In this video, we're gonna discuss the solution to question 14 from the practice final exam for math 12-20, in which case we're asked to consider the series where we take the sum where k equals two to infinity of one over k times the natural log of k squared. And that's to say the natural log of k, that whole quantity of squared right there. There's two parts of this question. This question is gonna ask us to do some remainder estimates, some error estimates associated to approximating integrals, sorry, approximating series with respect to partial sums. And it's broken up in two parts. The first part you can see on the screen right now, which actually has a statement right here. The series can be found convergent by the integral test. So this is not something that you have to prove. This is given to us that the integral test will provide that this thing is convergent. Now you are asked to verify by computing the following formula, which be aware that again, you're not gonna cite the integral test. This is already going on here, but if one was using the integral test, you'd have to compute essentially this integral right here. Now there is one important difference I wanna mention that the series starts off at k equals two, but the integral is gonna start off with n. So we're having a placeholder right here, which we could easily insert two into that to determine the convergence by the integral test. Now in order to calculate this improper integral, I would recommend using the u substitution, take u to be the natural log of x, and therefore du equals one over x dx. And you'll notice that the dx of course is there and then the one over x is there as well. And so then this would translate as we switch the variable here, you're gonna get a du over u squared. I also wanna change the bounds, right? As you plug in into this formula, you're gonna get the natural log of n as your lower bound. And as we do infinity right here, treating this as a limit, we take the natural log of infinity that is take the limit as x approaches infinity of the natural log of x, and that itself will become infinity. So we still have this improper integral. Now integrating this thing right here, well by the power rule, since we have a one over u squared, we can treat that as u to the negative two that would raise the power by one to be u to the negative one that is one over u. And then divide by that exponent, which is a negative one, you get a negative one over u for the anti-derivative and evaluate this from negative natural log of n to infinity. Now because of the negative sign, I actually wanna switch it to be a positive, so I'm gonna switch the order of the limits there. And so we get one over u as you evaluate from infinity to the natural log of n. And then as you evaluate these expressions right here, you're gonna get one over the natural log of n minus one over infinity. Of course, one over infinity is to be interpreted as a limit. We're taking the limit as u approaches infinity of one over u, and that'll go off towards zero. And so this integral is equal to one over the natural log of n, and this is what part a is asking us to do. Now going back to this idea with the integral test, if you plugged in n equals two into this formula, you would see that this is a finite number. So therefore the integral is convergent, which implies the series is convergent via this integral test. So then look at part b here. What is the smallest choice for n that would guarantee that the partial sum where k raised us from two to n of one over k times the natural log of k squared? What would be the smallest choice of n to guarantee that this partial sum would be an accurate approximation of the series to within one over the natural log of 100, right? And so this is a statement about error bounds right here. So this is some prescribed error, and we need to find that our remainder, rn of x needs to be less than this. Now the important thing to remember about the integral test, and this is what we mentioned earlier, is that the remainder of the integral test will be bounded above by the integral from n to infinity of the function one over x times the natural log of x squared dx. And as we showed in part a, this is equal to one over the natural log of n, right? And so this is supposed to be less than or equal to one over the natural log of 100. And so this inequality right here we need to solve. Well, taking reciprocals, we see that the natural log of n must be greater than or equal to the natural log of 100. The inequality switches direction when you take reciprocals, and then exponentially able sides, which is an increasing function that doesn't change the direction of the inequality, we're gonna get that n needs to be greater than or equal to 100. So 100 is the smallest number that we can guarantee that this thing will be accurate to this prescribed amount of error. And so in this exercise what we did here is we, on part a, we computed the error bound associated to the series, and then on part b, we used it to determine how accurate, how many ends do we need in order to guarantee accurate to a certain level. And so you'll see something like this very similar on the final exam. Of course, it might not be an error bound associated to the integral test. It could be some of the other error bounds that we've seen this semester. So be prepared to answer any of those.


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All of this is well and good provided we know that we are per bar is equal to be lower bar. And that condition the if there is irritating because it tells you all of this nice story works provided we are per bar is equal to be lower bar and we already have seen an example where it is where the two are not equal. So question then becomes what can how can you resolve this? This is where we basically need a next new idea, you need a new idea you need a new way to think about the strategic situation. All this reasoning is so far is good, but we have we have sort of limited ourselves to a particular way of viewing the options at hand, which is that a player has to play a particular row or a particular column. If you think of essentially the strategies that players are exposed to in a game the strategies that they have in a game in many cases these strategies can be thought of as let us say you know suppose a general wants to decide you know how much which of his he has to decide whether he wants to take this route or that route that is thought of one kind of way of visualizing the strategy. Instead of saying that I want to should I go to this route or should I go to that route instead of having that sort of dilemma a general might also ask if I have 1000 troops how many should I send to this route and how many should I send to that route. So many times the kind of strategies that we have with us can be interpreted as something on as a set of options on such that we do not have to pick only one of those options but rather we can decide that how much of our resources are to be allocated to each option. Say for example, so in the case of the general he has to decide I have 1000 troops maybe I send 300 here and 700 here or if you are a fund manager you have 1 lakh rupees maybe I put 25000 in this project and 25000 in that project. So this way once you start thinking about it this way then the options that you have that a player has are not just merely to commit to a particular row or a column but rather to decide the extent of commitment to each row or column. Now this extent of commitment can be thought of in many different ways one is that as I said is a resource allocation so you can think how much resources am I devoting to each option. The other way is to say well what I am going to do is I am going to pick a row or a column at random and I am going to pick it at random but I am going to choose very wisely the probability with which I am going to be choosing each of my choices. This now expands the strategy space. So now you are not just picking a particular row or a particular column as a player what you are actually doing is picking a every row essentially with some probability and what you have to decide is the probabilities that you are going to assign to each row or each column. So this is what is called a mixed strategy. A mixed strategy is basically a randomized choice of a pure strategy. So this is one way of interpreting it but this is mathematically this is good enough so we will just use this description is a randomized choice of a pure strategy. What is a pure strategy whatever we have these strategies we were talking of so far they are what are called we will call them pure strategies. Pure strategies are definite choices of rows or column mixed strategies are randomized choices on top of pure strategies. So these pure strategies are what you know rows and columns and a randomized choice of the same is what is called a mixed strategy. So formally a mixed strategy is a probability distribution on the space of pure strategies or equivalently the space of pure strategies currently a random variable takes values in the set of so mixed strategies just like pure strategies are for each player the mixed strategy is also for each player. Each player now has to do make a randomized choice over his set of pure strategies. So the probability with which you play with which you the player plays is the choice that he has to nominate. So it is then many people use this word randomized in a kind of loose way many people use the word randomized in a kind of loose way where they when they say pick something at random they actually means of pick it uniformly at random ok everything with equal probability but that is not what we mean here by random we mean with the probability distribution and the probability distribution has to be chosen with in a strategic way is this clear. So then in this case now can you tell me mathematically what is the what would be the probability distribution for the row player. So the row player the pure strategies for the row player for the row player the pure strategies are the rows are the rows ok and suppose there are m rows m rows suppose for then what are his what what is a mixed strategy for the row player a mixed strategy for the row player is now a probability distribution on this set of m rows right so how do I describe that I need to tell you a probability with which I am going to choose every row ok. So let us let us write it like this let y i is the probability of choosing row i probability of choosing row i ok this is the probability of choosing row i now what must these y i satisfy how many y i's are there there are m of them ok how and what should these y i's satisfy yeah so this because this is a probability distribution it has to satisfy that so firstly so let me just write it like this let y be this y 1 to y m ok a composite vector just I put them together y 1 to y m there are m of them and these are all greater than equal to 0 right and they also satisfy that the sum of these y i's is equal to 1 so this here this let us call this capital Y this capital Y is the set of mixed strategies for the row player so every mixed strategy for the row player can be written in is basically x can be expressed in this form it basically is a vector of length m now the components are greater than equal to 0 and the sum to 1 ok and you interpret the ith component as the probability with which player that the row player is going to play row i ok alright what is similarly now for the column player let us denote it by z suppose there are n columns then the what is a mixed strategy for the column player the mixed strategy for the column player is a vector now z 1 to z n these z's are all greater than equal to 0 these z's are all greater than equal to 0 and they have the property that if you sum them sum these z's they sum to 1 let us let us call this as a set capital Z and this is the set of mixed strategies for the column player now if they play these strategies a strategy y if the row player plays a strategy y from capital Y and z and column player plays a strategy z from capital Z then is they are going to now get a payoff which is going to be which is going to be a random variable because it is going to randomly choose an actual column and an actual an actual row he just decides the probability with which they are being chosen using capital Y using these y and z ok so players decide the probabilities with which these are to be chosen but they have to actually act a column or a row ok so which means that now the row that is chosen so row i is going to be chosen randomly row j is going to be chosen randomly so the players would get a payoff a i j ok when row i is chosen and row j is chosen now what is the probability with which i is chosen and j is chosen y i z j y ok but why are they independent non cooperative the game is non cooperative players cannot communicate with each other they have to randomize independently right so because they randomize independently see at the end of the day if i want to define a random payoff i have to define for you the joint distribution of the row and column i have only defined for you the marginal distributions which is the probability of choosing a row and the probability of choosing a column separately right now from the marginals if i want to be able to regenerate the joint in general i would need some more more information but then that would also require the players to coordinate between themselves if they have to correlate them their choices right so since the players cannot communicate with each other this automatically means that player the choices are being made independently ok so the probability that you see row i and column j being chosen is the probability that you see row i being chosen times the probability that you see row j being chosen ok so the payoff now that the players are going to get is this random payoff they get this payoff with this probability ok and then so whenever there is a stochastic payoff involved so there is you can this can be shown very very formally but essentially remember that what you need what the player must do then is to look at the expected value so the expected value of this is what players have to have to know this is actually the payoff that there is so yeah so there is a there is a theory of utility from which you can show that under the set of axioms of rationality what a player must do is maximize the expected payoff or expected utility and in short so whenever there is a stochastic outcome what you need to look at is the expected value of it you could have looked at other things you could have looked at its variance you could have looked at its tail probability you could have looked at its max etc etc why should you look at its mean well there is a there is a there is a reason for that yeah yes yes yes yeah yeah so naturally because every you know I have to compute the expected value yeah okay so the in other words the the let us call this something let us call this j of y comma z that is equal to equal to this and in fact I can write this out in more compact form and this is just simply y transpose a z so I can think of y and z these as column vectors okay so I come these two capital y and capital z these two I will think of these as column vectors column vector if these are column vectors then this sum is essentially just can be written in this sort of form it is y transpose a z is clear so now what you have is a zero sum game but where the strategies are y and z earlier the strategies were i and j now the strategies are y and z where the row player is looking to pick a distribution on the rows to minimize to get the least expected value here which is the least value of j the column player is looking to pick a distribution on the columns to get the maximum value of j okay it is still a zero sum game but with these now as their strategies the distributions as their strategies so what the players have to do is strategically decide with what probabilities are they going to be playing each of their each of their particular rows or row or column so we can once again define something analogous to what we did earlier since this is just again a zero sum game but in a different strategy space I can once again talk of the same logic that I did so far each player is looking to make maximum damage to the other each player can think of the worst case damage that the other can do and try to minimize that worst case damage yeah correct yeah so the strategies now are the y's and z's yes which conditional probability yes so the players pick a distribution and that is and play with that that is the that is the assumption so it is the player the game is just played once just what they need to decide is the distribution okay so the randomized choice is a very is a very convenient thing because it can be applied in any situation that interpretation of a mixed strategy but the problem with that is also that you know and it is also you know gives you a proper interpretation as a probability measure and then you can compute expectations and so on the problem with that is you know there is the way to if you want to give it an operational interpretation like exactly how is the game played out many many people then try to think of the game being played multiple times okay so if the game so but remember that is not what is being done here we are not assuming that the game is played multiple times and this is not the frequency with which so why is not the frequency with which player i chooses rho i if the game was being played multiple times the players will also strategize in a different way knowing that you know this is the game is going to be played in such and such way and that leads to a different analysis altogether it is called a repeated game that is not what is being done here it is not the frequency with which they are playing these strategies it is a random choice so you should be comfortable thinking of probability without thinking of frequency of use okay so it is a random choice of arising out of a sophisticated design of the probability distribution is this clear so a vector y star in capital y is a mixed security strategy for the row player if look at this his payoff look at the worst case damage that the column player could do to him okay and the this here is called the mixed security level denoted as Vm okay Vm upper bar okay and likewise a vector that star nz is a mixed security strategy column player if okay so this this is how we can define now the corresponding security strategies so these are security strategies in the sense of security strategy district so they are in the sense of distributions so in terms of mixed strategies what are the security strategies they should be playing so what kind of distribution gives them a certain guarantees the players a certain amount of certain payoff that is what is being defined here okay now because now so how many mixed strategies does a player have how many mixed strategies does the player have infinitely many right necessarily because every distribution probability distribution is a mixed on pure strategies is a mixed strategy right so if he has at least two pure strategies he will have infinitely many mixed strategy so the set of mixed set of strategies now has become infinite okay it is the when you go to mixed strategies automatically the set of strategies now becomes becomes infinite so it is actually not that straightforward to now say even that a by a security strategy actually exists showing that there exists such a y star that satisfies this particular property is itself not itself requires a proof you need to prove that there exists a y star which satisfies it earlier all you did was you know you could just check over columns then rows and so on and you could immediately derive that now why does that even exist a distribution like this has to be shown distribution that is better than all other distribution okay so that is that is one this thing and so once you show once the question of existence is along along with the question of existence you also have therefore a question of whether mixed security levels can be thought of as well defined alright so so this this needs some amount of work so this needs some analysis to you need to show that there exists actually a mixed strategy for each layer but assuming there exists one we now we we will we have the same properties that we had earlier we have that we always have vm upper bar greater than equal to vm lower bar this was this can be shown in just the same logic that we did we had earlier okay so we always have this particular thing now we move to this particular regime of where where now players are allowed to randomize but we need to still justify what is it that is being how exactly are players gaining from randomization okay so to see how players gain from randomization let us let us do one let us observe one simple property can you tell me what is the relation between vm upper bar and v upper bar how are these related vm upper bar is smaller why you are taking okay so one that is one of the arguments that that is so so vm upper bar is the claim is vm upper bar is smaller than v upper bar and the reason that is the case is because mixed strategies are more general than pure strategy right pure strategy can be thought of as a mixed strategy with where only particular pure strategy is given probability 1 and all other strategies are given probability 0 but is that enough because if you see how vm has been defined remember okay yes the mixed strategies are more general for than the pure strategies but you are also maximizing over now earlier you are doing max over j now you are doing max over z so the maximization is also being done over a larger set okay so so that is so that is where the subtlety is basically and the answer is correct so it is true that vm is smaller so in fact I will write out the more general thing we of course have this thing that I have written out here but we also have v upper bar of a is greater than equal to vm upper bar of a is greater than equal to vm lower bar of a which is in turn greater than equal to v lower bar of a okay and so let us let us actually prove one of these inequalities so let us prove this one for example okay so I am going to assume that a mixed security strategy exists okay for the moment so what is a mixed security strategy it is a y star such that y star transpose az max over this this is less than equal to max over z y transpose az so actually we can only focus on the left hand side and just look at this more carefully this y star transpose a is a row vector multiplying with a column vector z having components z1 to zn right now what are these these z1 to zn z1 to zn are simply these these this is together a probability distribution right so these are all essentially some kind of weights they add up to 1 they are all greater than equal to so when you want to maximize this over z okay we have we wanted to maximize this thing over z okay we want to maximize this quantity over z we have to basically decide what weights should these components z1 to zn get how what should be the weights precisely so I look at the column that has the largest value okay here I look at the column that has the largest value and pick that one and give that z probability 1 and all the others probability 0 weight equal to 1 and all the others weight 0 so so this actually therefore is equal to so the left hand side here this is actually equal to the max over j of or actually let me just write this for the right hand side that will make things easier for me so I will write this for y transpose right so you pick the largest column largest value from this row vector y transpose a give that particular guy to weight 1 and everything else 0 that has to be the maximum value over all over all possible weighted combinations like this okay so now therefore now you have basically the same thing that we had earlier because this is actually now so now minimizing this minimizing this over y in y minimizing the max over j of y transpose a j this is naturally more general than minimizing over every row because if I took up because I can take y to be a pure strategy and then I would get just aij there so if y is a pure strategy y transpose a j becomes equal to just the pure strategy i let us say and this becomes aij right so that means if y is a pure strategy means what it gives will probability 1 to rho i and all other rows get probability 0 then in that case this become so therefore this is therefore more general is than minimizing over rows itself so consequently the minimizing value has to be lower because you are minimizing over a larger set right so minimizing over uh minimizing the minimum value has to be lower has to be lower because the set of mixed strategies is a larger set so consequently we get this inequality here that v m upper bar has to be less than equal to v v upper bar same thing can be argued even on the other side and we get that v v m lower bar is greater than equal to v lower bar the first one yeah yeah yeah the same same sort of argument as before so I can just show this to you so so you just have you have j of y comma z as this right and take any any this this is always uh uh greater than equal to the min over min over y in y y transpose a z and it is always less than equal to the max over z in z of y transpose a z okay so and again I get if you want I can put a dash here if you are getting confused this is always the case and so now what I have on the left hand side is a function of y and I have right hand side is a function of z function of y alone and z alone and it is all the left hand side is always greater than equal to the right hand side so which means the least value of the left hand side is greater than equal to the largest value of the right hand side okay so that and then so the min over y y max over z in z of y transpose a z this is greater than equal to max over z min over y this is this is this here is your Vm lower bar and this is Vm upper bar so actually this this does not require you know this kind of form in fact you can do this for any function take a function of two variables the min max is always going to be greater than equal to the maximum that is that holds for any function okay all that it still has the same issues still there you know so okay so I do not want to take away the punch line but essentially we still have this here the inequality it is no different from the inequality we started with which was this is greater than equal to this okay so what will happen in the next class is that I will show that this is in fact equal V bar of a not equal to that is because there could be in general this is this is certainly more general than the than that okay all right so the reason for that is okay maybe I can just talk about that here yeah so why are these not equal so we we just showed that V upper bar is greater than equal to V Vm upper bar but then why are they not equal the reason they are not equal is if you see this this expression here I just said that if you take y to be a pure strategy take y to be a pure strategy i then the then this then this just reduces to aij now the reason this is this is not the same as minimizing over pure strategies is because this now the resulting expression that you have here is not linear in y anymore the this expression here was linear in z for a fixed y it was linear in z so therefore you you had to just find the weight at the coefficient with the larger the largest coefficient and give that the full weight whereas if you see this here this is not linear in y anymore this is the max of linear functions and the maximum of linear functions is actually is is you know the way it looks would be maximum of linear function take this function take this function what would be the maximum of these two it would be this region up to this point you know up to this point the second one is larger after that point the other one becomes larger and this is now a max of several such linear functions right n of these linear functions so it is not linear anymore and because it is not linear anymore it is not you cannot claim that this is that the the same way as before you know you cannot pick a component see because the component has now gone inside here it is hidden inside this maximization even if you did pick a component they would still be outside a max over j which will keep switching based on what what y you have chosen the maximizing j right for some wise for some wise it will be this j that is maximum some some otherwise it will be this j that is maximum yes so so okay so it that is I was going to show that next time but actually so what you are asking is this is this is this going to be strict in general right yes so there you can show many functions for which this is okay but but this is already telling us one justification for moving to mixed strategies the randomization has benefited both players each player has improved his security level by randomization right his pure strategies yeah no so that so that is where this is settled so so you will so we will again jumping ahead a little bit let us but the for the moment let us just just justify why we are why we have why it makes sense to allow players the option to randomize it because by randomization they are you know you cannot been once their security levels have improved you cannot basically deny them that option essentially they have they have the one's security level improves which means that it means that you know if they could they would randomize okay all right so what what I will show next time is is is basically the champion theorem here which is that this is equal okay so all the things that we were you know fantasizing about that would happen if we upper bar is equal to be lower bar would now happen for free because we upper bar and we will be m upper bar would be equal to be lower bar okay so there will always be a saddle point etc etc all those consequences will follow but in the space of mixed strategies not in the space of your strategies okay all that


White Sox are losing five to one in the bottom of the seven.  And they don't wanna be losing because they're supposed to be a good team but they're not really a good team.  He screams, yells, gives his buddy a hug. What a scene that is. And the White Sox got momentum. Let's do it, let's do it, let's do it. Tim Anderson steps to the plate. Now in the third inning, he had a call go, not his way. That up and in pitch was called a strike. He didn't like that and that same at bat, Karinczak throws it again and he does an awful swing because he's gotta protect because it's called a strike and he strikes out. So he's got that on his mind but he's trying to overcome it and say, no, let's just get some stuff done. There's two outs where it's only a two run game. Now let's get on base, keep it rolling, keep it moving. Good mood, good mood, I'm in a good mood. I'm not thinking about the blown call earlier. Oh my God.     And this is where it is. I mean, that's pretty close and it's very odd. You didn't get a rung up on it but it is a second of the game. I mean, it's over the plight. Is it too high? That box isn't real. It looks like it's kind of high enough. I don't know, it looks, it's not that bad. He doesn't like it, umpire doesn't like that.   Gets really uncomfortably close to his face.     That's terrible. You're terrible. That's terrible. He says that's twice. Twice you got me on that same pitch. Made some nice contact. Look at this, brim to brim, helmet versus hat. Helmet's always gonna win out. It's just stronger. Whoa, hey, don't bump me again. No bumping. Toss me out.   What was that? Kinda has to get ejected because the star player got ejected. Toss me out.  Okay, you're gone. You're gone. Don't come after me. You don't care. Tellin' the ruses set after the game. I think I saw the umpire moving forward quite a bit which they're taught not to do that. I didn't see any contact that I know. So he's just out here telling us he didn't see any contact but he's old. Maybe he doesn't have good eyesight but this old man saw it. Oh, he hit him. He touched him. And look at this. Just a little dance into his forehead. Just a little wiggle, wiggle on the hat. Umpire doesn't know what's going on. The brims are makin' out a little bit. I like this guy in the background. He's just got his seat. Maybe he went to Seat Geek, used code Johnboy, got $20 off his first purchase. Clap and so happy, so happy. Oh yeah, what? Come on, him and his buddy. Let's get him. Let's get him. Oh yeah, what? What? Umpire chewing his gum, having fun. Anderson got ejected and then suspended for three games, goin' brim to brim.


Item Number – SCP-485 Object Class – Safe Special Containment Procedures – SCP-485 is to be kept in a locked safe deposit box at all times, with the key to be kept in a secure location. Description – SCP-485 appears to be a standard retractable pen, with an unusually easy-to-click button. The pen itself was accidentally stolen by Dr. Daheej, upon renewing his life insurance policy. The pen once belonged to Agent R. of R. Life Insurance, Inc. Each time the pen's tip is extended, a random person known to the user dies by an unknown cause. Since the button's action is abnormally smooth, subjects during testing were noted to rapidly click the pen without conscious thought, or realization of what was happening. Full discovery occurred upon Dr. R. R. falling dead mid-sentence, as Dr. Daheej was absently clicking his pen near his desk. Daheej called his wife, only to discover no answer at any normally reachable locations, including her place of employment. Supervisor R. R. was found dead, with a mildly surprised look on his face. Pen was given SCP status, testing to follow shortly. The pen's action was confirmed by a reclusive Class D personnel, who only knew 39 living people, all met since his internment at location F*** on Base. Said personnel successfully dispatched upwards of 90% of the remaining test subjects on hand, as they had all been selected from the same dormitory wing on Base. Procedure for obtaining live testing personnel has been updated to require more randomization in the selection process. Addendum Due to Dr. Daheej's recent personal tragedy involving nearly all of his friends and family, SCP-485 is hereby remanded to off-person custody in a locked safe deposit box. Note, at least he stopped that damn infernal clicking at all hours at his desk. Now if he would just stop crying. Dr. Bright Lesson Complete If you missed the previous orientation, go watch SCP-484, Memory Stealing Drug, right now. Or for the complete course, watch this playlist.


It's Wilson Smith isn't that black.   Oh my god.    How could I stop? Kakarot It's not a Dragon Ball Z character. Oh, you can't oh my bad. My bad. My bad. There we go. There we go my bad Yo, y'all wanted to see the subtitles.  I Was doing you a favor Thank me. I expected a thank you What what what? What is this about?  I can't do this guys.  Come on Every every shot He's wearing the covert fire He's doing the Usap God, what does that say? Muramura she must call that wasn't that bad.  What is this anime? They're they're allowed to do this What are you Seth? They're allowed to do this How did it get through with this? Why can't I do this on my streams?   It's Will Smith. Will Smith isn't that black?    Why isn't it?  Why is that why they zoomed in on it? Is that what it's called the Sharon gotten the shot again? I'm believable, man.  It's gay Tom, and that's what it is. It's not getting Tom.  I was in Japan. I was in like a Manga store. It was like three floors and of course the basement is like the hentai, right? I saw like a 50 year old dude.   Yeah, I said it Goku's from fortnight.  That's actually not that bad average day in Ohio What did Aaron drag them into the thing I'm surprised they're not shirtless What's blurred out It's like a monkey and a doll wasn't enough.  This is what you see when you walked into What is it?  Is that a dick?   Is he a tomato?  This is another casual conversation in Tokyo That's what I'm talking about.  I don't know what that was I'm gonna try this yo w and chat if I should try this on stream.  We're gonna do it.   Oh my god. I thought I was racist. What does that mean? What's the blurt out word? I want to know and I want to say it out loud. I'll wait. I'll wait.  It's four letters Unsure. Whoa bath. I visited a bath up.    Is that another reference of this sea? What is that one piece? Is this a one piece reference? It's one piece.   I'm never going again. I'm never leaving my house If this is what japan is like, I must have been in the right part.  Should I do it?  What he passed the test he wasn't black enough Why are these animals hanging out?   He's driving. He's driving guys. Nobody's naked in a car.     This show is way too meta Is that what you call it meta when it's like very conscious about what it is or something or it's breaking the fourth?  I might not be able to handle it. Oh, you could handle it.  I could see in your face.   I hope so You could get lotioned up and 200 oh my you got lotion me up You can 200 million is that like a secret position you can 200 million between my boobies.  I'm gonna tell my girl that tomorrow.    It's crazy before this takes the cake. Literally.  We saw a nut sack kid Remember ball sack kid from one punch man, bro. So maybe he's talking about him You know man people actually into this in japan. I saw a bunch of them. So so this I understand I understand this completely That better this spider-man better be in this fucking anime Dad the pita parka better be on the other frame it is Oh god, oh god, I think that's my room What what what why are we raising our hands we have a question for the teacher All right guys, that's it.   I forgot This this is this is something else. This is actually something else. I actually want to watch this so bad It's finrall's voice. Wait, who's finrall? I know black clover, but Rosa tomato. Yeah, man.  I'm gonna be catch up after this this anime We included a hard toothbrush on your crotch to be safe Yeah, I remember when the nurse told me that So I honestly can't believe this is real This this isn't real.  Are you watching this, baby This is what I want.   He's in here too.        I know what those four stars mean There's no other word.   I'm gonna do it to you.   I dare you.  All right watch faja. I'm i'm a chuki.  Is that why they blacked out wil smith's eyes before? But I don't think that was wil smith because like I said wil smith isn't that black.  Why'd they do this to vegeta vagina?  Thank you.   Why does it look like this? We're gonna do lisa osd angel bleed after this.  This is acid the anime That's what the a stands for an anime acid.    I'll be really gonna do this Lollie yeah, I meant candy My likes of lollipops were hidden.


The goal of this study was to create a criterion equation for predicting the heat output of heat transfer from multiple pipes stacked vertically in order to determine the amount of heat being transferred from each pipe. To do so, the researchers used computational data from ANSYS Fluent Software and created a criterion equation for a single tube. They then derived criteria equations from the data they had collected and processed it mathematically. Finally, they used the least squares approximation method to calculate the criterion equations. This article was authored by Andrei Kaptur, Josef Husver, Branislav Dorek, and others.


So a few days on the podcast Tyler and I were talking about the best Linux desktops And one of the desktops that we were talking about was mate and our comments there kind of float around the idea that not a lot of people actually use mate and We were both kind of confused by this because from what we both remembered It was actually a pretty good desktop environment So what I thought I would do today is actually take a look at mate and ask the question Should you give it a try because it does actually Exist so let's go ahead and take a look at mate So here we have Ubuntu mate and I chose this version for good reason because this is the flagship distro for mate the main developer who does mate development is Also the maintainer or at least the chief maintainer of Ubuntu mate So all of the cool features that mate has are Integrated the best inside of Ubuntu mate Whereas if you install this on like Arch or Fedora or some other distro You're gonna find that a lot of the features that are built into Ubuntu mate are missing So things like the mate twig tool usually aren't included in the mate packages on other distros Same thing with the boutique, which is the software center stuff like that Now the first thing we should talk about is look-and-feel because the look-and-feel of mate is something that is going to be very Polarizing for a lot of people and the reason why I say that is because the reason why mate exists is because the developers at the time Preferred the look of GNOME 2 when GNOME 3 was developed and released So if you haven't been around Linux for all that long You'll probably not know that GNOME 3 was a major departure from what GNOME had looked like for a long time And well, this is what GNOME looked like for a long time This is the GNOME 2 paradigm and you have two bars on the screen one at the top one at the bottom and It's something that from a workflow perspective a lot of people got really used to and when GNOME 3 came out and they hid the icons away and the customization was all gone and it was slower than sin and it was not very good the Development team or at least a several developers got together and decided to fork GNOME 2 and come up with mate And that's kind of the story behind it in a brief few words So when you talk about look-and-feel You're going to expect something that is a little bit older and while I'm not saying that the look-and-feel is Out of date what I am saying is that you can expect this to be a consistent look-and-feel for probably the entire time Mate exists because they have chosen this look for a reason now one of the things that makes mate cool specifically Ubuntu mate is that despite this being the paradigm that they've chosen this look and feel is what they've chosen they have Provided you a tool to change that layout if you prefer something different So if you open up the menu here and search for mate tweak you'll find this application here and Basically what this application does is it gives you a few extra options for customization and stuff like that But the cool thing is that it allows you to choose between different panel layouts So the default one on mate is called contemporary But they have several other options So you could try Cupertino and then it'll bring up this option here and this is what Cupertino looks like It's more of a Mac like experience you can also choose familiar and that looks like this now Personally, I don't see that much of a difference between that and the contemporary look But there are a few things that are a little bit different the top panel is a little bit bigger Some of the applets are in different places things like that They also have one here called mutiny and as you might expect this looks like unity now You saw the error that came up that happens every once in a while when you switch between these layouts You can reload the layout if you want to and have those errors go away But this is the layout you'd use if you were used to the unity desktop There's also one here for pantheon, which is also similar to the Cupertino one So this is more elementary OS, but it's still very Mac like then there is Redmond and as you might expect This is very much a Windows like experience. So you have a start menu down here at the bottom There's no extra bar up the top. That's a windows version and then you have traditional Which is a even more gnomed to like experience So you have the two bars again and you have the Old style menu system up here instead of the Whisker menu or whatever that's called where it's a more modern menu system The coolest aspect of this however is that you can save your own layout So if you were to create a panel structure where the panel is on the left hand side Let's just say you created that and you have all of your Applets and stuff like that and the places where you want them and you have the menu where you want it you can Save that layout as your own and then switch away from it come back to it You can have several different layouts if you prefer to change it up That is really freaking cool because it's definitely not something you'll see In basically any other desktop environment Another area that mate does really well in is customization in terms of themes So out of the box you actually get a few really excellent themes to try out and use and when you select a theme It actually has like a packaging effect where when you change the theme it changes Everything except for like the wallpaper. So if we choose this one here You'll see that not only do the Applications and the bars change, but if we go into the file manager, which is called kaha. You will also see that the Folders and icons have changed. So let me actually change that icon again and you'll see that the icon theme has changed And you can scroll down here and see that there are several other themes. So if we choose say The purple one they'd become purple now really what all this is doing is allowing you to choose Accent colors and that is a neat thing to do. I don't know why they call them separate themes It seems like it'd just be easier to come up with a Accent color system instead of having several different themes But this is the way they've chosen to do it now Just like with the panel layout system you can come up with your own theme combination So you can choose different icon packs different themes just like that and because this uses gtk3 You can use pretty much any gtk3 Thing that you find online and they don't hide this behind any genom tweaks or anything This is part of the system preferences. So you can get into this anytime you want You don't have to worry about installing anything extra They also make it really easy to install those new themes by being able to have an install button right here Which will allow you to select the file and then it'll install it right for you Which is really nice another nice little tweak that they've added is an application that allows you to Completely customize how your menu system works So just no matter which menu system you're using whether it's this one or the whisker menu or whatever it's called This application lets you change what applications are shown what categories they are how they're ordered Whether or not they have separators in them, you can change the favorites things like that All that stuff can be done from this application and while this isn't unique to mate It is definitely something that is not that common Now the software boutique is unique to ubuntu mate You can get it on other distros if you want, but it is specifically built for this version of mate Because it pulls from the ubuntu repose So if you're using another distribution that is based on ubuntu The software boutique will probably work pretty well for you if you're on arch It probably would not work at all as far as i'm aware. I'm actually not sure about that But for sure it's definitely built for ubuntu mate And one of the things that's cool about it is that not only does it look really nice But it just functions really well. So you can add different repositories to it You can do a bunch of searches just like you would expect to be able to do It's really well categorized as well So you're not going to have the problem like linux mint has where All of their applications are kind of bifurcated and that they show multiple entries of each application based on where they're coming from So if you search for thunderbird in linux mint, you'd see three applications called thunderbird All of them are exactly the same. They just come from different places You don't have that problem here and while this isn't the fullest features like not everything in the ubuntu repositories is listed here The things that are are well done. So you can click on the details and it'll give you some details of the Application you're looking to download in addition to the details on the applications that are appropriate to do so They do also show you screenshots. So one of the things that I really enjoy about the software boutique Is that the screenshots that are here Can actually be made bigger. So in a lot of software front ends that have screenshots, they're not clickable they just are there and Most of the time that means that the screenshots are really small and are basically useless with this You can see the full size of the screenshot. It just pops up now That's not resizable or anything like that But that's about as big as it's ever going to need to be And you can see the whole thing which is really nice Now the last thing that I want to talk about in terms of the software boutique is that you can add a Whole bunch of apps to a list and then install them all one right after another now That's not something that you can do in any other software front end besides a panax So if you've ever used manjaro, you can select a whole bunch of applications and then have it install them Like in a queue you can also do that here with the software boutique You can add things to the queue and then it will install them one right after another And all you have to do is click the install button and you as you can see now I have two things here right in the queue and then it would just apply the changes Just like you'd see in pamac, which is like I said, this is that's really cool It's not something that you see in any other Software front end in terms of GUI's and stuff like that now you can obviously do that in the command line really easily But the GUI front end managers usually don't have that feature So at the end of the day mate is an amazing desktop I really do enjoy and I always kind of have I've had some issues When it comes to it running on my hardware for some reason when I first switched to Linux I really liked mate and I used it for a while But then after a bit of using it it just stopped running on my computer now I've switched to computer since then and I haven't used mate since then So I don't know if they fixed that or not or if it was just that computer But the point is is that I really enjoy Mate and I have This thing where dark modes are a great thing like I really enjoy dark modes And I think that mate has one of the best dark modes that you can find at any Linux distro It's just kind of out of this world. You look at this and it's just really well put together Very consistent And the combination of some of the colors that they've chosen are just really really good So I think that out of all the desktop environments that I've tried mate is still one of my favorites And I really wish it was more popular because I think a lot of people would enjoy it more now. Obviously There are some downsides. So like I said at the beginning mate does have A future problem In that it's always going to look like this. Okay, and that's okay Like the developers have chosen Their desktop environment to look like this and that's the way it's always going to stay because of the genesis of mate They're kind of stuck in that, you know, I'm too paradigm That's basically the way it's going to look forever more and if you like that kind of thing You're going to be very very happy with this look and feel even With a buntu mate where they give you some options for different panel layouts The default mate experience is going to remain the same throughout its life cycle for however long it exists You're never going to be having that feeling in the back of your mind where they might be doing a visual refresh Sometimes soon and you just have to wait for it. So if you use gnom, you know that eventually gnom is going to do a redesign That's the way gnom has worked forever Now it might take 10 years or something like that Eventually gnom 40 and the 40 series is going to turn into the 50 series or whatever they call it next, you know And usually that will come with a major redesign like the most recent one in gnom 40 was a pretty big redesign of gnom Still had a lot of the same paradigm, but it was a lot of new features a lot of different visual Changes mate is not ever going to probably do that without significantly changing their mission statement Which is to maintain the gnom to paradigm and like I said, there's nothing really wrong with that It's just you have to kind of know that going in that this is what you're getting and I think that that is Again, an okay thing. It's just something you got to keep in mind Now that's one of the reasons why I recommend if you're going to use mate to use a buntu mate because It comes with mate tweak right out of the box It comes with all those panel layouts for you already right out of the box And you can use any of those that you want now that doesn't mean you can't get mate tweak on other distros You can you can download that and have it work just fine But the preconfigured panel layouts are as far as I know Exclusive to a buntu mate. So if you want those things, this is the distro that you want to choose on it Plus because the developer of a buntu mate and mate itself are the same person All of the new exciting features usually come to a buntu mate first all of the Development cycles for mate are pretty much lined up with a buntu itself. So when the Interim a buntu releases come out. Usually that's when a new mate releases released now Sometimes there are some gaps in between there, but for the most part that seems to be true So that is mate. I personally think like I said, it's a very very good distro with one of the best dark themes You can find and if you like the two-bar panel layout or any of the others that buntu mate kind of gives you the Look and feel of mate is still really really good And I find myself again wishing that it was a little bit more popular So if you have thoughts on mate, you can leave those in the comment section below I'd love to hear from you if you want to follow me on twitter You can do so at linuxcast. You can follow me on mastodon or odyssey Those links will be in the video description just below the like button If you could possibly hit the like button, I really appreciate it does So premiumly help the channel The youtube algorithm just relies on that kind of stuff. It eats it up like a junkie does So hit that like button. I really do appreciate it You're supposed to say smash that like button. I guess as a youtuber I I've never really understood why you'd want to smash something but Whatever hit the like button if you would please you can support me on patreon at patreon.com Slash linuxcast just like all these fine people. Thanks to everybody who does support me on patreon and youtube I truly do appreciate it without you guys these videos would just not be possible Seriously without patreon and youtube that probably would make one video a week. So due to these guys I can make more videos every single day. Make sure you subscribe. Thanks a great for watching. I'll see you next time


On Iím talking a bit about my work that fits in directly with the talk that you just heard, dealing with cell types, but I want to start by talking about behaviour, because in the end thatís what weíd like to get to. So my labís interested in trying to understand synaptic mechanisms of sensory perception, we like to get a causal, and mechanistic understanding of just how very, very simple forms of sensory perception arise, a wrth gwrs, sy'n gweithiofa fewn cysylltu'r chwarae i gyffredinol amgyrchumerau deilio y cefnod yn swyddiadau, mae'n ychynig mewn proses. Rydyn ni ydych gyffredinol. Rydyn ni'n ddweud cysylltu'r chwarae i gyd i cysylltu'r hwn ac mae'r cysylltu'r chwarae i gael cysylltu i gael cysylltu y cefnod yn swyddiadau gwneud. ond bydd o gweithio'r bobl gyntaf, ac rydych yn storio'n eu cyfnod i gyda niwroffa gwasanaeth o gwasanaethserau gwneud a'r wneud yn y ddylch yn gweithio'r cywrs hon. Felly mae'n erioed i chi'n gweithio y gweithiannol o'r niwroffa gwasanaethau gwneud y gweithiannol, ac ymdweud ysgol cysylltu llunio'r prosesrwyr. Rwy'n dechrau i'r cynnwys cystafol rhywbeth, ac rwy'n dechrau i ddim yn rhan o'r ffordd. Yn cael ei gweld y dyfodol, y dyfodol, ydy'r pethau'n gweithio'n gwerthfyniadau'r prosesrwyr, ond rwy'n dechrau i'r prosesrwyr, SFK is convenient in terms of having access to genetic tools, and MICE have one whisker system that it is useful to get quantitative understanding of what is going on. Further processed in the primary somatosensory cortex. In addition to having a feed forward sensory pathway there is active motor components, an area of primal motor cortex, bwysig a bwysig yn ddechrau'r byddol yng ngyfnodau yn ddweud sy'n ddweud y cwysgwr arwain. Fe'n ddweud, mae'n rhaid pethau sydd yn ffordd y cyfnodd yn yr unig a phobl iawn, yn ffordd iawn i ddweud eich cyfnodd â ddweud yn ddweud, a mae'n ddweud o'r ddweud o'r ddweud. Ond, mae'n ddweud i'r ddweud o'r ddweud o'r ddweud o'r ddweud, oherwydd rwy'n iechyd yn rhaid i'r systemol, Felly mae'n golygu o wieg o dechrau fel dechrau wedi'u falch. Mae dyfodod o'r rhwylo yn bwrw, a dyfodod o hyd y trafnod mewn bethau'ro yn bwysig. Felly, gallwch yn wneud byth o'r unrhyw bobl maes o'r bwysig gyda'r ffinafol a'r maesau. Efallai, y dyfod y ddechrau i'r maes, gyda'r maes iTrsyn yn 1986 o ran rhai. Mae'n tyfu i'r maes yn argyflogol yw mynd i gyrwych â cyd-foclwyr yma, a sut nid i bethau ymwneud eich platfform ar gyfer hynny, a ydych chi'n gorfod cymaint ar y blaenau yma? Mae'r cerd-fodol ar y ffordd yn y platfform yma a'r pwgiau cyfwyr yn ymwneud yma dywed y gallu ymddangos ei pynd ikergynno'r platform fel yna'r pwgiau. Ac mae'n ymdyn nhw, o ran yr ysbyt yw, yn y platfform yr endo'r platfform a pwgio'n gwneud i ymdyn nhw'r pwyllteid. ac roedd yn ystod gweithio ac yn trwyddo. Yr unrhyw ddweud yma'n mynd i gweithio ymweld yma yma ymarfer o'r ffilm sydd yn ymlaen. Ymryd o'r gweithio'r cyfrifolau'r cyfrifolau'r cyfrifolau'r cyfrifolau yma sy'n gallu gweithio'r cyfrifolau ar y platfoedd yma i ymlaen i'r tynnu. Ymlaen oedd y cyfrifolau ar y platfoedd yma, ymlaen o'r cyfrifolau ar y platfoedd, yw'r cyfrifolau, yw ddweud yw'r cyfrifolau, ac ydy'r ddweud y cyfnod i gynhalu. I chyddo i'n meddwl bod dwi'n gymryd yn gweithio'r proses. Mae'r cyfnod yn solygu'r gyda'r hollu. Mae'n ynnig i'w blwyddyn yn ymgyrch i'r cyfnod y targfod ac yn gweld o'r cyfrifio'r gwahodd y tîm. O'r gweithiau yn ei gwirio'r celf sydd wedi bod yma bod ymlaen i celfwyrwyr senfritio'r gwnaeth o fyddech chi'w o blighwyr aio wedi'u gwasanaeth bai hwn o'r gyfer dweud o'r swydd ac mae'r ddefnyddio'r cyflogau ac yn bwysig, mae'n rhaid i'r cyflogiau g yr teini newydd yn rhaid o'r cyflogau rhai apwyr. Felly y mwyaf ar hyn o bobl yma yma yma ar ôl pryd ar yr oedd wedi'i gweld yn gweld yn gweithio'r celfwyrwyr a'r gennymau ychydig i ddweud yma'r lefnodau cymrydau a'r gyflawni ar gyfer y Llyfrgellau Gwyrdol, a phos ymgyrchai'r mynd i'ch bod gafodd oherwydd i gyfer eich gwirioneddau gyda'r gyfer gyfoedd iawn. Mae'n gofynu'r trafodaeth yma o'r gofynu'r Llyfrgellau Gwyrdol yn fyrwgellau'r cael eu gwirioneddau.  Mae'r wneud i gynnwys ar hyn o'r nôl i'r fawr yn i'r fawr, ac ydych chi'n gawr yn cael ei wneud i'r gawr yn cael eu newon, ac mae'n gwneud yn cael eu gawr yn cael eu 20% yn y ddisgrifennu cymdeithasol. Ac mae'r fawr yn cael eu ddifol o'r newon, yn fawr, yn cael eu fawr yn cael eu newon, fel i'r fawr yn cael eu cyllidau fawr yn cael eu ddifol, a'n iawn i'n amgylchedau ei ddechrau yn cael eu ddifol i ddifol.  Yn ymweld, yn ymweld, mae'n ddau'r cyfrigurion ar y maes bryd. Ond mae'n ddweud yn ymdweud yn y gweithio'r cyfrigurion gwahanol. Mae'n ddweud yma, mae'n ddweud yma, a'n ddweud yn y maes bryd yn y gyfrigurion gwahanol. Mae'n ddweud yn ymdweud, ac mae'n ddweud yn y gweithio'r gyfrigurion gwahanol, mae'n ddweud yn y gaf 67gfmau. A rwy'n edrych yn fawr i gael'r wneud o ddegwyddiadau i gyflwynoedd diolcholion o'r Lluwpxiontau yn adroddodd ar ddegwyddiadau a'r ddegwyddiadau ar gyfer yn yma, yn oedau yn gweithio'r dreuniau sydd yn cymryd i'r dreuniau.  It moves on this order of tens of�� op, of군s on maybe five microns or so, depending a little bit on how active the mouse is and it turns out that that type of movement artifact doesn't interfere dramatically with the whole России recording technique that I want to show you and that we have within high quality membrane potential recordings from these neurons. Now gave the urgent neurons, our device sort of a i'r sefydliad cyflwyno yng Nghyrgrifol, a rydym yn fawr ddaf yn gallu y Wirewyr Caiwgwch Reoli, te体oliad ddim yn gweld ff virus, i'r grwp c moes i'n sefydliad i'r grwp hwnnw'r Gaba Ergwyr Nghyrgrifol. Yn y gallwch yn gweld Gaba Ergwyr Nghyrgrifol yng Nghyrgrifol, sydd heb gêmwyr piwydig wrth gwneud gael Gheiddiogol i fod yn ei ddweud gyda'r newons gwneud mewn gwirol iawn, i byddwch ar gyfer y bwyd drwsio, ac rwy'n ddweud rwy'n dweud â siaradwyr Cymru yn yr un yn ddeni'r gwirol iawn. Yn rwy'n dod o'r parwapau a'r gwirol iawn yn gyfreilor na anghydd cynyodaeth a'r yn rhyngwly kolygowodol iawn 5-HT 3a, y cwmbrachau'r gwirol iawnr ar gyfer y gwirol iawn, mae'n defnyddio', yn gweiniogol, yn cael bod rhywbeth wedi gwirol iawn. Roedd yna y mae'n meddwl yn seithio heimerciaeth and compare with a total number of Gabaergic neurons, they find that they can more or less account for all the numbers of neurons with very little overlap in this classification scheme. We think that this is one that's interesting and appropriate and also quantitatively it just fits in well with the cell types and cell numbers that we found in primarysem Psych gern予s of their wake behaving mouse. In our recordings that we used the two-photo microscope, We see our green fluorescent cells. We can use different types of genetically engineered mice to differentiate them, and we find the same cell types as Godfisher and Bernado Rudi identified. There are somatosstaten expressing neurons, fast-pigging, labourergic neurons that expressed parvalbumin, non-fast-pigging, labourergic neurons that don't express parvalbumin or somatosstaten. They fall into roughly this subset as a division of the labourergic neurons inside layer 2, 3. a dyna maen nhw'n gwneud i'w rwyntio'r cyffredinol y llunio niogwyddych, a gwneud i'n wneud i'ch gyd yn y ddechrau. Ac mae'n pethau ychydig o'r problemol yma, dwi'n gwaith yma y tuffordi gefnogi, oedd eich cyd-io'r gwneud i'ch nhw'n gweithio'r ddifrwyng. A mae'n gweithio'r gwneud o'r pethau o'r gwneud eich mynedd. Felly, gwneud yn yn ffasbwynt i'r gyfer yn gyfnodig gyda'r gwneurolydau, N�heddech yw'r bydd n ending Diolch�, hwn ydy'r unrhyw gan yau hwnnw yw'r fHS, mae o hyd yn o��� yng Ngheithnogaeth scaf yn gyflow peathent, ond maeinäu pili Instatol Ap but man o野f 5, r phrall g呼b sydd cou nicely, i buddillueu gallu othrygu am y droi initiallyny ar GymrydDP fuel ar Carryabordなんだ ac efo'r Larygiynaeth fwrdd cyhoedliannos gwelwyr.  Felly mae hynny'n gael ei hyffroud이 gyda llunion. I think that's sort of obvious. They also have differences in terms of their just standard electrophysiological properties. The input resistance, for example, of the somatostatin cells is much higher than for the other types of neurons. Consequently, they also have a much lower real base so they're very sensitive to injection of small currents and they'll readily fire action potentials under many conditions. So this is sort of just the basic intrinsic properties of these neurons. A nice thing, of course, about recording in vivo is that there are spontaneous membrane potential fluctuations that may be relevant to the animal's behavior. So in the first instance we look and see what happens in the animal during what state that we call quiet wakefulness where the animal is not moving. We do high speed video filming of the animal and in particular we film the position of the whiskers and when the whisker isn't moving then we call that quiet wakefulness. And during quiet wakefulness there are slow membrane potential fluctuations in basically all types of neurons that we recorded from. So excited neurons have large amplitude membrane potential fluctuations. So here's the scale bar, 20 millivolts, one second. So these are slow changes in membrane potential. There are of course also fast changes in membrane potential but there are these slow envelopes that are obvious in excited neurons in non-fast-biking gap, ergic neurons, fast-biking gap, ergic neurons and the somatostatin cells are unusual. They seem to lack these slow oscillations or at least they're much smaller than in any of the other cell types. You can also see this if you look at the spectrograph here in the Fourier transform of the membrane potential. You see a large peak here for the fast bikers, non-fast bikers and excited neurons. They have a lot of power here in the slow frequencies and that's about half in the somatostatin expressing gap, ergic neurons. So the somatostatin neurons seem to have unique membrane potential dynamics that all the other types of neurons have been recorded in the superficial layers of the neocortex. They're also the most depolarised neurons, all the ones we've recorded from, more depolarised than the other gap-ergic neurons that in themselves are much more depolarised than excitatory neurons and both somatostatin and fast-biking gap-ergic neurons and to a small extent the non-fast-biking gap-ergic neurons are firing spontaneously quite high rates of action potentials which is different from the excitatory neurons which are almost silent under these conditions. They have a median spike rate of 0.1 hertz under conditions that are quite weak from this. So that's all very well. We see the membrane potential of individual neurons here. Of course we would also like to relate that then to the neighbours and so Luke Jean-Tier, when he was in my lab, began doing double recordings from nearby neurons again in the awake head restrained mouse and here he's recording from two excitatory neurons and you see again the slow membrane potential fluctuations that are characteristic of quite wakefulness and the grey neuron and the black neuron have almost identical sub-freshhold membrane potential fluctuations but action potential firing turns out to be uncorrelated. So membrane potentials of all neurons let's say as a first order approximation all go together so the whole neocortex under quite wakefulness is swinging up and down by these huge changes in membrane potential so again 20 millivolts, these are massive swings in membrane potential and all the excitatory neurons in the superficial layers are more or less doing the same thing. The same is also true of the GABAergic neurons. You take a fast biker and you compare it to the excitatory neuron recorded nearby and you'll again see very high correlations in membrane potential fluctuations between GABAergic neurons and the glutamatergic pyramidal cells nearby. And you can do the same thing for non-fast biker neurons, you can take fast biker, non-fast biker neurons, you can take any combination you want and we always see high correlations in these slow membrane potentials during quite wakefulness. On the other hand, if you look at the somatostatin neurons you see that things are a little bit different. First of all of course I told you that the actual slow membrane potential fluctuations are already much less in these neurons than in any of the others but if one then looks more carefully and you start doing cross correlations you'll see that actually there's a small weak anti-correlation where the hyperpolarisation in somatostatin cells follows excitation in the other cell types and so what we think is happening is that the GABAergic neurons will depolarise at the same time as the excitatory neurons and probably they'll drive an inhibition of the somatostatin neurons at the time where the other neurons are receiving excitation. In addition, the somatostatin neurons might lack one of the important excitatory inputs at all the other cell types. So all the other cell types, if it's an excitatory to an excitatory connection, excitatory to fast biking, excitatory to non-fast biking, single spike is very nicely translated to an excitatory post-synaptic potential so there's a nice, as a word, a high release probability of these synapses. On the other hand, in vitro work that's been done by a variety of labs like that Sackman's laboratory, Barry Connor's laboratory, Henry Markham's laboratory has shown that the excitatory synapse to the somatostatin neuron or the martinati cell as it's also sometimes called is a facilitating synapse so a single spike may only give a very small EPSP and so it could be that another reason here for, as we were seeing, no correlation is that it also actually lacks the major excitatory input that all the other cells are seeing around it and in one particular example, Luke Shonte was lucky enough to get a connected pair of neurons in awake animals so we think this is the first case of a synaptic connection studied in an awake mouse. So here's our excitatory neuron, here's a somatostatin neuron and when current is injected into the excitatory neuron Luke noticed that the somatostatin neuron would start firing action potentials by itself and you could do this repeatedly and here you see that you can actually drive the somatostatin neurons to quite high firing rates. When you then hyperpolarise the somatostatin cell you have to remember these are very excitable, these neurons so you can easily hyperpolarise them with just small currents so here injects 100 picoam pair, firing is blocked in the somatostatin cell it continues injecting currents into the excitatory neuron firing action potentials and you'll see that these early action potentials these first one, two, three, four action potentials actually don't give rise to an EPSP it's only the fifth spike here that gives rise to this quite large input and presumably as you keep going with these further inputs these are the ones that in the end were driving spikes under the normal condition and so I think it's entirely feasible to think that in many cases one reason that the somatostatin cells are out of phase and out of sync with all the others is that actually they simply lack excitatory input because the firing rates in the excitatory neurons turns out to be very low and the median rates at 0.1 hertz so it's very rare to get a huge spike train like this from an excitatory neuron occurring and so we think that's one reason that there may be this situation that you have an anti-correlation that's present in these somatostatin neurons different from all the other neighbours that are highly correlated in their membrane potential fluctuations so that's a little bit about the spontaneous activity of these neurons during quiet wakefulness but of course we normally think that this is a primary sensory area it should be involved in sensory processing and so we're also interested to see what happens when the whiskers are deflected and in this case what we do as an experimenter we take the whisker and we simply deflect it we move it briefly for one millisecond we give it a little jolt and this then activates the sensory pathway that I discussed and we call this a passive whisker stimulus in the sense that we deliver the stimulus it's not the animal that's decided to get the information we delivered it so at this dotted line here with a small bit of piezo that gives us one millisecond deflection of the whisker and all neurons basically depolarise so an excitatory neuron will depolarise non-fast bikers they depolarise fast bikers they depolarise the fast bikers are the ones that respond best in terms of getting action potential output then come the non-fast bikers and the excitatory neurons are fairly poor in terms of their response probability many of them don't fire spikes a few of them do and that then averages out to giving you a small brief amount of firing once again the somatostatin neurons these potential martinati like neurons are unusual you stimulate and this is the only type of neuron that we found that hyperpolarises in response to sensory stimulation we've never seen this before we've been recording for over a decade in this brain area and we've never found neurons that hyperpolarise in response to sensory stimulation until we came to these somatostatin neurons they also decrease firing rates so they're spontaneously quite active firing around 5 hertz you stimulate and they stop briefly for a brief period of time and they do this robustly so somatostatin neurons are also unique in the sense that they're inhibited by sensory stimuli quite different to all the other neurons that are excited and fire higher action potential firing rates finally I started off by telling you that the main way that the mouse acquires sensory information is when it actively moves its whiskers to touch objects and so the first thing one might want to look at is to see what happens when the animal is moving its whisker and not contacting an object but at least it's an active process so here we do high speed video filming we see what the animal is doing with its whisker here it's sitting still for long periods of time this is this period of quiet wakefulness and then every now and then it'll start moving its whiskers it's interested somehow in its environment there's a major change in brain state and one thing that happens are the somatostatin neurons hyperpolarise, they turn off the animal stops moving its whiskers there's a little bit of jitter around here and it's whisker, there's a little bit of hyperpolarisation here the animals calm again and their action potentials have been fired now we introduce an object these grey bars here so we put an object in the way so now when the animal is moving its whisker it's actually touching something this I guess is the situation but the animal normally gets its major impact we know in excite neurons fastbiking neurons and non fastbikers that active touch as we call it when the whisker contacts an object induces a depolarising sensory response here there's no obvious sign of depolarisation occurring if you look here on sort of the average trace you'll see that in fact there's a small hyperpolarisation here also at least the somatostatin neurons are clearly not getting interested in active touch once again they turn off and so the somatostatin neurons seem to be unique and different from all the other nearby neurons they hyperpolarise and reduce action potential firing whenever anything interesting is going on in this brain area whenever there's a sensory input whenever there's an active bout of whisking or when the animal is actively touching something so these are neurons that seem to turn off when there's something interesting going on in that brain area now somatostatin neurons are interesting in the sense that they have an axonal projection that innovates layer 1 and so whenever these somatostatin neurons are firing action potentials they're releasing GABA up here in layer 1 and so you might imagine there could be interesting processes going on in the layer 1 dendrites when we turn off inhibition if you turn off distal inhibition you'd expect maybe that the distal dendrites might become more active and so we had a look using genetically encoded calcium indicator GCAM3 we express it in excitatory neurons and when the animal is sitting quiet and we look in the layer 1 dendrites here there's very little going on when the animal moves its whiskers we see dendrites but I don't know if you can see the splines but it does light up and it lights up robustly so apparently as these somatostatin neurons turn off as the animal is moving its whiskers we release inhibition and it looks like the distal dendrites have become more active and start maybe firing calcium spikes or NMDA spikes so there are many things that happen in the circuits during whisking and so we wanted to have a more direct check also on what's happening and so we applied optogenetics we express haloradopsin 3.0 we now also switch over to Cree driver mouse line from Taniguchi and when we turn on the yellow light there's a hyperpolarised somatostatin cells and we can see a complete shut off of action central firing so the optogenetics works nicely and the interesting thing of course is to record in the nearby excitatory neurons when you turn off the somatostatin cells the slow oscillations continue to change in brain state but we do see that there's getting these multiple spike bursts that we think are characteristic of distal dendritic input that turns out to be slow and that could be then driving the calcium signals that we saw previously so the functional role we think now turning back to sort of the big picture where the animal is moving around exploring its environment there must be motor signals in motor cortex motor cortex sends profound projections to layer 1 of primary somatosensory cortex and also deeper layers these somatostatin neurons look like they're well placed to control this part of the input they can decide whether this layer 1 input from motor cortex should be playing an interesting role or not when the animal is actively exploring somatostatin cells turn off and they may then allow and gate this motor input into primed somatosensory cortex and that might then be a critical role in terms of establishing sensory motor integration in other sensory cortices it may be that these somatostatin neurons are involved in just regulating in general top-down feedback we think of this M1 signal as a top-down signal and many other brain areas receive top-down input into M1 and so it could be that somatostatin cells are playing a similar role in other brain areas I want to finish here by thanking Luke Zhongte who is a guy who did all the whole cell recordings Eve Cramer did the calcium imaging Hiroki Taniguchi and Josh Wang from Colesping Harbour generated and Jochen Steiger helped us with immunistic chemistry and I'd like to thank you for your attention We can take a few short questions Betty I think you said something and then just kept on going about the spikes and it's clear that the the membrane potentials are very correlated Did I hear you correctly that the spikes are not? Yeah, so that's absolutely true so maybe just to specify quickly excitatory to excitatory neurons so spike rates are low so it's not that we have really great data on this but if we take the spike data that we have there's no correlation it's just a flat line that the spike rates are that's not true for the excitatory versus GABAergic neurons or GABAergic their spike rates are much higher and they more or less follow the envelope of these slow membrane potential fluctuations but for the excitatory neurons the slow membrane potential is not enough to bring it to spike threshold so the excitatory neurons are hyperporized by about 10 millivolts the slow oscillation has about the same amplitude and so they still need another 10 millivolts to hit spike thresholds spike thresholds pretty much the same in all these cells and so we think there's an additional thing that needs to come in to follow the excitatory neurons and it looks like they need an additional big 10 millivolts input to arrive Okay Any further questions? We are very much convinced Thank you very much


Tomorrow we'll bring innovations like the heat pump, which electrically heats your house in winter and cools it in summer. At the agency, heat pumps, we see as one of the next major clean technologies that the world needs to focus on. We've seen huge gains in solar, we've seen huge gains with electric vehicles. Heat pumps is the next in line to have their moment.  Fossil fuel boiler uses fossil fuels, burns them to create heat to warm our homes. Heat pump is a little bit different in that these refrigerants that are used in heat pumps, they boil at really low temperatures and this is part of the secret sauce that allows them to be able to move this heat around effectively. So it would boil on one side by absorbing some of that heat, you then condense that and then release that heat then on the other side. It's much more efficient because it's not trying to create this heat but taking it from elsewhere in the environment and moving it to where you want that heat to be. Heat pumps can provide the same level of comfort as a traditional heating equipment in both existing buildings and new buildings. And as a matter of fact, the countries with the highest level of heat pump adoption are Finland and Norway, Sweden, countries with very low temperatures during the winter season. Because of how much more efficient they are, the switch even in grids that are highly dependent on coal and other polluting fossil fuels creates an improvement and a reduction in emissions and improves air quality by reducing the pollution in the air. So it's already a good move today and this is just going to keep getting better over time as more renewables come on the grid, new commitments globally, including the one at COP for tripling renewables is already going to really rapidly shift how we get our energy and reduce the volume of fossil fuels used to produce that electricity.


Hello and welcome to CMC Markets on Tuesday the 8th of April and this week's weekly market update and it's certainly been an eventful few days. We've seen a fairly neutral I would say non-farm payrolls report on Friday and after initially pushing higher towards the 1900 area the S&P very very quickly turned tail and went straight back down again and a lot of the declines that we've been seeing over the past few days have been largely as a result of a sell-off in what are categorised as the high momentum high growth stocks and I think that's sort of filtered through into the broader market. Obviously there's also been some concerns about what's going on in the Ukraine at the moment and a raising of tensions there. Last week we also saw the European Central Bank keep rates on hold though Mr Draghi did sort of raise the prospect of QE some way down the line but I still think that even though they are talking about it they still remain an awful long way away from doing anything in any way recognisable as what we would understand as QE and on the scale of the Bank of England and the Federal Reserve have done it and I think that's largely why we've seen the euro go higher and the European markets go lower. No prospect of QE no prospect of stimulus you look at the economic data that's coming out of the US and coming out of Europe it's not bad but it's not particularly great and when you've got the Fed later this week publishing its latest minutes the prospect of further stimulus reduction over the course of the next few months really means that you need stocks to start outperforming to carry on the gains that we've been seeing over the past few months. So you may have gathered from that introduction I'm going to be looking at the S&P 500 and the euro dollar and I'm going to start with the S&P 500. Now those of you who are listening to my non-farm payrolls webcast on Friday will know this particular chart that I'm about to put on the screen now. It's the daily S&P 500 chart and as we can see the we've got to break out higher of that triangular consolidation that we've been in since mid-February and at the beginning of March we broke higher we were unable to break above the 1900 level and I said that if we went back inside the triangle then the prospect the light that it was a quite high prospect that we'd go back and test the lower line on that particular triangle and that's essentially what we've done over the past couple of days. The key level now on the S&P 500 is the 1840 level which basically intersects that trend line and the March lows. If we take out the March lows at 1830 then I think the sell-off that we've seen over the past few days could actually feed in on itself and actually push quite a bit lower towards the 1800 level and maybe even as low as 1750. So that window between 1830 and 1840 is a very important level. Moving swiftly on to Eurodollar, Mr Draghi last week didn't pull the trigger on any QE, he didn't reduce rates, he didn't put the deposit rate negative and as a result we've seen a reversal in the Eurodollar and as can be seen from this daily chart again the support at 13670 where we have the 100-day moving average as well as trend line support from the 12760 lows that we saw in the middle of last year that so far is containing any downside in Eurodollar. Also on Monday we saw a bullish engulfing day and that again is an indicator of positive sentiment and as a significant likelihood we could well retest the highs that we saw earlier in March. I'm going to finish up with a quick look at the Australian dollar and this is a chart I've been looking at for quite some time now and I think it's a chart that I've shown you guys on previous occasions. We've now broken above the 200-day moving average, we've also broken above that neckline that I've identified with respect to the inverse head and shoulders. Now China announced a form of mini stimulus at the end of last week, we've got Chinese data later this week, trade data and I think there is a good chance we could see an improvement there and we've also got Australian unemployment data later this week. If any of those numbers are good and there's a good chance they could well be then the potential for a higher Aussie remains very much on the table as long as we stay above the 200-day moving average and the neckline support from those highs that I've drawn on the chart in front of you. So if we project a breakout from that head and shoulders to from that head to the neckline higher then we certainly have potential now that we've broken above 93 cents to go at least another 200 or 300 points to around about 95 or 96. So certainly worth keeping an eye on the Aussie dollar. So to sum up the key events to keep an eye out for this week are obviously the FOMC minutes which are due to be released on Wednesday evening. I think the key takeaways from there are what new criteria will the Fed be looking at with respect to their decisions on future monetary policy decisions. Also the latest Chinese trade data for March. Will there be an improvement in the exports and the imports data and will the balance turn back to surplus and also the latest Bank of England meeting though we're not really expecting too many surprises from that. Until next week thanks very much for listening. This is Michael Houston talking to you from CMC Markets.