Thank you. That concludes the debate on three years on Brexit and Workers Right. It's now time to move on to the next item of business, which is an announcement by the Economy and Fair Work Committee on enquiries into just transition for the Grangemouth Area and disabled employment gap and I call on Clear Baker, convener of the committee to make the announcement. Thank you. I welcome this opportunity to highlight two inquiries the Economy and Fair Work Committee is undertaking. Yesterday, members of the committee visited Enable Works and All-In Dundee. They are a consortium supporting people with disabilities into meaningful employment and supports employers to identify and provide job opportunities. Thank you also to Dovetail for the tool of their factory. On Monday, members of the committee will visit Glasgow to see the work being done by the National Autistic Society Scotland to support young people into employment. Those visits are part of our on-going work to look at Scotland's disability employment gap and what needs to be done to ensure that the Government meets its target to significantly reduce that gap. Our call for views is open for another couple of weeks. I also wish to highlight the economy and fair work committee inquiry into how we can support, incentivise and de-risk the transition to net zero in a way that will benefit businesses and people. The committee has agreed that the first focus of this work will be GrangeMouse. We know that transition to net zero is something that we must all turn our attention to and this work will consider the impact and opportunities for the GrangeMouse area. If any member would like to find out more about either of these pieces of work please do not hesitate to contact my clerks. Thank you. The next item of business is consideration of business motion 7735 in the name of George Adam on behalf of the parliamentary bureau setting out a business programme. I call on George Adam to move the motion. Thank you, Presiding Officer. I'm moved. Thank you, Minister. I call on Stephen Kerr to speak to and move amendment 7735.1. Thank you, Presiding Officer. My amendment seeks to insert a ministerial statement next week on the disruption in our schools. As the teachers continue their industrial action, causing no end of disruption, the First Minister and the Cabinet Secretary continue to pursue inaction as a strategy. Teachers who do not want to strike have been left with no options. Parents are having to arrange childcare, pupils aren't in school and are suffering further disruption to their education on top of the disruption caused by two years of the pandemic. That is why, Presiding Officer, I'm on my feet yet again asking for a statement. It feels like every time we get the Cabinet Secretary to come to the chamber to answer questions, whether it be on educational attainment, the apprenticeship programme, the current strikes, she must be forced into it. This is not the attitude of a Cabinet Secretary who is on top of her brief. It's not the attitude of a Cabinet Secretary who is energised and engaged in her subject area. The attitude of the Scottish Government seems disengaged to the point of laziness. Michael Marra Labour is happy to support calls for a statement on the strikes that are debilitating families and schools across the country. Speaking to trade unions this afternoon, they said to me that effectively these negotiations have ground to a halt. Is that not a disgrace? It is a disgrace because, Presiding Officer, many in this chamber, alongside parents in pupils in schools across the country will have the deepest sympathy for striking teachers. I have sympathy with a profession that seems increasingly to be held in contempt by the Scottish Government. The Scottish Government is negotiating a pay-de deal. It is now over 300 days overdue and we see nothing of the First Minister in any of this. She was fast enough to rush in front of cameras as she has over the past few days, but she shows no animation whatsoever to settle this dispute with Scotland's teachers. Presiding Officer, I will give way to this Parliament. John Mason Would the member like to tell the chamber how much she thinks should be offered to the teachers? Is it 10%, 15% or more and where that money should come from? John Mason, if we could get the Cabinet Secretary to come to the chamber to bring us up to date with the negotiations and where things stand, perhaps we can discuss that sort of detail. Presiding Officer, this Parliament needs answers and I ask for the support today of colleagues to get a ministerial statement at the beginning of next week on this issue. We need to find out what the Cabinet Secretary is doing. Is she negotiating with the teachers and the councils? That we know as of 17 January she hasn't attended any of the negotiation sessions. I'll give way one more time. Willie Rennie, does Stephen Kerr find it surprising that the Cabinet Secretary is so reluctant to update the chamber about this once-in-a-lifetime industrial dispute when they spent the whole afternoon boasting about their industrial relations exercise? Stephen Kerr Willie Rennie is right. There are inherent contradictions in what we hear from the front bench and their attitude towards the teachers' union and this dispute. Has the First Minister met any of the teaching unions? According to correspondence, which I would share with the chamber, I have seen this week that she has been missing in action. Despite her personal intervention in the local government pay dispute, in the train drivers dispute, she has yet to set a hand on the teachers' strike. No wonder members of a branch of one of the teaching unions that the EIS has written to me saying, the reason we are writing to you, Mr Kerr, is because throughout this dispute we have yet to see or hear from the First Minister. We obviously want to get this dispute resolved and get back to teaching our young people, but we need the First Minister to enable us to do this. If you see her, could you please let her know that we are looking for her? That is from the EIS. Furthermore, the EIS says that it is disingenuous and unacceptable for the Scottish Government and COSLA to continue to misrepresent negotiations as positive and constructive. Are they positive? Are they constructive? We do not know whether they are positive or whether they are constructive, because all we get from the cabinet secretary are meaningless platitudes in the form of press statements while the strikes continue. The cabinet secretary must appear before Parliament. Her laid-back, hands-off approach has failed parents, pupils, communities and teachers. I urge members to support my amendment today so that we can scrutinise the cabinet secretary. Mr Kerr, could I ask you please to move your amendment? For the opportunity to speak again, I move my amendment. Thank you. I call on George Adam to respond on behalf of the parliamentary bureau. Thank you, Presiding Officer. You would be a bit shocked to know that we are actually talking parliamentary business here, because Mr Kerr and I went off on one, I think that the term is there, I told you to speak. Mr Kerr has said this on numerous occasions about asking requests for a statement for next week, but this is the first time that we have heard that request for a statement at the bureau, because, as Mr Kerr rightly knows, there is a process in which the Conservatives are very familiar with by which a statement can be requested. Mr Kerr understands this as he was the Tory business manager and he did it regularly in the past. However, that was not raised at the bureau at all. As always, Presiding Officer, we will consider any statement request raised by business managers through the official route. What we have here, Presiding Officer, is the Conservative Party indulging in opposition for opposition's sake. It would be helpful if we could move away from these political shenanigans and discuss requests for business at the bureau as per the norm. The first question is that amendment 7735.1 in the name of Stephen Kerr, which seeks to amend business motion 7735 in the name of George Adam on behalf of the parliamentary bureau setting out a business programme, be agreed. Are we all agreed? The Parliament is not agreed, therefore we will move to a vote. Now there will be a brief pause to allow members to access the bill on the digital voting system. Can I ask all those members who have voted previously today to refresh their device? Thank you.


Thank you. So first I would like to thank the organizer for the school, the conference, and the opportunity to talk. So I'm going to present this joint result with Sylvain Crovisier and Henri Sariq. Okay, let's start. So well first I for the second time this week you will have a short introduction to entropy So why should we care what we do we do is it so it's essentially you can you want to count or bits in a certain way and You can do it for measures you can do it for from the point of view of topology and It leads to a lot of Interesting fascinating stuff you can use it to classify Classes of dynamical systems in the probabilistic setting in the symbolic setting even for in the smooth setting we see and As was mentioned in the Talk by Keith Well, when you have it's especially interesting when you have systems with say some high publicity Which have because of this a lot of invariant measure and then entropy becomes a way of Selecting measures Interesting measure. So how do you count? So let me repeat Only for the second time this week The one way to do it, which is the let's say the boy and where the boy and in a burgway Which is you you fix yourself? Precision a scale. This is the epsilon a small positive number and then when you Consider some time and then you will say, okay I will not make any difference between two points whose orbit stay epsilon close within I mean during time and Okay, that gives you a metric and hence a notion of balls and once you have these balls You can define covering numbers for subsets That's just the minimum number of balls in this sense that you need to to cover your subset and You can then extend it to measures as Just by saying now you're not interested really in covering a Definite given subset, but just anything with a significant measure and One half was already introduced in the previous lecture Okay, and then once you have this number then you can say, okay I'm going to now define for instance topological entropy just by saying, okay I let the scale goes to epsilon for fixed scale. I just compute the exponential growth rate Of the covering numbers I mentioned before Okay, and then if you have a nice If you're in a reasonable setting a nice setting then you can just say okay The topological entropy is just when I want to cover everything Okay, and for measure I mean Catox formula tells you that at least in the algorithm case you can essentially do the same Adjust this time instead of covering everything. You just cover a subset of significant measure Okay, just so feel free to interrupt me. Otherwise these things so you see them for the second time this day, so Okay, and then one of the key Thing which is the rational principle that tells you that actually it is what you see when you're looking at measures is Reflects in some sense all that can be seen in your system as soon as you You are in this topological a compact setting Okay, and there is a very nice proof by Mishorevich Which is also interesting because the way it is The proof goes is to say okay if you try to actually distribute point or actually equidistribute measures measure on epsilon n Separated Points then so you try to build some kind of equidistributed measure when you let n goes to infinity You will get something which has close to the Full entropy so this is one way to say okay, this is one more reason to think that Measures maximizing the entropy are going to be an exciting thing. Okay. Anyway, that's Something we can decide for ourselves now. When do they exist? So Okay, first what I should say is that their existence is in some sense much less general than The setting of the rational principle you need something more than continuity and compactness one of the thing which was mentioned By keys is expansivity so if not to orbit stay close to each other For all times at least in fact positive and negative then This will imply that the entropy function of other measure with upper costumy continuous so then You achieve your mark the supremum is achieved. This means you have a measure of maximum entropy This same upper semi continuity argument applies in fact as soon as you have a infinity map on a compact manifold this is due to your new house using young Dean's theory But interestingly so Not only C0 is not enough, but actually for every finite smoothness you have counter example so the this was shown by misery which in a Dimension four or more and actually you can build Also examples at as soon as it look at question makes sense in dimension two Okay, now the subject so this was for Existence which essentially Well, you have this at least very this very Well still general theorem of new house that as you just see infinity a personal continuity existence Even if you don't really know anything about the dynamic you have this Kind of functional analytic a reason that gives you measures of maximum entropy. So now the more difficult Stuff is Well, what about the number? I mean as was mentioned if ever for instance you have a system with zero Entropy then all invariant measures are measures of maximum entropy and this is well and actually this you can use this to To to see something very easy, but still which you have to keep in mind Which is it's easy to have systems with uncountably many measures maximizing the entropy. So What is the solution to this exercise? You just take Your favorite system which has a measure with maximum entropy. So let's say a sinfinity map on some compact manifold and then you take the product with let's say the identity of the circle and while using things about the entropy of Product and things like this you can easily check that well now Not only you have if you so you had at least one measure of maximum entropy for F because it was infinity And now you have Uncontably many ergodic measures of maximum entropy. So you have to To I mean you need something for this I mean to hope that you will have finiteness. So what kind of condition wouldn't show finiteness? What type of system so one of the first type of system for which it was known our subshift or finite type Okay, let me just Point out that for existence we had this Expansivity condition and the expansivity condition is automatically satisfied for any shift on a finite alphabet and you see here to get we have this example of existence and now among all this shift the one for which it is classical at least to That they have finitely many measures of maximum entropy they have a much more rigid structure and that's the idea Usually when you can prove finiteness, it's because you know a lot of things about your system about your dynamics This is the opposite to the question of existence Okay, and then it was shown that This is this also holds in some sense if you build if you go Classically through a Markov partition This is a consequence of the let's say the Paris result that this is also true in the smooth setting for uniformly hyperbolic different morphisms and so well hyperbolicity gives you a Well a setting where you can hope to show that You have finitely many So for uniformly hyperbolic this this was done in the 70s. So what about non-uniform? Okay, is it true that when you have something which is non-uniformly hyperbolic Let's say all measures are hyperbolic in this in the case in sense in the sense that they have no the only opponent exponent will be Will this give me Uniqueness or finiteness or something like this Okay, so the first type of symbol in the symbolic category The answer is somewhat. Yes So well you have to to assume something because well for substitute or finite that you had By the nature of things only finitely many pieces So you would get finiteness of measures of maximum entropy For the their generalization to infinite But countable alphabets you can have of course infinite you can take one system and take Countably many copies of it. So you do not you cannot hope to have finiteness without adding an assumption But for instance go a bit show the I mean the result that makes sense here Which is that if you ask you if you assume your disability Then actually you have at most one measure Maximizing the entropy for this type. So in the symbolic setting you have this nice I mean the the result has this natural generalization and Okay, what about The smooth setting so actually it's not enough so already for Smooth but with finite smoothness interval map So assuming positive entropy, I mean I've made the remark before that otherwise The question is Doesn't make sense Well, you can check it's not very difficult to build example where you see that in finite smoothness You can still have infinitely many measures of maximum entropy Actually, there are countably many that is not this is better than the general situation But still you can have infinitely many The fact that you have here because of reals inequality which will appear in a second You know that when you have positive entropy measures with entropy close to the maximum will have a uniform lower bound on their exponent So in some sense you do not have uniform high publicity, but you have Well as somewhat strong form of non uniform except you seen high publicity still it is not enough What do you need more? So for sin infinity it works. I mean you have if you take a sin infinity interval map with With Which is infinity smooth not only it has measures of maximum entropy by new house, but actually it has finitely many of them and what is the So what is So that's reals inequality that there's you that So this is in dimension one for maps I mean I'm quoting the special case in dimension one for maps or in dimension two for Differomorphisms of surfaces So sorry You see that if the if you have a lower bound on the entropy of the measure then you have the lower bound on the largest Yapunov exponent, okay, so if you want So what is the extra thing that you get from you go when you go from here to here it's it's Well, it's what we'll see. Okay, so that's the that's the this theorem now We want to extend it to dimension two so dimension so this was dimension one for maps and we expect usually that when Things are nice with us then what's holds for interval map should hold in a Adapted form maybe for surface differ morphism So for a long time there was no What what no progress in this with respect to this question and then a few years ago Saric built so succeeded in building a kind of symbolic dynamics for C1 plus alpha Surface differ morphism with positive topological entropy and one of the consequence of his construction is that the as in the For the interval in slow smoothness the set of measures of maximum entropy is countable It cannot be uncountable As in the general case Okay, but in fact is I mean and we will build on his result So to to show the the finite net so this is the the main theorem so it's repeat It's a joint work with a silver and Omri Okay, you take Any compact surface and he's infinity if your morphism on this surface The hyperboleicity assumption here is that the topological entropy is positive Okay, and then you get I mean the most important thing is that thus You have only finitely many ergodic measures that maximize the entropy Okay, and it's even nicer in the sense that if you assume a natural condition for your disability Of your difumorphism that is topological transitivity. You really get uniqueness Okay, so this is a this is a Result it somehow completes my PhD thesis With a little help from my friends. So now I'm going to try to to explain Some things that how you prove this oh, sorry, I forgot so once actually the so we will see we prove a little bit more and This has to let me quote two Things that we get let's say for the price of the previous theorem two more things so the first one is You can apply this to equilibrium states and especially holder continues Small potentials. So what does mean a small potential? It means that they satisfy this condition which actually Somewhat somewhere appeared at some place in the key stock The point of this condition Usually usually in this business is that you can check that it immediately implies that measures that equilibrium measures measures that mu that Maximizes the sum of the entropy plus the average of the potential the integral of the potential This measure under this condition They will have positive topological entropy They will have positive entropy and then actually the positive is not something abstract It's the difference between the right-hand side and the left-hand side so once we have Well, we will see that the same argument that proved the The theorem about measures of maximal entropy actually applies then to equilibrium states Under this condition, sorry. Yeah, they were so what we will obtain is that the Intersection of the support of the support of two measures like this will have zero topological entropy More than that. I don't know and the other Stuff which I don't want really to to read is that actually we prove a theorem about CR different morphisms and then Everything gets a little bit more complicated but so instead of having the condition that the topological entropy is Non-zero you have that it has to be bigger than some threshold Where in the numerator you see essentially the lift sheets constant and in the denominator you see the smoothness And this has to do with what you have lots of estimates like this First in a young beam theory or when you try to compute Some or in South theorem and we'll see that's that's how it it comes from It's on some the interest of having a CR statement is maybe to understand better What's going on in this infinity case where essentially everything becomes zero? Okay, and then you get the same conclusion, okay, so now Okay, that's me so what is the strategy of the proof so there are three Let's say three parts one part is to introduce a Kind of spectral decomposition, which will be based on the Homoclinic relationship, but between measures not directly between points then we prove So we had this Big theorem of sorry that I quoted or at least I quoted some consequence already This theorem is very powerful But it's also very difficult to to establish and in particular You need a construction, which is quite abstract and it's really difficult to understand how what's going on on the manifold is reflected into what's going on on the symbolic dynamics so Here the point of introducing these Okay, sorry there is a mistake. It's not hyperbolic measure class. It's homoclinic measure class that might I mean the measures are hyperbolic too But that the world that should be there is Homoclinic measure class. So the point is to have this notion which is Clear let's say canonically defined on the surface and to understand it on the on surrog Symbolic dynamics and this is where comes the into play the local version of sorry theorem will get symbolic Essentially symbolic coding for each of these homoclinic measure class So then you have these So so and finally so you have this spectral decomposition into These natural pieces, you know by the local version of sorry theorem that each piece will have At most one measure of maximal entropy and now to conclude you only need to show that Only funny too many pieces can have entropy above some threshold I mean if you have all this then you have the the main theorem Okay, and oh yeah, so what I should say is that we use I mean this type of ideas is very close to what Federico, Hannah, Alita, Zibi and Raoul us did for SRB measures on surfaces So some of the problems are different The results are different too, but the idea that but they they also had I mean they they Introduce this idea that you should look at a version of homoclinic class for invariant measures and also that you that in dimension to you can use a well plan of topology and that it Simple let's say simple figures tells you that a lot of stuff that if you so I mean it's it's different but It's in the same spirit Okay, so what are more precisely the ingredients so as I said the basic I mean the big thing is the Saric's coding for surface Differmorphism and We use a more specifically how I mean He shows that In some sense the size of the alphabet of the symbols that you need to use in his coding is strongly related to How good or how bad is the high publicity on the surface for a given point I mean I will give a slightly less mysterious statement when I Go into the horrible details later but that's the Okay, the second argument is This thing about plan of topology, so let me make Drawing which is what it said it looks a little bit stupid, but still one has to To do it what is a rectangle for us So a rectangle is just you have so suppose somewhere you have a Hyperbolic set with its so you have this Hyperbolic set lambda often it will be a horseshoe so so transit topologically transitive so locally maximum Okay, this is the Sorry Yes invariant So this is lambda What if you not too sure about the other words it's the the last ones that matter most so my Rectangle is just Well, sometimes a rectangle is just a rectangle so the rectangle here is just the open set so but the boundary pieces of leaves of Of the dynamical four liations of this uniformly hyperbolic horseshoe, okay, so this is really I just Well, and essentially I'm going to when things intersect in Well, the boundary in a non-trivial way their boundaries have to intersect and Then I know things That's the second ingredient Okay to build these rectangles to show that you can cover a Lot of measure with them we will use a piecin theory and especially to build the relevant horseshoes linked to To hyperbolic measure we will use catholic horseshoe theorem That tells you that when you have a measure with Hyperbolic measure, so it knows you only have enough exponent you can find a horseshoe which has topological entropy almost equal to that of the measure and Which is homo clinically related to the measure And which is close to the measure in lots of different senses Okay, and sorry and one one of the things that we that is known about these horseshoes is that so you have this so the collection of the stable sets gives you a foliation or lamination technically with continuously I mean the leaves are CR and they depend continuously on the point So it's not exactly a foliation is Let's call it dynamical lamination or dynamical Foliation and these things are known to have positive transverse half-dough dimension and there is even there is a lower bound for these things Which I mean the lower bound comes into play when you want to do the CR case for the C infinity case You just have to know that the transverse dimension is always positive Okay, and so when we do so we are going to to do this Jordan theorem thing to show that essentially when for instance when When you have let's say two rectangles that intersect in a non-trivial way There you see immediately that the boundaries have to Well, that's a definition let's say of intersecting One meets the other no no one covers the other then you see that the boundary have to intersect Well as sets and then the question you ask immediately yourself is okay Well, you know, maybe not immediately but after the next slide is whether this intersection between smooth curves are transverse or not Okay, the topology of course doesn't tell you anything about it, but then that's where South theorem or an adaptation of it in the For dynamical for Asian where you have this kind of partial smoothness Very classical Comes into play and here you have the other Bound that tells you that for C infinity in the C infinity setting if you have Affoliation This type of affiliation then well the you can look at the sub foliation defined by leaf By leaves which are tangent to some smooth curve And you will get that the dimension of these bad guys is actually zero And when you compare with the previous thing you see that Well, when you have an intersection not between curves, so now what will happen? Well, I will come back to that later. So when you are looking at two given curves, of course, these curves could intersect Non-transversally, but if you use that these curves actually are accumulated by a whole Dynamical foliation like here then using these two ways these two arguments You can show that well, maybe not this curve But another curve Which is just as good as it as the first one will have this transverse Intersection that you're hoping for. Okay, so essentially while we at point two We had topological intersection and then from three and four you get nice transverse intersection and Finally the finiteness and what is the extra secret ingredient to a hyperbolicity? it's yamlil theory and more precisely so what you Yamlil theory gives you a way to uniformly control the tail entropy which was introduced by Mr. Ivits under the name of conditional topological entropy Which I caused for some time Local entropy, but okay Which is the this simple it's a very simple quantity in fact, but maybe it doesn't look like that, but Well, which is okay you at each scale epsilon what you do You you look at the complexity that is the topological entropy defined just by asking yourself How many balls do I need to cover this subset? So here the subset you want to cover is any let's say kind of tubular neighborhood of a given orbit When you are close to a given orbit Close at scale epsilon how many entropy can you will use? May you see when? You keep looking at this epsilon tubular neighborhood, but now you look with a very much smaller Microscope a much smaller scale and that's the topological entropy of this set Okay, this is for one the neighborhood of one given orbit now you can take the supremum of all orbits Okay, and Well here this is for at scale epsilon now as in the definition of the entropy You should let epsilon goes to zero. This is the tail entropy of F Okay, and it's also called the tail entropy because one of the key property which is completely obvious from the definition is that When you compute let's say the entropy of a subset or of a merger it doesn't matter Okay, you will you get immediately from this definition the estimate That if you stop your computation if you do your computation of entropy at a given scale with a given precision Then actually what you can miss out is bounded Just by this quantity So it gives you a uniformity in the so it gives you a it's a bound. It's a first bound now the I mean Sex entropy theory will give you much finer bound, but it gives you a uniform bound on the Uniformity or non-uniformity of epsilon and when you are seeing infinity the these things go Goes to zero this number goes to zero. So you get uniform convergence Okay, that makes lots of people that I know happy But here for us it's even more basic than that it tells us that essentially for a given smooth map There is a scale at which if we compute the entropy we see almost everything. We don't need to go To go arbitrarily small scale. Okay, and if it's not since infinity Yeah, no, no, sorry. There is a No, this is I forgot to take the limit when epsilon goes to zero. Thank you for should be clear for I mean I I said it quickly But yeah, it's worth repeating Yeah, of course the Okay, okay, so that's the That's the list of things you should be ready before you start cooking So let us start So the first ingredient is to define this homo clinic measure class here. I got it Correct. It's homo clinic So this is a very well. This is a classical idea Let's say according to the definition of Vivian Baladi something that was very well known before you started your PhD so You take so first you take two points you say that they are homo clinically related If the following hold so I'm not saying the points are periodic for now So I have to assume that they have reasonable stable and unstable set let's say what what what is produced by piecin stable theorem that is you look at the set of points which converts exponentially in the future or in the past To the orbit of the point you are considering and I want these to be nice guys Okay, just so that what I'm really interested in saying will make sense and now the homo clinic relation I mean goes back to maybe smell or Is to say okay, I want the unstable Of One to cross the stable of the other in a transverse way Okay, so the picture is Like this, okay, let me keep my colors. You have This will be Okay, let me say this is Okay, and this is the stable P the unstable of Of P and then you can imagine the rest of the notation Okay, this is so you want this Okay, you once you have defined this for substance points you extend it to subset when there is no It's completely trivial. I mean this is just a definition anyway It just takes care. I mean this partition just takes care even in the classical case of Periodic orbits you need to pay attention About I mean the where you are on the periodic orbit. So that's why you need to have these these sorry these Partitions and you want that essentially you have a kind of synchronization and the the matching parts should be homo clinically related Okay, so this you can apply this now to horses, which I mentioned before And Now using the lambda lemma you can check that Apply to horses to this is really a well. It's an equivalence relation and Because of well everything is uniform and so on it's enough to find two points which are related in each or shoe to Actually establish that they are themselves related in the sense that you have all points for which The periods don't forbid. I mean the that are not the off a Modular the periods will be How more clinically related which is the definition of the subsets being related Okay, so something that cannot I haven't yet defined here. So let's just keep that Okay, and as I said the classical case which go back to a new house in the 70s is to apply this To hyperbolic periodic orbits, so of course, you know how they have stable and stable manifold And this is what you call homo clinic class. So there are two with two definitions which you can define that okay the The people I speak with they like the closure and here we will also like the closure So if you have a hyperbolic periodic orbit, it's homo clinic class is the closure of the set of hyperbolic periodic orbits, which are homo clinically related in this sense to the first orbit Okay, and that's it's well known that Well, for instance, you want generically you can define a spectral decomposition using these well These things appear in a spectral decomposition. I don't want to I don't have the time to well Okay, and now what I'm really interested in is in defining these four measures like in a similar way to to what Federico, how he did a slightly different way, but yeah So when I have to ergodic hyperbolic measure, well, I said they are related if they are You have a full measure subsets which are related in the previous sense Okay, and now the homo clinic measure class Well, it's just the The class for this relation and you can check that it's an equivalence relation on this set of measures and it generalizes the classical definition in the sense that when you have Hyperbolic periodic orbit, they define the hyperbolic measures and the two notions then are the same Okay, and you can check that actually At least in the scene infinity case. Well, don't pay too much attention essentially with respect to positive entropy measures ergodic measures It's essentially the same to speak of hyperbolic measure or to speak of measure carried by these homo clinic classes, which are the closure of Homoclinically related periodic points, so it's Almost it's not exactly the same. We don't know exactly what could be what is the difference. They could be Some difference. Let's say at the level of entropy zero, which is why we want to to deal with the measure stuff Okay, and one of the things we could know that one of the benefit of Going back to this more classical notion What the homo clinic class is a compact invariant set is that if you have a C infinity map the entropy function stays stays Upper semi-continuous when you restrict to the compact invariant set and therefore you still have by new house the exist the local existence of Measure that maximizes locally the entropy and this is for existence Okay Okay, then there is a local uniqueness theorem, which I'm not going to really to speak about since I have no time oops Okay, what is the Okay, this is what I want to to mention now It's just the corollary the corollary tell me it tells me that now I had this Global sorry theorem, but global with a control on hyperbolicity and Well linking the hyperbolicity for the map to how Smalls in the symbols I must use I cannot really explain more in the few minutes that remain and But here the the what we are at 10 is this now you can focus on a homo clinic measure class and They are only they can all be lifted somehow to a single piece of the Symbolic dynamics and the consequence of this is that each piece will have at most one measure of maximal entropy I mean we actually have one measure that maximum exactly one measure that maximizes the entropy among the class and this measure either it is of Entropy which is the topological entropy of the map or it's something lower And then it doesn't count as a measure of maximal entropy for the whole thing, but essentially you have here you have the local uniqueness and now the well In a zero seconds the finite multiplicity That we want to prove now can be formulated as this if you take any positive Number then the You can look at the homo clinic a measure class Which have entropy in the sense that they carry measure with entropy bigger than this positive number and This is a finite subset and this when you combine this with your previous Uniqueness theorem you get the main theorem. How much time do I have? It's over. Okay, so let So that's the proof You know all my secrets now Okay, let's me just conclude very quickly. So I would like to say that What it is? So in some sense it completes my 20 years old PhD Now it leaves you Some problem especially so now we prove uniqueness for finite Smoothness actually we don't yet have we think we can have but it's not Really a counter example that would extend to really show that C infinity is necessary Okay, I don't want to know no time to Mention two and three and then of course so a further question which is much less Well, which is really open we don't really know to how to to deal with it now is You have this spectral decomposition. Can you get more information? Especially in this is spectral decomposition appears Entropies and periods of the various species. What can you say about that? And then this would give us? classification of surface Defiomorphism Okay, and then Well, what about higher dimension so maybe You really make and tells tell us something about the case of three-dimensional flows which should be well interval maps should be like different morphisms of surfaces which should be like Flows in three-dimension well, maybe we don't have to wait 20 years for that and Now the bigger question is what happens for different morphisms in higher dimension So we know that some extra assumption is needed. It's not clear why it's not clear which one Well, we do the job are really necessary or whatever anyway, so we already three minutes Over time, so thank you


You got your papers out, all ready to go. Number two, I think I got some feedback yesterday that my quiz was a little too hard, so it's a little easier maybe, but no promises. So this is your quiz question number one. It has to deal with the anatomy of the iris on the pupil. And it is important to know what you're looking at and what is normal. So the question here is, and it's even multiple choice, so it's a little easier, I think, is what is the normal location of the center of the pupil compared to the center of the eye? Is it inferonazole? Is it supronazole? Is it inferotemporal, or is it suprotemporal? Does anybody know? Yeah? Well, I mean, did you answer it on your paper already? You got it? Does anybody know? It is inferonazole, and it's unfortunately no rhyme or reason. It's just kind of where mostly anatomically things end up. So just important to know when you're looking at a normal iris and normal pupil, you're going to have some displacement from the center of the iris of the center of the pupil. Question number two. So I want you to list three signs of Horner syndrome other than meiosis, ptosis, and anhydrosis. And I think I could think of maybe eight. So you get three. It's not too bad, right? So I'll give you 15 seconds. Seconds left. There we go. You ready? Can somebody scream some out for me? Sorry? Perfect. That's a good one. Anything else? Like how am I sign this involvement? No. No, it's not a sign. What is happening? How about flu and ophthalmos? That's a really great one. Or an elevation. What is happening? You're having a seizure because it's too stressed. All right, so this is a list, right? So again, ptosis, anhydrosis, your classic medical school teaching. You're not in medical school anymore. You're ophthalmologist. So you should have a bigger list of things that are associated with Horner syndrome in terms of the signs. So dilation lag is your classic, classic thing we talk about with Horner syndrome. So really important to think about that. Reverse ptosis, of course, is associated with the sympathetic innervation of the inferior eyelid retractors, which is equivalent to the mular muscle in the upper lid. So it's a reverse ptosis. And as Dr. Warner had mentioned, it gives you an appearance of pseudoanophthalmos. When you do your exophthalmometry, of course, it is not the case. And that's why it's called pseudoanophthalmos. But the appearance of the ptosis and reverse ptosis gives you that sunken eye look. The conjunctival hyperemia is really important as well. And that's just related to the removal of the sympathetic tone of the vessels. And so a lot of the time, what patients end up being treated for when it's not picked up correctly is for some kind of corneal or dry eye or infection or allergic reaction in the eye, because that eye just looks red. So unless you pick up the subtle ptosis and subtle anisocorrhea, they can't end up being treated for anterior segment problems, which are not anterior segment problems. So again, really important to keep in mind when you're looking at somebody with unilateral red eye and maybe some other neurological symptoms. Iris heterochromia is also an important sign. It is traditionally thought of as a congenital hornar syndrome sign. And it develops in children, because if sympathetic innervation is disrupted at the time where the melanocytes produce pigment and deposit pigment in the iris, you basically get anisocorrhea. So if you have a unilateral hornar syndrome, you get anisocorrhea. And the iris that is lighter is the one that is the abnormal iris. And classically, the timing for that is thought to be probably up to two years of age. So there's been some studies done on the development of the color of the iris in children. And up to two years is when you can actually have development. So even if you have a theoretically, even if you have a acquired hornar syndrome after one year of life, then you still could end up with iris heterochromia. Again, abnormal iris is the lighter one. The sympathetic innervation is required for melanocytes to produce pigment. You can get transient increase in accommodation, because of course, you just get a parasympathetic drive. As your sympathetic drive is impaired, again, temporarily transiently, you can get reduced intraculopressure for the same reason. Has anybody heard of Harlequin sign or what that is, or Harlequin syndrome? Very good. Yeah, so that, again, is one of the findings. And which side would it be the hornar syndrome on? So Christian, which side would the hornar syndrome be on in Harlequin? Sorry? The normal side. Correct. So again, think that that's actually the opposite side. But the sign is called for the facial flushing.  And if you remove sympathetic input, you actually get a straight, half the hair straight, or some part of the hair is straight, and the other side is curly. So I really don't know the explanation. I don't know if Dr. Warner, you have heard of why that's the case. But I don't think we've figured that out yet. They scared me so much it made my hair curly. This is true. All right, so there is a case. So we have a 63-year-old patient. And she came into clinic just last month with a two and a half week history of Anisechoria. And the Anisechoria was greater in the dark. So I am going to get one of the maybe PGI chews to describe to me what you see. So this is a photograph of our patient in a room light. And she's looking far away. She's looking at distance.  So. Holy Mary. All right, Chris? Upritalia is a nebosis. And there's also people that are smaller than the right injection in the right eye. Oh, in the right eye, you mean? Oh, OK. Anything else that you think is on the photo? The nebosis in that left eye. Good. So what's the MRD? I just estimate. Yeah, and then what do you think of the right? The right eye, maybe four and then. I agree that. So that gives you two signs of Horner syndrome. So we've got ptosis and reverse ptosis. Reverse ptosis, good. That's pretty good, right? So apparent on ophthalmos, I think, is a really nice thing that's exemplified here. Just looks like that eye sunken because of that appearance of the ptosis and reverse ptosis. So, but you know, I already told you, right, that the anisecary was greater in the dark. So you kind of have your differential narrowed down a little bit. But it also helps you, again, just that subtle ptosis, reverse ptosis, apparent on ophthalmos. And you have the anisecaria. And you put it together. One thing she does not have, she doesn't have iris heterochromia. So you probably, it's not congenital. And she's got the achemosis around there. So something must have happened to her. So, yeah. Is her eyelash a little left side? More curly. Well, almost some cops have been told that she stayed. No, I think it's just the other right there. It's just the darker background. You don't see them as well. And so then this is a picture of the same patient. And this is her looking at near. So you're basically looking to constriction to near. And she had that. And then here is a photograph of exposure, light exposure to the right. And you're looking for a kind of consensual response. And if that, and that is indeed present. And then we did this. So the light has turned off. This is five seconds. This is 15 seconds. What do you see there? Five seconds. 15 seconds. Very good. So this is a sign of Horner's syndrome called dilation lag. And again, a really nice thing to look for, because it really, you can even avoid, in this patient it's kind of classic.  So you're getting the idea that this is Horner's syndrome. And in majority cases, actually, it's pretty convincing. So even drop testing is not necessary. And we actually didn't do drop testing in this patient, because I think all the signs were pointing to Horner's syndrome. And this patient actually had a surgical resection of her thyroid. And she developed a really large hematoma on her neck. And supposedly, that was compressing her sympathetic pathway. I will have to caution you. I do remember seeing one case in residency where a patient had had a tumor resection in her neck. And she developed Horner's syndrome afterwards. And it's easy to assume, well, this is just post-surgical changes, nothing to worry about. And this was about probably six weeks after she had had her resection. But there were some other things going on. So we decided to reimage her. And she actually had recurrence of that tumor in the short period of time in the same area, compressing her sympathetic chain. So just be aware of looking for other things and not just discounting things to post-surgical changes, because multiple things could be going on in the same patient. So we actually offered this patient repeat imaging. But she chose not to do that. And we're just going to observe her and just make sure that she does well. And when was the surgical time? Yeah, it was about four weeks ago. Yeah, like three or four weeks ago. Didn't it make this injury up? Yeah. Well, I think this is probably maybe post-surgical or something like that. I don't know where they went into it. But the ecumosis had no relevance to it. Well, it had relevance because it was post-surgical. But it wasn't a traumatic event or anything like that. OK, so the next case is a three-month-old baby. And the parents bring him in because about one and a half weeks ago, they noticed anisocorrhea. And so maybe we'll get Nico to comment on what you see here. And I always, it's sometimes important to mention pertinent negatives in this case. So what are pertinent negatives in this case? The upper eyelids use symmetry for its notosis. Very good. What other signs of horner did we talk about that he does not have? Look at his face. So it doesn't have any symmetry in the flushing, right? So that's important to note. And stepping back, even before you think about something like horner syndrome, he does have anisocorrhea. So what's another important pertinent negative that is nicely exemplified with the corneal reflexes in this photograph? Yeah, so they're central, and there's no apparent deviation. So presume that this child did have right-horner syndrome, right, have a little bit of meiosis on the right. Would we expect iris heterochromia in this child? Three months. No, so as I mentioned, right, so it, well, it usually takes about six months for it to become apparent, but up to two years sometimes. I guess it depends on the natural pigmentation, right? So I'm a child. OK, then this is the room in the light. This is the dark room photograph. Nico? So? Yeah, we actually didn't think that it was that different. It was less than a millimeter, about a millimeter or so, or less. And it was relatively symmetric, and we're comfortable because there was no ptosis, no other concerning findings. So we are going to be watching this little guy, and we thought he had physiologic anisechorrhea. So we have question three from your quiz. And again, it's a multiple choice. Yeah, sorry, yeah, the parents had looked at the photos, and he's had it since birth, so. Or at least like, at least the first month for sure. All right, what's the answer to this one? It is C, and the concern with apoclonidine and bromonidine is what? Yeah, CNS oppression. So we really do not like to use any of the derivatives in children, and it depends on kind of the source you look at, some sources say even up to eight years of age. Majority of sources say maybe two years of age, and after that, it becomes relatively safe. But it just has to do with CNS penetration of both drugs in children as compared to adults. So do not give bromonidine or apoclonidine to children. Cocaine is actually safe in children for testing. So what age? So like I said, so most sources say about two years, but some say up to eight. So I would just avoid it in children if you have access to cocaine in general. I did want to mention a little bit more about physiologic anisechorrhea. You did mention a few points about it, but up to 20% of population actually do have physiologic anisechorrhea and walking around with unequal pupils. Usually it's less than half a millimeter difference, but classically we talk about less than one millimeter. And the amount can vary depending on time of day, and it can actually flip eyes as well. So you can see that traditionally anisechorrhea is the same in light or dark, but it can be more obvious in the dark like in our baby as you can see just because dark conditions just makes things I guess a little bit more obvious. So the confusion often comes in, especially when you have an older person with physiologic anisechorrhea and then they have maybe involutional ptosis. And so drop testing is important in physiologic anisechorrhea in case you were wondering why would we test if all these features are present. It's not often clear as can be. Okay, so here's the third one. This is a baby I saw, I think it was maybe a third or fourth year resident and mom sent me this picture. So what sign is this? Yeah, so what sign is the pathology on? So theoretically it should really help you localize where Horner syndrome is. And of course, and you seem to know kind of a little bit more about the anatomy of facial sweating and, no? No, okay. Anybody? Why does that maybe help you localize things? Well, so the way that the pathway for basically vasoconstriction of vasomotor and pseudomotor fibers goes is a little bit different than your pupillary sympathetic pathway. And very similar, it just goes down a little further down the T spine, but when it travels to the superior cervical ganglion it actually splits and fibers that innervate the upper medial forehead actually travel differently than do the fibers that innervate the lower face. So it kind of gives you an idea that, if you have a bit of asymmetry, you know that if the whole face is affected that it's likely either first or second order neuron, but if it's just part of the face like the superior medial forehead then it kind of helps you localize things a little bit. Now I have to say that in kids there's been some publications about the fact that it's not necessarily true and there's thought to be some transynaptic degeneration that happens that we don't actually see an adult. So in adults this may be helpful, but there's been several cases in children where drop testing actually localizes to a different location than the facial asymmetry and the facial flushing. So I will have to caution you against that in children, in adults, it's a little bit more consistent in terms of kind of the asymmetry. Now you did mention that we don't really test for anhydrosis. You can in children, especially if they cry, it's actually like in this case, kind of a nice example of how we can actually see the anhydrosis and the facial flushing that's asymmetric. Some people talk about using like a spoon or even like a prism in clinic and running it over the forehead and seeing the difference of how slick it is depending on the side of the forehead you're testing for. So and I mean, I've, you know, I saw a patient with Harlequin syndrome we actually made him run up and down the stairs just to see kind of where to reproduce those signs. So you can do certain things to bring out anhydrosis and asymmetric flushing. You know, it is a little bit more effort. So maybe that's why we don't talk about it. Yeah, that's true. And so I just want to mention this because I knew we weren't going to talk about too much in the actual didactic portion of the talk is that, you know, like if you think cornering children, like you got to think neuroblastoma, you know, and it's sometimes difficult, especially if a child presents a two years of age to know if it's congenital or quiet, especially if there's no history of birth trauma. So you really, you need to think about that first. And one other point I wanted to make here is the kind of the congenital side of things. Why would congenital agenesis of internal carotid artery cause Horner syndrome? Where does sympathetics go? You need that to kind of guide that. Correct. So if you have developmental agenesis of the internal carotid, you're just not going to have your sympathetics travel to that area. So just again, connection between what your causes are to the anatomical understanding of the pathway are really, really important. Okay, so Lee, do you want to describe this one? Three minutes. Well, you know what? Actually, we're going to go to this. This is one other thing that we did not cover that I wanted to cover today. So I know he's telling you what is going on, but I did want you to, no, I'm not, I'm going to show you this.  So the patient is basically looking at near, evoking a near response. So what's happening there? No, well, later, but sorry. So he tries light first, that doesn't work. Then he tries near response and that constricts the pupil. What's that called? Sorry? Light near. Yeah, so light near dissociation. Slowly is moving. Yeah, so light near dissociation. So this is your quiz question four and what I want you to do, this is a little bit of help for you, but I want you to name an anatomic site and then etiology of causes of light near dissociation and I want you to name five of those. A few more seconds. So the first site, of course, is retina. So if you have severe retinal damage, that can give you light near dissociation because of the input effect. Short posterior ciliary nerves get affected in either PRP or peripheral neuropathies of different kinds that can give you light near dissociation. As Nico had nicely explained, adi's pupil site of pathology is ciliary ganglion, so you need to know that. With cranial nerve three, aberrant regeneration can be a cause of light near dissociation, for example, when adduction is coupled with meiosis, et cetera. So that's important to know. Argalobrobrits and pupils localize to the tectum of the midbrain due to the inflammatory effect. And then we've seen a few cases of dorsal midbrain syndrome that are due to either tumors or hydrocephals or other compressive things. And quiz question five is two systemic findings in adi's pupil. This was covered, so we should. And a quick one here. This should just be a quick look. What's this? Can somebody describe the photo quickly? Maybe Lee, sorry, I took away your chance and it's a chance to redeem yourself. And what's this sign called? The toothpick sign or the Q-tip sign? Why is that there? Correct, so he's trying to elevate the eyelid. Eyes down and out, you have anisocorrhea as expected. So as Nico quickly mentioned, you need to image this patient. And this is the last one here. And this is a patient here that has anisocorrhea that was greater in the lip room. And this is him right here. And this is him after installation first of dilute pyloh and then second of 1% pyloh. So what's your diagnosis here? Okay, I'm always running out of time, but these are your quiz questions and those are your points. And I will collect the scores.


What is one thing that celebrities in Kenya do, that you consider something you just can't do? Something that I can do ignoring fans, like I can't stop, I can't stop for a fan to take a photo, you understand? I can't reply a DM if I have an opportunity, so one thing I don't like doing to my fans is being a snob. Ya, because I've been snobbed by people, people who snob me right now, sorry to say, we're in the same industry right now. They go for meeting brief, I am there, but there are people who snob me so badly when I was there. But I've never even told them because I'm not here to say on any, at you or Mulinidoraw, who is laughing now, no, no, no. I've been through these things, I've been snobbed, I've been humiliated, so I really try not to do the same to my fans because they are the people that have grown me. A behavior that you had to change for you to move forward in life? No, I had to quit smoking, and yeah, quite a smoking. And there is another addiction, I won't mention, I also quit that. So that, I mean, the actually two addictions for the last five years have been amazing for me since then. I'm fine, thank you so much, we thank God. By the way, this is my first time interviewing you, by the way. Ya, ya, I've been interviewing many people, I've been attacking. All your brothers, I spoke to them. That is the first time they actually did an interview in their life. Aha. They have never. This is about it, you know they are your big brothers, they came through for you. What are your thoughts about that, and what do you have to say to them? Ah, quite an emotional moment, they are emotional feelings, but I just want to appreciate them for their support. They don't go for shows, they came that time. I saw them, I was surprised. And I don't know, now appenda to Sana. Ya. Now to Mia Terrence, because people came through when Corona Terrence. Pole, pole, pole. So people came through, what is the most surprising thing about that event? The most surprising thing is to me, it was a confirmation from God. It's like an affirmation that my son go, this is what I called you for, go for it. I brought these people, I didn't see people, me I saw love. Ya. Those volumes of people, that was love, that was love.  That is God. Ya. That was God, that is God. Yes. Wow now, okay particular movie you know, any watch on screen. Uli kwa na pressure, kutahenda je. I know you are just confident that kutahenda 2. Wa, wa, wa, wa. I have so much pressure, but I have to give it up to one person that is Vinichepi, my wife, for standing there in the gap. She is actually the person who was pushing more. She was a person who was doing the organization. I was so much freaked, but I say it, God, I've done what I was supposed to do. I've done all the marketing I know. I've spoken to everyone that I know, you take it over from there. Ya. That's what I did. And I just say, even when we were shooting, even when we were planning, I told guys, in ya mungu, because we have never done that. I've never spent so much money on a project, never. That was the first project, every expensive project that I saw, spend a lot in terms of energy, in terms of attention. And when I see all these people come, I say, ya ni mungu wewe, wewe ni mungu. Nuktapa ni anzi kulia. Ucilia, ucilia Terrence. But now talking about films, looks like you've launched your career in film already. Because we're here because of volume, the series, it's on Netflix Terrence. This is your first role, you are on Netflix. What are your thoughts about that and how was the experience working with Tosh Gitonga? Amazing, amazing. Again, I say this is God. First of all, I just want to congratulate Tosh Gitonga. For those who don't know, he's redoing this movie again. We had shot it again, something happened, one of the cast. And we did it again. I think when he gets time, we can explain to you what happened. And he never gave up on this project. And when he called me, Tosh Gitonga is the first person whoever put me on TV on a commercial, TVC, TV commercial. It was a safari kum. And he paid me good money. That was long time ago. That was like seven, eight years ago. He becomes the first person also today to put me on Netflix. He put me on Netflix before my movie put me on Netflix. So it's such a good coincidence. And this set was so much amazing because I'm doing something that I'm not used to do. It's not your normal Papa Fred, normal Kiateka, normal Kamami. It's a different role. And it challenged me, but I thank God that it went well and people have loved it.  The thing that I shot, you see, all the camera gear, everything that I used camera, Tosh gave me the part here for free. So it's been a brava. But God bless you so much and I'm happy to be here. Yes. Tell us about that. Amazing. So I went to Tosh. As I said, Wachishwa was very costly in terms of equipment and everything. I went to Tosh and told him I need to do this movie. I told him actually last year. Because last year I did a series. It's called Wababa Nation. I did that series. Tosh gave me the equipment. There is a camera gear. He gave me the camera gear through his company camera gear and primary pictures. When I was shooting Wachishwa, I looked at the budget and said, bro, this is the kind of production that I want. This is the quality that I want to produce. I went to Tosh and told him, I want you to help me with camera for certain days. He said, it's alright bro, come for it. I didn't believe. Because he's on the quality camera. If you saw what we did on Icon, those are quality cameras. If I was to hire them, for example, they would have cost me 3 million. Yes. But it gave me for free. And I don't take that for granted. And he's been so supportive. Because I call him for everything. And I told him, what do you think? And he advised. When he called me for the movie, he said, hey bro, kuja? Kuja is a movie. Nanda kulipa. And he pays. He pays good. I said, kuja nanda kulipa. I said, say bro. Wachatuni kuja. Wachatuni kuja. Kuja is stuck in Superstar. Nikule Temaretka. Ni ni ni ni ni. Because na sa idea na humeni sa idea. So, I feel like this guy has that heart of giving you gear for free. Then giving you a movie that he'll appear on Netflix and still pays you. And he got, aku bless you sana tosh. God bless you. Ya. Nimi onapale kumchondor. Se ma'i cheren sa betengeneza, pesa mingi sana. Yes. Pesa umetengeneza. Nimi mwen kuze vacation munenda wapi December. Ku do kishi amili shukurani. First of all, where I am right now, I'm not into minting money. Whatever I'm looking for in terms of money, I'm looking for money to invest in my art. What I've been able to shoot and the money that I get from whatever. It took me two years to shoot Wachatuni because I was saving. Ya. And I approached our partners. What I normally do, I sell a vision to people. I sell a dream. Right now I'm telling you, in terms of cost, nukumenshonia kamera. Ie njetoshani nipatia, nge-dikos 3 million. But nipeo for free. Nelewa, nukumenshonia. But at the end of the day, you have to put down a budget and say me, if this is what this movie cost. Either you got it for free or not. So, sezi se mati nimetengeneza ma pesa. But I also appreciate I don't want to complain. Whatever I have, I thank God that I'm able to sustain myself. My family, I can cater for my basic needs. Neneza patia, atotwata healthy, issuarens, you know. I can try and build a few things. In that, nisekwena stragul sana kamamsani. In that, whatever I want to achieve as an artist, I'm able to achieve. So I do a lot of saving. Every income that I get, I do like 30% before anything. For the sake of my art and why I want to take my brand. So, I can't complain. Among all your characters, Terence, which is your favourite and which one do you consider the easiest to execute? Every character that I have from Terence Creative, the brand, all of them appreciate them because each brand has taken me from one level to another. I started with Kamami. It introduced me to the social media world. I brought up Kiateka. I can't play Kamali. I handle all my my characters equally and I try to give them each of them their attention that they require for them to pop out. So I can't sit here and say, this is better than that. Each character contributes to Brand Terence Creative. So I treat them equally and I pay attention to all and I invest in all equally. Yes. I ask you, Malizia, quick for your question. Number one, what is one trait that you appreciate the most in your wife? Very consistent. Never giving up and she's very loving and forgiving. Yes. The biggest lesson life has taught you so far? The biggest lesson that life has taught me not every friend is meant to work with you through your entire life journey. Okay. Now next question is what character traits if a friend possesses they can no longer be your friend or rather just a person possesses they can't be your friend? Someone who intimidates the poor. Okay. Someone who is so much proud. Someone that disrespects God. Those one I cannot. Yeah, because if you, I normally say if you're not, don't look down upon anyone unless you want to leave them up. So if you don't come away in blasphemous, we respect God, we're any pretender, you know. Those are the traits that I do away with. I normally don't lose friends, I categorize them. So I put you in your category. Nadia, are you? Right, alright, alright. Next up. I quit and so you need. But I don't like pretends. I like real.  So if you can't be real offline then I don't see how we will be real online. So we have to be real offline before we come online. Second last question. What is one thing that celebrities in Kenya do that you consider something you just can't do? Something that I can do ignoring funds like I can't stop. I can't stop for a fund to take a photo, you understand. I can't reply at DM if I have an opportunity. So one thing I don't like doing to my fans is being a snob. Because I've been snobbed. By people people who snob me right now, sorry to say, we're in the same industry right now. They go for meeting brief. I am there. But there are people who snob me so badly when I was there. But I've never even told them because I'm not here to say on any at you or on any other how. Who is laughing now? No. I've been through these things. I've been snobbed. I've been humiliated. So I really try ataka mani mechoka. I really try not to do the same to my fans because they are the people that have grown me. A behavior that you had to change for you to move forward in life? Too, I had to quit smoking. Ya, quite a smoking. And there is another addiction. I won't mention. I also quit that. There are actually two addictions. For the last five years have been amazing for me since I quit. Bonus question.  What is that one value that you want to instil in all of them? What I want to instil in my daughters is value humanity and the future. The future. I normally say the future will question you. So whatever you do today just remember that the future will question you tomorrow. So you have to be very responsible and very careful with what you do today because the future will question you. And when it's question new you better have the answers. Alright guys, there you have it from Terence Creative. Asante. And congratulations. Thank you for watching our Netflix and of course getting us to watch your film Icon the Movie. Ya, wakujekwa www.terence.ke So we are streaming it from 22nd.


Now this should be the pie you make for Thanksgiving. This is it. This is the shining star, okay? And it's the best of both worlds because it's the sweet potato and the pecan pie in one. Hey, it's Timmy with Collard Valley Cups. Good to see you. We are making a sweet potato souffle pie. Sweet potato with pecans. All right. Out with the streusel top, I am actually making my sweet potato souffle recipe that's in my first cookbook, except that I'm having it. So I'm using a half cup of brown sugar packed, about a half cup of nuts, and we're going to chop this up with this chopper right quick. The first time somebody sent me this as a gift, and the first time I used it, I've never used one, and I had it on flat surface, and I was like, oh, you have to chop with that in a bowl. And it works really good in a bowl, and I didn't know. And so I get to use it today, because it's working great. Then we're going to add the butter, okay? So we're going to add, this is actually margarine, I guess about three tablespoons, three and a half tablespoons, something like that, close enough. And then we want to put just a little bit of flour in it. I'm going to say about two tablespoons, maybe, and we're just going to chop it all up. Actually, I'm going to, well, I don't know if my blending fork is clean, I used it to do the pie crusts. Let me get my blending fork. So you're just going to mix this up. Now a lot of people like marshmallows on their sweet potatoes, and some people like oatmeal, and I've tried it all different kinds of way, and some people like coconut, but this is just what I like. I don't like coconut, I don't like the oatmeal, I don't like the marshmallows, I like it this way. You make it how you like it, because you're going to like it the way your mama made it, or the way your grandmother made it. Keep pressing it in until you get a nice consistency strudel, strudel, whatever you call it, and that way you can sprinkle it on the top of the pie. So we have our potatoes, and this is going to be in a steamer pot, and I'm just going to put a little water in them, put a lid on them, steam them, but when I first opened them up they were just bright colored, and because we didn't hurry up and get them in here, they turned just a little bit brown. That's just three really small to medium sized sweet potatoes. So we're mixing up the sweet potatoes, one reason I do this is because I like it creamy and fluffy.  You know what I'm talking about, it's got a lot of fiber in it, so if you use a whisk and you mix it up really well first, and you turn it off and pick it up, pick it up, you can, if it's real hairy, then they're just stringing all over the end of the mixer, and I actually get them out. This one looks fine. It's fine for it to have a little fiber, but you just don't want it to be, you know, grotesque fibers, fibers, and you may surprise sometimes you get a potato that you just really need to help out a little bit. So we're going to start with our potatoes. It takes about a cup and a half to make a pot, okay, stick a margarine, it's a little bit more than a quarter stick, but that'll just make it take better, right, and then we're going to put in a half a cup of sugar, half a sugar, put in a half a cup, you know, good, I have a jumbo egg left, maybe I don't, it's pretty big, extra large, I'm going to put in an extra large egg, that's ready to mill, and we are all adding some whipping cream, so I'm going to use my supply recipe. It's nice and fluffy and creamy, it's in the sink, and we're going to get out it once a lot, right, come here baby. Now this is a pre-bake until it's brown like you would for a pudding pie, but just a little bit of pre-bake so that your crust gets nice and done on the bottom with one that I like to pre-bake every crust, okay, if you're going to store by it, don't worry about it, but sure, you roll it out thin, we're going to put this in here, be the pie you make for Thanksgiving, this is it, this is the shining star, okay, make sure you get enough potatoes in there, I could have used probably another half a cup of potatoes easy, and don't worry about measuring it, just perfect because it will fluff up because it has those eggs in there, or that big egg in there, now we're going to put on the streusel, I don't know my mama always made it, this is my mama's recipe, and boy does everybody love it, okay we're going to use every bit of it, and this is like I said, if you have my first cookbook, just use my sweet potato souffle recipe, and half it, and put half of the filling in the pie, half of the streusel on the top, and you will have a sweet potato pie, what we have, go ahead and show them how pretty it looks with my leaves on the top, but this is the perfect pie for Thanksgiving y'all, they made things in Publix, but you know, if you make it at home with my recipe it will be even better, but if you're in a pinch, use theirs, I'm going to put this in the oven, and it's the best of both worlds it's the sweet potato and the pecan pie in one, it pretty much really is, the top tastes like a pecan pie, so we're going to get this back in my little oven and we're going to cook it for about, it's probably going to take about 40 minutes or so, you're going to want the sweet potatoes to be fluffy, and be done all the way through, and they'll start fluffing up around the edge first, and you'll see the pie rise around the outside edge, and then once that middle part comes up and stands up and starts to fluff too, then you know your pie is ready, if you're afraid that your ring is going to get too brown, make you a ring with, we call it tinfoil, or get you one of these, their cheapest dirt, and lay it around the edges, once it gets to the goodness that, I mean, you know, as brown as you want it, then lay this on the top of the pie crust, okay, I'll show you how it works, Chris, go ahead and show them, you just come in here and you just lay it down on the top like that, once you feel like that your crust is as brown as you want it, alright, we're going to turn this pie on, I'm going to bake this at 350, and I'm going to put it on 40 minutes, I'll check it a little early and put the ring around it if I need to, I use, I make it just like I do my sweet taste of clay, so if I put it in a pie crust, we have made a homemade pie crust today, I have got one mayo sithriath and flour and butter, and I've got one that's made out of plain flour with butter flavored crisco, okay, I'm going to use this one, this one is a lot more dense, you can tell, and thicker, and this one's real light and airy, okay, this one is the one I'm going to use for our pie today, for this pie, and this is just a one and a half cup of flour with a half a cup of shortening, a tiny bit of salt, and five to eight tablespoons of ice cold water, okay, so there it is, and you just lightly flour your surface, and I'm just going to press down to start with, now I'm going to go ahead and roll it out as much as I can, just like, there's a stupid nap in here, I'm telling you, when you turn on a camera, it's amazing what comes around, so when you roll a pie crust, you're really supposed to roll, turn, roll, turn, roll, turn, and it's just, you know, monotonous, and I'm an impatient person, so it's kind of hard for me to keep wanting to turn, and turn, and turn, and but that's the key to getting it nice and round, okay, so just dust it with some flour lightly, roll, turn, roll, turn, roll, and the crust needs to be pretty big, it needs to be rolled out about an inch and a half past the edge of your pie plate, and I'll show you how to measure that once I think we're getting closer, now let me just show you, here's the pie plate, and we're not quite there because you want to be about an inch and a half past the outside of the pie plate, and you can wet it and piece it back together in places if you need to, if you got a couple of little stubborn places, okay, that one's going to work, now what I'm going to do is I'm going to sit this here, I'm actually going to trim it before I put it in the pan, quite big enough on this side, I have to trim it, but it just makes it easier once you get it in there if you do, I used the backside of that knife so it wouldn't cut up my table, okay, now I'm going to pick up this plate, and you can dust this a little bit if you want to, if you're afraid it's going to stick to it, but it shouldn't, and then we're just going to roll it up on this and just roll it out in the pie plate, now you're going to pick it up and make sure that it fits very tight down in the bottom, and then now we're going to do the edges, I just take my fingers and pinch to make a pretty, and you can kind of make it a diagonal shape, oh that's what you do, it's simple, and sometimes you got a little more crust than others, it's just according to how you aimed it in the plate, and you can kind of fold it over and make it and mold it because it's still soft, it's got plenty of shortening in it, so it should be pretty when you're done, a lot of people make videos in all the different kind of ways you can do your set edges and all that, but I just do it this way, I think if somebody's getting a homemade pie crust they should just be happy, I think it's pretty, it's always beautiful when it comes out of the oven, it's simple and easy to do, because all you need is just your fingers, and then I usually go over it one more time to make it more uniform, and now we're going to mix up sweet potato filling for this, now you don't have to pre-bake a pie crust, but I like to, so I'm actually going to place this one behind us in my little convection oven and let it start pre-baking just a little bit, I like to pre-bake on about 10 minutes, so we're going to put some holes in it, I'm going to put this rack in my convection oven, I'm going to get out something to prick some holes in it, you can use a fork of course, and you do this just so that it don't blow up and get all bubbly and mess up the pre-crust, it has to be preheated, it's a convection microwave, I am going to put it on convection, and I usually keep it on about 400 when I do this, now if you're baking them in a regular, but you could go 375, and we're going to go about 8 minutes, and I'm going to press the start button, now we're going to make our sweet potato filling for our pie, so I'm just going to, you know what, we could cut out a couple of leaves, let's do that right quick, we're going to take this and we're going to cut out a couple of leaves to go on the top of our pie, it only takes a second, so I'm just going to ball it up a little bit, smash it, roll it, you can tell it's going to be flaky, I want you all to see this, do you see that, how that separated, do you see that right there, and then look at how these layers are in there, see how they're, it's going to be a delicious crust, I can guarantee that, it looks flaky on the table, okay, so what I do, when I do this, roll it out thin, now you can get little cookie cutters and things like that, or you can just use a knife and make some leaves, trying to look at a, I like to be able to look at a leaf, but there's really not any in here to look at, so I'm just going to make one, this is going to be the big one for the top, and then I'll make a couple of little ones, okay let's make a couple of little leaves, we'll do three, don't fret over stuff, if you don't have a, just you know, it'll look like a leaf, leaves are all different sizes and shapes, so we'll put these on the top of the pie, well you know what, we don't have streusel on the top, but we'll still put them on there, you could put hearts, you could put, I mean whatever you know, whatever the occasion is, there's the little leaves, and here's a nice larger leaf for the middle, alright, so we got a little extra dough, it's not money though, thanks for watching Colored Valley Cooks, where we cook Black Momma D.


Okay, so good afternoon. So this is actually the continuation of the previous talk about Maintaining accessibility on a long run through testing So just to make a quick poll do what do you think is the accessibility problem of this? What is the problem with GNU plots for? the colors red and green is the In the worst choice of colors to do because a lot of people actually can't distinguish and then Like 8% of the people of the male people cannot distinguish between the two Or at least have problems and then with group plot 5 they improved this so you see I mean just wondering How many people here please raise your hand if you are colorblind in the room is there somebody no But that's 8% normally so statistically there should be 1% at least Anyway So what is accessibility? What to make it simple it's making something usable by everybody whatever the specific needs situation Etc. So of course, it's blind people deaf people etc. But also people with cognition issues I don't know all people have problems with Understanding your your software things like this on motor issues You cannot press a shortcut because you need your both and both your two hands and you don't you have only one and Quite often it can be you because you have a package and you cannot type with the two hands or a Lot of people here have low vision and you're lucky because you have glasses with which you can wear all the time all the time, but Some people cannot have this There's a poll which says actually 10% of the people are really handicapped in their daily life and 20% would say that they are limited in their daily life due to Conditions whatever the thing is it's it's really it really is a matter for everybody actually and For free software, this is really about freedom zero the freedom to run the program for any purpose Okay to run but More to that and to be able to use the program and then there's the second Freedom freedom number one. This is free software. You can modify it. That cannot happen. I will explain why It's question of priority as was mentioned previously. It should be prioritized It's actually just like security and internationalization In the rest of the talk really try at some points thinking yes, this is like security and Internationalization it's the same kind of we have to keep it in mind all the time and The question is who is doing this the problem is it concerns just some fraction of the people they are they are already having a hard time using computers and Having the skills to actually program modify the program. It's even less people and Then you have people who have programming skills and could do something on this But then being aware and understanding what needs to be done. It's even less people So there's really extremely small fraction of the people who can actually work on this So the sentence this is free software. You can modify it that cannot work actually You could say okay, let's pay some people to do this Okay, so we have some people which monitor all the software in the free software world So we would need a lot of people keeping getting updated with all the evolutions we have here and there And so we have for instance in January at EGALIA who does this on everyday life But he cannot do everything. It's not possible and spending your whole day. It's just debugging things It's really more than painful. So no, it's it's not fearful as a solution so the support has to be Spread among every developers Integrating into their development process just like security just like internationalization Nobody develops a software without taking a security issues into account nowadays or at least they shouldn't really Accessibility is the same kind of priority Just to give the low things so the You know rights of persons with disabilities So I put everything so you can read it offline, but basically discrimination is Exclusion on the basis of disability including denial of reasonable accommodation So even if you don't do this on purpose, it's considered exclusion and reasonable What does it mean not imposing a disproportionate or undue burden? Okay? It's not much more clear, but at least it has a legal meaning and disproportionate The question is how to make it proportionate So we will propose a regression testing So there are two things For start we want to avoid introducing new issues. So everything that is Developed nowadays should not have accessibility issues by pointing them out as soon as the development While the programmer is programming the tools tells it. Oh, this is bad. This is bad This is bad. Here is how you should fix it and then the programmer learns and then he will not do the Mistakes again. So that's an extremely important thing to not go back Make sure that we don't have new issues While we still have the old issues That we have to work on so we have a list and then okay We have to work, but it's a second priority after making sure new things don't get regression So what are we talking about technically? Just extremely briefly the idea is we want to make the same software accessible For a lot of reasons I don't detail but basically we can't reimplement LibreOffice for instance So we have to make it accessible The idea is you have your application and then the screen reader uses an accessibility bus to access the abstract representation of the application and This is basically a tree of widget and then okay. You have all the information cool a lot of toolkits Provide this information. That's fine But the problem is it doesn't mean that it's necessarily usable because maybe you have this dialog box and Maybe you implemented it that way So you have labels and then you have text and there's nothing that relates one with the other So ideally you would say there is a label for some text But maybe you have just written your code that way or maybe it's the XML file you use which imposes that way of doing it Okay, we could say sorry about this You could say that the screen reader should have a script to fix and to know that it should relate one with the other But it's not viable on the long term because the screen reader then gets a lot of ugly hacks And it's not maintainable on the long term with each new release You have to fix to update the hacks. It's not really something we want Instead you should just declare properly the relationships between the widgets. Sorry To declare them properly means you say that this text is labeled by this label. So that's what we will focus on Just some takeaway slides. I don't detail them because I don't have the time But basically design logically without taking into account graphic things use standard widgets use labeled widgets make sure you have logical rejections hips and keep it simple and Making it simple will help everybody actually to use your software You can try accessibility tools You can enable enable the screen reader and see what happens and try to use just a keyboard Don't cheat and see what shows up on the braille device If you want there is a debugger to check exactly what is there okay, but Maybe it's not something that we should promote because it shows that it's quite a lot of work to work on accessibility Well, maybe we can do a lot of things without going that far So trying to use automatic tests in continuous integration And that's what we propose as a first as a first step now To try to avoid some classes of new issues and still have a fix me list to fix the previous one The idea is that that way we can make people aware of the question with easy enough to fix issues And then okay, they take that into account and then maybe later on we can expand the kind of things We want people to keep in mind all the time when they are developing So about regressions, you know about what regression so you move one step forward But actually you go two steps forward and two steps backward because a new feature breaks an old feature a bug fix Breaks a feature you have regressions here and there so you need regression testing and user testing Concerning accessibility. It's way worse Usually when you make one step forward, you actually have ten steps backwards and new features are just not usable at all quite often And bug fixes break usability completely quite often And user testing doesn't work because there aren't so many concerned users and it's difficult for them to test the development versions of your software And the developers themselves don't have any idea on how to actually fix it because they are not accessibility experts So how to test this what what should be done So regression testing could be an idea to make them learn progressively So new features they should be hopefully usable that is there are shortcuts There are logic relationships is that convenient maybe not but at least the new feature with some effort should be accessible I mean the person who actually needs accessibility maybe it's not convenient but at least it can achieve the task with more time that should be ideally be needed But at least it does work and for the old features we should make sure that they remain usable So there are three things we are thinking about right now which are relatively simple So labels with widgets all widgets should have some label which says what it is about except maybe some special cases Labels conversely if they are there for the visual rendering that's probably for a reason And so if there's a label without a widget attached to it probably there's something problem Like somewhere and also shortcuts all the widgets should be reachable through shortcuts So maybe pressing tab or maybe it's in the toolbar and so you have an F something shortcut to be able to access it quickly So maybe these are the really simple rules that could be tested automatically that we can enforce and make sure that they will always work And that's already a huge progress compared to what we have nowadays So how to test this? We could try to test online so run the application and check that we have labeling But it's quite expensive it's low and okay but which source line corresponds to that widget it's difficult Maybe we can do that inside the toolkit but it's also the same problem how do you get back to the source code Okay maybe there's research to be done here Static analysis passing the source code I don't really see how to do this at the moment I mean it looks not so easy But a lot of applications use Glade so XML files basically and so what we've been working on and will work this month Is a tool which shows the warning so saying that this widget doesn't have a label for This label doesn't have a widget attached and this widget doesn't have a label And there are actually like 16 lines apart so probably actually these two needs to be related and that's all So it's really simple to fix those and hopefully this tool will allow to make that easy So of course we have other issues like there are multiple named Mugnik for one widget Or the link is actually broken okay these kind of things we can debug automatically And we can include that in the build process So we've been running this on LibreOffice and we got like 8,000 warnings That's a lot we can start with compilation 8,000 warnings So we want to implement a notion of suppression which says okay these 8,000 warnings we have to fix them at some point But they zero we have zero warning and we remain at that And if there are new warnings okay we fix them and then when we have time When we take the time to do we fix those old warnings we have suppressed And then we should be able to make progress actually There are false positives sometimes you say no no this actually is not interesting to label or some things Probably we can automate some of these and mark those which we cannot automate because it's really on the semantic We will be working on that this month so to have a look at all of these Try to sort them out see with the people what they prefer the way they prefer etc So that's the HIPRA company and Martin Peuchot wrote the initial tool and which we will use and extend And that's funded by TDF so it's on some JIT from now Probably we would try to move it to some place like maybe at GNOME or JITLAB I don't know we can discuss our idea is that it should be as globally used as possible It doesn't have to be only for LibreOffice maybe there are LibreOffice specific things From what I've seen in the 8,000 warnings I probably not so many LibreOffice specific things I guess So to conclude it's really a problem for a lot of people and actually as I said before It actually helps everybody when you have shortcuts to do your daily work you actually save a lot of time So and making the software simple etc it really helps for a lot of things But we need to raise awareness on this and regression testing maybe is a nice tool Starting with just a few warnings and see how well it is accepted etc And then get to integrate accessibility in the development process itself To enforce the things that ok we have agreed on enforcing making sure that it's always like this Just like security and internationalization I haven't talked about keyboard shortcuts but yeah we will also work on this just not now Thanks so we stay here for the weekend maybe just one question So can the script be integrated inside Glade? So I asked on the Glade mailing list they didn't answer I'm not sure Glade doesn't seem to develop so much but yeah that was our idea Saying that ok there's that Glade tool and ok integrate The thing is a lot of people use UE files but without actually using the Glade library So I prefer that it's just one script that people use Just like lint like valcrin valcrin is not inside the compiler I don't know but I mean we are open to whatever Yeah 8000 yeah usually yes So for instance I didn't show it but the sort dialog box there are 8 warnings and yes there are 8 issues Quite often it's a small issue that is you have the word ascending and descending And you have to know that it's the sort things And it's just leaving ascending and descending with the sort word It's small but it helps a lot actually And it's really easy to fix