars or clicks of a certain size. And the large deviations of those objects also fall into this nonlinear large deviation theory. And so this nonlinear large deviation theory was introduced by Chatterjee and Dembeau. And the aim was really to unify all those large deviation problems and to find a criterion so that this strategy, which consists in those tilts, are the optimal ones. So let me now describe what is the criterion that they found. So their theory aimed to be quite general. So here we are moving to a slightly more abstract setting where we have a random vector on an. So canonically, you can think about this random vector as having id coordinates like Rademauer entries, for example. And now we are studying a smooth function of this vector. And the main question we want to ask is what is the last function of this vector? This is the large deviation of f of x in the large n limit. So what we saw is that so using those tilts, so using this family of probability measure, we can always more or less provide a lower bound on the probability that f of x is above t in terms of some vibrational problem. So this is provided that you have some concentration property under your tilted measure. So if f of x has enough concentration property under that measure, then you can using this strategy, you can give a lower bound, which is this one. And the nonlinear large division theory aims at understanding when is this lower bound actually sharp and when can we reverse this inequality. So Chatterjee and Dumbo found the following criterion. So they proved that if you take x, which is uniformly sampled on the discrete hypercube, then this lower bound is indeed sharp if the set of gradients of the function f is of low complexity. So this means that the gradient does not span into too many directions. More precisely, they gave a criterion in terms of low metric entropy. So they were asking for the criterion is that you can cover your set of gradients by a small number of L2 balls of radius delta square root 10. So remember that as we are on the discrete hypercube, you have a certain function defined on this hypercube. So you have two to the n vertices. And on each vertices, you have one gradient. So essentially, for generic functions f, the number of the covering number of the set of gradients will be exponential in the dimension. It will be essentially the number of vertices. So this criterion actually asks for a sub-exponential covering number of the set of gradients. We can also discuss why we are asking for a mesh, which is in delta over square root 10. And the reason is that square root 10 is the diameter of the hypercube. So you can see that if you make a narrow on the gradient, which is of order delta over square root 10, you're going to make an error between the function f and its tangent, which is of order delta. So on every convex subset where the gradient is constant, with an error, which is delta over square root 10, you're going to make an error of order delta between the tangent and the function. OK, so more precisely, what they did is that they gave a quantitative upper bound on the probability that f of x is above some level t. So they proved that you can get some error terms with respect to this rate function i of t. So the error terms are of two types. So there is this first one, which is a polynomial in those derivatives, which is very complicated. But it's explicit, and it depends on the derivatives up to the second order. And then you have another error term, which comes from the complexity of the set of gradients. So the bound is maybe more complicated than this in reality, but this is how the structure of their bounds. So what you can see is that if this probability here is of order minus vn, so if you know what is the large deviation speed, then this bound is meaningful if you the covering numbers of the set of gradients by balls of radius delta of square root n is a little o of the speed. So maybe let's see now some examples of functions f, where this bound is actually meaningful, so functions which have a gradient of low complexity. So the first example is just like linear forms. Then the covering numbers of the gradient is trivial. You can also look at an example of a function which is related to the Curie-Weiss model. So you take this quadratic form, the sum of xi xj for i different than j. So you can normalize it by 1 over n square in order to study the deviations of order 1 of this function f. So here you can prove that the speed of large deviation is just n. So the gradient at any point x, you can see that it's almost a constant vector, so that the set of gradients of this function is almost one dimensional. And as it is almost a one dimensional set, so it has covering numbers which are polynomial in the dimension. So the log of the covering number is only logarithmic, and therefore it's indeed a little o of the speed of large deviations. So maybe now an example of function which is not of low complexity. So if you look at the larger second value of the Vigno matrix, then so here, so n, so big n should be n, little n choose 2. OK? So we know for this model that for this function that the speed of large deviation should be n, little n. However, the gradient of this function is essentially the top eigenvector. So you see that if you look at the image of the gradient, it spans the whole sphere. So in particular, this has a covering number which is exponential in dimension. So it's an exponential n, and therefore this is not a function of low complexity. So a function of low complexity is a function where the gradient really spans into a few directions somehow. So what about the normalized traces of powers of x over square root n? So the bad news is that it's a function which is not of low complexity. The gradient spans into too many directions. But what we can show is use a probabilistic argument to reduce the complexity. So what we show is that we can actually reduce ourselves to the large deviations of a function of low complexity if we truncate the trace. So what we can show is that in the large deviation scale, somehow the deviations are only due to the edges of the spectrum, and therefore we can truncate the trace. So here I'm denoting the trace subscript k to be the trace where you keep only the k largest eigenvalue in absolute value. And so using concentration arguments, one can show that the part of the trace which corresponds to the n minus k smallest eigenvalue where k is a small fraction of n, this part of the trace concentrates at the large deviation speed, which is n to the 1 plus 2 over d. So that we are reduced to study this truncated trace. So we also have a condition on the growth on how many eigenvalues we are still keeping in the truncated trace. But it's actually sufficient to reduce the complexity enough. So for this truncated trace, what you can see is that now the set of gradients actually is only a subset of matrices of rank k. And therefore, this has a potential to be of flow complexity. If k is low enough, so we can actually show that this function is of flow complexity. So however, if you look at, so we should come back to the bound of Chaterjien-Dembault. So we fixed the complexity error term, but we still have this smoothness error term which makes it difficult to apply this bound in this context for our example of the normalized traces. So motivated by this example, I gave an improvement on their bound using different techniques. So what I showed is that we can remove this smoothness term. The counterpart is that I have to ask for a covering number, not only of the set of gradients, but of the convex hull of the set of gradients. So it may increase enormously the complexity for certain examples. For example, if you take a function where the set of gradients is all the unit vectors. So this has a low complexity in Chaterjien-Dembault's bound, but this has a very high complexity in the bound which is here actually because the convex hull is a cube and this has a huge complexity. So however, so introducing this convexity here makes the bound a bit neater. And for many examples, it gives an improvement. So in particular, we are able to use this new bound to derive the large deviation upper tail of the moments of the empirical eigenvalue distribution and show that this variational problem here is describing the upper tail and that it corresponds to actually saying that certain changes of measure are optimal. So to conclude, I just want to remind you so that from this estimate, we can derive a large deviation principle for those traces in the case of big pneumatrices with shafts of Gaussian tails. And this complements the result of Guyonet and Husson on the top eigenvalue for this model of big pneumatrices. So I thank you for your attention.


Guess I was muted false Sorry about that Shannon, this is full This is the second half of a case. No, that was my fault Julian This is the second half of a case that started with pick your team seven all spots sold straight up And there is another full case split between pick your teams nine and ten That's available on the site right now We can do more of this tonight Carson Wentz 50 out of 75 Indianapolis Colts, Sean O'Leary last spot mojo and Mack Jones Patriots base rookie Sean Maddock Yet Pat Freyermuth relic 109 out of 125 for the Steelers Wayne Stock and first auto is JC Horn for the Carolina Panthers. That's eight out of 30 35 son of Joe Horn Carolina Panthers Patrick Davis Kenne and Wong Wu 39 out of 99 little peekaboo two-color patch auto for the Vikings Pat Wolff Starting off with Jim Kelly 47 out of 75 Buffalo Bills David Bararino and Elijah Mitchell rookie For the San Francisco 49ers Brandon lots of lip We've got a rookie influx relic of Cadarius Tony 100 out of 125 for the Giants and Philip Nguyen And a redemption will save that Check out the patch auto for color patch auto Tylen Wallace that is six out of 50 sizeable signatures nice four-color patch there silver ink auto and the redemption Midnight signatures. Okay card 20 T Tua Tua Taga by Loa midnight signatures dolphins and Derrick Gordon Those midnight signatures are one of the nicest looking sets to very nice second year to a Taga by Loa T For which one I'm not getting what you're saying auto cracks dying That redemption wasn't a tray sermon. Okay Well, here's a tray sermon for you Or Tray Lance 67 out of 75 49ers Brandon lots of lip and Tommy tremble for the Panthers Patrick Davis Cadarius Tony relic almost two colors 10 out of 10 Giants Philip Nguyen Midnights or sorry spotlight signatures Ryan Tannehill gold ink three out of 25 Titans Roy Schappic and Josh Palmer three-color patch auto to 199 for the Chargers Pat Wolff Excited to see what you can do. I think he Chargers just cut Tyron Johnson. So I think there's a good chance that he might Get the white wide receiver three treatment Just start the season Be too bad for a I think we got him in the fifth round He'll at least get some decent time this year Even if he's not wide receiver three right off the bat halfway through guys three more boxes to go Let's find a NFL shield Jake Funk 54 out of 75 for the Rams Sean O'Leary. Oh, yeah JC Horn for the Panthers Patrick Davis and very nice four-color patch Trevor Lawrence 11 out of 25 Jaguars Sean Maddock, yeah, that was a nice Tannehill a little tanny there Kyle Trask Three out of 25 rookie auto Tampa Bay Buccaneers Sean Maddock. That's not good ring two three-color Anthony Schwartz 75 out of 99 For the Cleveland Browns Glen Campbell Silver ink auto Let's get you to trade Lance make up for it I didn't see who the card is but I'm gonna tell you right now whoever it is there. They need to work on their signature. It is God Absolute embarrassment. That is 19 out of 25 Travis Etienne for the Jaguars Sean Maddock and Carlos boogie Batchum for the bills David Bararino Justin Herbert relic that is 57 out of 99 chargers Pat Wolf Patrick Surtain The second 108 out of 199 His sticker look like it's like a blue tint to it it does That's interesting Denver Broncos Julian Schwartz or sorry shilts Four-color patch auto seven out of 25. Come on Jalen Darden Tampa Bay Buccaneers Sean Maddock nice patch player could be great. That is a garbage I don't even know if he's trying to like Is he trying to make it like a TD? Or sorry JD That'd be clever And last box mojo Let's get it for you Brandon That is Brandon I use 60 out of 75 for the 49ers Brandon lot to lip They put so much work into this T Higgins Yeah, they put a lot of work into redoing this this year. You got Travis Etienne 93 out of 99 Jags Sean Maddock. Yeah, they retooled it. The midnight signatures are great spotlight signatures are great Sam Elinger, I feel like you could probably space out his first and last name a little bit I don't think they spaced that at all. They gave him a one-name Sam Elinger They didn't put a space between his name T Higgins clearly two words Sam Elinger one word Indianapolis Colts Sean O'Leary I guess I mean I Guess it's like if the name's long That's kind of weird But to finish it off a mere Smith Marseille 93 out of 99 silver ink auto Minnesota Vikings Pat Wolf there you go guys that wraps up that case. We do have a fresh case In pick your teams nine and ten in the store now But nice second half 2021 Penini black football six box half case break pick your team number eight from jaspercasebricks.com is in the books I'm Sean jaspercasebricks.com. Thanks for hanging out. We'll see you next time


FNN. The Tiger. Financial News Network. News Update. Hi everyone, hope everyone had a good weekend, long weekend. We're looking at the Dow this Tuesday, the very last day of May. We're looking at May the 31st. We've got the Dow down 324. That's 32,892. That's spiral up to the 50 period exponential moving average and grey leg on Friday. For me it was nothing to be complaining. We've been long, but it was a big surprise. Just the amount of buying that came in. Now we're going back a chunk today. High was 33,160 just under the high of Friday which was 33213. So you can expect that there should be a peak A here. You can expect even a two day pullback. But I suspect that we are going to see at least a test of that 50 period moving average again. That's going to be the big test. Is that going to tell us that we can go much higher? I'll talk about that in my show coming up. The Tiger technicians hour at 10 o'clock eastern time. But right now we've got the 10 o'clock Tiger Financial News Network update. We're looking at the should be a down date. The SB is down 46 and 41. 12 had a spectacular move on Friday to continue that move up. The QQQ is also taking a bit of a breather. We're looking at the QQQ, the NDX100 training vehicle down 350 and 30540. Yes, very good move. It isn't as good looking as the other two indices, but pretty decent rally from the IWM, the Russell 2000 pulling back as well down to 68186. Didn't quite get to the 50 period moving average. That was a really nice break from 168 to the 187-ish area. Now we're looking at the gold and gold is in fact pulling back a bit. It's down 1849. The dollar is holding quite well actually. It is up 59 ticks at 101.94. It's really crude oil that we're looking at. Crude oil is up $3.45 at 118.50. Touched 119.98 in the continuous contract. Leg E went right to the Fibonacci 161.8 expansion. We'll see where it can go much higher than that. We're here and we're looking at the TLT, which is bonds. Bonds are down sharply, down 253 at 116.56. Meaning that yields are once again up to this 50 in the day of the TLT, yields are going up. I'll be back for the Tiger technicians. I hope you can stay check out my people on my daily newsletter.


QuickBooks Online 2024. Enter transactions for owner deposit and loan deposit using bank feeds. Get ready and some coffee because we're going to be like bookkeeping Einstein with QuickBooks Online 2024. First a word from our sponsor. 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trimmed it down a bit okay it's an improvement if you would like a commercial free experience consider subscribing to our website at accounting instruction dot com or accounting instruction dot think of it dot com here we are in our quick books online bank feed practice file we set up in a prior presentation opening the major financial statement reports like we do every time the reports on the left hand side in the favorites right clicking on that balance sheet report to open a link at a new tab right clicking the profit and loss to open a link at a new tab and once again right clicking on the trusty tb trial balance to open a link at a new tab if you don't have that trial balance in the favorites you can search for it let's tab to the right do some formatting here close up that hamburger put the button on the hamburger we're going to select the ranging changing the range change 010124 tab 022924 tab drop down let's see it month by month let's run it to refresh it let's tab to the right close up the hamburger again and then change that range 010124 tab 022924 tab and then select the drop down and we're going to say months run it to refresh it again let's tab to the right one more time we're closing the hamburger we've seen that the tomato is properly placed and so now we can close that hamburger and then change we'll still poke around at it changing the range change 010124 to 022924 and then drop down we want the months and then we're going to run it to refresh it okay let's go back to the balance sheet so now we're looking at the deposit side of things with the bank feeds last time we looked at the easiest kind of system where we have our deposits and they're all going to be just deposited directly to an income account which can only really happen if you're in the type of industry that allows that to happen however we still need to distinguish between the kind of deposits that are coming from the customer and the kind of deposits that might not be coming from the customer such as those coming from us the owner or from a bank in the form of a loan for example if we miscategorize those what will happen is we're going to end up with income that is not really income it's from us or it's from the loan which from the U.S. income tax perspective would be very bad because then we'd have to pay taxes on our own income is what we would end up doing probably and that wouldn't be good let's take a look at the flow chart to just recap the revenue side of things and how the bank feeds fits into that system so when we're looking at the revenue side of things it depends on the industry we are in as to how the bank feeds might work within our system last time we looked at the simplest system where if we have gig work which is get paid by youtube we can wait till it clears the bank we'll be able to see who it came from hopefully because it's an electronic transfer and then we could just create an account called like youtube income for example and record that or we might have a situation where we're at a cash register if you're at a cash register situation or you're making sales during the day and then you're going to deposit the cash into the account at the end of the night and or you have credit card sales you could wait until the money actually hits the bank account and then just record everything as revenue using the deposit form with the bank feeds in that kind of system and you wouldn't have the electronic transfer showing you who the money came from but that's okay in some instances because you wouldn't know who the money came from anyways because you're just selling to the public it's not like you're getting all of their contact information when you're at like a cash register type of situation however oftentimes you might also want to have an internal control that would be checking the money that you have in the cash register to the receipts before you make the deposit in which case you would have to basically make the deposit and then use the bank feeds as a checking feature and then we have an accrual system where you would have to actually invoice the client track accounts receivable that transaction not having cash involved in it and therefore the bank feeds will not help you with that although you can then think about connecting the bank feeds possibly to the invoice or the receipt payment or the deposit we'll talk about that later so let's imagine the first system right now where we're putting money directly into the bank possibly in the system where we're taking cash and we're just putting we're just going to deposit the cash into the bank and and wait till it clears the bank feeds and then recording it as revenue so if that were the case that would work fine but we would want to make sure that we can distinguish that from other kinds of deposits that we might make into the system from ourselves so let's go back to the first tab and let's go into the transactions closing up the hamburgie here's our bank feed transaction now if we had a deposit let's go into our deposits and filter by just money in so if we had a deposit that was just cash it might look something like this right just a cash deposit and like i say if it was if it was coming from customers and we were waiting till it clears the bank and we record that as revenue we can use that as our normal process however if we the owner put money into the bank then it might look the same and we have to have a system to make sure that we catch the fact that that should not be recorded as revenue but rather as an owner investment and usually you can see that because it's going to be possibly for a larger dollar amount maybe and possibly because it's going to be even in nature there's not going to be any pennies or anything involved which is often the case with sales especially if you have to deal with sales tax calculations okay and the other thing i just want to point out is the accounts that will be effective so let's go to the balance sheet deposits will will obviously be increasing the checking account the other side is going to be going into the equity side of things instead of into the income statement so let's just recap our our balance sheet accounts we've got assets liabilities and the equity so assets minus liabilities equals basically the equity kind of like the book value of the company when we first start the company what will typically end up happening is we need to buy machinery and equipment and inventory possibly to help us generate revenue and therefore we need to get initial cash into the business how do we do that possibly we take out a loan and that would be one way that we would have a deposit other than from customers and or we ourselves as the owners put money into the business so let's first think about that first one we the owner are putting money into the business hopefully this doesn't happen all the time but only when we're starting the business and when we're increasing the size of the business because as the business starts running we're hoping it generates revenue and cash and we take money out of the business which we saw in a prior presentation so you're not going to see putting money in the business all the time hopefully but when it happens we have to distinguish it from like another deposit so the draws of the business when we took out we put in the draws if you're a sole proprietor and you're putting money into the business you could put it into simply the owner's equity or like the retained earnings account but oftentimes you might want to do a similar thing as withdrawals and create an owner investment account to record the equity that's going in just making sure that it's an equity type of account if it were a partnership then you might have like five partners or something like that you would then need a capital account like the owner's equity a draws account and a an owner investment account per partner you actually might make a parent account as the partner's capital account and then subordinate accounts of draws owner investment type of accounts in it and then possibly the portion made of the net income since you have to deal with this net income that's in here that's pulling in that's not actually an account if it was a corporation then the you'll recall that this account would be called retained earnings and then the draws because everybody has to take the same draws are called dividends and then the money that comes into the business from the owners are called shareholders that's the capital when they buy the initial capital from the company not on the secondary market okay so that's going to be the idea let's go back to the first tab we're imagining we're a sole proprietor let's say this is us putting money into the business so we're going to say all right so this is going to be an the vendor is going to be owner owner this is going to be a customer so owner customer we're not really a customer but we have to choose customer or vendor so i'm going to put an owner or customer and then i'm going to create an account so we're going to say new account and then it's going to be an equity type this is the key it must be equity and then we have to do estimated health insurance health saving uh uh uh i'm just going to call it owner's equity for that subcategory and then i'm going to name it uh owner investment so owner investment it's not going to be a subcategory of anything let's save it and close it and so we're not going to assign a class now this is one that you're probably not going to assign a rule to because it's not something that's going to happen all the time and when you see that come up you probably want to just make sure that you can identify it so we might not want to have a rule for it and we want to be careful that we don't create a normal rule that would include the deposit automatically recording it as income with the rule we want to make sure when we're making the rules it will be able to distinguish money that's coming from a customer as a deposit and money that's coming from us or a loan so let's go ahead and uh confirm it and then if i go into the the the balance sheet and run it it would be increasing the checking account with a deposit and the other side is going to be down here in the owner's investment so if i go into the owner's investment then we can see the detail here it was recorded once again of course with a deposit form that being the typical form used i'm going to check on it when the checking account is increased that's the form used and there is our deposit closing that back out going back there it is now like with the draws the deposits typically will close out in normal bookkeeping to the equity account on a yearly basis at least but quickbooks doesn't automatically roll it into that account so if you want to close it out you you would have to do in a journal entry to do that on a yearly basis but if you don't do it it's not the end of the world it's just that this will then represent investments for the life of the business as opposed for the current period for example if i go to the next year this income will roll into the equity let me show you we're going to go 010125 to 010125 run it and you can see that the income is gone it went into equity but it did not roll in the investment and the draws which typically would be closed out under normal normal bookkeeping so you could do that manually with a journal entry okay 010124 to 0229 uh 24 the other way that we might have income come into the business that's not from a customer would typically be like a loan situation so if we have a loan there's a couple things to just keep in mind with the loans we kind of jump into a whole a whole can of worms as they say when we get into the loans because as the bookkeeper you might treat the loans a few different ways depending on on who you're working with in terms of your accountant and what kind of separation of duties you have so for example if you took out a loan and you and you just got money so you said you got a business loan and the money's increased in the checking account you'd see it come through the bank feeds and the other side's just going to go to a loan well that's going to be pretty easy to initially put on the books because because the full amount is going to be received in cash however oftentimes loans are financing equipment so you might be purchasing equipment for example and then you're taking on a loan as part of the purchase of that equipment so in that case you're going to see the the money come in uh to the bank feeds or or you know you're going you're going to actually see a partial payment possibly when you pay for the equipment putting down a down payment or something like that but you're not going to see the loan money going into the account so in that case if that were the scenario you have a few different options one you can you can talk to your accountant and have them you know possibly help you to to make sure that you're recording the transaction uh properly recording the equipment at the cost of the equipment the loan balance on on the books and the cash deposit or you could just say hey look i'm going to do everything on a cash based system over here on the bookkeeping side and then when myself or the accountant does the adjustments at the end of the year for taxes and possibly external reporting they can take care of the other issues meaning i'm just going to record the the the payment for the machinery not including the loan just the cash payment that i paid for it even though i financed it i'm going to keep the receipts of the transaction i'm going to when i add the machinery here i would like to actually include the purchase documentation and the loan documentation possibly as an attachment so that when i provide this to my cpa or my accountant at the end of the year they'll be able to see that to properly identify the equipment on the sub ledger and they'll be able to break out the loan properly which is something they might have to deal with anyways right because they're going to have to create an amortization table and whatnot so that might actually be a fairly easy thing to do anyways because they're still going to have to do it and then they could basically and then at the end of the year they're going to take that documentation and make an adjustment to properly record the machinery and equipment on the books including the loan to properly record the loan on the books at the same time so that's one issue with the loans uh how are you going to record it on the books the other issue is breaking out interest and principal and short term versus long term we'll take a look at those in a second let's first put the loan on the books let's go to the first tab let's imagine that the full amount we we got the loan that and the full amount came into bank feeds it was just went into our checking account we didn't finance the equipment so let's just imagine this strike payment was actually a loan from the bank so i'm going to pretend that this was a loan i'm going to go into it i'm going to say this i'm going to call it a vendor of a stripe bank loan is going to be the vendor just so we can identify it as a loan and i'm going to say tab save category now on the categories i'm going to call it an other current liability now here's another issue with a loan you if you pay it in installments you might have a current portion and a long term portion of the loan but it's useful to put all loans into one account so that so that you can tie them out to the loan balance i prefer putting all the loans into the current portion rather than the long term portion of the loan and then breaking out the long term portion if necessary if there is a long term portion annually if we need to which we may not always need to do if we're just doing the books for taxes because we might not need the balance sheet information for taxes so i'll talk more about that in a second i'm going to put it into other current liabilities it's going to be a loan so loans i'm just going to say loans loans to others and then i'm going to call it loan payable now also just realize that if you had multiple loans which is often the case for some businesses that finance equipment for example you might want to make a parent account called loans payable and then make a subsidiary account for all of your loans breaking out the loans possibly by institution but you probably also want the last four digits of the loan number i'm just going to put the last four digits of like a loan number just to show you that process here because that can help you to identify the loans so then i'm going to say let's save it now no class now this this is this is something that we might want to add an attachment to because again when we have this for the accountant side of things we might need them to create an amortization table to help us break out the interest and principal so it might be useful to do that we probably don't need a rule because we don't do loans all the time this isn't something that's going to be repetitive so the rule most likely would not be applicable here so let's go ahead and record it and check it out so if i go to the balance sheet we would have then an increase to the checking account and then the other side is on the balance sheet in a loan payable it should be on the balance sheet there it is loan payable so if i go into that we're going to see the transaction deposit loan payable if i go into it it's still going to be with the use of a deposit form so that looks good i'm going to close this out go back now if i did not identify it as a loan and i recorded the deposit as income uh same which the same thing would happen if i didn't identify my investment it would then record over here on the profit and loss as income which would make it our income statement look better it looks like we got more income but that's not that wouldn't be good for us for taxes because we have an income tax in the united states and we want our taxable income to be lower not higher right so that so we don't want we don't want to record income over here for sure if it was from a loan or if it was from the the owner so we have it properly broken out as a loan so just a couple other things to note on the loan while we're on the the loan information and thinking about how it's going to be impacting the bank feeds once we have the loan on the books the next question is how do we handle the payments for the loans sometimes the loan will actually give you the institution they gave you the loan will give you an amortization table but oftentimes they will not they'll just give you the terms of the loan because you can create your own amortization table from it so an amortization table looks something like this where you where you break out the principal and interest so you can calculate this is not the same loan but just note that you could you can build one in excel you can also use online just search for amortization table creation software or something and you'll get an online calculator for it i like using the online calculator as a double check and doing it in excel myself because then i can use it for other as an integration for other things as well but in any case so if it was a five-year loan it would be 60 months the rate in our case five percent this would be the monthly rate this is the payment so that will help you to break out the interest in principle which is one reason the financial institutions don't do it or give it to you possibly if they don't have to because then you can see how much interest you're you're actually paying but i also need to see the interest on a per payment basis so you can see this first payment we're going to say in this case we're paying the same amount each month which is often the case for installment loans like similar to a mortgage might not always be the case for a business loan but it's a pretty common kind of structure for a loan but in order to have the payments be the same the allocation between interest and principal reduction will differ and that's the trade-off so that's kind of like the issue so once we create the amortization schedule whenever we make a payment on the loan if we're trying to tie out to the amortization table we have to break out the interest in principle which is difficult to do with the bank fees so in other words you might try to automate the payments that you make on the loan on the on the decrease side of things money out you might say look i'm going to just say if this was a loan payment here i'm just going to break it out and and have this and automate this go into the loan now you could possibly put splits and have multiple accounts affected because there's going to be three accounts affected rather than two accounts however it's still you still won't basically be able to do it because every payment has a different allocation of interest in principle so that becomes kind of an issue for the bank fees you can't you can't just easily make a rule to record all the loan payments properly so that the loan balance will tie out after each payment so you have to basically do an adjustment to make that work if you want to automate it then you can do a system where you're saying okay i'm not going to do that what i'm going to do is i'm just going to record the payment as it comes to the bank feed to the loan balance in other words i'm just going to record the payment to the loan balance here ignoring the interest which is kind of like the rent on the purchasing power of the money and then and then at the end of the year i'm going to to provide this documentation to my accountant or cpa who can then create the amortization table if they need to and then they can break out the proper amount of interest with a journal entry they can do an adjusting entry to properly record the interest that actually works pretty well as long as you communicate well with your accountant because then you and or you can do it yourself right because then you can automate the payments on the loans without having to do anything during the year to to to get that done and then you can basically just do an adjusting entry for tax purposes possibly breaking out the interest so that you get possibly a deduction if that's applicable for your taxes for the interest expense okay so that's one thing the other thing that that you might have some options on is is the idea that you might need to break out the short-term and long-term portion of the loan so normally for external reporting purposes the the current liabilities are those that will be due within a year and long-term liabilities are those that are due after a year that's useful to people reading the financial statements because they want to know if you have enough current assets to pay off your current liabilities which are due shortly right if not then you're going to run into a cash flow problem and possibly be a going concern meaning have the like ability to go out of you might have to go out of business or something right so so so we need to break that but with a loan you can see if we make a monthly payment that means that part of the payment is short-term and part of the payment is long-term or part of the loan is short-term part is long-term so then the question is well uh am i going to break out short-term and long-term portion each month no probably not the easiest way to do that would be to break out the short-term and long-term at the end of the year when you need to possibly and you possibly might not even need to do that if you're a small business that is that is just recording a schedule c why because the schedule c is just the income statement basically you don't need the balance sheet on it so if you're doing your books primarily for for taxes you do need to break out the interest because that'll hit the income statement and possibly create a deduction for you but you may not need to break out the short-term and long-term portion of the loan because that's on the balance sheet and therefore may not impact your taxes if you have a basic schedule c tax return if you have a corporate tax return an s corporation possibly then maybe you need to then you might need to break it out but even then you may not you know depending on the circumstances so so there so there so there's that so then you'd have to so how would you break it out then you take your amortization schedule and you would and you would break out the short-term and long-term which i won't get into in detail in here but you could just you know look count the 12 payments out and have the short-term and long-term portion which again is something the accountant can do so couple so that's just a couple things to note when you want to make sure that the deposits from yourself and you're and from a loan if those come through you can distinguish them from deposits from client customers so that you don't record them as revenue number one the the deposits that come from yourself you're typically going to be putting into the equity section as owner investments if a sole proprietorship or a partnership and or a partnership capital investments or something and then and then it would be the sale of stock right would be the issuance of the stock for a corporation and then with the loans you have a few options in terms of of recording the loan if you purchased equipment and how you're going to deal with that do you want to stay in a cash-based system and be more reliant on yourself or your accountant at the end of the year to properly then do adjusting entries which can make it easier to automate your system or do you want to put more detail in as you're doing the bookkeeping for the purchase price of the equipment and then with the payments do you want to be breaking out each payment between interest and principal as they're paid which means less easy to automate or could you rely on the accountant to break out the proper amount of interest at your end or yourself with an adjusting entry and then and then do you need to be breaking out short-term and long-term portion of the loans you might not if to even if you do need to you probably only want to do that periodically so that you can still have each of the loan accounts tie into the amortization tables all right so let's go to the to the trial balance run it this is where we stand at this point in time if your numbers tie out to these numbers great if not it might be a date range issue you could change the date range and see if that is the issue if it is you can drill down on the numbers go to the source document change the date uh from the source document