Complex Question Formation Statement Questions Statement questions can be used to express surprise or disbelief. You're not married? They won the game? He does? For added effect, you can add a WH word. You did what? She went where? Negative questions. Aren't you going to the dance? Haven't you been there before? Isn't that Dr. Zimbongo? Questions with OR. Is it the blue one or the red one? Would you like some tea or coffee?


OK, so I think we can move on. And the next speaker is Ignacia Cancino Aguirre, talking about metabolic variability in mycobacteria. Ignacia? Hello? Yeah? So good morning, everybody. I'm Ignacia Cancino, and I'm a PhD student at Inriaca Nobel in France under the supervision of Hida de Jong and Delphine Robert. And I'll talk to you about this new project that we started, that it's about the analysis of mycobacterial metabolism using genome-scale metabolic models. So just out of motivation or context, mycobacterium tuberculosis is a bacteria that causes tuberculosis. It's a disease that kills more than 1.6 million people every year. And as you can see, it's present in almost every country. And despite all the efforts to eradicate it with vaccines and antibiotics, it's still present. And also, it's become more and more resistant to antibiotics, so it's like a big problem. But MTB, or mycobacterium tuberculosis, is part of this genus, the mycobacterium genus, which comprises around 200 mycobacteria. And so it's part of this genus, along with other pathogens like mycobacterium lepra and mycobacterium ulcerans, et cetera. So we were very interested in looking at the genus level of mycobacteria, because they're very interesting. Even if they're genetically kind of similar compared to other bacteria, they show different phenotypes. So half of the genus divides in slow growers and the other half in fast growers. And there's one clade that is kind of intermediate growth, but that it's weirdly defined. So this is very interesting. And there's been attempts to understand a bit why, but not that many. It is interesting because a lot of the slow growers are also pathogenic bacteria, but not all. So just as an example, some of the slow growers there's MTB, there's ulcerans, mycobacterium marinum, that is pathogenic usually to fish, but there's been clinical cases of infecting kids. And there's also other, the fast growers are mycobacterium spegmatis, for example, that is non-pathogenic, and it's found in the environment. But it's not clear this pathogenicity to growth rate relationship because there's other bacteria like mycobacterium abscessus, which is also pathogenic, but it's a fast grower. But how do they define what is a fast grower and what is a slow grower? So usually, and this has been done for 100 years, whenever they find a new, let's say, mycobacteria, they plate it in this LJ complex media, rich media, and then they let it grow, and then they see how long they take to form colonies. And if they take longer than seven days to form colonies, then they will consider them as slow growers. And if it's less than that, it would be a fast grower. And this LJ media, it's very complex. It has egg and potato starch and things, and it was developed in the 1800s almost. But it's still being used for clinical diagnosis and isolation of mycobacteria. But it's very interesting that even that growing in this media, you could see also the relationship in the phylogenetic tree. So there's been, of course, some attempts to understand this difference in growth rates. But it's really not that well-studied as one would think of versus difference in lag. They've always mentioned growth rate, and they haven't really mentioned lag time. So I'm not that sure. Yes. I mean, it could be lag. But then sometimes when you grow it in liquid media, sometimes you measure observance, then there's no lag. It's just very, very slow growing. But yeah, it could be also the lag time, I guess. Yeah, so some of the issues to understand this difference. One is very costly experimentally, not just money, but also time-wise, because they grow very slow. I mean, yeah, they can take like, I don't know, two to three weeks to do one growth curve. Some of them don't even grow in liquid media. Because they're pathogens, you need these biosafety level three laps or biosafety level two laps. So yeah, there's not that many studies. And a lot of studies focus more on MTB infection in host cells. Then also pathogenicity is kind of a weird defined concept, because there's no clear definition, at least in this area, about it. Like some people say, OK, if it infects somebody, then it's pathogenic. Some people say, oh, but if it infects, let's say, many people with healthy immune system, then it's pathogenic. If not, it's just opportunistic. Some of them infect other mammals. Also, they don't necessarily optimize their proteome allocation. So if you want to see it that way, we saw in a Terry's talk last week, he studied smegmatis, which is the fast grower for us. But for E. coli is a very slow grower. And they weren't optimizing their proteome allocation to grow more. They would invest in other functions of the cell. And also, if you would explain it by the number of our RNA operon copy numbers, they have very low copy numbers. So most of them have like one or two. And still not clear, because some fast growers, most of fast growers have two copies, and most of slow growers have one. But a few of the fast growers have one, and then, yeah. So it's not like a clear relation. And also, these studies have been done by very few bacteria. So I guess you could maybe look more into that, if you want, because they're usually done in maybe four or five of these bacteria. But anyways, this is not enough for us, I guess, to really understand why they're growing differently. So we were thinking that one way of studying this growth rate variability is by studying their metabolism. Because you can study all the reactions that are happening, that account for biomass production, and then you can relate it to their growth rate. So the approach of this project is using genome scale metabolic models, as we have heard these past two weeks. And they model the metabolite dynamics in the cells. And then they relate the stoichiometric matrix that has the stoichiometric coefficients for all of the metabolites in reactions. And then you multiply it by a vector of the reaction rate. And then if we assume that they're in a stationary state, then we can equal that to 0 for the internal metabolites. And then we can also constrain these fluxes with either experimental information or thermodynamic information, like directions, et cetera. And then we will have a constrained space of solution for this linear system. And then we can analyze it in different ways as we saw. So we thought that this method could be useful for us to understand why they're varying in growth rate. But of course, there are some issues. And some issues with this approach is that there's only two genome scale models for mycobacteria. So mostly for MTB. And then there is some strains of TB that have been done. And then mycobacterium bulb is BCG, which is actually the one that they use for vaccines. But they're very, very similar as well. And actually, they merge these models at one point and use that one to analyze both of them. Recently, they have of course differentiated them a bit more. So yeah, that's the only mycobacteria that has a model. So we would have to reconstruct more. And then of course, there's the experimental limitation size I mentioned before. You need a biosafety level three and biosafety level two labs. Some of them don't grow on liquid media. Like mycobacterium ulcerone doesn't grow on liquid media. And some of them, I mean, and a lot of them take a lot of time to grow. And also to go from solid plates to the liquid flask, it would take like a month or something to adapt to those conditions. And they also tend to clump a lot. So it's a bit annoying to do these growth curves on liquid media. But luckily, there's the reference genomes available on NCBI. And there's also experimental information on single bacteria or single species. And there could be some information in general about the phenotypes and maybe some pathways. And we also have this, that I forgot to say it, a collaboration with the Francis Creek Institute in London, where they focus a lot on micro-bacterial metabolism and antibiotic resistance. And they have these biosafety level three labs. And they do very nice stuff as well. So the idea of the project is to develop genome-scale metabolic models for the different micro-bacterial species. And so validate those. Then at the same time, obtain exchange rates and growth rates for these different bacteria grown on the same conditions. And then after we have these two components, the idea is to analyze them. And because I said that micro-bacteria don't really optimize things, strategies, we would do the analysis by uniform sampling because we don't want to assume optimality. And then the idea is to compare how the flaxes behave in the network between the different types of micro-bacteria. So first of all, we started by asking ourselves, OK, but can we actually infer the intracellular flaxes with the already published model of TB? Because if not, then this approach wouldn't really hold. And so we found one data set of carbon-13 measurements of the intracellular flaxes. And so we constrained our models with the exchange rates that they measured and a few thermodynamical information like reaction direction and the growth rates. And then we used uniform sampling. And then we also removed some of these infeasible loops with cycle-free flux. Maybe some of you might know it. So we found that this is only four of the reactions. We have the results for all of them in the network. There's like 1,300 reactions. And we found that for most of them, our simulations were at least in the range of the experimental value. So we have the blue curve, which is our simulation from the sampling. And then the red dashed lines are the experimental value. So we thought, OK, even if the mode is not necessarily the exact value, they're still in the range. And then we can infer flaxes, at least, with this model. So then we continued. And then we started the part of reconstructing GM scale metabolic models, which is like a actually long and tedious process. So we tried to use automatic tools because in the beginning, we wanted to do it for the 200 species. And so there was no way that I, a PhD student, like learning about this would do it in three years. So we looked at some automatic tools that are already, I would say, widely used. I mean, they're from 2018. Carth me, maybe some of you have heard it. And they create already like a connected network. So they do align the genome to a database. But then they also make sure that they are connected. But the issue with this is that sometimes it tends to add more reactions that there actually are. So you still do need a step of manual refinement, or maybe some gap feeling. I mean, it's not too automatic. And we also, because we saw this in the beginning, and we're not satisfied with the model it was creating, we also implemented some other filters for Carth me. So yeah, some like playing with the alignment parameters. And we also updated the database they had with this new MTV model that we thought it would be useful. So then we tested. So we tried this pipeline with tuberculosis, because there's already a curated model for that. And then we tested it with this growth metrics. So in the lab, they grow TB in single carbon or single nitrogen sources. And then they say if they see some growth, it doesn't matter the rates. But just if they see some growth, they would classify it as one, and if not, zero. And so we did the same with our model, doing FBA. And just, I mean, we didn't care about the value of the growth rate, but just if it was higher than zero. And so we actually, in our model, it got very similar predictions to the reference model that is already published, which is nice because it was mostly done automatically. And it's slightly better than the reference, but not too much. It's actually very similar, except that it has more reactions. So it has 1,700 reactions and 1,200 metabolites. So this was nice. But then we're in the part of the working progress, which is applying this pipeline to other species. So in the beginning, we thought of doing it for the 200 species. But then because it still needs some manual refinement, we thought of, for the 200 species, just doing functional genome analysis. So to see which genes that codify for enzymes that have reactions associated to them, which ones are present in the slow growers and in the fast growers. So not really quantitative. But then we would take from those species 18 that we're actually growing in the lab and that we are producing this growth metric. So does it grow in single carbon sources or not? Because those we can actually validate them with some data. So then we would do the models of those, validate them with these phenotype data sets. And then from those, because doing the growth curves take a very long time, we thought of starting with at least five species that have this difference in growth rates and actually do the growth curves of those and measure growth rate and metabolite exchanges. So that would be like, that would be five species. And yeah, and that would also be more carefully curated. So then this is the experimental part, which I'm helping out but I'm not the only one doing it. We have a researcher in the creek that's actually continuing the experiments, but we kind of discussed it together and I did a few of these curves. So we chose to do the growth curves of five species. So from those, we chose three fast growers and two slow growers. And for the fast growers, there's one that's pathogenic and the others are not. And then for the slow growers are both pathogenic. And then we decided to grow it in a defined media because the LJ media that is actually used to to classify them as fast and slow. It's a complex media and there's many stuff and it's very variable. So we cannot really rely on it to have these quantitative rates. And so we used 7H9 media, which is like a very gold standard media for mycobacteria and it kind of is not the same composition, but it does resemble the phenotype seen with the LJ media. And then we would use the optimal temperature of those and yeah, about temperature. There's two of these that grow at 30 degrees and others at 37. So we would use the optimal temperatures of those. Yeah, and then it would be aerobic growth. So shaking the flasks. And we thought about, okay, which media should we test? And then we decided to do it on the 7H9 that has a glycerol glutamate and glucose as carbon sources. And then we also thought, okay, maybe we could also see how they behave or how they change their growth rates if you just throw it on a single carbon source media. So we chose glutamate and glucose. We tried also with glycerol, but they tend to clump a lot, a few of them. So then OD measurements are not really reliable, even if you're using detergent. And then the idea is to measure growth and also measure metabolite uptake for those over time. So all in all, the project is to study micro-bacterial metabolism to hopefully explain better why they have this growth rate variability. The approach that we're using is this constraint-based modeling and implementing experimental data. We're in the process of reconstructing the models for the other micro-bacterial species and testing those at the same time, obtaining experimental information. And so what is left to do, which I think is the most nice part of the project is actually comparing the flux spaces between the different species and sea if we could find hopefully some clues of why they are acting different with respect to growth rates or maybe why some pathways are more active, let's say in some group than others. So just to finish, I want to thank my lab, my supervisors, Elfin and Hida, and we have a new postdoc now that's also helping a lot with the bioinformatics and our collaborators at the creek. So the principal investigator is Luis Pedro Carvalho and Azeli, she's helping me with experiments there. So yeah, thanks then. Question? Thanks a lot, we have time for questions. Hi, thanks. So, I mean, I know you're not on the experimental side, but can you elaborate a bit more on why you chose to take glucose, glutamate and glyceros, so what was kind of the rationale behind selecting those carbon sources? Yeah, so I mean, they were based on the gold standard media for TB or for mycobacterial identification, which is apart from the LJ that's complex, the 7H9 middle group media. So that media has these three carbon sources and then already because there's been most of studies, they do it on this media. We have more experimental information to kind of validate our models, for example, and also to compare and, yeah, so we didn't want to create a new media from scratch. So that's why we chose those three carbon sources. Other questions? Yeah, this is a curiosity, so it's the first time that I think about this mycobacterium, but it seems almost like there's this established pattern of the slow grows being more virulent or being more pathogenic. From the physiology, is there any, what's like the typical explanation that people give? Are they? So there's not like a clear answer also because there's a lot of the fast score that are becoming more pathogenic. Apparently they've seen that the pathogenic one, they have lost some genes so they can only grow intracellularly. Yeah, they have some proteins, I think that they say that related to virulence, but they're not, but like the fast growers also have them, but just like a difference in those proteins. So yeah, it's not actually that clear, the physiology of them. Actually, I want to follow up on this question. Can you maybe, I don't know, say where the fast growing or non-pathogenic bacteria found in which kind of environments? Because I imagine, so for example, for E. coli, we see that UPEC has way lower growth rates than our lab strains, of course they've also been involved. So maybe there's also something going on with they actually benefit for changing colonization habitats when they grow slower, I don't know. Yeah, so most of the fast growers, they have been found in soil and water bodies. There's no specific trend, but just more like environments, I would say. While the pathogenic are usually found intracellularly, I guess because they already infect. And yeah, I think it has to do also, there were some studies looking at that the fast growers can use more diversity of resources, while the pathogenic ones, they can take only a few of those. So I think it does affect that. So for MTB, let's say, the kind of environment that it grows in when it is a pathogen, is that known, what is that environment and can that be sort of simulated in these flux balance sort of theoretical studies? Yeah, so MTB grows on macrophages in the phagosome of macrophages in the body. And there has been actually very interesting studies with these published GM scale model of TB on the host, so macrophage model and the TB model and how they interact. So yes, it can be modeled. Also, you could also do it in the lab. So what they do in the Louise lab, they take macrophages from blood of donors and then they infect with TB and then they study different things, like I don't know how pH changes, for example, and things like this. But I actually wanted to, in the beginning, I mean, I thought of like, oh, what if we can do growth curves in this macrophage-like media, but there's actually no macrophage-like media at the moment. They really just take the macrophages, but that takes forever. I mean, it takes even longer. And the thing, not just the time, but also it changes from patient to patient. So if you have fresh blood, I don't know, with better macrophages, then it's a nice experiment. But then next week you get new blood and then it's like not that great. I don't know, and they don't really have information of the patient because it's confidential. So yeah, I think it would be very, we talked about this in the lab and it was like, oh, it would be very nice to have a synthetic media that resembles the macrophages, but then I think that's like another work. And so everybody has been pushing it, kind of. But I think it would be very nice to do that. Yeah. Any other question? Okay, let's thank the speaker again. Okay, see you.


Welcome folks, we have the Dow Industries trading down $7.76, Nasdaq's up $4.66, S&Ps are up $130. That's a downdraft folks, and the Nasdaq have over 4% and the S&Ps over 3, and the Dow Industries 2.4. Gold, gold contract down $47 trading at $18.28 an ounce. We have Silver down $0.73, $21.19 an ounce, Light Sweet Crude flat $1.2031, notes and bonds. You talk about a move here man, this is quite a move. You get the 10-year down a point and a half at $1.1508, the 30-year off 3 points at $132.15. We have the 10-year right now yielding 3.369%, monster move, and another monster move out here is Kingdala. Kingdala's up $934 ticks trading $105.03, Kingdala very well could be an ABC structure on the way up. It did a .382 retracement on the way back, heading for the highs again, if it breaks the highs, guess what, it will be pretty intense because what it would set up, the ABC structure is about $108, but what it would set up is that it would set up that you could go ahead of $120 actually, that's the $2,000 high. Euro is at $104, yen is at $138, the British pound is at $124 to $1 USD, $121 to $1 USD. We get over and take a look at the spy and we'll see whether we're going to get the volume inside the S&Ps for an ABC structure down. We broke the B point and at this particular point it doesn't need many shares, it's only going to need 30 million shares into the close and we can get it. The NDX is going to be a confirmed ABC structure down. The NDX looks to me like it's going to have the volume in space. Right now you've already done 66 million shares, I think it needs 93, 91, you'll do that in the next hour, so that's an ABC structure down and it's a monster ABC structure down on. And then on top of that you're coming up to option expiration this Friday and what does happen folks is that January and June are the largest option expiration, so stay tuned for the firepower. Gold, gold contractor, bottom line is pulling back. We went top side on Friday with volume and guess what, just gave it back. We are at a price point of 1826, we hit a low of 1824, the low Friday was 1826 and it took off like a rocket ship so this is all about the dollar, that's the bottom line. Notes and bonds, they just continue to want lower price, higher yield. Stay right there folks, come right back.


Freedom is not to do what you want, but what you ought.  Has anybody ever seen a horse just roaming about and not have a master? We have not seen that in natural life. We're not seen that ever. A donkey just roaming about and nobody has to claim for it. Same thing happens when we receive deliverance, when we receive freedom, we don't receive freedom just to be free. We receive freedom that we can have and be bound to a different master and that's Jesus Christ. And then church, there's this, how can I say a sick thinking that people come to church and say, I wanna be set free from depression, I wanna be set free from drugs so I can do what I want. You guys heard that before?  You know, I want Jesus to deliver me so I can do what I want. You know why Satan fell from heaven? Because Satan wanted to be God. Satanism, it's not worshiping evil or anything. Satanists, they worship self. They worship and they do whatever they want. There's something worse than being addicted to drugs. It's becoming a God. It's doing what you want because that's why Satan has fallen from heaven.  So we have to understand that freedom is not, though we can do what we want, but we can do what we ought to do is to have our relationship with Jesus Christ. Amen church. Freedom is not just being delivered from evil but replacing that evil with Jesus Christ. Amen church. We are to be free with the purpose. We are to be delivered with a purpose and our purpose is to win souls and make disciples. Amen church. Being free is a dangerous ground. Being free is dangerous when you are not filled. It is dangerous to be free when you're not occupied and when you'll not have a master. We have to understand, the Bible clearly talks about, it says that if you're not hot and if you're not cold, Jesus Christ will spree you out of your mouth. It is dangerous for us to sit in the middle, to be able to just attend church and not get involved, not to get to know Jesus Christ because it's a dangerous ground. Sooner or later, you'll begin to slide back and when people come to the altar call and they give their life to Jesus and I get a chance to meet with them, to talk to them and I tell them one thing, do everything you can to get involved. Do everything you can not to be free because that freedom is a disguise. Is the freedom that you think I can do whatever I want whereas Satan is lurking behind that freedom and he'll capture you right back. You have to understand, you will never be free. You'll be a slave to something. You'll either be slave to sin or to Jesus Christ. You'll be either a slave to Jesus or to Satan. You cannot live a life that is free. It's not possible. Sooner or later, you'll understand, if you will not become a slave to Jesus Christ, you'll become slave to depression. You'll become slave to suicidal thoughts. You become slave to sickness.  You will be a slave to something and to be a slave to Jesus Christ is that as we want because Jesus Christ says, I came to give life and life more abundantly, amen. When Jesus Christ has become your master, when Jesus Christ becomes your everything, that is a life worth living. That is a life with peace. That is a life with comfort. That is a life that when somebody looks and says, you know, I wish to have that life because that is a life that is found in Jesus Christ. Amen, church.


Exceptionally dry conditions throughout the area have contributed to several small wildfires over the past week. It's rare, but not uncommon to have these conditions during the dog days of summer. The Bemidji Fire Department has the area's status listed at its high risk for wildfires. If we don't receive any rain within the next few days, we could see the risk for fire danger increase. While there are no burning bans currently in place, firefighters are asking everyone to act responsible when having a campfire.   It has to be logs, three foot ring contained by rocks, bricks or something like that. And it has to have, it can't be within 25 feet of a structure and it has to have a manicured grass all around it. Unrelated to the dry conditions, the Bemidji Fire Department will not be issuing any burning permits at this time because of an air quality alert that has been issued by the Minnesota Pollution Control Agency. The alert was issued because of smoke from Canadian wildfires currently moving into the state. The air quality alert will be in effect through noon on Sunday.


Alright guys, good to see you again. Good afternoon. Today I'm going to tell you about an algorithm that's used in the system identification. It's called expectation maximization and we are still thinking about structural learning where we have a set of equations that describes the state update and we have a set of equations describe the measurement and what we want to know are the parameters in these equations the A, the B, the C and the noises and in the particular task that I want to show you today the approach differs very much from the work that I showed you on on subspace analysis in that subspace analysis is was used by control theorists. Expectation maximization is a learning rule that's used iterative people in machine learning and you know they're just different fields they've used different tools. The fundamental power of the state space the subspace approach is that it gives you an estimate of the number of hidden states the size of the vector x. In the process that I'm going to show you today you have to assume that you have to make a guess about that number and then based on that you're going to come up with the best estimate that you have of the the parameters of system A, B and C and this expectation maximization as applied to the state space equation finding those parameters something that was described about the same time as the subspace analysis and it was the late 90s when the paper was written. So that's what we're going to be talking about today and to start things off I want to so this is now the last parts of the chapter 9 and what what I want to start with is how to apply the algorithms that we've been learning the subspace analysis and for example today's to you know you've collected some data from some individual some system that learns and you want to identify that learner and we did this a few years ago in a task where people were asked to make an eye movement so they had a stimulus they were given a target here they made a saccade to that target and then what happened is that we jumped the target so that we made it so that after the end of their saccade the target that used to be here now it appeared here so at the end of the movement it appeared that there was this error this error here and this error caused adaptation so for example if you look at the experiment so here's here's the way the experiment went the position of the target T was on the y-axis trial is on the x-axis and x is trial y is the change in the position of the target delta T here and so it began with a delta T that was negative and then you know it went positive and then to zero and what people did is that they adapted so that they began to reduce this error so they began to learn and there was a set break forgot a little bit learn set break forgot a little bit they learned something like this then the perturbation was reversed as follows and then what happened was that we took data like this and we said all right what are the states that describe this learner and what was the parameters associated with that learning system so let me write down the equations for such a thing so suppose that we can imagine the learner as having a state x and what we're interested in is describing how it changes the state so there's some state x but maybe we don't know its size and this represents a memory state in the learner and that changes from trial to trial as follows what was going to happen is that this this system is going to in this case we assume it's a vector B right in the matrix that's going to be learning from it's going to learn from errors I'm going to call this y tilde that's the error in trial and plus epsilon x so the state update equation looks like this it's going to have some memory state x as many dimensions as you like it's going to learn from error y tilde that's going to be this B that tells us how much is going to learn from error and then the action that the learner produces the thing that I can measure is y that's his action maybe saccade length the saccade that he makes depends on where the target is t in trial and and maybe he's there's got some bias in him so that whenever I show him the target at 10 degrees he always makes a saccade to 9 degrees so I'm going to have this bias here I'm going to call it y B some constant bias in his actions and then his performance also depends on the state x his memory states so I'm going to have c transpose x of n plus epsilon y so this is my system of equations that I want to fit to the behavior of the subject so there's some state that this individual has and that state changes as a function of error and tends to decay to zero without error and he performs an action y that I can measure that action depends on where the target was some inherent bias that he has and this his states that tell him how those states are related to the particular actions making so I don't know see I don't know a I don't know B and I don't know the noises what I do know is why the action that the subject produce on trial and and where I put the target on that trial T so I can estimate this tilde here why till the error as being the difference between the action that he did and the consequences of it so I can say y tilde of n is equal to where I put the target T of n plus say I put a perturbation to that target and we call that you have it this is the perturbation that I did this is what I plotted here you have it is the perturbation that I call the delta T which is basically the change in the target that I made this is this is the perturbation that I produced so this is this is where the target was this is where target ended up the difference between that and what the subject actually did which is the action that he performed it's it's going to be yb what what what it's going to be y of n minus y of b y of n plus yb so this is what he expected to happen this is what actually did happen the target was moved by some amount and here's what he expected to happen to it that's equal to let's see T cancels here it's going to become u of n this cancels here minus c transpose x of n minus epsilon y so this is the state update equation this is the measurement equation and this is what goes into here y tilde is the difference between you what I did and what the subject expected so now I'm going to put this back into this equation now so I have x of n plus 1 is equal to a x of n plus b times y tilde which is u of n minus c transpose x of n epsilon y plus epsilon x which is equal to a minus b c transpose x of n plus b u of n minus b epsilon y plus epsilon x that's my state update equation it written in the canonical form so I have this matrix that I'm going to be estimating this vector that I'm going to be estimating and these noises here so when people perform actions they may have a bias so it may not be that when you give them a target they may not move to the target they may consistently understood it yeah yeah it's it's the idea that the idea that you have I give you something to do you do it and what for whatever reason you don't go where I ask you to do you do something other than that but you do it consistently you have a bias in your behavior so we want to take that into account when we want to find the difference between what you predicted and what you observed so if you had known that you had a bias by the time you get to the end of your movement this error here is not really an error it's just you predicted it so that's why I'm taking taking that into account this way no it means so it's it's in fitting these things I'm sorry it's so difficult to see the darn thing in fitting these things to behavior what what one of the important things is that what is error right and what error is is the difference between it's a difference between what I observe minus what I predicted so what is what did I predict well I don't really know what you predicted all I can see is that what I would imagine is that your prediction should be based on all the previous data is that you know on on average you have this bias in your performance so that must be what you would predict on that trial so I'm guessing that would be the case which is why I put this bias here in here in principle we have to guess what is error that you're learning from and in this case there's if there's bias in your performance I assume that doesn't go into your errors okay so okay so what this means is that when one fits data like this what one gets is so let me just fill this in so here's here's the data here's the performance you know what one gets is that there is some that ends up with two states here just like what David showed you guys in the in the two-state model what one gets is that there's a fast state that rapidly learns forgets rapidly learns forgets and then there's a slow state that slowly builds and one can fit this kind of states-based model to actual data and you get this two-state process out of it now the lecture today is about the problem of fitting such system of equations to data using a different concept a concept of expectation maximization yeah and our problem remains the same the particular problem that I want to solve equal to a x of n plus b u of n plus epsilon x where this has variance q and y of n is equal to c x of n plus epsilon y this has variance r and what our problem is as follows what we want to do is to estimate the parameters of the system let me call that theta and the parameters of system are a b c we have the noises are q and we have the initial state x hat and the initial covariance p0 our uncertainty about that state this is these are things that we want to estimate and on the other hand what we also don't know are the states x hat from trial one to trial n so we don't know the states and we don't know the parameters in em what one does is that what one says is that fix the parameters in the expectation step we fix theta we find x hat going from one to n and of course the way we do that is via the common filter if we knew the parameters we could find the states in the m step what we do is that we fix the states we find theta okay so to do the e step you guys know how to do that the m step is what's interesting which is if we knew the states how would we find the best estimate associated with the parameters and it's an iterative process if you go back and forth and you do this until you find that it converges so the critical thing in our formulation is going to be describing what's called the complete log likelihood and what the complete log likelihood what that means is that you want to find the probability of all the states and all the observations given that you had the inputs and the parameters theta so it's a likelihood function right unusual likelihood function only has complete log likelihood it has also the hidden states so what I'm going to do is to write for you what the complete log likelihood is and so just like every other time when we do a likelihood we find the conditions that maximizes that likelihood so we're going to write the probability of all the hidden variables x all the hidden states and all the observations the joint probability assuming that we know the parameters of the system assuming that we know the inputs of the system you and then once we've written up that the probability that's likelihood we find the log of that we find then the maximization of that likelihood we find the parameter theta that maximizes that likelihood that's what we're going to do today so the key step is this this we know how to do this the e-step the m-step is find the parameter theta that maximizes this quantity so let's begin so suppose that I only have the following like likelihood so I have the probability of x0 x1 y1 given u1 suppose that's only we only have one observation y1 and we only have one product so what is this probability so this is equal to p of y1 given so this joint probability I'm going to write it as a conditional probability so probability just to remind us the joint probability so p of a and b is p of a given b times probability of b p of a given p of a and b given c is equal to p of a given c times probability of c probability of that b occurring given given c so probability of y1 I'm going to write it in terms of u1 and so y1 given u1 and x0 and x1 times the probability of x0 and x1 given you want so this probability here is equal to probability of y1 given just x1 right because y1 only depends on and this probability here p of x0 and x1 I can write it as p of x1 given u1 and x0 times probability of x0 given u1 which is equal to this doesn't have any such there is no dependence between x0 and u1 so then I get probability of y1 given x1 times probability of x1 given u1 and sorry x0 okay so that's that's my first sorry let me this is what we're going to do is we're going to go from u of 0 so to me to write this I need to have u0 here because u0 is going to make a change from x0 to x1 so I apologize for that this is u0 okay all right so next step is I want to write what is the probability of x0 x1 x2 y1 y2 given u0 and u1 so I'm just going to add to this now if I have two measurements yeah yeah yeah yeah it's a vector yep good question right so we have two measurements now y1 and y2 rather than just one okay so that's all so before I only had one measurement just why one I have two measurements I want to write where am I going because I want to write this probability all the x's from one to n all the y's from one to n I guess is this still confusing do you see it okay well see x0 is a part of theta right x0 yeah yeah so I'm going to have to you know if if if I fix this I have to find what x0 is it's part of the one of the things I don't know all right so this guy let me I think I'm going to write it over here it's going to be kind of long well maybe you'll fit so p of x0 x1 x2 y1 y2 given u0 and u1 this is equal to p of y1 y2 given u going from 0 to 1 x going from 0 to 2 times p of x going from 0 to 2 given u going from 0 to 1 which is I'm going to break this up so this is p of y1 let's start with y2 I guess y2 given u01 x02 y1 times p of y1 given u0 to 1 x0 to 2 second term p of x from 0 to 2 um let's start with p of x2 given u0 to 1 x1 to 2 times p of x1 to 2 u of 0 to 1 um okay so this term here this is just equal to p of y2 given x2 right because y2 only depends on x2 this term here p of y1 given this is just equal to this is the only thing that matters is p of y1 given x2 sorry x1 um this term here p of x2 what matters here is x1 and u1 then I have this term here which I have to break here x2 given u1 0 and then x x1 times p of x1 u01 um this term and then this stays as it is this comes stop p of x1 this is just 0 x1 doesn't depend on um oh wait uh oh this is y yeah so this is this is not right so if I take x2 out of here what I left behind is 0 and 1 then I get um so okay I have this this x2 depends on x1 and u1 then this term here 0 and 1 okay now we're in good shape all right so this this term here is just p of x0 because it doesn't depend on um oh actually this is just 0 uh yeah that's fine okay so I can write the my as follows this is equal to just like that derivation that I have there is a multiplication of i going from our little n let's call it going from one to n of the first probability so what is this probability here p of y given x this is going to be p of y of n given x of n times n going from one to n of p of of n plus what um x of n I did I write it x of I wrote it as x of n plus four given u of n x of n times p of x0 um yep it is we're gonna we're gonna try to find it why no because no so um so in this step we have to find theta right and theta includes x0 so so x0 is going to be a normal with an expected value x hat with variance p yeah yeah sorry I forgot it thank you okay so we can write these things right because we know the relationship so we can write p of y of n given x of n what what that is so let's let's write it so p of y of n given x of n that's a normal with mean um c times x hat of n and variance uh r which is equal to um 1 over square root of 2 pi raised to the power m m is the length of the vector y times this variance covariance it's it's determinant um in the denominator times an exponential of minus one half um y minus c x hat of n transpose r minus 1 y minus c x hat of n so just cx I guess this is right so that's that's the probability of y given x now you have that the next term that we need to know is probability of x of n plus 1 given u of n and x of n that's um um it's normal with mean a x of n plus b u of n and variance q does that make sense that's what this equation is all right so what we need to do is find the log of this quantity I just wrote down for you what this is I wrote down what this is and this is just some some mean and variance x and with some you know it has some mean and variance that's going to be p at time zero at the step zero so we're going to find the log of this function write that down so the log of of this thing that I've put there look the the log of that likelihood function is going to be the sum of n is equal to 1 to n that's going to be the multiplication there of this the log of this of this quantity here and let's write that down let's see what that would be let me begin with what's inside the exponential so I'm going to have a minus one half y minus c x of n transpose r minus one y minus c x of n and I'm going to have this term here so the term that I care about is determinants that has r in it because r is one of the things that I need to find of the parameters that I don't know so what that's going to be is minus one half n times log of r because remember r is the determinant here being raised to the power of minus one half so we get them because there's n of these things that are multiplied by each other so there's minus one half times n times the determinant of r next what I have is the and then I have some constants you know associated with two pi raised to the m let's forget about that because we don't need that next thing that I have is the multiplication of this times this sum here of the n that are being multiplied that normal so I'm going to have another exponent minus one half of x of n plus one minus a x of n minus b u of n transpose times q minus one times x of n plus one minus a x of n minus b u of n right that's the exponent of this normal distribution yes they are sorry correct thank you very much very good so I think that's right so now what I need to do is maximize this log likelihood so to do that what I need to do is that what am I maximizing it with respect to what we want to find the derivative of this with respect to all the things that we don't know all those things that we don't know a b c r q x hat and p I also have my I forgot there's also the normal associated with the there's also minus one half the probability of x zero which is I guess that would be my so the probability of x zero is normal with mean let's call it um mu I guess so this is x zero minus mu I guess I've been calling it x hat of zero haven't I so let me call this x hat of zero that's our log of the complete likelihood so what we're going to do is that for each of the parameters we're interested in we're going to find the derivative of this with respect to that parameter now the idea is that you have started with some estimate of a b c r q x hat and p you begin with some estimate now what you do is do you maximize this log likelihood to find you know a better estimate so we know this because we began with some estimate for theta we found the best estimate for x hat now what we're going to do is that okay given that we have this estimate of x hat and some prior belief about what these things are find a better estimate for them and and we can do that so we're going to maximize this this this likelihood so through that you notice that there are these are variables right so this is every term here every multiplication here is going to become a scalar because it's just a probability just a number so we're going to be finding derivative of scalar quantities with respect to these matrices so we're going to have to find the derivative of x of n transpose c transpose r minus 1 y with respect to r or with respect to c these are matrices that's okay we can find derivatives of you know of scalar variables with respect to matrices it's just going to become a matrix so derivative of the scalar variables with respect to a matrix is going to give us another matrix and there's some useful idea in your on the website there's a file called useful math and along the things that are there are how to find derivatives of scalar quantities and for example the derivative of the quantity a transpose xb where a and b are vectors dx is is the quantity a b transpose and the derivative of let's see the other one that we're going to need here is derivative of a transpose x transpose c xb dx x is here is a quadratic term the reason why we're going to need that is that some of these multiplications here is going to give us a quadratic term so for example this multiplication here quadratic in a so we're going to have to know how to find the derivative of a scalar quantity in which their matrix is being multiplied by itself this is equal to of two terms um it's c transpose a transpose c h so let's uh let's do some of these derivatives so to do that what i'm going to do is multiply out one of them c matrix c here so we have x hat we don't know c how to in terms of the quantities that have seen it so the log of that likelihood so that's going to be a sum let's see i'm going to have y of n transpose r minus 1 times cx of n and i'm going to have minus xn transpose c transpose r minus 1 y of n this is a scalar quantity which means that these two terms are the same terms because this is the same as this this is the transpose of that term um so that's equal to minus one half two times um two times y of n transpose r minus one c x of n plus so forth okay find the derivative of these and i don't have any more c's right those are the that's the only place where c appears so i want to find the derivative of this with respect to the matrix c this is what i'm going to use this term here so i have this quantity where this is a transpose and this is b what i'm going to end up with is this transpose so i'm going to get minus one half the two cancels out i'm going to get minus r minus one y of n x of n transpose for the first term looks good this and this says yeah this is a this looks like a matrix of the it's shaped and then for the second term this this is a quadratic in c i'm going to use this so i'm going to get x is what i'm finding the uh the the derivative with in this case so that's just don't don't confuse that with this so i've used x and c here i've used x and c here but they mean different things so in this case this is a transpose and r is here c this is b so i'm going to get r minus one c x of n x of n transpose i'm going to get two of these check my notes see if i got that right i actually did it right so we said that equal to zero and what we find is that um uh sorry this this two goes away to because i have minus one half in the front of it so this is just uh this is just this i have um r minus one c x of n x of n transpose is equal to r minus one y of n x of n transpose so c is equal to um sorry i forgot all this all this has a sum in front of it i forgot the sum so c i'm going to put a hat on top of it that's my estimate of what c is it's going to be equal to the sum y of n x of n transpose times um this term here the sum inverse so what we're going to do we're going to replace these values here with our expected values for this so um i have x as the mean and so if i if i put the expected value for these guys what i have is that the sum one to n y of n x hat of n transpose this i can compute right and this is multiplied by um the expected value of x of n x x of n transpose minus one expected value expected value of x x transpose what is that how can i compute that the quantity in principle what's the expected value of x x transpose well you remember the equation for variance right so what's the equation for variance variance of x expected value of x minus is expected value right so this is the variance equation p variance of x the expected value of um x gotta catch those stupid mistakes otherwise we'd be going in circles okay so this we have this quantity variance of x the value is y p and this we have as well so this quantity here is the sum of p of n the uncertainty of the state in trial n plus the expected value x hat of n x hat of n transpose that's my estimate of c if i know x hat which is what we're assuming so we begin with some estimate of ab and all those things we use the common filter to estimate x hats and non-certainties now we go back and re-estimate all the parameters ab c and d using our state x hat i can compute okay yeah go ahead what's the expected value of c so c is c is so the c that will maximize the log likelihood is this right the hat value of c the expected value of c is going to be the expected value of things inside here my estimate of c is going to be the expected value of it that maximizes the log likelihood so this is the c that maximizes the log likelihood right but but i don't have x right x is a random variable all i can do is say okay well what's the expected value of c if that depends on the expected value of x and its variance yeah or really it's a trick that just says well we're going to replace these x's which are random variables with their expected value and this quantity here is like a variance okay all right so let me do one more of this it's going to be basically exactly the same except that we're going to do it for let's see which another one that's in the second one i was going to do it for was a so why is this why does this make sense so look look at this equation so why is this equation by x n transpose and then solve for c that's what that is so you should when you look at it you see okay well where does this come from it comes from multiplying both sides of the equation by x n transpose effectively what this is so there is a relationship between that and this um let me do it for a so in your book you have it for all the parameters but um there's no magic here obviously just finding these two rules and those derivatives and because the derivatives are from the scalar quantities the basic result here so this is similar to um how we're going to do a basically we're going to end up when we you know what we're going to do is that we're going to multiply out the second equation this part here slide that out we're going to get some scalar quantities that have matrix a in it are going to look like this some of them are going to be the quadratic form like this we're going to find just like I've done here but the result is x of n transpose so we're going to see that let me just multiply it out even though this is not the way that's what I have and then I use the expected one to transpose multiplied by some expected value and you notice that this estimate with some estimate of a b in all these things you compute x hats but you compute x hats you get these expected values and then now that you have your x hats you compute all the old values of x and b the iterative process and you have the similar equations for you know that you can compute the derivative of this with respect to b the derivative of this with respect to respect to r and initial p and x hat okay so in machine learning em very powerful tool and it's this iterative process by which you assume in the case of this structural learning problem that you you begin with some estimate of the e-step so you fix data hat use the Coleman filter to find x hat step you fix x hat and you find a new estimate yes some parameter yes yeah so let me think what we're going to end up with is a new estimate of x hat no I don't I don't know when you maximize this when you find the derivative with respect to x hat we're going to get an x zero in there yeah yeah yeah but um what I don't know is um what's the what's our you don't have an x zero here as our as our given because I have I don't I'm kind of confused myself I don't know let me think about it I don't know good question I need to make a homework assignment for this so that everything's clarified all right by actually doing it all right guys good luck with this with


My name is Anthony Conti. I'm a neurosurgeon at JFK Neuroscience Institute specializing in complex and reconstructive spine surgery. My treatment care philosophy is to do what's best for my patients and treat them like they're a member of my family. It's to treat the whole self and know that pain and different brain and spine pathologies take a significant not just physical but mental My main goal is to minimize their pain while maximizing their quality of life whether that be through surgery or through conservative measures. I won't hesitate to recommend to a patient that they should undergo surgery if I feel that it's the right thing or if I feel that they will achieve significant improvement in their quality of life and in their pain control. I also won't hesitate to tell patients that I don't think surgery is the right option. To see a patient go from having significant pain or spinal deformity or debility from spinal deformity issues to a point where surgery or conservative measures can get them back on their feet to get them back to doing the activities that they love and to see how much their quality of life is improved during the span of our relationship together is one of the most rewarding things that I can ask for as a surgeon.


Can you please tell us your name and where you are from my name is Sylvia and I live here in Pasco And can you tell us who do you have here with you today? This is my son Derek? Hello Derek. Can you please tell us? The problem that you had and your testimony, please Before Derek came to live with us over a year ago He has been hospitalized many many times and some of those times were in the intensive care unit he suffered from asthma severe asthma and Was not able to do most of the things that children do at their age And can you tell us how long was Derek suffering from asthma since birth? Okay, so because he was suffering a lot with asthma. Where did you guys go to find a solution? Well Derek had Pediatrician neomologist that was in charge of his medical care and Then anytime that he had an emergency then he was taken to the emergency room Did he ever have to use any inhalers or medications? Yes, he was on medication daily medication two different inhalers every day Okay, so can you please explain to us what happened during the prayer line a year ago when Derek was prayed for? Well before Derek came to us. We started praying for him February the last year we were praying for people with asthma So we were praying for him When he came to us, I stopped the medication when he moved to live with me I stopped the medication We went to the doctor and she asked me if he was taking his medication and I said no I took it from him and she gave me a look and she said why he needs it and say I don't believe he needs it So she said fine. We're gonna do it your way. But if he start feeling bad, we're gonna put him back on the daily medication Okay, so I know this is funny But this is actually a very serious situation where you know, she has a child that is suffering from asthma and the doctors thought you were Going a little bit out of your mind with taking the medication away, which is usually something that is not Often done. So can you please tell us what happened at the prayer line after he was prayed for? Yeah two days ago July 4th is Being one year that we have been successfully without any daily medication for asthma So can you please tell us what are a couple of things that he can do now that he was not able to do before clearly? He is very cheery so Well now he can spend more time outside he can play with other children he can be himself and He have learned a lot too because his developmental was a little delayed because he was spending a lot of time in the hospital And Derek, can you come over here really fast? Can you take a really big deep breath for us? Yeah, good job So can you please tell us some advice for anyone who has maybe a child that is Suffering with an illness or is going through some medical problems. What would you advise them? Well, first of all, never stop praying for your children and that's to the parents never stop praying Believe and hold on to the promise of God that by his tribes and we are healed and Even when you believe like I did that he was healed never stop praying after that either just continue praying Amen. Thank you so much Thank you, Derek you may take your seat


Hello and welcome to this session in which we will discuss compliance attestation. Compliance attestation is part of the statements on standards for attestation engagement which what we've been working with in this chapter and just to review real quick we have three level of service we could have an examination engagement, review engagement, agreed upon procedures and we can have those applied to various subject matters such as prospective financial information which we already completed reporting on pro forma financial information which we already completed today we're going to be discussing in compliance attestation so compliance attestation is part of this process it's a subject matter now what can we do with compliance attestation so we can do an examination review or agreed upon procedure those are the level of services for compliance attestation we can do examination and notice here there's a trend there's always you can always do an examination can you do a review matter of fact you cannot do a review on compliance attestation matter of fact once again it's clearly stated in the literature that you cannot do a review on compliance attestation and you could also do agreed upon procedures so for compliance attestation examination and agreed upon procedures now you might be saying why am I keep on repeating myself believe it or not many questions about attestation engagements on the CPA exam are derived from this table or understanding this table also will help you understand how to answer the questions now I just want to clarify that we are not dealing with report on in compliance in connection with the financial statement audit this is for another lesson and we are not dealing about a report on compliance and internal control over compliance as part of a single audit engagement that's also another lesson this is the single audit federal assistant program so we are dealing with compliance attestation that deals with the statements on standards for attestation engagement the first term we want to learn about is compliance with a specified requirement what does that mean once once you see that statement it means the entities is in compliance with the specified laws regulation rules contract grant or whatever that topic is so they are in compliance compliance attestation engagement could take two forms you can have a compliance with a specified requirement whatever that specified requirement is could be specified to laws regulation rules contract or agreed upon procedures related to internal control over compliance so just make sure once you see the internal control just its internal control over the compliance just make sure you're aware of this so the practitioner and could be engaged to report could report on three things basically directly on the subject matter let's assume you have a contract that's the subject matter are they in compliance with the subject matter or assertions about the subject matter management is making certain assertion or on the internal control over compliance simply put one and two is related to one and two is two basically but you can report on the subject matter as well as the assertions about the subject matter now bear in mind the practitioners compliance report don't have any legal power now why do I mention this because sometime on the CPA exam they'll try to trick you into making you believe the answer is somehow illegal this compliance report has legal authority it does not before we proceed any further I have a public announcement about my company forehead lectures dot com forehead accounting lectures is a supplemental educational tool that's going to help you with your CPA exam preparation as well as your accounting courses my CPA material is aligned with your CPA review course such as becker roger wiley gleam miles my accounting courses are aligned with your accounting courses broken down by chapter and topics my resources consist of lectures multiple choice questions true false questions as well as exercises go ahead start your free trial today no obligation no credit card required now there are preconditions for both examinations and agreed upon procedures before you start management should accept responsibility for compliance you're not going to do an examination if the party that's asking you to do an examination is not taking responsibility for this also management accept responsibility for the entity's internal control over compliance so simply put if you're gonna examine or do any agreed upon procedures they have to take responsibility now man I said management it's the responsible party but we're gonna say management you know for ease evaluate also management evaluate the entity's compliance with specified requirements also the management did some compliance evaluate the compliance and no written assertions about those no compliance engagement simply put you will not go into performing an examination if the party that's asking you to do what they don't give you any written assertions for agreed upon procedures let's be a little bit more specific agreed upon procedures we can have agreed them agreed upon procedures on compliance with specific requirements wherever those requirements are or we can have it on the entity's internal control over compliance with specified requirement or we could have it on both basically the agreed upon procedures to do both the compliance with the specified requirement and the internal control over the compliance which is why not let's have really everything covered so remember in an aup agreed upon procedures you have findings that's what you report your report findings what for well what do you think it's for well to help the users in evaluating the the entity's compliance with specified requirements so basically to meet number one or to help the entity's internal control determine whether they are they have an internal control over compliance to deal with two which is basically we're saying the same thing just kind of reinforcing this concept remember agreed upon procedures is between specific parties it could be two it could be three parties but it's specific parties so what you do how do you carry the procedures you follow the agreement whatever the agreement is what you're supposed to do and you limit your restrict the report to the specified parties because it is by nature every time you hear agreed upon procedures remember it's limited it's restricted by its nature it's agreed upon between two parties the practitioner and someone else you could have a third party but that you would restrict it also to that third party assume in the third party agrees to what we are doing an examination again it has a higher level of assurance examination can be done on the entity's compliance with laws regulation contract or grant or assertions about the compliance with specific requirement so it's either the subject matter or the assertions again you have to have preconditions we mentioned the preconditions the responsibility of management but for examination we have a fourth condition and that's we can obtain sufficient appropriate evidence to support management assertion or assertions again examination we have to be aware of this and in examination we give an opinion to give an opinion you need to have sufficient appropriate evidence so if management cannot provide the sufficient appropriate evidence to support the opinion then we cannot carry an examination so that's a little bit different than it agreed upon procedures and in examination procedures first we have to understand the compliance requirement what are we do what are we complying with regulation contract rules regulation that's the first thing review the prior engagement if it's available in any regulatory reports if that's what you are working with ask or inquire with appropriate personnel talk to the people who are responsible of the of the of this process of the subject matter perform risk assessment and design step to address those risks obtain a written representation letter or written representation and document all the steps above it's very important to understand what goes on a representation letter basically a recap of everything that we did so basically representation letter is management telling us in their own words management is responsible for the internal control over compliance management performed evaluation on on the entities of the entity's compliance with internal control the management disclosed all known non-compliance made all relevant documents available provided information about communication with any relevant parties such as regulatory agencies internal auditors and other practitioners this way management is coming clean just made they tell us they did they gave us everything that will make our life easy to carry that compliance because we want to protect ourselves because of the management don't take responsibility or will hide anything then we are at risk of missing something so we want to make sure they come out and they tell us those things now the best way to kind of summarize all of this is to look at reports maybe one for an examination one for an agreed upon procedures to wrap it up because a report is the end product and in the end product basically would recap everything but it will be formal one page recapping everything so this way you'll understand in an actual example what the end product would look like whether it's an examination or an agreed upon procedures and what should you do now go to far hat lectures and work mcqs to understand this concept better those could be easy cpa questions don't shortchange yourself take it seriously good luck study hard and stay safe


Everybody forced here upping 2022 Bowman inception baseball hobby 16 box full case number five random divisions results link is in chat Results are on screen, too. Let's get started everybody best of luck 16 boxes here we go Gold ALS Tyler Whitaker 49 out of 50 blue auto and Alcantara Michael McGree v 58 of 99 Hope you're right Travis Hope you're right and an AL West auto Anthony Gutierrez 38 of 200 Blue foil Oscar Colos 14 of 99 AL central nice colos and Alcantara auto Ronnie air can tarot 95 out of 200.  Now West blue foil 16 of 99 Ryan Bliss Dual Jersey auto for the AL West Pedro Leone 68 of 200 AL West and AL Central gold auto Brian Acuna 25 of 50 It's a nice hit so far nice Acuna gold Say guys, it's just prison basketball and tea basketball tonight as well Got some PYT Phoenix football spots left Phoenix football tiered full case and just a few impeccable football teams left as well That's what we got for you tonight blue foil Armando Cruz 39 of 99 and at least Mundo Cruz NLE start over here. You're so our Garcia 154 of 200 and AL East auto Luis Mesa fuchsia 22 of 75 Blue foil AL East Trey Sweeney now 40 of 99 Dual Jersey auto AL East again Marcello Meyer 159 of 200 there we go Congrats AL East again That's going to mag nice Marcello And NLE sought out Andrew painter 316 of 399 Internationals once a month other than that it'd be should be less than a week We get shipped out depends on how we're staffed What's what we're you know breaking depends on a lot of things, but yeah, usually less than a week if Faller falls right Jackson Job gold foil 50 of 50 for the AL Central Yes max some people use it. I'm not entirely sure Exactly how it would go with us, but yeah, maybe Brian can help you out Silver signings Ricardo Cabrera 95 100 NL central nice Cabrera and NL central again at Hedbert Perez out of 194 of 200 Got an orange Royce Markintana 9 of 25 for the NLE Nice one NLE tonight in Tana. Got nor have era auto AL Central 286 of 399 No, Justin. There's spots in national treasures basketball prison basketball Phoenix football and impeccable football and Promodial prospects auto for the NL West Benny Montgomery to 75 nice Benny smack if you want more frequent shipping We offer that you just have to email us you just have to request it for your international You want more frequent shipping or like overnight or whatever it may be Like some people want orders overnighted sometimes Just email us do our best to get things done for people Fuchsia 38 of 75 NL central Christian Hernandez, obviously more than once a month for international You'll have to pay like anything more expended than normal. You have to you have to pay since it's all free for us Anyway, it's Christian Hernandez there. God gold auto Victor Labrada 12 out of 50 AL West AL West gold and blue auto McEl Triana 37 and 99 NL central half way through pretty solid so far Couple mad cards other nice hits as well Yeah, like if you have something you want to get and get so you can get in your hands and get it sold or something like that Just let us know Gold headbert Perez 25 out of 50 NL central Obviously shipping changes depending on where you are, you know, whatever it may be if you want to insure it all that stuff So yeah, we do a lot of that because some people buy like Like sealed cases and stuff from us. They want to like overnight it or whatever it may be so Edward Perez we got an NLE start a Spencer Schwellenbach 115 of 399 Obviously it's not all the time, but yeah Schwellenbach NL East and AL West Denzer Guzman auto 30 of 75 you should foil you should Dustin Harris 5 out of 75 AL West No, just and there won't be Samuel's of Vala orange out of the 25 NL West Laces of Vala and Primordial prospects auto Jonathan media 14 out of 99 for the NL central I wouldn't put a discount on a on a random team stop break when it's At least halfway full because that's not fair to everyone else. That's already bought into the break Yeah, see that one has that one's over halfway We got a ways that we got a little bit of time to get there. So Looks like we're down to eight on prism two on Phoenix PYT two on impeccable PYT still 14 on national treasures everybody fuchsia Kyle Manzardo to 75 AL East Gold foil auto Ryan Holgate NL central 46 of 50 Trying to go to the fair Brian or at the Ferris wheel and blue foil out of Christian hand as NL central to 99 Yep triple threads after this got blue foil and in some polino for the AL East number 24 out of 99. Oh, yeah I don't yeah, Brian you buy and I'll be unfair. I just not give you a team blue foil auto Sam Bachman 49 at 99 AL West and NL central gold primordial prospects auto Hendry Mendez 33 of 50 Yeah, again, sorry, we're running behind guys just trying to get a bunch of breaks filled tonight Slow nights happen. It's the first time that we've been Waiting to fill breaks in a long time though. So It's pretty rare. We've done really well past few weeks Thank you everybody Even if you're not buying inside been buying the recently. Thank you blue foil Alan Serra 14 of 99 NL central We've got Huge release day Wednesday. Will Bednar NL West of 399 on the auto Yonatan class a 1 of 99 auto for the AL West primordial prospects it's kind of a Little a little left to be desired on the autograph there Got Bowman's best baseball Don Russ basketball and immaculate football Biggest release day we've had in months. I would say probably since the holidays Gold Marco Luciano NL West 49 out of 50. Oh, yeah, Brian, of course, man Ryan spikes AL East auto number 316 of 399 spikes and AL West auto Dustin Harris to 75 Let's close out with a with a with a huge one here in the last couple boxes Dustin Harris AL West we will recap this one guys. This is longer break. So we'll recap this one for sure even though we're behind It's a replay, but I don't care. I don't care. I don't know what happened. It's spring training raise tomorrow I don't know what happened Why would I know what happened in that game? Blue foil Daniel Vasquez number 98 of 99 for the AL central AL East on an outtouch Bradley 206 of 399 And NL central gold auto Jay Allen 39 of 50 nice Jay Allen NL central so good in this so many names Blue foil Averson, Artega 43 of 99 NL West and Alcantara again here. Yo, Hengik Pinango 17 to 399 in the auto And we are gonna finish with a nice hit a very nice hit at that NL central Pinango NL West Jordan Lawler primordial prospects auto orange to 25 Sick Lawler Yeah, six at 25 Jordan Lawler Congrats Congrats NL West Give me one sec. We'll do a quick recap everybody. All right, all of our autos All right, that was that was a big stretch illegal big stretch. All right We had yo Hengik Pinango Dustin Harris Jay Allen Taj Bradley Ryan spikes Luis Mesa. Yo, so our Garcia Yonatan class a will bednar Sam Bachman Henry Mendez gold Christian and Hernandez Ryan Holgate gold Jonathan Mejia Samuel Zavala orange Denzer Guzman Sensor Shwell and Bach Victor Labrada on the gold Mikkel Triana Benny Montgomery Nor hey Vera Royce Marquintana. That is a non-auto got Hedbert Perez Ricardo Cabrera Jackson Job non-auto Andrew Painter Brian Acunha a Pedro Leone Ryan Bliss non-auto runnier can tarot Michael McGreevy Anthony Gutierrez Orange Jordan Lawler to 25 for the NL West For the AL East Marcello Meyer to 200 the dual Jersey auto and gold to 25 AL East blaze Jordan auto Great hits. Thanks again, everybody triple threads up next


One special type of permutation is called a transposition, and these are also very important in our study of permutation groups. So a permutation in general is going to rearrange things, but a transposition is going to swap just two elements. I'm going to replace one thing with something, and I'm going to replace the something with the first thing. So in cycle notation, this transposition is also a two-cycle. X is going to be replaced with Y. Y is going to be replaced with X. So here's a very, very, very, very useful result. Every permutation can be written as a product of transpositions. Now it's very important to read the fine print on this, and here in this particular case there isn't any. And what's noteworthy here is what this theorem is not claiming. The theorem is not claiming that this product is unique. I may have different products of transpositions that give me a given permutation. The transpositions might not be disjoint. The transpositions may actually have elements in common. And so, for example, let's see if we can do that. So here is a permutation, and I want to find two different products of transpositions that are both equal to this same permutation. Now, if we want to do this, it may actually be easiest to write our permutation sigma in Coshino. So let's see what our product of cycles does to our elements A, B, C, D, and E. So again, the first cycle is applied, then the second cycle is applied. So A, first cycle says do nothing to it, and then second cycle A replaces with B. So B do nothing followed by replace it with C. C replace it with D, then do nothing. D replace it with C, but then C gets replaced with A. So D goes to A. Third cycle, third last term, E do nothing followed by do nothing. So this product of cycles gives us this particular permutation. So now let's apply transpositions to get the permutation, and we'll record those transpositions as we go. So remember, a transposition involved is switching to and only to elements, and our goal is to end up with B, C, D, A, E. So what can I do? Well, maybe I'll get a B into the first location. So I'll move B into the first location, which means I have to move A back to where B was. So my first transposition is going to be A, B. I'm going to swap A and B, that's recorded as this cycle A, B, and importantly, nothing else changes. So that is going to be C, D, E. So my first positions all set up. So I want to get a C into this second position, so maybe I'll swap these two, C and A. So that's going to give me the transposition C, A, A, C. And again, only these two change, all the rest, B, D, and E, they all stay the same. And let's say I have B, I have C, now I want to swap these two, A and D. So I'll swap these two, that's my transposition A, D, and all the other terms stay the same. And then now I have my final permutation as I want it to be. And it's the product of the transpositions A, B, followed by A, C, followed by A, D. Now I want to find two different products of transpositions that give me this particular permutation. So let's wipe out that sequence of transpositions and try to find a different one. So let's see. So the first time I worked by getting the B, C, D, A, and E. So maybe this time I'll work from the other end, I'll try to get an A in this last position here. So that means I need to move A over to here and D replaces A. So there's my first transposition A, D, and again all the others stay in the same place. Now I want to get a D in this third position, so I'll swap D and C. That puts those there. And then again all the other things stay in the same place. I want to get a C in this position, so I'll swap C and B. And there's my third transposition, all the others stay in place. And so here I have a transposition A, D, followed by C, D, followed by B, C. And again two very different products of transpositions that give you exactly the same permutation. So again part of the goal of abstract algebra is to build up certain habits of thinking mathematically. And so here's a very useful mathematical habit which is constantly asking yourself whether there is an underlying pattern or is it merely a coincidence. So in this particular case we wrote this permutation sigma as the product of transpositions, either A, D, A, C, A, B, again A, B first, then A, C, then A, D. The other way we could have written this permutation is A, D, C, D, B, C. And they're different, but there is something the same. They both have this transposition A, D. And so the question is, is that an important pattern? Maybe there's something special about these or is it a coincidence? And so could be a avoided it. If it's an actual pattern, there's no way we'd be able to avoid including A, D. But if it's a coincidence then we could have avoided it. So let's see. So again my permutation takes A, B, C, D, E and transforms it into B, C, D, A, E. And so the question is, I want to avoid swapping A and D. So is there any way that I could have done that? So let's see. Well here's another way to look at it. Is it a coincidence that neither of these included E? So let's see if I can avoid that. Let's see if I can start by including a transposition that involves E. So let's see this as a product of transpositions. Let's start off by including E and maybe I'll swap E and, how about A? So I'll swap E and A. So there's my first transposition. E swaps with A and again B, C and D are all the same. And let's see. Well okay so I want to get E and B. I'll swap those two so I get B in the first location. And again all the others stay the same. Let's see B is good. I'll swap E and C so I'll get C in my second location. Again all the others stay the same. I'll swap E and D so I get D in the right place. All the others stay the same. And then I'll finally swap E and A. So A is in the right location. E is in the right location and all the others stay the same. And so this permutation can be written as this product of transpositions. And if we look carefully we see two things happen. First of all we don't have the transposition A, D. It's nowhere in this list. In fact none of the transpositions we used. A, D, A, C, A, B, B, C, D, A, D. None of these transpositions are in here. So the transpositions that we get not only is the product not unique, but there seems to be very little that the set of transpositions have in common. And so this asking whether it's a pattern or a coincidence it certainly seems to be a coincidence that both of these had A, D in them because we could easily have avoided it. In fact it seems that there's no actual pattern. This has three transpositions. This has three transpositions. This has five transpi... Hold on, wait a minute. That's three. That's three. That's five. Wait a minute. There is something of a pattern starting to emerge. So again in the spirit of from one problem make many we might find other products of transpositions that give us that permutation. And if we do that one of the things we'll find is that all of those decompositions do share one feature. If a composition of transpositions make up that permutation sigma the number of transpositions that we require while the number is going to vary the nature of those is going to vary every set of decompositions is going to be odd. We're going to have an odd number of transpositions. And maybe again we'll make many problems out of one if I pick some other permutations and find transpositions that give us those permutations. One of the things we're going to find is that if I can write a permutation as a product of an odd number of transpositions then any other decompositions that produce that permutation will also require an odd number of transpositions. And likewise any permutation that can be written as a product of an even number of transpositions will always be expressible as a product of an even number of transpositions even though the actual number is going to vary. And after a while we'll accumulate enough evidence that these observations seem like they do form an underlying pattern and so it will be worth trying to prove our claim. And we'll take a look at that next.


Hey guys, it's Tilly and I am back with a quick video on my favourite booktubers. Pretty much watch booktube religiously. For those of you who do not know what booktube is, it is basically like YouTube but for books. So it's all like done on YouTube but it's like the slang term we call people who do mostly book videos. I am pretty much obsessed with watching book haul videos, book reading wrap ups, I love bookshelf tours, I love everything that's bookish and it is just like one of my all-time favourite things to do when I'm like getting ready in the morning or like have nothing to do all day. I just watch like a booktube all the time. So of course I have managed to accumulate quite a few favourite booktubers and I'm going to give them all like a shout out now because I just love them so much. So it's going to be in no particular order because I love some of these people equally that I can't even rate them. I just love them and there's so much love to give. First up we have one of my really good friends, she's amazing, she's a queen, she's beautiful and kind and just an absolute sweetheart and that is Tanika from Flipping Through the Pages. She has like really amazing videos and you have so much fun watching them because they're so easy to watch and like she's so kind and open and all of a sudden you've like lost like three hours of your day because you've been watching all of her videos. It's happened to me like three times now and I blame you Tanika for why I've been late to work once. But she's an absolute darling and I know that in the future me and her are going to be doing some collabs because we both live in the same city and that's like the most exciting thing because not only have I found someone who loves the same things as me but we also get along really well and like I said she's like a queen. Next up we have my girl, my girl who I love so so much. I met her at the start of the year and we hit it off like this and I have never been happier to have someone as my friend and that my friends is Chami from really like Wildfire. Chami is like the funniest and happiest person that I know.  She doesn't just do book videos as well, she does all different ones and to be honest they're all amazing. We have lived from stories for coffee and I love watching her videos, her voice, her face, her background, her books, everything about it is just so perfect and I just could watch them forever and ever and ever. Once again she has videos that you just find yourself watching and losing like a daylight over because they're all so good and she has such a good range of books as well like she doesn't just stick to doing like book holds and book reviews she brings up all new ones like journal flip through, she has like book vlogs and it's just so good. Like if you guys aren't sure what book video you guys are looking for her channel will definitely have it. Mary from books and cookies and if you guys want to sing a real-life angel on your screens you need to go to her channel and watch her now because she is such a beautiful person and so kind and I just love everything about Mary. Not only is her bookkeeping channel really really good but she's also like the best person ever. Angus from AW Studio's books. He is another really amazing editor in his videos. Like I have no idea what he does. It is most likely witchcraft but he makes them look so good and he is also really phenomenal at doing these videos. They're fun and creative and they just hold your attention from beginning to end. Sam Barnes from Ozfan Boy. Ow I hit my ear. I absolutely adore watching Sam's videos and talking to Sam. He is such a funny and sassy and great person in general and you can see in his videos when you watch them as well. Felicity from Foster Fangirl and you guys need to go check out her channel. She once again does other things besides books like right now there's just like the bachelorette recaps all over here and you know if you are like me kind of obsessed with the bachelorette like I've only watched like one episode but I live for the recaps of the TV series. Felicity also does a lot of book reviews and it's really good because she's informative and fun about them and you kind of just know if you're going to read the book or not and most likely buy the book. Four more to go so we haven't got long. Next up we have Books K which is Cassia. I've recently subscribed to her and I pretty much like binge watched all of her videos. They are so good. I absolutely love her bookshelves in the background. They're so amazing and her videos are just yeah so easy to watch like you lose yourself in them. Jen from Miss Henry Reyes and I really wish that I could like reach through my screen sometimes and just go hang out with Jen because I love everything about her. Her videos are amazing.  I love her voice and I can just like listen to her voice while I sleep and that to not be in a creepy way at all. She also has so many wonderful videos um you can find yourself just going through them all and finding so many favorites. Kat from the little book owl and I absolutely adore her videos like everybody else's videos that I've mentioned but within hers every time I watch them I find myself coming away with like a really good opinion on the books or like the topics that she's talking about because she's so informative in her videos and I really really enjoy that and at the same time she also has some that are so great that I find myself like smiling when I think about them later as well. And lastly we have Allie from Hardback Hoarder and I love everything about her channel from the way it's set up to all the videos that she posts. She posts so regularly as well and her videos are so much fun. She's so creative and I just love watching them all. At the moment she's doing writing prompt videos leading up to NaNoRemo which is just suddenly hit me how close that is. I will be uploading a NaNoRemo video probably like before this or after this. It's like cute up but I don't know when I'm actually posting it because I'm a terrible person. Anyway getting sidetracked make sure that you do check out her channel she's so much fun and I love watching it and just yes I have repeated myself a few times there. I will leave links to all of these wonderful booktubers below and I encourage you all to go and check them out because if you guys like watching my videos I can assure you you will love watching all of theirs especially because so many of them have inspired me in my booktubing and pretty much me in general. They're just such inspirations and great people so go check them out and enjoy booktube and book videos and buy loads of books. Thank you guys for watching and hopefully I shall see you guys again soon and until then I hope you guys have a wonderful book each day and great things happen to you. For those of you who don't know what NaNoRemo is, it is basically a national novel writing month so you have to write 50,000 words in 30 days.


We build everything, we build all these telescopes, all the infrastructures so we can get the best possible data. And this data will be used by the scientists to do great science. Around ten different teams which are shaping the whole Akada software. A very, very strong integration between different teams with the same objective, which is to make the observatory work. Akada is the software system that will control the area of telescopes and acquire the data from their cameras. Last night for the first time with the CTAO control software we could see the Crap Nebula. For us it's a huge achievement, it's kind of a combination point for the team.