Hey gang, welcome to today's video. Welcome to my channel if you've never been here before. This is a full day of eating I am an intuitive eater. That means that I do eat what my body is wanting and needing in each moment That took me a lot of years to get the hang of. You can't expect to overcome Certain eating issues right away by intuitively eating. You really do have to learn how to get in tune with your body Figure out what your body's signals are. I do have other videos on my channel that can help better explain that So please do check those out. Please hit that subscribe button down below So you get all the future videos that explain that. I have maintained a healthy weight this way I eat mostly paleo. While paleo may seem like just another buzzword made up by the diet industry This trendy plan focuses on eating the whole foods that have kept humans healthy for centuries The core principles are simple absolutely no processed food dairy or refined sugars If your stone age ancestors didn't eat it neither should you. So today I'm out and about I have a meeting at a retirement home to talk about the health and wellness things that I do I will be in search of a new laptop because you know YouTube you take up a lot of space and need some better equipment. I'm still running the same laptop I bought years and years and years ago. They don't even sell it anymore So yeah, I'll be shopping for that. Anyway, let's get into this video Here's what I have for breakfast and I have no idea what I'm having for the rest of the day We'll find out as we go along Make sure you peel the avocado instead of scooping it because the dark green part contains the most nutrients KSK's best non bloaty protein powder ever 80 calories 16 grams of protein The only ingredients are spreaded brown rice protein organic natural vanilla flavor and organic Stevia for sweetening What more could you ask for? My tea was I eat 30 a.m.  It is now 111. So I've got apple Healthy pop. This is Zevia. Let me tell you the ingredients carbonated water Stevia leaf extract Tartaric acid natural flavors caffeine and citric acid so not the absolute best Most optimally healthy thing neither am I 80 20. This is my pop of choice. I was a coca-cola lover so that's how I deal with that and Always water. So this is what I'm gonna do now Have the meeting with the guy and I'll catch up with you next time. I decided to eat something All right, so left that meeting. I'm now gonna have this quest bar 21 grams of protein One gram of sugar certified gluten-free the ingredients on here again much like myself not 100% optimally healthy, but Delicious, so here's what the macros look like 14 grams of fiber in here one gram of sugar 21 grams of protein five grams of fat only a hundred and eighty calories for 21 grams of protein This is bomb. I love all of the quest bars. So that's what I'm gonna have I'm gonna go head out to a new gym that is opening supposedly this Wednesday Check that gym out. See when it's opening talk to that guy and I'll see you later. I'm back home again It's not time for dinner. It is time for a snack. It's about 330 right now this bread I found at Longos Unbelievably delicious stone melt slow-crafted authentic sourdough rye with organic flaxseed in it If somebody not a celiac person, but somebody that has a sensitivity to gluten like myself Eat sourdough. It is not that bad for you because the souring process of the dough if it is Authentic sourdough breaks down the protein gliadin found in gluten, which is the cause of The gluten problems for many. Yes, there are things like pesticides herbicides fungicides Chemicals and such that do cause sensitivities as well. So for my snack I am having a slice of that. I may have some yogurt berries and Ungranola as well Bridge when I get to it for now. Definitely a slice of this delicious bread.  It was amazing Okay, so this is one of my favorite snacks It's also what I have either as a before bed snack or as a dessert because it is quite healthy for you, but Greek yogurt this one scotchadakis Okay, if you're a Greek, I apologize that I just completely probably butchered that well a very very heavy heavy Burtaiton tonight. We had a very dares dareson bite. Let's go ahead terraces English for the bit to have the pet But it's really really thick. It's delicious. So I like that brand even the zero percent pretty thick Kakao nibs I repurposed the bath and body works candle jars because they have the rubber sealing on the inside a lid So handy This is ungranola. I'm gonna put a photo on the screen here of what brand it was I can't remember because I put it in here, but it's just like granola full of nuts almonds coconut flakes There is no oat or grain in it. So it's better for your gut Delicious berries strawberries raspberries and blueberries because some of us want it all this is date syrup So much better for you the ingredients are 100 organic dates Obviously, this is from home sense because Everything is from home sense. And as soon as I said home sense she was so excited and look at this Awesome thing and then powdered peanut butter. This is the no sugar added version. So powdered peanut butter You're not getting as much of the healthy fat. So I'm not Necessarily suggesting that this is better than all natural peanut butter. I do think you should use all natural peanut butter You're a fake and a phony and I wish I'd never laid eyes on you But I like the powdered stuff for ease of throwing into smoothies and stuff like that So this is what I'm using 90% less calories from fat. So That's not a good thing if it's healthy fats. You want all those fats But just as an example for two tablespoons, which would be 200 calories with the natural peanut butter This is 45 calories for two tablespoons and six grams of protein. You're only getting 1.5 grams of fats though So I'm gonna whip this up Doesn't that look delicious? I'm actually not going to use the cacao nibs date paste or Powder peanut butter right now because I just want this as a little snack because I'm about to make dinner quite soon So I don't want to get too full by the way the protein on this yogurt One serving 18 grams of protein crazy So this is what it's going to be for now and uh, I'll catch you at dinner time It is dinner time. So I am going to have potato sweet potato fries in the air fryer I am cooking for two. So there's white potato as well. That's going to be mashed We are having raised without antibiotics chicken breasts broccoli peas extra peas in case these aren't enough for two and gluten free gravy to Either pour over everything or dip the chicken in We're gonna use these pots for some of it instant pot for one potato for the mash air fryer for the fries It's going to be quite the production. But here we go I'm feeling slightly nervous. The chicken is in the frying pan. I put garlic powder paprika and Time leaves on the chicken delicious. This is the gluten free gravy Got peas and broccoli in there the air fryer is going with my sweet potato fries The white mashed potato will be going in here. That's where we're at I accidentally left my sweet potato fries in the air fryer for a bit too long So they're kind of crispy, but that's fine. They'll still be delicious Here's the gravy Nice and thick chicken gravy this chicken because of the seasonings I put on it almost looks breaded It is cooked to perfection. Juicy delicious Meh veggies are veggies, you know, so this is my finished plate. Oh my um, that looks Amazing it is six on the dot right now gonna have dinner at six I might have some dessert later. I might go to the gym for a little bit, but we don't know yet We'll see anyway. I'm gonna eat this if I end up having dessert It would likely be a blended banana with some cacao powder some maple syrup some dairy free milk Sometimes I put granola and the date syrup on top of that I'm not really feeling dessert as I did have quite a full day. I didn't do much activity today So I'm not as hungry today as other days But that is just an example of what I would have for dessert here is a photo of that So you can at least see it So that's my full day of eating. I know it's not incredibly exciting It does change day to day based on what I'm up to what I'm out and about doing I often grab food on the go I have lots of tips and tricks on how to stay healthy no matter where you're at Including airports, which I will be hitting up in may I am going to be talking about healthy ways of travel as I do take a trip to Arizona to Sedona. So stay tuned for that Please do hit the subscribe button down below. That really is where the support does come from If you thought this video was helpful informative or entertaining at all Please do give it a thumbs up down there for me as that does help support it too And let me know to continue creating content like this Please click that little bell notification icon if you would like notifications of the next time I do post any new videos And until next time have super amounts of fun in your life Have super amounts of fun enjoying all the food that you eat in a day You don't need to be trying to copy anyone else's diet Just eat in a way that makes your body feel your best and I'll see you next time. Bye


A guide to enterprise open source, authored by Dr. Ibrahim Haddad with a forward by David Marr, produced by Linux Foundation Research in partnership with LFAI and Data. In vertical software stacks across industries, open source penetration ranges from 20 to 85% of the overall software used. OSS has become a foundation for new commercial products and services and is essential to many organizations' software development workflow. OSS adapts to different business models, regardless of the industry vertical in question. OSS can improve enterprise product development and improve enterprise talent and skills development. Through open source participation, enterprise developers can build on the work of others, experiment with new features, and focus more of their efforts on differentiation. Participation in open source projects, positions organizations to leverage external R&D, spot opportunities to commercialize discoveries, and increase enterprise speed to market. Here are some of the best practices for enterprise. Identify reliances on open source software. Clarify needed open source skills. Identify your enterprise's open source objective, strategy, and opportunities. Set up your organization to implement open source. Identify career paths for open source talent and leadership development. Organizations face significant challenges in five specific areas with open source. Culture, processes, tools, continuity, and education. Mastery of open source requires a strategy that encompasses open source consumption, participation, contribution, and leadership. Read the full report at linuxfoundation.org slash research.


I'm very happy to be here and so today I will speak about universal optimality of E8 and the leach lattice. And so today I will explain what universal optimality is, what is this property and during the next five lectures I will try to prove to prove this property. And so this this notion of universal optimality it comes from the field of energy minimization. So here is a very classical problem considered in mathematics and physics sometimes in computer science. So we have some metric space and in this metric space we want to choose a collection of points and we suppose that these points interact with each other and the energy of interaction it depends only on pairwise distances between points in the set. And then the game we are playing we are trying to minimize this energy. And so in this series of lectures we will not speak about general metric spaces but we will speak about Euclidean space. And so here is our and so let's I'll just formalize what I have just said. So what we do we fix some potential function or potential profile so it would be function from the interval 0 infinity which is somehow the values which distances between points can take and it takes values so our energy is always real positive or negative and so now if we have for example a finite set so we say that potential p energy of a finite set in the Euclidean space it will be the following quantity. So this will be the sum over all pairs of points and we assume points to be different so self-energy is not taken into account as in many physical problems. So then we would like to minimize a quantity like this and so here are straight brackets they denote the Euclidean norm and so but of course somehow because we are working in Euclidean space maybe being able to compute this energy only for finite sets is not very interesting for us because for example we think about possible for example physical applications and then we want to study something like a crystal so we would like to also to give a definition which would work for infinite configurations but again about doing giving a reasonable definition which works for all sets it's a bit too difficult so we will restrict ourselves to good subsets so namely we call them point configurations and so a point configuration in the Euclidean space it would be a non-empty discrete subset of the Euclidean space and so what it means it means that every ball every closed ball it contains only finitely many elements of this set and so now what we can do now we can define energy for so maybe just small piece of notation for the future so we will denote by b with lower index r of x still depend on d it will be the closed ball of radius r about x in the Euclidean space and so now how do we compute the energy of point configuration which might contain infinitely many points so we do it by limiting procedures so what we take we will take our our so we'll take all pairs of points which line the intersection of our configuration with an open ball of radius r about 0 and then the compute the energy of this subset but now what it will do I will take this r bigger and bigger and bigger and so now I will also need what I will need I will need some kind of a renormalization I will divide this energy by the number of points in the intersection and so now I would like to take a limit of as r goes to infinity and of course such a limit might not exist for some configurations and for some potentials p so I take limit inferior and so I will call this quantity this will be the lower p energy of a point configuration and so as we see in this definition this lower energy it is something like average energy of interaction of one point with all the others so for this we need this normalization factor here and so now in some cases just a limit like this would exist and then we say that this is not the lower energy but just the p energy of C so now if limit exists or the same expression as here number it's p energy and so just a small remark is that with this definition so our energy p energy it can be some real number or it can be minus or plus infinity and so now what we want to do we want to what's the name says energy minimization we want to find configurations with minimal possible energy but now to somehow to rule out trivial solutions we need to introduce another notion which is the notion of density of a configuration so we say that so that the point configuration it has density 0 if the following holds if the following limit exists and equals to row so the now so density it would be the average number of points per volume and we computed in an obvious way so we take our configuration again intersect it with a big ball we center it 0 and divide with all this by the volume of the ball and if this number exists then we say that it is a density of our configuration and so now when we try to so let's maybe before we come to minimization let's do a few examples which will illustrate these two concepts so one nice example of a configuration in Euclidean space it is a lattice suppose that lambda is a lattice and so in this case of the density of lettuce it is just the inverse of its co-volume so the density will be just one over the words co-volume and so also now we can apply our definition of p energy and then we see that the p energy of a lattice will be the following quantity so it will be this number assuming that the sum converges absolutely are you assuming any positivity properties not at the moment but this will come come in a bit later but actually in the for the energies we are interested in they will be positive so they will do consider repelling potentials and yeah also this assumption will be true so we'll consider energies whichever like fast decay of course our general definition it allows also maybe to define number when this assumption is not true but we will not consider examples like like this or maybe we'll consider one of them but later in the series of lectures and so here is another example which will play a role a bit later so the lattices are very nice configurations but unfortunately there are too few of them so because being a lattice it's a very restrictive condition so we would like to relax it a bit a little bit and instead of considering lattices what we can do we can consider periodic configurations so from analytic point of view can periodic configurations are still nice they have usually well-defined density also it's easy to compute the energy for periodic configuration and at the same time we can say that almost any configuration can be somehow approximated by a periodic one at least if it's in some reasonable sense so so let's consider now next example would be periodic configurations so for this we fix a lattice lambda and then the configuration is lambda periodic if C plus L it will be again C for all elements in lambda and in this case it's also very easy to compute the density so density it will be the number of elements of C modulo lambda and because you know that configurations they are discrete sets so we know that this is some finite number again divided by the co-volume of lambda and so maybe what's a bit more involved computation it is how to compute the energy so here again we assume that our potential decays fast enough so what we can do we can take some over all elements of C mod lambda and we will consider separately x and y which are different modulo lambda and then we have a sum like this some over all elements in the lattice and in the case if x and y coincide modulo lambda then we just have to sum over the lattice without zero element we will get a sum like this and so now let's define so now what does it mean to minimize p energy so maybe maybe at this point you have some questions to the examples oh yes yes you're right thank you and so now what we would like to do we would like to fix our potential and to find the configuration which minimizes the p energy of course here one obvious problem is that for example if our potential is repelling then the points will just like go away to infinity we'll get something like that empty configuration is the best or that point should be as far away from each other as possible and so one way to overcome this is what is sometimes done in physics to make to do somehow change the shape of a potential which somehow makes this trivial solution impossible and another way the way which we will as which we will choose we will fix the density we will say that we are searching for a minimum only among configurations with some fixed density definition so we say again so let see be a point configuration configuration suppose that it has this density row and we assume that row is a positive integer and also let p not integer sorry positive real number be any function then we say that c minimizes p energy if it's p energy exists and every other configuration so every configuration in the same Euclidean space of the same density as of this time has lower p energy at least equal to this number and so another terminology for this is to say that c would be a ground state for p terminology stolen from physics and so now what we in general expect we expect that of course this ground states they will know what what happens if we for example fix density and then change our energy profiles somehow we expect that of course the set of ground states it will also change for together with a energy profile and it's quite easy to come up with easy examples like that but maybe maybe there is a nice family of p energies such that several energies have the same ground state and so these questions they bring us closer to the notion of universal optimality so how the ground state do the ground states depend on the energy profile p and so first idea is of course that they can depend a lot and so here's one example so let's consider a Gaussian core model and let's look at it in our favorite gledian space R3 and so Gaussian core model it's quite often used in physics and chemistry so first it is quite simple on one hand and on the other hand it is also rather realistic and useful so what we do here we fix some positive number alpha and we define our potential function to be the Gaussian with this exponent and so now here one observation it is that because of the symmetry Gaussian has it is what we can do we can fix a density and change exponent alpha and study ground states or on the other hand what we can do we can fix alpha for example to be pi and then change densities and search for ground states for different densities and this will be essentially the same problem so here's so what we can do so fix and change alpha and see how ground states will depend on alpha and this is actually equivalent to the fixing alpha which I like to be pi and then change density and because this is somehow used more often maybe let me just use this terminology for for a moment and so if we have fixed alpha oops sorry and therefore our energy becomes this function so what experiments tell us about the ground states for different densities the first is if density is smaller than one or much smaller than one then we know that face centered cubic lattice it seems to be the winner in this case and so what is a fade center cubic lattice it's a lattice like this which for example gives us the best packing it would take a usual cubic lattice Z3 and then in the center of each face of a cube switchers which give us a tiling of a Euclidean space we choose one more one more point and now if rho is bigger than one then here it seems like that there is another obvious winner which would be a body center cubic lattice and this lattice is they actually do all to each other after right scaling and the body center cubic lattice it looks like this so again we have we take a usual cubic lattice Z3 and now we add one more ball in a center of each of these cubes which we can imagine they are tiling our whole space so this will be a geometrically different lattice and for big values of rho this one seems to be the best so we see that there is certainly a dependence of ground states on the energy even for this very nice family of potentials difficult to come up with a nicer family but now something quite interesting happens around density which equals to one and so this was observed in the 70s by Stillinger so what he have found that if density is about is close to one then actually face coexistence of these two lattices it will have better energy than each of them separately so and so how it looks like so we divide our Euclidean space into two parts and here we consider so our total density has to be rho but we make for example half of them to be cro one and another half or two such that their average is rho and on this side we for example arrange our points in a maybe FCC lattice of density also we have to rescale it and on this side we will make it as a business lattice of another density and because of this play with different densities it turns out that we can achieve some improvement sorry but boundary does not play that much role right because bug like the dimension of the boundary is small right and like in that list in terms of our definition somehow the density of all thing is still well defined and the energy is still well defined right exactly that's why I don't understand how it can help what he proposed yeah I think it happens because because he has he has two different densities on two different sides and again so it has to do with the convexity of this you can draw a graph of like how how for example the energy of such a lattice depends on density and how let energy of this one depends on it and then around one there is something like a kink and he uses this kink to create an improvement so in the case after case of maybe two doesn't it's not something very strict right now but it looks like would look something like this no maybe not like this maybe maybe okay maybe I should draw it but he does use the somehow convexity properties of these two graphs of the energy of this lattice how it depends on density and energy of this lattice how it depends on density so we see that the ground state and it can depend in some rather complicated way is just to make sure that I'm not totally mad is it true that raw is equal to one plus two over two yes I suppose so yes and so how however to universal but universal optimality it is exactly this phenomenon that in some metric spaces we can find the very like a nice family natural family of potentials for example like Gauchan's and the same configuration will be a winner for all elements in this family and also to make it a bit more formal we will need one definition so we say that the function g again from the interval zero infinity to the real numbers is completely monotonic if it is infinitely differentiable and satisfies the following condition so it has to be like a perfect repelling potential so it is positive it is decaying and it is convex so and this pattern goes with all the derivatives so it's derivative derivatives they have alternating signs and so this will be true for all positive k for all non-negative k and here is one example so what kind of function is this for example an exponential function with a negative exponent will satisfy this condition so and so here is the definition of universal optimality which was given by Henry Kohn and Abinav Kumar so they say that the configuration is universally optimal if it is a minimizes energy for all functions p which are completely monotonic functions of a squared distance so it is a slightly stronger condition than just being completely monotonic so we say that so now a point integration c with density with some positive density rho is universally optimal if it minimizes p energy p so whenever p is a completely monotonic distance of a completely monotonic function of squared distance so p it is g of a squared and g is completely monotonic yeah but I think it is actually necessary so at least at least there are configurations which do do do this so I mean I mean we do to have like less less conditions on on on g power laws okay the power laws are also also fall into this category yes and you cover potentials sorry you cover potentials oh it's expanded one hour okay so this I'm not I'm not sure about maybe maybe mix of power and exponential it's a better function you know that much anyway yeah but maybe okay maybe maybe maybe not because the best of functions sounds like it's something oscillating right so this okay maybe yeah but this I have to check check the condition and here are the small remarks on how to be if you want our function to be sorry configuration to be universally optimal it actually it's sufficient that it minimizes energy for all Gaussians and this happens because of the following theorem which is quite old and classical probably it's theorem by Bernstein at least in some of its formulations and it says that every completely monotonic function can be written as a convergent integral of the following shape for some measure on measure mu on the interval zero infinity I was surprised by this not patients should not use our meaning our square it's kind of confusing but it is like this is to use the R squared it is somehow stronger condition and because somehow if you have a because I think if we go because it's not a very difficult computation but if we had something which was for example here function p it also will be completely monotonic if it's but somehow just completely monotonic is not enough for us for our needs and so for example like a conceit corollary for for this would be so that that C is universally optimal it is equivalent to see minimizes the energy for p equals to the E minus alpha R squared and here for all positive alpha so now I have a question how do I bring back the upper blackboard and so now we gave this very nice definition so not we but Henry Cohen and Abinav Kumar gave this definition but now of course the question is is there at least one object which satisfies this definition and as we have seen in for example in dimension 3 we don't hope for an object like this so in dimension 3 it will not exist and so Cohen and Kumar they actually studied the same question also in a compact metric spaces like on spheres and projective spaces and they found many particular examples of this universally optimal configurations and they also found a few in Euclidean space the first easy rather easy example it is that the lattice of integer numbers in dimension one it is universally optimal which is of course maybe not so surprising because what can be better than the lattice of integers so integer numbers inside R it is universally optimal and they've also conjectured the universal optimality for the few more lattices so they conjectured that the A2 lattice which is a hexagonal usual hexagonal lattice in R2 and also E8 lattice which leaves in eight dimensional Euclidean space and the leach lattice which leaves inside 24 dimensional Euclidean space that these three lattices are also universally optimal and so now the theorem which I would like to present in this series of lectures it's a joint result obtained together with Henry Cohen Abinav Kumar Steven Miller and Danila Ratchenko and so it says that the lattices E8 the leach lattice they are universally optimal one case is open so Z is now A2 yes A2 yes A2 is still open and some power it turns to be more difficult than E8 and leach lattice yeah but maybe I will come to this little bit of the in the last lecture so I'll see why things which works and big dimensions why they don't work in small dimensions and so maybe now what I don't know what would you like to make a small break so maybe maybe we can make a small five minute break and then I will explain tell a bit more about the methods of the proof and so at the second part of the lecture I would like to speak about methods of the proof of this theorem and so the proof it in print yeah I guess so it does follow from this result after after some limiting procedure but it's not it's not difficult because packing problem it also can be formulated as this energy minimization problem for some suitable like one way for this potential it's that it for example energy is infinitive two points come too close together and just zero if they are if the distance is enough of course it's somehow it's contradicts a little bit our rules for the potential but but it's somehow but it's very close to and so let me tell you know about like our sex our strategy of the proof and so the key ingredient of the proof are the linear programming bounds and I will introduce this technique in a moment and so essentially what this method is it means that we have this very difficult nonlinear problem about configure about point configurations but we replace our difficult problem by an easier one we relax it so to say by a different a question which we now ask not about points in our space but rather about functions on this space and so the problem which we will study it will be actually now it will be certain convex problem in the space of functions and because it's a convex problem here this word linear programming comes from which is a bit no strange and maybe also old-fashioned terminology but at least it works very well in some nice cases as I will tell show you in a minute and as we have to work to do this convex problem in the space of functions so it's convex it's nice but what now what is not so nice that our problem becomes infinite dimensional and for this we will need some trivial facts from Fourier analysis and in particular we will need to establish new Fourier interpolation formula and now the last piece of our strategy it is after we first relax our problem to some convex problem which magically turns out that even after relaxation we still get a precise result for this very nice e8 and leash lattices then we do manage to solve this problem by introducing new Fourier techniques what we were able to do we will reduce our question about of universal optimality to some to the proof of a positivity of some function of two variables and unfortunately this step we could not find a better way to solve it other than check it numerically so the last would be the numerical verification positivity of a certain function and for example after some transformations we can think of it as a function for example on this unit square and so let me start with the first point which would be the linear programming bounds so here we'll need two technical definitions so one of them we will recall the definition of a Schwartz function so the Schwartz function on the f-credian space it is a function which is infinitely differentiable and also the function itself and all its derivative they decay faster than any inverse power so and also we know that and this will be true for all positive numbers alpha for example we can take them to be integers and for all multi indices beta and here also one piece of notation so as we have to use a Fourier analysis we have to introduce Fourier transform and so here I just because there are several different conventions about how to write down the Fourier transform I will write my favorite way of introducing it and the following and so here by the dot I will denote the usual scalar product so standard inner product gradient space and so now when we have this notations we can formulate what a linear programming is and so this method is used quite often in metric geometry and then analyzing optimal configurations and so usually for each space for each kind of problem there is a separate adaptation and so Henry Cohen and Abinav Kumar they developed a nice adaptation of linear programming to this energy minimization in Euclidean space again let P be any function any energy profile so but this time we do want it to be a repelling energy profile so we don't allow P to take negative values and we suppose that F is a we were able to construct a Schwartz function and so we suppose that this Schwartz function satisfies several nice conditions so first we suppose that F is bounded above by P to all points except for zero and also that the Fourier transform of F is non-negative then we know that then every configuration of Rd with density rho it will have lower P energy which is at least this number which will be rho times the value of Fourier transform of F at point zero minus the value of F at point zero so we have obtained an estimate for possible P energy and so now let me give you a short proof of this statement and so this is what I say that we have somehow replaced our problem about finding good content about configurations of points by convex problem for functions because now our problem becomes just finding such suitable F and the conditions which we have one F they are convex conditions so F has to satisfy these two inequalities and also this value has to be optimal for us and in general as we will see now in a proof that this is a sort of clearly a relaxation of our problem so in general what we obtained this the question about F it is a weaker statement it will just give us the lower bound in most of the cases but of course we will not replace our initial problem and so let's do the proof and so here now I will just to make my life a bit easier I will not do the proof for general configuration but I will prove this statement for periodic configurations so suppose that C be a periodic the lambda periodic configuration and lambda is some lattice so then we have the following we can write the P energy of this configuration on the following quays so and so now at this point we just used the computations which we have done before when we considered periodic configurations so now what we do we can estimate this number from below using the proof in the fact that F does not exceed P so we can write in the following quay and now because F is already defined at zero where P was not we can rewrite this in the following slightly nicer way maybe more symmetric so we will write the sum over all x and y in C modulo lambda not excluding the case where x is equal to y and now the only term which we will have to subtract would be F of 0 and so now what we do at this point we use the Poisson summation so we write our sum like this and again so here lambda star is a dual lattice so it would be the set of all mu such that mu times L is an integer for all elements of the initial lattice L and so now we do maybe the somehow the most non trivial part of the of our proof so what we will do we will replace this double sum by absolute value squared of a single sum so we leave our summation over dual lattice and so now here the trick comes so we have written a sum like this and so now okay okay sure it should be F and so I think now it's not correct and so now a good thing which car which we see here is that this the absolute number squared of course it's a non negative number so here we can use our conditions from the theorem that the Fourier transform of F was a non non negative so we can again estimate this number maybe I'll do it in this black part so now we throw away all the terms in our sum over the dual lattice except of the the one where mu equals to zero and so now this the the sum of exponentials if mu equals to zero it's very easy to compute it it will be just the number of elements of C modulo lambda and we have to take it squared and now this is if we see that we can cancel something cancels out here and what we will get we'll get the number of elements in our configuration modulo lambda divided by the co-volume of lambda and this is just the density of the configuration so so this proves our statement and so the general case where we consider not only periodic configurations it was actually so general case was proven by Korn and Corsi Ireland and so now we can look at the proof and we what we try to see is in which case we can hope for a sharp bound so in the proof we have seen that we when we prove so we could get a sharp bound only if all the inequalities which we have written in our proof they are actually equalities and when by each of these estimates we essentially did not lose anything and again some by considering different case and doing numerical experiments we do know that actually sharp obtaining sharp bound by this method it is a very rare occasion so usually we get just some estimate but this estimate is not good enough to completely resolve the problem but still in some cases it does happen we do get sharp bounds so when can it happen so again suppose that so we make the following assumption suppose that lattice suppose that our optimal configuration that is actually a lattice and that it minimizes p energy for some p and we suppose that this can be proven by constructing appropriate function f your programming method first function f so it means that in all the our inequalities on that blackboard we we don't have any losses so and so this give us quite restrictive conditions on the function f so first we know that our function of x it has to be equal to p of x for all x which are in in our latest lambda maybe accept for zero and also we know that the value of the Fourier transform of our function it has to be exactly zero for all y which are in the dual lattice again without zero and so now the question is so something that we observed numerically that actually in in some cases these conditions knowing these two conditions it is enough to identify the Schwarz function f uniquely so only by giving these two kinds of restrictions we can then reconstruct f at least in the space of Schwarz functions and so here is another result which I would like to present during these six lectures and hopefully also to prove it so it is the following interpolation formula here maybe before I write the formulas so one more remark so we see that these two conditions these two equalities have to hold but also they have to hold to the second order because of the inequalities which we have so if our function p is nice and smooth then it means that f has to coincide with p at all lattice points but it also it has to satisfy up to also the first derivative has to satisfy to coincide and the same happens for the Fourier transform because we know that f at point y is zero but also I've had it is a non-negative so it means that it is the derivative of f hat also has to vanish at this point and so now the question is whether we can reconstruct function by knowing its values and values of its Fourier transform and their first derivatives and some discrete set of points and so suppose that d and and 0 be either 8 and 1 or 24 and 2 then every f in the space of radial Schwartz function so here we consider not any Schwartz functions but only Schwartz functions which are invariant under rotations around 0 so any radial Schwartz function is uniquely determined by the following values so we have to compute f of square root of 2n its derivative at this point Fourier transform and the derivative so it's Fourier transform and this should be you know you should know these numbers for all integers and which are bigger or equal than to number and 0 and and 0 it depends on a dimension so if dimension is 8 then and 0 is 1 and if dimension is 24 then and 0 is 2 and so more precisely we can write in the following way we know that there exists an interpolation basis consisting of functions a n b n a n tilde and p n tilde and they are all radial Schwartz functions and again so we have a such four sequences of numbers with index n which starts from n 0 and so this basis is defined by the following property so such that for every function f we have the following formula so equation by i f for interpolation formula so we know that f of x equal to the following sum so n goes from n 0 to infinity and here we have so f of square root of 2n times a n of x plus its derivative value of Fourier transform at this point and so also what is important is that this series it will converge absolutely and of course the convergence is not very difficult because we started with our function f which was a Schwartz function and it means that these values over which we are interpolating they are already decaying very fast so the only thing we have to ensure that the values of these functions a n and b n and a n tilde and b n tilde they don't grow too fast for example that they grow at most polynomially in index n for fixed x and then we'll know that this serious converges okay so actually we proved that they can be arbitrary sequences yes so in any dimension if we to take for example Schwartz functions and consider these its values such for example all square roots of integers and its values and the same Fourier side we know that there will be some relations between these sequences but there will be only finitely many of f of not finitely many but it will be finite dimensional space of relations and then it will be actually described by some space of I would say modular forms or modular forms like with general sense but but I will come how probably explain this on our next lecture a bit more and so and so let me write a little bit about the properties of these functions a n and b n so so it's actually it follows from our claim that this formula it is an interpolation formula for example it should works for functions a n and b n themselves and so what does it mean that they are interpolating basis so they have the following properties so so it means that for integers any pair of integers m and n which are bigger or equal to n 0 we know that for example functions a n if you evaluate them at points square root of 2m so they will be it will be this value will be equal to 1 if n is equal to m and it will be 0 otherwise and at the same time the derivatives of this function they will vanish and the value of its Fourier transform at such points they will also vanish and the derivatives of the Fourier transform is also vanish and for the function bn we will have a slightly different story so here are the values of the function bn they will vanish at all our chosen points on the other hand the derivatives they will vanish everywhere except for one point where m is equal to n and the values of bn and the values of the derivatives they will both vanish on the Fourier side and another useful symmetry here it is that if the Fourier transform of a n it will be actually equal to the function at a n tilde and the Fourier transform of b n it will be equal to b n tilde so the Fourier transform in all these is taken in one dimension r squared or in rd? no no it stays taken in rd but we work with radial functions so it's in a sense it is one can think of it that because all our functions they will think of them as a d-dimensional function to take Fourier transform but essentially they are one-dimensional so this Fourier transform it could be replaced by some Bessel transform for one-dimensional functions and the derivative is the derivative of the function of r squared okay yes so here the derivative it's actually the derivative of one-dimensional function so it's somehow radial derivative in radial direction thank you and so here maybe I'll use some notation so we'll denote by lambda 8 this would be the E8 lattice lambda 24 this sub-index 24 this would be the leach lattice so these are very famous mathematical objects and maybe they don't need too much introduction but I'll just remind that these both lattices they are even and unimodular lattices and so even it means that if we take any vector L in this lattice then its Euclidean norm will be a square root of even integer and unimodular it means that the co-volume of the lattice is one and also one important fact it is that the so the shortest vector of course shortest non-zero vector in lambda d it will has length or has Euclidean norm square root of 2 and 0 where in 0 is like in the formulation of our interpolation formula and so now when we have an interpolation formula and we know this properties of the optimal axillary function what we can do we can combine this together and construct our axillary function and so by combining what I have just said so now we see that the only possible axillary function that could prove a sharp bound for for this fun for the lattice lambda d where d is either 8 or 24 at least the auxiliary function among among Schwarz functions would be the following one so this would be the function f of x which is the following sum because we know that such a function that will coincide with p up to second order in all vectors of of lambda and also it will vanish at all the vectors of as a Fourier transform of f it will vanish at all the non-zero vectors of the dual lattice which in our case is actually the lattice itself and so now but now of course we have extracted this information only from knowing the equalities but in in the proof of Conan Elkis about linear programming we know that knowing equalities is not enough we also have to prove the inequalities and this is what will prove the universal optimal the universal optimality for us so so we also need to know what happens to the function f in all other points now it suffices to check f of x actually does not exceed p except for zero and also that the Fourier transform of f is non-negative for all points y in the dimensional Euclidean space so we need to have a picture which looks something like this so so if we have our potential which looks like something like this then our function f has to be like this and Fourier transform has to be something like this yes so this we will do this for the gaussians right and so again so this is what you said so we will remember that lambda d it is universal optimal if and only if it is a ground state for all gaussians and so now a few words about how to how to approach this problem so now we have to prove some inequalities for now we do see where the proving positivity of a function of two variables comes from now we have somehow two variables here one of them is alpha the exponent of a gaussian and another is x which is a length of a vector and we need to prove some inequalities on our function for all parameters x and alpha and so come out to do this what will be very useful is to have an explicit formula for our function f which somehow would be we also get it if you could have explicit formula for example for this for interpolating basis functions and so now I will finish but now okay there is a trick which actually allows to do it only on one side I will also show it to you now in a moment but so let's let's first I'll write on how to first how to make these functions explicit so that we can work with them and prove inequalities and second part is also how to like instead of proving two inequalities how to prove only one so now we consider the the following generating functions right by f capital of tau and x the following functions so first function the function like this and second one the function like this the same only with still does and so here in these functions here x it will be a variable on space and tau parameter tau it's an element in the upper half plane so it's a complex number with a positive imaginary part and so now what we see that if we substitute tau to be i times alpha the purely imaginary number then what we will get here we'll get the function which we had before this will be this auxiliary function for the Gaussian with parameter alpha so now the inequalities now the inequalities capital f of i alpha x smaller than equal e to the minus pi alpha x squared for positive real alpha and all x in the Euclidean space and now we can take the Fourier transform of this function but we take a Fourier transform with respect to the second argument in the function so we consider alpha just as a parameter and compute the Fourier transform again for all alpha and for all y in the Euclidean space and so now these inequalities they will imply the universal optimality of the lattice lambda d all the letters were interested in and so and so here now I will show you a trick which helps us to compute this function capital f of tau and x explicitly and therefore it will also help us to find for example the interpolating basis and the auxiliary functions we are interested in and so the trick is the following so now what we can do we can apply our interpolation formula to the complex Gaussian so the Gaussian with yes yes yes also I so what we do now we want to so so we now in applying interpolation formula which is now in the middle upper blackboard to the following functions to the complex Gaussian p with index tau of x it would be e to the minus pi i tau Euclidean norm of x squared and then what we will see so that it is equivalent to the following expression which involves our generating functions capital f and capital tilde it's equivalent to saying that 2 e pi i tau times the Euclidean norm of x squared equals to the f capital f of tau x plus the following and now because the Fourier transform acts nicely on Gaussians so here as a from the last two terms in our interpolating formula we will get also not exactly the capital f tilde but the function which is closely related to it so it's the function which is obtained by capital f tilde by a simple modular transformation function like this so we have got a functional equation which looks like this and we secretly actually would have also two other functional equations for these two functions so secretly we also have we also know that this both functions they are so to say linearly periodic we know that if we take f of tau plus 1 x minus 2 f of if we take the second difference with respect to tau so this will vanish and the same will happen for capital tilde for the capital f tilde oh yes minus one over tau think minus one over tau and so now we have this free equations for f and f tilde and now these three equations they actually they allow us to find these functions explicitly and this is something we will speak about on the on our next lecture tomorrow so somehow somehow because we want our interpolation formula to to be convergent so this gives us already some gross assumptions on f and these functional equations together with gross assumptions they will allow us found f and f tilde explicitly and so I think I have one minute left so I can maybe show you how to instead of proving two inequalities how can we prove only one inequality so now we can see that actually if we prove this inequality it will also apply this one and it follows from the functional equation and the fact that the Fourier transform of capital f with respect to the second argument will be just f tilde in equal this inequality f of i will equal 0 for it implies is actually bounded by e to the minus p again for all and so how do we see it we see it from first we know that if you take f capital this would be just tilde and this formally this follows from the properties of the functions and the interpolating basis it will follow from from this property and second what we just have to use we have to use the functional equation so so we know that f of i alpha x it will be equal to the e minus pi alpha the Euclidean norm of x squared minus this number and so here we use the fact that f tilde is actually equal to the Fourier transform of f and here we use the fact that our d is divisible by 8 the dimension is divisible by 8 and so here at this step we can use our assumption which we have made so we see that this is bounded by the exponential by the Gaussian this is exactly what we needed to prove so instead of proving two inequalities we actually need to prove only one of them so thank you very much okay so I did not formulate it like this in the theorem but it but it is actually the property yes yes okay so they actually have to do with dimension right so it's amazing that this lattice comes out special if I follow your experience I would say I would guess that the other light is that one might have looked at like 8 to twice the 8 or the 16 or the 23 nemyo lattices don't satisfy this so they will not work yes yes yes so they do it by 8 is just a small part of the story of course of course I think it's and also we still hope that something is something you know something is going on with for example in dimension 2 and also in dimension 1 so yeah so arithmetic properties are important but I think they're quite subtle here question about interpolation formula so are there other Dean and not for which it works I think I actually it works for every dimension with some okay so maybe of course like this and zero it will always do depend on it on a dimension and this number it can be actually like how exactly do depends it can be described by dimension of some space of modular forms and also like what's a bit special about in this case which might not always be true is that like for example here we can start our formula from the same number and zero everywhere and in general it could happen that yeah like like the total deficit in dimension is not divisible by 4 and then we have to divide maybe they take I don't know more values on free a site or more derivatives so is it possible to find explicitly this function f capital for any dimension yes there are also some I think in the sense that we have to make some choices like for example to choose where to start your summation and after that it is possible so you only need to specify these two pairs because there are examples of the latest yes yes because there are also some maybe not so pleasant technical details details which you did not want to work them in like in a full generality but yeah but we concentrated on these two cases only because because of our application


What up everybody? I'm Joe for JaspysCaseBreaks.com with our final Jaspys The Diamond Dozen. Baseball case break. 12 cards in here. It's our very own repack product curated by us. Just for you. Just for you. This is our final case. We only produced 9 cases, so a lot of these may be checked off the board, but there's got to be some stuff left. Big thanks to this group for making it happen. Thanks to the people who bought their spots straight up. And congrats to the people who won their spots in the filler. Number 41. All 30 teams are in. Let's roll it. Let's randomize it. 1 and a 4. 5 times. 1, 2, 3, 4 and 5. James down to Michael after 5. And now for the teams. Fingers crossed. Good luck. Trade at your own risk. A lot of those cell shades were probably, most of them were probably pulled. This is the final case. 1 and a 4. 5 times for the teams. 1, 2, 3, 4 and 5. I think that does ring a bell. Mariners down to Angels after 5. James with the Mariners, Danny with the Cubs, Nester with the Reds, Ed with the Diamondback, Steve with the Pirates, Ed with the Braves, Eric with the Rangers, Rory with the Padres, Chad with the Marlins, Nester with the Brew Crew, Jimmy with the Phillies, Tristan with the Tigers, Melissa with the Met, Nicholas with the Guardians, Thomas with my Dodgers, Chad with the Nats, Rory with the Royals, Melissa with the Red Sox, Jason Waters with the A's, John with the Blue Jays, Danny with the Yankees, James with the Astros, Nester with the Cardinals, Danny with the Rockies, Eric with the Twins, James with the Rays, Jared with the White Sox, Michael with the Giants, Carlos with the Orioles, and Michael with the Los Angeles, California, Angels of Anaheim in Orange County. Let's sort by column A or column B that is alphabetically. And we're going to pause the video just for a short bit. When we come back, we're going to see if there's any trades and then we'll have the break. Stick around. Be right back. All right. Welcome back, everyone. The scary trade that has happened. These guys weren't scared. They were like, screw it. I'll trade. They were feeling frisky. Danny is out of the Yankee spot and into the Astros spot. Put a T there for trade. James is out of the Astros spot and into the Yankee spot. Put a T there for trade. TWC trade window closed. TWC. We should run a promo where someone gets TWC tattooed on them with the Jaspy logo that they can close the trade window whenever they want to. All right. Don't do it. I'm kidding. Wednesday the 12th, Random Team 9, our final box, which is case number seven. I think we still have the paperwork here. That was the last one remaining. Thanks, everybody. I feel like we filled these nine cases up fairly briskly. I appreciate that. It was a lot of fun. All right. Thanks again to this group here for making it happen. Appreciate it. Believe it or not, Rick, there are some jerks out there. You can see on the top camera. Was there a filler card in here? All right. There's some graded cards. I'm going to do the non-graded cards first. Then the prize, the filler. There's two fillers in here. Two different prizes. We'll do that before we do the graded cards. First one, Anthony Rizzo. All-Star Rookie Team, Anthony Rizzo. Nice. Eight out of 25. This is from a 2020 set. It's more of a flashback sort of card, I guess. That's going to go to the Cubbies. Danny with the Cubs. We have for the Anaheim Angels, Tim Salmon. Part of the Joe Jaspy All-Fish Team, a one-of-one. Michael P with the Angels. All aboard the Big Hit Express. Next up is Tim Anderson. I think he recently got injured. Get well soon, Tim. That's a one-of-one. Another one, White Sox. Jared with the White Sox. All aboard. All right. Next one is Raphael Devers. 10 out of 10. Nice flawless baseball Devers for Melissa and Boston. And if you like flawless, ladies and gentlemen, Jaspy's CaseRace.com, we've got a one briefcase random team break. ABC, always be closing. Next up is Jacob DeGrom, 7 out of 25. Triple Relic and Autograph from Museum Collection. That's for the Metropolitan's. That'll be for Melissa. Back to back. She's heating up. She's on fire from downtown. Next up is Mike Traut. He's the first best fish in Angels history. Tim Salmon, as Oliver was mentioning, second best fish in Angel history. Was Mike Karp ever on the Angels? All right. A couple more numbered cards. We've got Fernando Datis Jr. Rory and the Padres. There you go, Rory, from Spectra. Spectacular Autograph. Is that numbered? No, I don't think it's numbered. There you go. And we've got, trust me, she'll like it too. Two out of 10. Dual Relic and Autograph. Frank Thomas. That's Toronto edition of Frank Thomas, by the way. And that's going to go to John and the Blue Jays. We've got the first filler card. It's the Brewers. Get a box of 2021 Bowman Chrome Sapphire edition. Congrats to Nestor and the Brewers. The other one, Tigers. That's Tristan with Detroit. You get a box of 2021 tier one baseball. Nice. All right. A couple of graded cards. We have a PSA 10. Luis Robert from 2020 Bowman Chrome Sapphire. 32 out of 75. That's Jared with the White Sox. And the last one. Ka-boom! You're on Alvarez. 2022 Absolute Baseball PSA 9. And that is for Houston. That's Danny and the Astros drawing blood in that trade. There you go, gang. I'm Joe for jazzy's casebreaks.com. Thanks for watching. Thanks for breaking with us. I'll see you next time for the next break. Bye-bye.


ThinkTekAway, civil engagement lives here. Welcome to the Asia Review. I'm your host, Bill Sharp, back after a four-month period of absence during research in China. And it's good to see everybody out there today. Our program today is the Pacific Island Nation's Leadership Program with Taiwan. And our guest, I'm going to let them introduce herself first. Christina Monroe. Super. Senior Manager with East West Center of Leadership Programs. Great. I'm Laura Kahikina, Director of Environmental Services with the City and County of Honolulu. Great. Well, it's great to have you guys here with us. And I know, Christina, you just got back from Palau, so we really appreciate you being in here today. Yes. Glad to be here. Well, tell us about the program. What's the program seek to achieve? Sure. So the Pacific Island's Development Program is a five-year-old program with generous funding from the government of Taiwan, from China. And it has now served 122 fellows from 15 different island nations, both here in Hawaii. They spend about a month here in Hawaii and a month in Taiwan. Wow. Wow. So, now, just tell us what some of the Pacific Island nations are that are included in this. Sure. Vanuatu, Papua New Guinea, Salamence, Samoa, federated states of Micronesia, to name a few. Wow. Yeah, I mean, of course, the Pacific Island is a cover, a really wide, broad area. Yeah. Well, what kind of this program started? What was the impetus for this program? It was really the Taiwanese government coming to our state department and saying, we would like to invest in these island nations and foster their growth and their leadership capacity within both their government, NGO, business sectors. And the state department then coming to East West Center, knowing we could do the job having had the Pacific Island development program since the 80s and thinking we could do it and so far so good. Wow. That's great. That is really great. And just how long is the program? It is approximately two months. Two months. Okay. Great. And so, the folks that participate in the program, these are developmental officials from all these Pacific Island nations? Different things. Others might work for the Palau Conservation Society. Others might work for the Tourism Authority, the National Congress. A lot in government, but again, some business, some NGO in really all sectors. Great. Great. So, Lori, now what's your role in all of this been? So my role, I was actually kind of taken aback when East West Center first contacted me. I had no idea this program existed, but I was thoroughly impressed. But they were more interested in the city and counties, landfill and age power facilities.  Some of these other countries, they don't necessarily deal with it in an environmentally friendly way such as city and county does. So we gave tours of our facilities. And then also, my role when I spoke to the participants was to talk about leadership and management. So like I guess as Christine mentioned, I'm one of the mentors of this program. Oh, that's really interesting. So basically, you're here in Honolulu because you work for the city and county, but you're kind of an advisor to the program? When they ask me to participate, whenever they have new students come in, then they come in to our facilities and I will meet with them. Oh, wow. That's great. That is really great. Well, I think everybody knows that the Pacific Islands are probably an area which has been at different times kind of overlooked and probably can benefit from a lot of this sort of attention. As I recall, this program was started when Kurt Camel was the assistant secretary of state. You're exactly right. And he was very, very keen on the Pacific Islands. His book, which I think is a fabulous book, one of his books called Pivot is all about how the U.S., well, not all about but gives a lot of focus to the Pacific Islands and how the U.S. needs to ramp its game up. Yes. He's still a great friend and advocate of all our leadership programs and especially this one. Yeah, we're thankful for the role he played. That is great. That is great. Okay. Now, okay, so we have the East West Center. We have the Taiwan government and East West Center means U.S. government. A good portion of our funding comes from government. That's true. I don't know how you count the movers and shakers behind this program. Do you count them as two or do you count them as three? East West Center and U.S. Governor all rolled into one? How do we do that? Yeah, sure. Taiwan, of course, being the primary funder for this one is our go-to. We ask their inputs, of course, and they guide us. But what we really respect about them as a funder is that they trust what we do. They like what we do. We're in constant dialogue with them and the IDIA folks there to find out what's going on with them. What would they like to see more or less of in the program? So they're closest friends in the process. That's great. That's great. I know that I just came back from China and Taiwan a few weeks ago and on the way back to Hawaii, I stopped in Taiwan and had a meeting with some folks in the Ministry of Foreign Affairs and I know they're rather keen on this program. Yeah. I really agree. So now, when you're in Taiwan, where is the training carried out at? It's we work with the IDIA, Institute for Diplomacy and Foreign Affairs and they play a big role. So we stay right next door to them. They guide our meetings. They take us on site visits of importance which echo the important case studies of leadership they do here in Honolulu to see how things are done in Taiwan. So okay, do you stay mostly in Taipei or you're panned out and spread out throughout the country? Yes. A good portion of the time is in Taipei but they also have a final retreat and refraction space. It's a bit outside of town. So get out a little bit. Yes. Oh, that's super. That's super. Now, do you go along to Taiwan or are you just sort of holding the fork down? Just holding the best. It is an interesting idea. No, I just hold the fork down here. I see. That's great. That's great. You know, in Taiwan, Taiwan is very concerned about environmental issues and especially with the party that's ruling Taiwan at the minute, they're very big on being green, environmental issues. So it's interesting to hear you talk about some of those environmental issues. So how many folks do you have in your section at East West Center that handles this program? Yeah, we have about nine people that do Pacific Island initiatives and that could be a range, the North Pacific Women's Action Program led by Gretchen Alter. We also have Scott Croker. We have Nick Barker. Many people that are involved with different aspects of Pacific Island programming and this is one of those. That's great. That's great. And so as this program goes forward, how do you see it evolving? Great question. We like futures questions. And I think that's an important reason why Lori's with me here today that I think moving forward in our leadership programs, profiling Hawaii's leadership cases and community leaders that we respect and making sure people understand leadership questions aren't easy. There's dilemmas, there's trade-offs, there's a lot of complexity. And I think when they sit down and talk story with Lori from all these different islands, they share there's a camaraderie that comes from being island nations together, struggling with problems and as well the leadership case studies that Hawaii can provide. Not that we're better or more advanced but that we're part of this neighborhood of Pacific Islands and meeting friends, struggling with waste, whether that's solid or wastewater as Lori is. I think they feel a connection, a kind of relief and then also a lot of learning that comes from it. So moving forward, profiling what Hawaii does best and introducing them to those folks and having honest dialogues about the choices you have to make. Now I'm sure the program has had many successes but what's a kind of outstanding success that you might tell us about? Oh my goodness, that's a hard one. Do you want to say more about that time? No, no, no, no, not at all. If you need me to give you time. I'd love for her to describe a little bit more what they did with you when they had a conversation. Sure, when she first approached me, usually I asked for, what are some topics that I could put together PowerPoint, she'd say, no, no PowerPoint, just speak from your heart. And it's like, I don't know anything about this program. They had a reception prior to the meeting with me and I took down notes of everything what they were all interested in and a lot of them were environmental issues, clean water, what do you do with the sewage and leadership and management questions. So I just went one by one on some of those things, what they're interested in and I really enjoyed myself. I'm not used to speaking like that, usually it's a set PowerPoint and here's my notes and at the end questions, but it was so interactive. I really enjoyed it and I really do hope they invite me over every year for their program because it was educational for me too. You just take for granted what we have here. You flush the toilet, you turn on the water, it's there and you just meeting with them. I have a much greater appreciation for what we have here. Oh, that's great, that's great. Well, now that we talked about successes, what are some of the challenges, what's the biggest challenge? Sure, I think anytime we do residential leadership programs and we have a large suite of those at East West Center, I think people get really jazzed and they have a cohort of like-minded folks, they live with them, they eat with them, they have fun with them, they're doing trainings with them. That transition back home and how can what Lori talked about be used.  So how do we navigate this change with my new knowledge and not get too big for my britches? Change bureaucracy in a Pacific Island nation. Exactly, so they're empowered as an individual but how can we increasingly, and our challenge I think as trainers or facilitators is to give them tools that they're going to be able to share with their teams so that they're changing systems. They may feel jazzed but no one's going to care maybe when they get back so how can they make that real for their community and make it something useful to others around them. So a little bit more of the train the trainer model I think is useful giving them tools they can go back and teach others about and then they've got a team on board with them for the change they want to make. Right, and I mean these are all Pacific Island nations that you deal with but each Pacific Island nation is different, it has its own different culture, its own different customs, its own different language. So there's a lot of challenges aren't there? Yeah, absolutely having just been to Palau and Yap and Micronesia just seeing the difference between the four states in Micronesia and then Palau and Marshall's all really different. There's some, we're cousins, there's some shared challenges but they're also very unique in their geography and their systems and their history so being both respectful of their differences and that's just within the North Pacific. Then you throw in the South Pacific and a lot of differences and they themselves often maybe know more about the US than they do about each other. So building that Pacific camaraderie they might not have actually met someone from Melanesia and their Polynesian that sometimes not and so getting a pan Pacific cohort vibe and around shared challenges we're all dealing with waste but we're all from very different places that can be one of the biggest takeaways that some of the participants have is that pan Pacific family. That's a really interesting comment. I think what we'll do is we'll stop there. We're going to take a break. You're watching Asia in Review. I'm your host Bill Sharp. Our show today is Pacific Island Leadership Program with Taiwan. I have two guys here with me Christina and Laurie who are filling us in on this program and we'll be right back so don't go away. Hello everyone. I'm DeSoto Brown the co-host of Human Humane Architecture which is seen on Think Tech Hawaii every other Tuesday at 4 p.m. And with the show's host Martin Desbang we discuss architecture here in the Hawaiian Islands and how it not only affects the way we live but other aspects of our life not only here in Hawaii but internationally as well. So join us for Human Humane Architecture every other Tuesday at 4 p.m. on Think Tech Hawaii. Hey baby that's you. I want to know will you watch my show. I hope you do. It's on Tuesdays at one o'clock and it's out of the comfort zone and I'll be your host RV Kelly. See you there. Welcome back to Asia in Review. I'm your host Bill Sharp. Our program today is Pacific Island Leadership Program with Taiwan and my guests are Christina and Laurie and they're very much involved with this program. Christina is the boss and Laurie I guess you would call it as a consultant. Sure. A big boss on her own right. Yeah. So this is a really great program that really it gives so much help to Pacific Island nations and but OK the United States definitely has interest in Pacific Islands but there are other countries that do to Australia and New Zealand. Do you see did they have similar programs. Sure. Australia New Zealand especially invest heavily in leadership development. A lot of aid a lot of our fellows will work for Australian aid funded organizations so sure. And it's a some of our other programs the North Pacific Women's Action Program brings together funding from New Zealand and U.S. So definitely we're working together with other with other nations to to support collaborate with Pacific Island nations. OK. Now let me say Pacific all the country all the I don't want to say countries quite yet all the areas that the Pacific Islands you're dealing with these are independent nations with there's still some European colonies in the Pacific. Do you deal with colonies as well. Sure yeah and some have special relationships like Tahiti with France. There's there's definitely different levels of relationships with past or current European or U.S. There's American Samoa although of course the compact agreement with Micronesia so yeah a different relationship with different countries. That's great that's great that's great. I'm just a question on the tip of my tongue I almost lost it. OK now when you're in Taiwan you're you said you were mostly in Taipei right. But what are some of the other areas in Taiwan that you go to to carry out the training. It's a good question and next time I hope to go myself. So I can answer that question better of other staff members normally escort them. So I see. So I'm probably not the best person to ask that to be honest. OK. But a lot of it is looking at case studies. They have our important department so mostly in Taipei but again they end in a retreat that's outside of town and that's also to get away kind of from the urban so they can enjoy a closing retreat in the outskirts. So the real focus is on leadership development. Right. Do you guys get into like village development land reform or that kind of thing. Or is that out of your scope of concern. No no it's a great question. East West Center leadership programs generally work with the individuals sometimes with teams but primarily we get to all those issues but not in a way that we're directly doing like an international aid or an international development office would do we more work with individuals embedded in those systems give them tools give them ideas that are more that they apply to their context so we might not know about specifically about wastewater in a certain village but that's why when we bring them here to Honolulu we give them general leadership foundational leadership skills and then we have them do different case studies with Lori looking at solid waste and wastewater. We also go go to NOAA we go to Paycom we go to the women's correction facility looking at deep deep sea research that's happening so we do a lot of different leadership case studies in the community that would give them that context specific to insert into their work. How would you characterize Pacific Island leadership is there a Pacific Island mode of leadership. Oh boy that's a dangerous question like it would be here in Hawaii to generalize is is difficult. I think one thing working with the Pacific Islands 15 nations that we do we realize how it's unlikely to be able to generalize across the 15 I think there's some shared and some things that Hawaii shares as well. I think there's an importance of elder reverence and elder knowledge. I think there's a challenge between indigenous and Western knowledge systems and how that's kind of where I wanted to go. Because I know that can be tricky. Sure. Yeah that can be very very tricky. But I think I interrupted you. No no but I think you know it's something Hawaii has as well. It's a blessing we have to be able to have different systems to make sense of not just getting from one system but then it takes some negotiation around that and who's the authority just coming back from. Yeah they have a fourth branch of government in addition to the three we have and that's the traditional leaders. So how did and they are consulted just like a branch of government. And so how they merge and do that is unique to say how Palau is doing it. So exciting to see that. Could you very broadly say that Pacific Island leadership is consultative in nature that it seeks to create like army you know sometimes Western leadership is sometimes characterized as being a little bit set them up and knock them down. Kind of like well here we all guys we're going to do it my way. Sort of I guess that's a classical notion of Western leadership. Whereas I somehow have this notion that like I'm more familiar with East Asia than I am with Pacific Islands and and I think in the Far East there's more of a consultative collaborative approach to leadership and I have a sneaking suspicion that might be true in Pacific Islands but I don't really know. I think so I'm depending on your expertise. No and I'd be curious what what Lori thinks just in talking with them a little bit but I a lot in her mentorship but I think it comes from also having a small space I think geography does come to play here we have they we all have limited resources but islands as we know we're more aware of our resources and that means how we steward those and who gets to consult in it's probably going to need to be a bit more collaborative because we're aware of the limits of this space we occupy so maybe by force you can't you can't go west and run off and find vast tracks of land. So I think that that plays in just as when you look at the difference between Hawaii and mainland leadership you might be able to maybe maybe not but I think you could say something that that had to do with islands but I don't know what you think after all your experience in Hawaii. I can see it both ways because our resources are limited we sometimes do draw that line you know even between government state and city and and beds like no this is my responsibility this is yours so it's both both ways sometimes we're collaborative and sometimes it's here's the line. This is our Kuliana. For all our non-Hawaiian listeners Kuliana means turf. Very well put. That's really really interesting yeah that's really interesting yeah cross-cultural leadership that's that's that's a challenging enterprise. Well how about some of the feedback you've received on the program. Yeah obviously the government in Taiwan must like it or they wouldn't have renewed it. Yeah right yes and I should say that so we'll we just receive order five more years of funding so until 2022 so that's that's good feedback from them but I do think it's based on participant feedback I think and Laura you heard you heard from their opening ceremony. A little bit more about what they wanted to get out of it. I think we're hitting that pretty good and exceeding expectations in terms of building this pan-Pacific network. I think leaving with that really really opens their mind to other possibilities and seeing the differences and the similarities between other Pacific so the network itself we get a lot of feedback about that I just met about five in my travels I just met about five or six alumni and I think that feedback that it's it's opened them up to approaching problem solving or taking a more appreciative lens to problem solving and trying it from different directions that's pretty big feedback we get basically unlearning and relearning is just as important as learning in our programs and I think they they find that impactful. I see I see you. OK you're basically interested in leadership I know one of the great natural resources of Pacific Island nations are the great fishery resources. Do you have any interface with like fishery organizations and helping them maybe to ramp up their leadership skills. Sure. Sure. You can't walk too far in the Pacific and not not hit up against this huge resource. A lot of people are involved in and sure a lot of the fellows we have have some affiliation with government more likely government or or NGO some business interest related to to fisheries and that's yeah it's a it's a huge deal for them I think looking at even more recently looking at building infrastructure around say the canning of tuna and putting in those facilities so not just using it as a selling our resources but how can we do value add and that but that will get in you know to waste how would they deal with the waste of that and process that and every island's kind of making different calculations around that. There seems to be like a lot of emphasis on environmental protection. I don't know if this question sounds a little naive I'm going to stick my neck out here. Why. Why is there is this program seem to put so much emphasis on environmental protection. Oh. Did you want to answer that. Well you could say why it's important and then it probably blew back to why we had it. Actually what in in that reception a lot of them did come up with that environmental I think as Christina said we're on an island.  Our land is so we only have a very limited amount so how we deal with it. Some of the students what they've shared with me they do just have a landfill and they just dump everything there. There's no monitoring. Our landfill is very strict. What what what can be disposed of there when what time and we have to close it every day. We have to cover it where there's birds there's rubbers that people can sift through the landfills over there. That's not allowed here. And so I think just just opening their eyes on how things can are done here. It was really educational for them. Oh that's great that's great that's great. You know sometimes when I think of and this might sound just a little bit naive too. So you'll forgive me again I hope but sometimes when I think of a civic island nations as as you guys have pointed out several times today the land masses is somewhat limited and some of them are really challenged by which would say like their land is disappearing. And it has that is that an area which you kind of address leadership of how to preserve the land that you have. Sure. It's a it's a big issue. It's not a future issue for Pacific Islands. I think that's why they take a global lead on sea level. I've just been told that we have one minute left. So I have to notify you. Super important. Right. And as they have less land and have to move infrastructure what salination talked a lot with Laurie about that. It's something we'll have to deal with in Hawaii and they will too. Great. Great. Great. Well I think we've come to the end of our time here. I'd like to thank our guests for joining us today and we all need to pay more attention to Pacific Islands because they're unfortunately have been overlooked a bit and this program certainly does seeks to write the balance. I'd like to thank everybody for joining us today and I'd like to see you again next week when my guest will be Peter Olson Peter Olson is a former Pentagon consultant and strategist and he brings the wealth of knowledge here to share with all of us. So we'll see you again next week right here on Asian Review.