Thank one matrices with mismatched, please go ahead. Thank you. Thank you everyone for the opportunity to speak I'll be I'll be presenting some recent work that I've been working on with at least like a and I'll be presenting some recent work I've been working on with my least like a and flora and it's related to estimating Require matrices and in particular I'll be focusing on two problems. One is universal And the other one is large deviations so I'll first begin by introducing the general setup for this inference problem Since I'm a Mathematician, I will sort of also go over how I see the theory of large of large deviations I will go over the main results and how large the reserve connects to this Bayesian inference problem As well because I'm a mathematician I'm obligated to tell you at least some ideas of the proof and at the end I will serve To end with some open problems and what is next with respect to these problems? So let's let's start by defining the model that we'll be working with Let's consider a very simple and Somewhat Generic inference problem. So this inference problem is I want to infer some signal So I'm my signal has a very specific structure. It's a rank one matrix of dimension n by n and It will be generated by the outer product of a vector with IID entries So this factor x zero will encode my signal matrix and it's a vector in Rn and all of my entries will be generated independently from this probability measure P zero and I'm going to observe a noisy version of this signal So what do I mean by a noisy version of this signal? Well my noisy version will be a matrix Why which is another and by a matrix, but it's its entries will be generated randomly independently and conditionally on my signal matrix that I wanted to To observe so my my matrix why I'm going to assume that it will be symmetric because my signal will be my signals also I'm symmetric and These entries are why it will be generated from some output channel I'm going to denote it by this condition probability measure with this subscript out on the bottom and it's going to be generated conditioning on my signal and there's a funny little normalization term on the On my matrix This is there just because this is the right scale to look at things so that the problem isn't too hard and the problem Isn't too easy. It's sort of the the right scale where interesting things happen and A classical example of something that falls under this so much generic framework is the spike matrix problem So let's assume my signal is a random rank one matrix and I'm going to generate my data Why conditionally on my signal in the following form were generated from a standard normal? for not a standard normal from a normal the distributed random variable with mean given by the corresponding entry of my signal with variance one and This this is I'm equal in law as why is I'm equal to some additive Gaussian noise added to some normalized version of my signal matrix Okay, so my goal or my problem is I want to somehow estimate or want to guess what this signal matrix is from my observation and Classically, what's a nice guess for what my For what the best estimate will be well one way is out of all the possible functions of my data I want my estimator to minimize some some error when one thing we can do as well on average I want to minimize the differences of the squares of each of these entries of this matrix on average and The best estimator will be given by the by the conditioner expected value of my x zero given my my data y so Moving forward I sort of want to understand what this conditional expectation is because this will be the object that will minimize the mean square error in this problem associated to this problem is the conditional probability measure and By a base here, we have all the parts to sort of have a very nice explicit form for it So we can write the conditional probability that my X by my signal matrix is equal to any particular value conditionally on my observations Why I can use basiom to write as some ratio and I can use independence to write it as some product of all the entries of These of these of these objects and this p0x is is a on-product measure I just I just did not put the tensor on the top to simplify some notation and Related to this posterior probability, which is related to the optimal estimator is another quantity this Statistic wouldn't call it the overlap and this overlap will be defined as the inner products between two vectors One vector is my original x zero vector Which was what appeared in the signal and the other one is the inner product with my with my guess So a sample from my posterior probability measure from this G optimal that I'm going to call it and I'm going to take the inner product between these two objects and This sort of loosely measures how close my estimator is to the original signal so Sort of the magnitude of this corresponds to how many are entries I've Guessed correctly or or what's the angle between my estimator and the original signal? I want to guess and this this parameter this statistic is a very fundamental object and that if I want to compute interesting quantities such as the free energy The mineral means great error this behavior of this overlap sort of encodes the order parameters for these models So I'm good bit be a bit more precise of hopefully I can now motivate where does this overlap appear And why is it somewhat somewhat interesting? I'm just going to return to the spike matrix example because everything's simple and explicit for this problem From this model I have an explicit formula for the posterior as mentioned before I can write down what this is. So in some general formulas, I now have a somewhat explicit explicit form for this condition of probability measure and If I expand it out then Then there's gonna be a term of this Hamiltonian Which will it will appear in the exponent minus some term that only depends on why we don't really have to worry about it since it will sort of cancel with the factors on top and associated with this is somewhat called your free energy Which is one over and expected value of the log of the normalization term in this probability measure subtracted the terms only depend on why and This should just be the h n of x in the exponent here and this quantity this free energy sort of encodes the behaviors for this conditional probability and that if I take if I take the raises with respect to lambda parameter, I can recover certain moments of of the term that sort of encodes the behavior of this probability and Placically this limit of the free energy was proven. It's It's proven by the large and Milan is given as some variation of problem It's given by the supremum over some parameter of an explicit function that that depends on it prior in some very specific way and These overlaps are sort of important is In these in these types of models we observe something called overlap concentrations So the behaviors of these overlaps in the high-dimensional limit they sort of Average or deserve concentrate on its expected value. This was proven for in general after a small perturbation to this to this measure by John and From here we're sort of able to We have some really nice behaviors of these overlaps to these problems and this parameter q that that appears in this in this Optimization problem this some q corresponds to the expected value of the overlap up to some up to some smoothing of the gives measure So this is the classical setting and this is a classical result for spike Matrices we're gonna move on to a slightly more challenging setting This is more realistic setting in the sense that if you have a normal statistician like myself I might not know what the prior is and I don't know how the data is is I'm generated So I will make my own model and from here I can build another Another another condition of probability measure that might not be the right one So this y here was generated from the P zero and the p out that I defined way back But I'm gonna build my own model since I don't know what this is exactly. I have some guests on what the prior is I had some guests on what the on what the output is and I can define a I can define the associated probability measure with these guesses and again I can look at what the overlap is it is it's gonna be the inner product between maybe not the optimal estimator but some estimator based on my best guess and the original signal that we saw before and This mishmash setting is has been studied recently by many people in this in this room in particular Jean Barbier and Francesco Francesco camellia camelli Marco and Manuel So this is a somewhat more complicated setting for a friend. It will be called the mismatch setting and Again, let's just do a concrete example to Do our demonstrate these ideas. So let's return to the spike matrix example and Let's say that I know that my dad is generated from some from some spike Gaussian additive noise But I don't know what the prior is so I'm good to guess my guess is My signal will be generated with taking values plus one minus one with probability one half I Can build my conditional probability measure and again, I want to understand what's the free energy for these models for example, and the only difference here is my px here is different than the p0 that appear before and this this limit of a different energy was proven by Francesco and the co-offers so this limit of this free energy is given by some again some other variation of formula and This variation formula in this mismatch setting is already much more complicated than what we had before There was some explicit term that peered over there now I won't I won't go over what this is, but it'll be the solution to the SK model at some external field and some temperature beta I will make it a bit more precise later once I once I explain the other results but there's some it's there's some explicit formula for it. It's a bit more complicated and And I just want to show this just because in a mismatch setting even the limited free energy becomes much more complicated for these problems and now you're probably wondering or Why am I focusing on all of these spike matrix to these models? They are nice examples because objects are are explicit but how is this related to the general difference problem that we were interested in or die that was interested or that I introduced at the beginning and this connection will be connected through something called the universality of the overlaps and I'm going to be a bit more precise about what I mean about universality and Before I could explain what this universality is I want to introduce or at least review What large deviations are? So our least large deviations in the context for these inference problems So suppose we're back in the optimal case I know that my overlaps concentrate and if my overlaps concentrate Let's say I want to say something a bit more precise than just concentration Let's say I want to find some estimate on what's the probability that my overlap deviates from its from the value I just concentrate on so let's say I want to compete what's the probability that my random overlap deviates from its from its expected value and And I want to sort of make this precise with two parameters So I want to find out how fast is this exponential exponential decay So I find out what's the exponent on this on the exponential decay and also when you find out Well, what's the what's the coefficient in front and this coefficient can also depend on the empty So this is some form of concentration in Inequality we sort of want to find out what's the probability that it's that is sort of deviates from its expected value and Large and large deviations you can think of it as a more precise version of this So I might classify for any rare event a and to find some some constant and some speed so that I want to compete What's the probability that my overlap lies if in this set and this the set I want I'm going to insert and less than or Equal to I'm a sort of approximate equality at least up to the first order and If I take one of when to the alpha and the logs of both sides It sort of means I want to compute probabilities of this form So can you give us a probability that my overlap takes a certain value? We know that it I'm concentrated but at finite end. This is still a random object So I want to see well, what's the probability that it takes some off takes some value and this N of alpha and the speed sort of encodes Serving codes where this value is so All of these objects can be encoded by something called the rate function and the speed and this is encoded for something called the large deviations principle So we'll say that a sequence of measures in our case dark sequence and measures will be the laws of these overlaps under the Under some maybe some posterior measure either the optimal one or the one from mismatch So I want to understand the laws of these overlaps and it's encoded by two objects One is the rate function. This rate function is a nice function. It's lower semi Continuous if it is a even better rate function if it's a good rate function in all of its level sets are also compact So there's some there's some nice function I and There's a function a event which it encodes our speed and basically what it says is the log of the probability We had before will be upper and lower bounded by some infimums over the sets of this rate function and the intuition or how we can think of what this rate function is is The formula we had before of it dilemma one over end of the log of the probability of a set a is given by the negative Thememe over this set well on one end the one over end log of the probability is like the integral of my measure And on the other hand when a n is big then you would expect to just integral on the right hand side Will concentrate on the near map on the maximizers of i of x in this a which is precisely what we have here Or the minimizers I guess in this case because it's minus sign so This rate function i is sort of the density function Corresponding to the mu of n so you can think of this i of x as sort of Encoding the probabilities of these rare events in some simple way So this rate function encodes everything that we need to know up our understanding these rare events and a classical example for this or a concrete example is Is on is on chameleism which tells us the behaviors of a certain statistics, so let's take IID and IID random variables and want to compute what the sample mean is in this case, we know that a sample mean concentrates by the law of large numbers and We have an explicit formula for the probability that the sample mean debits or the sample mean takes certain values So this rate function will be given as the log of the expected value of its moment generating function You could take it some Lejeuner transform, which will be the supremum of its convex of this of lambda of x minus the minus the log moment generating function and this this Lejeuner transform of the log moment generating function encodes the probabilities for these rare events As in it was given as the up as this supreme over sets in the set that we are interested in Okay, so so this lambda star will be the rate function for sums of IID random variables And this has a direct application to what we had before in the sense that let's say our perfect information My estimator is precisely what my x zero is in this case My overlap just becomes the sums of the entries of my signal vector squared And this is a sum of IID eight variables because I'm assuming that the entries of my signal are IID So cremation actually tells us what the what the large deviations are for this overlap It says that the log of the probability on the overlap takes a value in any set We'll be upper and lower bounded by the infimums of this rate function Say by some supreme of some prime of lambda minus some log moment generating function And this form will be important to remember for the results are to say later on And now I guess the question is well Can we generalize this result when the case where my overlap has a very simple structure to the case when my estimators are from these general probabilities that we observed before and now I guess I'll be explaining what the main results are at least what we managed to show So the first result is a universality result To go in line with the topic sort of female disconference So I'm just going to find a few few objects So I'm going to find two log likelihoods one log likelihood is the log likelihood of my of how the data was I'm generated and the other one G without the zero is the log likelihood of My uninformed guess on what I think this log likelihood is going to find free free on different parameters I'm going to call them Fisher score parameters that they're just functions of Average over my data why assuming no signal? So I guess this is sort of the behavior of the way my dad is generated in the absence of any signal So in this in the spike matrix model just to be like average over standard normals because when there's no on signal then you just have the additive Gaussian noise and You have these three parameters that serve only depend on the first and second derivatives of my log likelihood functions and the inner products between them and In the simple case when our guess is perfect, so in the Bayesian optimal case when my One might guess for the log likelihood and the actual log likelihood are the same Then all these parameters are actually all encoded by one parameter called lambda then the mismatch case these parameters may be different I could define two likelihood functions. So one likelihood function is the is the Or one Probability measure will be the probability measure that we observe before just some normalization by some fun That only depends on why I'm just going to include that here or I'm going to subtract it off since since we need some extra normalization and The other probability measure. So this gn of y is the probability measure corresponding to the original reference problem and this other probability measure z and of beta or gn of beta will be a Gaussian measure corresponding to what appear to be in this in the spike matrix problem We had before except lambda parameters are replaced by these free temperature parameters We had before and this and this model this Hamiltonian isn't new This has been this is precisely the model studied in the work by by on Francesco And we're just looking at the giz measure for this model So here's our result for universality, so we got to assume a few things They could probably be weakened But I'm going to assume that the that the way that that is generated and my under form prior I'm going to assume those are compactly supported. I need to assume sufficient regularity on my log likelihood So it has to be at least three times differentiable and there's also some bounds on the On the first and deferred derivative. There's some funny condition as I need some consistent estimator estimator condition and the intuition for this is At least in the spike matrix model in the absence of a signal I know that my dad is generated centered so my additive noise is centered It means that as the student as the if I make my guess of how the dad is generated It also has to be centered so I do preserve the mean somehow. So that's the intuition behind what this consistent estimator condition is and I'll be looking at the joint law of two statistics So one is the overlap they saw before which is our inner product between our signal and my estimator And I also have some R1 when overlap the self overlap, which is just the length of my of my Sample the reason why I went to it went to look at the joint law of them both of these objects is The value of the norm or the norm of this X sort of encodes the behavior of this overlap So if my vectors X is very small the overlap would naturally take very small values Just by the Cauchy Schwartz in E in E quality and I sort of want the overlap to sort of measure how close we are I don't want this negative to be really influenced by the size of the vector So one way is I can like normalize it by the overlap or I can just look at the end look at the end joint law together So what my what the large deviations results says is that? If I take my beta parameter to be encoded by the Fisher score parameters I defined before which is the expected values of the part shows of the log of the log like it's so my beta's take this very specific values we saw before then the joint log of the overlaps under the original gives measure and under the gives measure that we saw That we saw with the beta half parameters. They satisfy the same almost sure large deviations principles so the probability is very events are the same and It's almost sure large deviations principle because these problem measures actually random they they are They depend on the the They are generally conditioning on the why so almost surely no matter how we How we generate them to satisfy the same large deviations principles They have the same probabilities rare events and you also get for free that the free energies are the same for these for these inference models Okay, so that's the universality part is that These spike matrix models that I introduced as toy models are precisely what we want to look at and The next object is well can we compute what this rate function is and now I will sort of go over what this P symbol? We saw before so just P symbol is it can be defined or this preasy function it can be defined with two two sequences of of Of on parameters there are some explicit form and I don't want to go too much into I'm deal of how this formula looks like but I just want to point out that if you recall what the What the on Kramer's theorem was there was a infimum over lambda and you of some linear part minus the log Moment generating function of some object. So this is the linear part It's the log moment generating function of the other object. So from Kramer's point of view. It's sort of generalizing the large deviations principle to when I have some extra terms in the exponent corresponding to my new Gibbs measure and If you're from a spin last point of view, you could think of this is the standard preasy formula But since I have some probability here. I went I have some extra part that sort of is Is influenced by the probability of this event and this is the The Kramer's theorem part. So you think of it as some spin last part added to it The Kramer's theorem part or the Kramer's theorem part You just add to it some spin last part if you're unfamiliar with either one there was just some explicit rate function out that we have and This is just to make things precise. This is a possible domain of all the overlap So if I take linear products of my overlap and myself overlap The possible values are sort of bounded within some sets So so these are these are possible values of my overlap. They can't take all values since you're generated from probabilities with them with them with certain assumptions out of support So so the max max values have to take certain values and the C encodes the sets of possible values and Our result is well We have a almost sure large the large deviations principle for the Gibbs measures so the joint law under our General beta parameter. So for any choice of beta parameters, it doesn't have to be the special ones But for any choice of beta parameters I will have a rate function which is given by the negative of the function that we had before on the supreme over It's possible values. So this rate function will be infinite if my values of my overlap SNM are not within its feasible values Which means that I'm just taking the log of a zero. So it would be negative infinity and if it is in the set of possible values then it's Then this large deviations or its or its rate function to probably are very fancy be encoded by this rate function here And it's almost sure in a sense that this gives measures random But for almost all realizations of w and x zero we have a we have that it satisfies the same Rate function, so this random probability measures holds this result holds almost surely for this randomly generated functions Gibbs functions and As a consequence if I take my betas to correspond to the parameters we had before We have a formula for the rate function I can also take rectangular sets to optimize over a self-overlap if you if you don't want so I have the large deviations of these overlaps from The inference problems I had before so almost surely for all observations for my y I have some as I have some rate function that's given by the same object as the beta parameters had before okay, and As another free result we get we could compute the limit of the free energy We so I get the limit of the free energy for free just by optimizing over the rate functions and If I know my rate function has a unique minimizer at some s and some m Then I know that my overlaps will converge to s and m almost surely So we have another way to show concentration for these models just by looking at the minimizers of these rate functions Okay, so those were the main results it was basically It's basically saying that The inference problems or these overlaps generated from these general inference problems Are the same as the overlaps generated from these spike problems with a very specific choice of beta parameters And we also have a function that Encodes the probabilities of these rare events So we know that these overlaps at least they're universal in the sense that their rare events are given by the same By the same types of rate functions and these are almost your large deviations principles Okay so I have 12 minutes to go over Some ideas of the proof and I think I will just have time to go over the ideas of the universe alley part and What I'll do is I'll first show a quench universe alley part and then to get to something that's almost sure we we use basically some concentration and I guess precise estimates on all the errors to sort of go from quench to almost sure so the log of The free energy behaves close to the its expected value This this the object before the the expected value in the object with the expected value will be will be close So so we could just study the expected value for now I basically to show universe alley. I want to show that these logs of these probabilities This is just the top term in the gives measure For any site a I want to show that this log of this probability of the object on top is is Can be reduced to the log of the probability of this e to the Hamiltonian of these free beta parameters on the bottom So how will we do that? Well? Because I assume enough regularity on my g I can take some first first and second first and second derivatives And because of the normalization on my X I X X J I could throw the third order term because this is of higher order I guess this is will be off on more grand this will be off of small order.  So we can use some matrix concentration in equalities replace that second term with this beta parameter that we had before This is precisely how we find the beta parameter in the second term and Now we just have to deal with this first term in this object and this first term in this object is I ID we assume that my entries were generate ID. So there's just some I ID random variable Time some X I X J and I know that perhaps in very the very large end This will probably behave like a standard normal or not. It's not a standard. No, but some normal with some shift so You could compute what the mean is of this object you get some beta parameter You can compute what the variance is you will get the other beta parameter and you can use universality of Universality in the sort of force pin glasses because you just have the ID entry times X I X J You can unravel it to say that I guess I could replace this with the equivalent Gaussian model and From here just log it is free energies The term in the exponent was precisely the H beta parameter that we had before So this this holds for all a so it shows that at least quenched all of these All of these all of these friends breezy free energies all of these on condition free energies So it reduced to the same thing up to some up to some little Small error that sort of goes to zero in the limit and since in the large division, but we take anti affinity That's that's that's really all we all we all we care about okay, and Now I wanted to go over the proof for the large deviations Maybe I will just say a few a few quick words about it is that these Conditional problem of these cut these free energies conditioned on some values of these overlaps these are called the france per easy france per easy france per easy potentials and The log of the probabilities that we wanted to study before these overlaps can be just written as the difference between the france per easy potential and the free energy which is without this without this This extra extra conditioning so I could write these these objects. I wanted to compute for their large divisions large deviations principle as the difference between two log partitioning functions one is conditioned on the overlaps taking some values and no one is not conditioned my overlaps taking certain values and I guess you can use Varda and Zama and just say well these these are coins I could just take any to do to zero I can add them in later So if you notice in the rate function, there were some some simple parameters that disappeared at the end Those are what you get when you just add them back in so to prove this We really only have to look at the behaviors of these gives measures under the first term by universality studying these these these gives measures will will basically give us the large deviations of the object that we had that we were interested in at the start and Because the free energy is concentrated by by some Concentration we're able to just look at the quench one so we're able to average over the radness in these in the way these measures are are Defined and then get the almost sure Almost sure object afterwards, but this is a bit easier said that done since These this indicator functions not really smooth with respect to x zero. So the concentration here is actually a bit more Delicate to show so to to go from quench to almost sure we Requires a bit of work Let's see so it's six minutes to lunch and this will take too long. So I would just ignore what the Ideas are for this object but maybe a Very quick word on on how I'm new to how I'm this is proved Um, this is I guess this proof of this was sort of generalizing to work on large on large deviations by my supervisor on the Dimitri pension echo back in back in my PhD thesis so he was sort of proving He proved a large deviations principle for the self-overlaps and what we did was we added and what happens when you're adding the R1 Zero overlap and just introduce some extra challenges in the sense that I guess there's some There we lose some smoothness by adding this just indicated functions You can smooth objects out in a in a nice way You can also add a perturbation to our probability measures for changing the large deviations principle So at the scale that we're looking at we can smooth out our measures a bit So we could get ultra matrices all the nice things that we that come with it I can use the our cab commissures to prove the lower bound and then I can use the ideas to prove Cramer's fear I guess it's a bit more complicated, but you could You you could basically use some tools from large some large Deviations to sort of finish the proof for the lower bound and You can also go from quench to to almost sure if we were a bit more careful with all the estimates Okay, so future problems and what are we interested in in the future? So it's a natural quit questions are can we generalize this to higher rank models? This was sort of done for Done for the classic spike matrix models Can we generalize similar results to instead the rank one case? Can we go to the higher in case? There's also the question is can we go to the tensor case? So instead of a x i x x j Can we assume that our rank one model is basically generated by some tensors or the look at the corresponding p-spin models for these objects? Another assumption is well, we assume that these y i j's are sort of generated independently and they had the same law IED so can we generalize this to when there's different different post years for each i and j and these are the Hetero-Hetero-Midgenius models that's been studied by the works of Reeves and Francesco and lastly We have some rate functions. We can study the phase the phase transitions for these models We can study well one is a replica symmetry breaking when did these objects concentrates when do you have ones that have a Unique minimizer so we haven't done that yet. We just have a rate function There's still lots to understand about the behaviors of these overlaps under these design rate functions and I guess we have some time for questions or not then it'll be time for lunch Yes, so thank you for your time. Thank you very much. Justine is there Thank you. It was a very nice talk. Okay. One thing that I didn't get is what was the The mismatch scheme on the likelihood the privilege of the data given a signal. What was the assumption on that one? Oh What would the assumptions on the Guesses for this mismatch. I see so one assumption is I needed my guess for the prior to be compactly supported This can probably likely be weakened The other assumption is for our mismatch is I need enough regular I need some smoothness so I need the on the log Likelihoods to be defendable enough times and the last estimate or the last condition I need on what my guess is for this is I need that this this quantity to be equal to to zero and the way that I Would like to interpret this or at least in this in the simple case this this What this condition means it means that in my original model if my original model without any signal So my structure my noise if my noise was centered then it means that if I'm basically guessing how my how my Observations will be on will be on generally I serve also need my noise to be centered So I also need I also need Need I'm just hold true because if this was not if this was not zero then there'll be an extra mean mean There'll be an extra mean term that sort of is of high order than then everything else will have a slightly different problem and A I'm comment is in the optimal case this If we have the right if we choose the right log Likelihood this object could be zero automatically So this is this is sort of automatically satisfied for the Bayesian optimal cases and it's an as an extra assumption You need so it's to be saying that mice that my statistician's guess cannot be really wrong I need I need to at least match match the means of the noise Okay, thank you last question Okay, the intuition behind the second overlap them. Can you just share the idea about it? Yes. Oh So, what's the intuition behind this some second this second overlap? I Guess we don't have to understand the The Joint laws if I want to only understand you over the original overlap I could also just just look at that but suppose you wanted to something a bit more precise this overlap We want this to sort of encode how how close our Guess was we want to sort of encode the angle behind this and in order for us to encode the angle acting So normalized by the length of these vectors so I sort of have to control the length of these of these estimates and I guess if I In some cases like if I just if I just flip flit some coins like plus or minus one This this overlap only takes one values But in some more generic problems my p of x may be supported on some interval then these Overlaps can take an a range of values and you don't want a small value from my estimator to really Influence what this overlap is or someone isolate the angle for these problems. So that's the intuition Why I want to do I understand what the joint law was He's modest Very nice work. I read it And I have a ton of questions of course the first one is so maybe you partially answer to this Have you tried to extend it to vector spins Yes, so I have not done it and I think it should be done the main challenge to understand to to go from this to vector spins are You have to go to basically a vector version of Chromersphere and that extra step it should be doable, but There's a bit of a bit more work to be done and the other may may obstacle that sort of Prevents us from going to vector spins is will we now have to just understand the joint laws of many estimates from for for In in state only one exio in the higher-rank case. There'll be many Exios serve after I said I can understand what the joint laws are and the nice news What that is the synchronization that was used to understand the classical vector spin models will also work Work for these models because things are at the right scale so we could still add to regularizing perturbation So I think the main challenge will be You'll be generalizing chromers theorem from the vector case or from the scalar case to the vector case And and making sure that nothing breaks for those photos okay in the follow-up question to this is in this Proof of your university you need to expand the g y is zero in the second argument right and to do that You need that the second entry of this g y Is small otherwise you cannot neglect the further terms. That's that's right. That's right Do you know when this for what kind of rank scaling this breaks down? I see I see yeah, so Francesco's come completely on correct any three times the French one also needs some bounds on what these what these what these are and it's and it's on written paper and So When are some examples of some log likelihoods where this will not work I I could say that it works in I guess models Corresponding to stochastic block models and models where it will not work I would assume that maybe if the white has heavier tails or something like that Then it then it will not work since the log of the probabilities might be too too big So so implicit here in the behaviors of this G is sort of some very precise Precise Precise or some maybe somewhat Restrictive conditions and what the log likelihoods can be so It'll be interesting to see how much we can remove that but this is Right now we just we just Assume assume some are uniform bound on these on these on these derivatives. I Have one question as well. So from the formulas that you get again do you get insights? from the form of the rate function when Do you expect to have? concentration in this mismatch settings or not Is there any insights you can extract from this? Yes. Yes. That is a very nice nice own question. It's sort of something that We haven't done and I guess one of the motivations for approving this Models are at least for on Florence and that is what is was to precisely understand how these are perhaps behave in these in these models but we just have a great function now and we haven't You haven't done any analysis, but hopefully in the future will be able to use this to understand To understand what were you where you mentioned or I guess that was why Florent and Menka were One of the reasons why why why they why they were Where they were interested in this in this problem, but it's not been done yet. Oh, but I think It has been done in In some settings, but it worked by by Francesca. I believe yes. Yes So so yeah, so so they just would correspond to the precisely for the unique unique minimizer case Yes, so they were they were able to show that these that use these overlaps overlaps Constituted for these models Okay All right, I don't see other questions. Maybe we can go for lunch and thank you again Justin


A Central Lakes College graduate took home some hardware last week at the State of Minnesota Trio Conference. Rob Robinson was one of two people to receive the prestigious achievers award at the conference held on April 4th. Trio is a program at colleges and universities across the country that provide academic services and assistance to first generation low income and disabled students. The two winners were selected from 69 Trio programs around the state and Rob is only the second CLC student for the grad to receive the award. Rob's story is evident and continues to be told at CLC. When Rob Robinson came to our program, he was in the second year here as a student. He officially was a student athlete, came here to play football and then realized that academics was a little higher on his priority list than he had originally realized. Because of that he came and saw us out in the Trio program realizing that we could help support him along the way on his academic journey. After graduating from CLC with an associate of arts degree, Rob went to graduate from the College of St. Scholastica with two bachelor degrees and currently works as a case manager at a local treatment center. If you've enjoyed this segment of Lakeland News, please consider making a tax deductible contribution to Lakeland Public Television.


to my channel and welcome back to another cooking video. So today my mom and I are working together. We're actually in her kitchen and we're gonna be sharing with you some of her best holiday recipes, which I think would pretty much fill a book. If you guys don't know, my mom actually has her own channel and I will be linking it below. She does post kind of at random, right? To random. To random. Anyways, so she has so many recipes just from years of doing catering events and things for family and friends. She did all of me and my brother's weddings and she definitely needs to write a cookbook, I think. So today's recipes are definitely more at an easy skill level, wouldn't you say? We're kind of. I would say we're gonna try to keep it that way so that you understand. Yes, yes. And also we will tell you what alternative tools you could use if you don't have a standup mixer and things like that. And there is one recipe here that's been really highly requested that I had done a while ago, probably over a year ago. I think so. Something like that. And that is my mom's sticky buns. They are, in my opinion, the absolute best and they're relatively simple to do once you understand how to do them. They are. So we're gonna be showing you that. We're also going to be having some savory things today, things that you could easily make for family and friends or enjoy at a gathering. So I think that we're ready to go. Cheers. Let's get started. The first recipe that we're gonna show you today is one that I can honestly remember my mom making even as a little girl. It was definitely around the holiday times that she would make these pinwheels. And you're gonna go ahead and mix together four ounces of cream cheese, 1 fourth cup of ranch dressing and a half cup of shredded cheese. It doesn't really matter what kind. You just want it to get to a creamy consistency. Then you can literally use any type of filling you want to. We went for a little more of a veggie style filling, kind of down the line of veggie pizza, so some baby bell peppers and some green onion, some ham. And you can just really go crazy. I love bacon bits in these. You can also switch it up with different types of cold cut lunch meat. And just having that creamy base makes everything really delicious. You can also use red pepper wraps, so you could have green and red wraps for Christmas time. You can add in spices.  And then the key for these is to roll them up and put some saran wrap around them. And then you'll want to leave them in the refrigerator for a few hours. Overnight is best, but if you only have a few hours, that works as well so that they're nice and firm and cold and easy to slice up. So the whole reason that we went ahead and made these pinwheels is because we wanted to put together a charcuterie board. And I believe I'm saying that right. You guys can correct me in the comments if I'm saying it wrong. So these are a bunch of the different things that we used and you can really use anything you want to. And I have some serious charcuterie board inspiration coming for you at the end of this video. My mom did a catering event for a family friend and she did a charcuterie board that was the size of a table. It is huge, you're gonna love it. So stick around until the end so you can check that out and get some ideas if that's what you're planning to do this holiday season for whoever you're celebrating Christmas with.  So she said you wanna use at least eight different items and you also wanna think down the line of things that would be sweet and things that would be salty even going down the spicy alley if you like things like that. Fruit, cookies, I mean you name it. You can really put together a lot of things and I think the more that you have on the board the more interesting it looks and the more fun it is to eat. Dips are also a great thing. And then another little tip she had for you is to make sure that you use things that are different sizes. So you have the small blueberries, you can use salted nuts and then larger cookies or different slices of meat and folding them different ways. Just have a lot of fun with it and make it your little art project. Something else I love about this idea is you can go ahead and make a bunch of the ingredients yourself to put together your board or you can simply pre-purchase a lot of things and nobody will ever know because it looks so homemade and so put together. Okay, so on to those famous sticky buns. So the first thing that you're gonna do is you're going to put together four cups of very warm water along with two tablespoons of yeast and one tablespoon of your sugar.   After your yeast is activated, you wanna add in your cup of softened salted butter and then you're gonna whisk up four room temperature eggs and dump those in as well. Next, you will start mixing. Now you can do this by hand and my mom said that the best thing to do by hand is start out with a wooden spoon and then as the dough gets thicker, use your hands in a bowl. So it's easy to do by hand. You don't have to have a mixer, but a mixer does make it go a little faster. So now she's adding in about, she said seven cups of flour. You're also going to want it adding your one cup of instant potatoes and I think that's the secret ingredient in this to be honest with you. I feel like that's what makes the dough so yummy and you're just gonna keep adding and allowing the mixer to mix together. She said since she does have a stand up mixer, after about seven cups, she switches to her hook which you're gonna see here in a minute, her dough hook and it just helps to mix things a little bit easier. After that, she adds in the rest of the flour. You're also gonna wanna make sure that your salt is in there, your sugar, all of the dough ingredients are mixed in with this and then whenever it's kind of pulling away from the bowl or if it's getting a little bit firmer as you're mixing it with your hands, that's whenever she gets it out of the bowl and kind of combines it a little bit and then puts it in the bowl to rise. You wanna cover up, she likes to use saran wrap. Some people use a dish towel, but I know my mom has used saran wrap for years whenever her bread dough or any type of dough is rising and you'll just wanna go ahead and set it on your stove top as your oven preheats. Now to make the sticky part, you're going to take a 13 by 18 pan and this recipe actually makes two of them and you're gonna put a stick of butter on the pan and throw it in the oven, let it melt up a little bit. Once it's melted, pull it out and you're going to put your brown sugar all over the bottom of the pan.  The next step while your dough is rising is you're going to make your frosting for the top. So you're gonna put together your powdered sugar, your vanilla, butter and water until it's combined and looks nice and creamy. Once your dough looks a little puffy and my mom said that it doesn't have to rise a whole lot, she said this dough is pretty forgiving. You can go ahead and take the cover off and divide the dough in half. We're gonna give you a couple ideas of what you can use this dough for. You don't have to put it in just a sheet, but you're gonna go ahead and take that half and stretch it out into this shape. I don't really know what you would call it.  So she just softens butter and takes her hands and puts it all over the top of it. Next, you're gonna go ahead and shake, liberally shake on some cinnamon and I know my mom said she often uses a lot. So you definitely want to go extra on the cinnamon.  Then she takes a pizza cutter and cuts it into 15 rolls. So as you can see, a visual is super helpful for this and if you're gonna make this recipe, you may wanna come back and watch this just to kind of be able to eyeball and make sure that your proportions are correct. The first pan she did in kind of the traditional manner and then this pan, we did something a little bit special. I know she does this around the holidays where she'll just get a can of pie filling. You can use blueberry, which you'll see in a second, cherry, strawberry, whatever you wanna use and she kind of twisted them a little differently just so that they could hold the pie filling and then she wanted to put together these crocs that she had picked up for some friends to be able to pass out some of her delicious sticky buns as gifts. So I think this is such a great idea and again, she went ahead and twisted them in, I don't know, a little, not so much a roll, but a twist so that they could hold some pie filling as well.  Now one other little note my mom had was don't ice these until they've cooled for maybe about 20 minutes as well because the icing will melt and it will run all down. If you want the icing to sit on top and look really pretty, it definitely helps to let them cool a bit. Okay, so like I said, I had to include this footage that my mom did because when it comes to food, my mom is honestly a genius. She just has a way of making food in art and I love it so much about her. She just does such an excellent job, especially whenever she's working at events. So this was an event that she did and she filmed it and she said, oh, you should show them the huge Shakuturi board that was requested for this event. So it was literally the size of a table as you'll see at the end, it's just huge. So enjoy, I hope that it inspires you if this is what you're putting together for the holidays. Thank you guys so much for watching today. If this inspired you, don't forget to give this video a like if you're new here, I'd love it if you subscribe to my channel and I will see you guys in my next video.


Good morning, everybody and welcome to this press conference if we've been too subtle with the branding You're joining the first press conference of the annual meeting of the World Economic Forum in Davos 2016 and It is a very special press conference because the question we're trying to answer today is how can we prepare a vaccine for Ebola? How can we be better prepared for the next outbreak and It's especially in the sense that we're joined By Gavi today and whenever we are asked at the forum.  Are you more than a talking shop? We're always happy to mention Gavi, which was born I can say 15 years ago here at the World Economic Forum in Davos and Has has done fantastic things just to give you a couple of numbers in the 15 years Gavi has vaccinated 500 million people in over 70 countries let let just let that number settle in So very pleased to have this press conference and without further ado I'm happy to introduce to do today's panel to you on my immediate left is Seth Berkeley Who's heading Gavi the vaccine alliance? Right in the middle is Julie Gerberding who's joining us from MST or as it's known in the Esmerich She's the vice president for strategic communications global public policy and population health Next to her. We're joined by Nungosi Oconio Iviola who is the chair of the board of Gavi? So thank you for joining us today and last but not least we're joined by professor Jeremy Farah Who is the director of the welcome trust and completes this panel wonderfully? Jeremy Sorry Seth. We'll we'll start off with you. So The question for the Ebola epidemic that I want to ask you is why was no vaccine available when this happened and And also if you could elaborate a little bit, what is your partnership with Burke or MST outside the US? please So Ebola is a disease that's been known now for more than 40 years and There's been lots of outbreaks, but they've been in the poorest countries in small numbers and as a result There is a complete market failure. There's no commercial market for such a vaccine I suppose I can say luckily but During the anthrax outbreaks in the US some investments were made because they thought Ebola might be a bio-terrorism Weapon and those were not completed of those vaccines were put in mothballs But when this very large outbreak occurred all the sudden those vaccines were pulled out plus new technologies that were there and It's amazing and I have to hand it to the pharmaceutical sector because the acceleration of this was done in record time normally we take 10 years to do a vaccine and As you saw here, we went into an efficacy trial and finished it in just a few years The the partnership with Merck is really about trying to make sure that in this interim until we have a licensed product Which of course is the critical outcome. We want that vaccine is available if there's another outbreak So the agreement is and it's an advanced purchase commitment against licensed product at the end Three components connected to this advanced purchase commitment The first is that they should submit a emergency use authorization listing with WHO That's a regulatory authority that would allow the vaccine to be used In the case of another emergency declared by by WHO second that they would produce 300,000 doses of vaccine and have those doses available in case there was an emergency these are Investigational doses obviously and then third that that they would make sure to submit a full regulatory application Lastly about this it's very important obviously for the world to have this vaccine Which is the only one that had efficacy trials and therefore is is the most promising available But also the science around this vaccine is critical because any other product that is being considered since this has human data As well as animal data and all the great work that the Merck scientists usually do it will frame You know all vaccines and so it's really important to do that I just want to lastly acknowledge that gail Smith who's here the USAID administrator the partnership around Gavi is quite broad It includes you know all of the major donor countries the recipient countries all the pharmaceutical companies and you know We're all committed to make this work and to try to make sure our vaccine is available So something like this doesn't happen again Thank you says Julie. Let me let me put you on the spot How how close how far away are we from from having enabled a vaccine? Well, first of all, I am very happy to be here to celebrate the 15th birthday of Gavi because I didn't realize It's a if that's all that the World Economic Forum did it's a miracle so congratulations on your 16th birthday sweet 16 I would say the the serious nature of the Problem that had to be addressed the Ebola outbreak was a wake-up call to a lot of people I think we had gotten complacent about Ebola as something that was usually a small problem in rural areas and could be fairly rapidly quenched but the scale and speed of what was really a far storm of Ebola in Western Africa really Reminded us once again that mother nature is the best terrorist and that we do need to take much more seriously our ability to Prepare in advance, but also to respond when something like this occurs. So The truth is this is an unprecedented speed to develop a vaccine product the fact that we have submitted the Necessary paperwork to the WHO and they've accepted our paperwork for review for the emergency use assessment Process it happened faster than it has for any single other product So in that sense the partnerships that grew up between Industry Gavi the WHO the governments of the affected countries USAID all of the various players CDC NIH Is really an unprecedented example of global collaboration and this speed would not have happened if we hadn't had that Capability and I will say that while there are many actors in that process the fact that Gavi was there at the center and had experience in Understanding what is necessary to bring a life-saving vaccine quickly to people who need it really was kind of the glue that kept the partnership Together, so I think Gavi for that for that leadership from a from a murk or as it's known here in Europe MSD perspective we We need to get this vaccine licensed and so our highest priority right now is to continue to assemble the science the safety data the immunogenicity data the efficacy data and Have full licensure both so that we can obtain a WHO recommendation and meet the requirements for the advanced purchase agreement But also so that we can use this product more broadly even in advance of an emergency so that where it's appropriate We could have pre existing protection For example among health workers or others who might be at risk and that is first and foremost our leading priority We are also Certainly ramping up to be able to make sure that we provide you those 300,000 doses In in a few months so that if there is a Recurrescence of the outbreak that we have doses of vaccine available and ready to roll when people need them And we know now how to use this in at least one way with the ring vaccination scheme so that we can Hopefully rapidly quench Subsequent outbreaks before they reach the size and scale that we experienced and then the last thing That we have committed to as a company is that when we have a licensed product We will make it available for the people in the poorest countries at the lowest possible Not for profit price and that means that we intend to be able to provide Wherever people need it a vaccine that is affordable and that the cost of the vaccine will not be a barrier to the kind of public health protection every Everybody deserves Thank You Julie. No go see In your native country in Nigeria Which is one of the most populous countries on earth out of the 11,000 people roughly we lost to abla I understand there were only eight people who died of abla. What was what was the what were the measures? You took what was the success story if you will in Nigeria? What happened there? Well, thank you very much Let me also use this occasion to say this is my first major public engagement as the Gavi Board chair and I'm really proud to be here to welcome Gail and as well and Say that one of the reasons that I'm excited to be chair of this board is because of the kind of public private partnership That we see Gavi involved in the fact that you can really use innovative ideas and Financing mechanisms to bring the public and private sector together to deliver and on an issue That is so important as they're bullet pandemic You know that the Afri whole of Africa was very very much impacted by this Particularly West Africa and as you see my country Nigeria We were lucky because we had a strong health system in place That we had used to deal with the polio We were able to deploy that to be able to manage this Pandemic and only eight people died, but let me say that 11,300 people were killed in West Africa 28,500 infected and there at least 17,000 survivors who are dealing with the Complications and the social state stigma that is attached to this So there's the loss of lives the fear You know that we all experienced about this pandemic And just to share terror of it That's on the human side You also as a former finance minister also paid a lot of attention to the economic side of it And you remember that the for Guinea, Liberia and Sierra Leone The the World Bank estimated Losses, you know in in a couple of of a couple of billion dollars In these countries the UN development program said that for West Africa as a whole it might even exceed three billion dollars So we this is just a lesson that if we don't pay attention and prepare ahead for these kinds of Pandemics, it's not only the loss of human life, but can devastate the whole region economically So to conclude I'm really proud. I think this is the kind of thing we need to do They using the advanced purchase commitment Preparing ahead and I want to also thank the pharmaceutical industry for what they are doing with us Thank you Jeremy, let me ask you The the welcome trust your your lifeblood is is R&D Why was the why was the process so difficult to get to the vaccine and one of the steps that you think Should should be taken to improve this for future cases It's very important to put Ebola in context since the since 2003 or 2004 These are not rare events. So In fact, I may be one of the few people in the world that's been involved and seen patients through SARS through bird flu through The pandemic of 2009 influenza We have MERS CoV in the Middle East at the moment, which is continuing to circulate we have zika in South and Central America I mean They these are regular events and actually if you ask yourself for any of those we actually we actually don't until today Have a clear Vaccine available for any of those. So in some ways we're using 19th century interventions When we come to have these epidemics and I think in future we need to see an Ebola And what Merck and Gavi have done in relation to this I think needs to set the precedent that we absolutely have to commit ourselves for those epidemics that we know about That we have vaccines that have been into man in the inter epidemic period such that when we come into an epidemic Which can be very explosive can disrupt society as we've heard and impact on both health and economic Economics that we have those vaccines ready to go and they can go at a moment's notice And I think that's what we've all got to commit ourselves to for the for the knowns The chicken goon years the the zikas the MERS the SARS And then we have to also think about the unknowns that we can't yet predict HIV Remember was an epidemic that that started and it's devastated the world And there are a number of those that we don't yet know about that we need to be prepared for Thank You Jeremy Maybe maybe one question to all of you quickly So, you know the forum is always keen to to have a multi-stakeholder engagement and that was mentioned that that Gavi is So so successfully doing it. We have about 40 something heads of state in government here If you had one wish to do these Gentlemen and ladies here representing the public sector in a nutshell. What would it be? Who stops it? Thanks. I think it's what Jeremy said is to take this seriously I noticed on the risk register for this year at the global economic forum Infectious disease is not in the top 10 and that's because it's not top of mind right now But when this happens and if you look at what HIV's done to the world And of course if a flu pandemic occurred a really severe one like the 1918 Spanish flu epidemic We could have 50 to 100 million deaths and the World Bank has said that the cost of that could be over a trillion dollars So we need to make sure that everybody has this top of mind And then that the resources and the political will is there to create the systems like Jeremy has talked about I Think we're all probably going to answer the question the same way and that really is from the framework of leadership commitment I too have gone through SARS monkey pox Wesson isle and so on and so forth and I can tell you that what happens when a government sees an emerging problem There's a very rapid response and in a non-partisan way people kick in and do the right thing But as soon as the problem goes away, so does the investment in the level of interest and we've got to get global leaders to stay the course We don't necessarily need citizens to be in a constant state of alarm about emerging infectious diseases But we do need the political leadership to keep this front and center on the agenda So that we can get out of this kind of her key jerky funding process and get into a situation We are truly prepared to manage these inevitable outbreaks I Thank you. Well, I just have maybe two very Precise messages one is No, one is safe The world is so small now that I would want all the leaders to pay attention You cannot say I'm at this end of the world or the other end. So it wouldn't affect me Whatever breaks out these days can affect anyone. So it's important to pay attention The second is in addition to the human dimension Remember the catastrophic financial and economic losses that could emerge and that can really Damage the economy in a way that has leaders probably don't think about I mean, you know thinking through the ball and what it did to really undermine the Economy of the country countries that were most affected should be a wake-up call to every leader I think the only comment I would make is that it is true This is a so-called market failure, but we've got to see this as public health and and that is the responsibility of all of us Governments USAID diffid the other governments around the world need to as they are doing Continue to support this. This is public health industry has to be a partner from the start And it also shows and today shows this again the importance of global organizations that bring us all together With it, you know, Gavi has played a critical role in moving this vaccine forward And if we don't have those global organizations where countries come together for the common good Sometimes we get cynical about those organizations. I think they remain absolutely critical to the future of public health Thank you very much We have a couple of minutes for questions from the floor if I could have an indication Yes, can we get a microphone if you could state your name and organization, please? Yes, my name is Isabelle Sacco I work for the Spanish new state and CFA Could you please remind us what in what country this vaccine was used during this last epidemic And how many people were vaccinated in these Trials that were what happened there. I heard last week from the WHO official that this vaccine had a 90% of Efficacity and could you please confirm this? I think the Published data available about the trial which are really the only efficacy data that we can speak to at this point in time Demonstrated a hundred percent efficacy and the Lancet report that came out at the end of July of 2015 of course there are more data that have been assembled since that point in time and the final Efficacy submission to the regulatory authorities is still in progress Good science takes time and getting all of the data together Including data from ongoing trials is still a work in progress. It's going as fast as I think we can expect it to go given the Timeline that we've been operating under but we we don't want to make any claims about the established efficacy until we have the science But it but it has been it was used extensively that the study was done in Guinea But studies have also been undertaken and people within Sierra Leone and in Liberia have received this vaccine Also, of course in the United States in Germany in Gabon in Kenya I mean this vaccine has now increasingly in more people and as Julie says that safety data will is all being gathered And that's the critical bit that adds to the efficacy data that you know about I think that also speaks to Seth's point earlier that this is the first vaccine to have Information about efficacy, but it helps understand additional vaccines that may emerge and helps create the standards for evaluation So it's not only helpful in getting a vaccine available for emergency use But it's also helpful in expanding the whole repertoire of what we know and need to know about future and even more advanced vaccines It's not also reiterate Seth's point earlier that that to do this in the confines of an epidemic Which is terrifying to be part of is chaotic and is a crisis to have got through and got efficacy data on a vaccine Is an enormous amazing tribute to the people in Guinea to Merck to MSF to WHO and Diffid and and Norway and welcome trust it who funded that I think it is a remarkable achievement Which really does need to be celebrated I would have to go back and check. I hate to say it, but I think it off top of my head. Is it 4,000? It's between 4 and 6,000. I can give you the number The exact number afterwards if you want but it's between 4 and 6,000 in that study in that study And then and then well over 10,000 if you look at all of the use of the product in different settings and and tests Yeah, thank you. Do we have any other questions? No, all questions have been answered wonderful. Thank you very much to a fantastic panel It's been it's been encouraging to hear about the great work that's being done there and thank you for the great partnership Thank you for watching


As a devoted fan of classic British television, I thought I had seen it all, which is the lost episode of Coronation Street. Yet while I stumbled upon one dreary evening shattered my perception of reality and left me questioning the very fabric of the shows I held dear. It was a chilly autumn night when I received an anonymous email claiming to possess a VHS recording of an episode of Emmerdale from 1979 that had never aired. Sceptical yet intrigued, I arranged to meet the center in a gimly lit alleyway, the perfect setting for a clandestine exchange. The tape was wrapped in a tattered cloth, its label barely legible. With trembling hands, I rushed home, eager to unravel the mystery concealed within the dusty cassette. As the tape worded to life, I was greeted by the familiar sights of the Yorkshire Dales. The opening credits rolled, but there was something off about them, a subtle distortion that sent a shiver down my spine. The episode began innocuously enough, with the villagers of Emmerdale going about their daily lives. However, as the storyline unfolded, a sense of a knee settled over me like a suffocating blanket. The plot revolved around a forgotten character, a recluse who lived on the outskirts of the village. Rumors swirled about his mysterious past, and the villagers whispered of dark beads committed under the cover of night. Curiosity drove me forward as I watched the events unfold, each seen more unsettling than the last. Shadows danced across the screen, and a sense of impending doom hung heavy in the air. As the episode reached its climax, the protagonist ventured into the depths of the woods, drawn by another worldly force. There amidst the gnarled trees and twisted brambles, he stumbled upon a dilapidated cottage shrouded in darkness. Inside, he discovered a room bathed in a neary blue light, its walls adorned with strange symbols and sigils. In the center of the room stood a mirror, its surface shimmering within a natural glow. Unable to resist its allure, the protagonist approached the mirror, only to be greeted by a chilling sight. His reflection stared back at him, but it was not his own face that he saw. Instead he beheld a twisted visage, a grotesque mockery of humanity. With a strangled cry, the protagonist recoiled in horror, but it was too late. The mirror had claimed him, dragging him into its dark depths and sealing his fate for all eternity. As the screen faded to black, a single message flashed across the screen. The mirror's purse. Beware the reflections of Emmerdale. And with that, the tape came to an abrupt end, leaving me alone in the darkness with nothing but my thoughts and the lingering chill of fear. To this day, I cannot shake the memory of that lost episode, nor the sense of dread that accompanies it. For somewhere, hidden within the annals of television history, lies a darkness that should never have been unearthed, a darkness that now threatens to consume us all.


We had just had our second board meeting as you recall this board, the advisory board on SSM MD model started in October last year. So after our second meeting we established what we called working groups, three working groups one of them was handling policy, regulation and rare advocacy. And then the second group was dealing with issues of infrastructure and technologies. And the third group was dealing with the partnerships and financing models. So they have worked so hard throughout the year and I'm happy to say that we now have produced a report assessing these looking at this situation analysis now in terms of ICT for disaster management but also looking at ICT for development and through the assessment looking at different good practices and they have come out with recommendations and proposing some actions. So today we were able to launch our report. What we hope to achieve first of all this report as it was launched today will be on the website of ITU, it will be public. But what is important is that from this report and from the recommendations of the working groups we have now sort of summarized what will be our action plan. And that action plan is looking at those three areas but you could say now these areas now can be summarized in about three pillars. One pillar would be advocacy itself together with the addressing it from the global angle. The second pillar will look at all the innovations you want, move this forward and of course the third one will be mobilization for financing mobilization. But what is important is that how do we change from the current use of ICT whenever there is infrastructure and so on, whenever there is a disaster and change is that as countries develop the ICT for development infrastructure as they put in place regulation, also regulation as they align since operators that they take into account the issue of disaster management or disaster mitigation.