So hello, everyone. Welcome to the first seminar of 2021. Today's talk is by Akbar Akim of Simon Fraser University on the complexity of CSB-based ideal membership problem. Yeah, thank you. Right. So, as Jakub said, I will be talking about the complexity of CSB-based ideal membership problem. And this is based on joint work with Andre Floto. So I'm going to start off with some definitions to state the problem. So let me start off with what do we mean by ideals and some like introduction to this algebraic geometric stuff. So through this talk, let F be a field, for instance, a field of complex number or real numbers. And then by fx1 to xn, we denote the ring of polynomials or f or maybe often I use capital X. And then an ideal is the subset of this ring of polynomials, basically a set of polynomials that satisfies three properties. So the first one is zero belongs to the ideal. The second property is that the ideal is closed on the addition. So if you have F and G in the ideal and then you sum them up, the result is also a polynomial in the ideal. And then the third property is sort of the ideal is absorbing the multiplication. So if you have this polynomial F in the ideal and then another polynomial H from the ring of polynomials and then you multiply them, you get something in the ideal. So it has these three properties. Let's see an example of ideal. So let's say we have these polynomials f1 to fm in the ring of polynomials. So we define this subset, which is basically the summation of hi fi, where hi are from ring of polynomials. So this gives us a set of polynomials, like sort of generated by this f1 to fm. Right. So you can check that this set, the way it is constructed satisfies the three properties of an ideal. So this set is basically an ideal. And it is called the ideal generated by f1 to fm. Okay. For instance, let's say I have polynomial one, so basically polynomial degree zero. So the ideal generated by this polynomial is basically the entire ring of polynomial. So as long as you have one in the generator set, then you get the whole ring of polynomial. So there is this fundamental theorem by Hilbert called like Hilbert basis theorem, which says every ideal of the ring of polynomial has a finite generating. So this generating set is not unique, is not unique, but it's, we have a finite generating set. So this gives us a way of representing ideal. So let's, let's get to the definition of ideal membership problem. So the input of this problem is an ideal and another polynomial f. And the question is, does f belong to i? So I'm going to check if the input polynomial f belongs to the ideal. Right. And as I said, this ideal i is represented to us by its generators, f1 to fm. And just to remind you the definition, if we have these generators, then the idea is going to be set of these polynomials, right. Okay, so in a more like a stronger version of this problem. So basically the search version of this problem we have this input polynomial f and then this generating polynomial f1 to fm. And now the question is, does there exist h1 to hm such that the equality holds. So basically you can generate f using this multiplicative polynomials h1 to hm and the generating polynomials, right. And so we want to find such h1 to hm from the ring of polynomial such that the equality holds. And this h1 to hm are called nullish.proofs of the fact that f is inside the ideal. Okay. So I'll give you a couple of seconds to stir this and digest. Right. Okay. So how do people generally like attack this type of problem. So basically for the search version when you want to find those proof nullish groups h1 to hm. So basically the first thing that comes to mind is like start dividing two polynomial division. So we have this input polynomial f and then this generators f1 to fm. And then if you start dividing f by this f1 to fm, we get the remainder, right. And if the remainder is zero, then we can say that the polynomial, the input polynomial f, belongs to the ideal. Okay. But we may not be lucky and the remainder may not be zero. Right. In that case, we cannot say anything for sure. We cannot say f is not in the ideal. Why is that? Because the order of division matters. Right. The way that we divide this input polynomial by this generating polynomial, it matters. Right. So let me elaborate on that by an example. So for instance, let's say this input polynomial is f, x squared y minus x y squared plus y. And then my generating polynomials are f1 equals x squared and f2 is x y minus 1. Then the ideal I'm looking at is generated by f1 and f2. All right. So now let's start dividing f by f2. Right. So if we start dividing f by f2 first, then we get this result which says f equals 0 f1 plus something times 2 and the remainder is minus x. Right. But if we start dividing by f1 first, and then divide by f2 after that, we get remainder zero. Okay. And the point that I want to make here is that this generator set, this generator set of ideal, they may not be well behaved in terms of division. So if you are unlucky and you get the nonzero remainder, then you cannot say for sure that the polynomial is not in the ideal. Right. So this is like basically the beginning of the story of Grobner bases where people are interested in finding sort of good generators. Right. So, well, now the more robust approach to solve this search version of ideal membership problem is to construct Grobner bases of the ideals, whatever they are. So the good property of this Grobner bases, basically, they are generators of the ideal, and they are pretty well behaved in terms of polynomial division. Right. So, basically, the most important property of this Grobner bases is that the remainder is unique, no matter in what order we do division. Okay. And so in order to solve the IP problem, what we do, we have this ideal, which is generating polynomial, then from those we construct Grobner bases. And then as soon as we have the Grobner bases, we do division polynomial division as long as we can in any order we want. And if they're the remainder is zero if and only if the polynomial is in the ideal. All right. Yeah, but life is not as simple we there are some drawbacks here. So first of all, this grobner bases are very sensitive to monomial ordering. Whenever we talk about polynomials or polynomial division, we have to set fix the monomial order, for instance, lexicographic order, or graded lexicographic, right. And if you change the ordering that you are working with, you see like drastic changes in the complexity of construction constructing Grobner bases. And we will see that this monomial orders, we don't like them in terms of PC, later on in the talk. And another drawback is that, so there is this general algorithm called book burgers algorithm for constructing Grobner bases. So this algorithm is sort of non deterministic. It's quite tedious to analyze the complexity of Grobner book burgers algorithm, which construct Grobner bases. So, while there are some upper bound and lower bound for the upper bounds for the complexity of this book burgers algorithm, but quite serious to analyze this algorithm and see for your specific problem which you are interested in, is it going to give you a polynomial time algorithm to construct Grobner bases or not. Okay. So this was about search version. Now let's go to the decision version of problem which we are not interested in finding those proofs h1 and hm h1 to hm. And we are just interested to say yes or no, the polynomial is in the ideal or not. So here we are interested in the geometry of variety. All right, let me define what variety. So a variety of an ideal is basically the set of all zeros of polynomials inside the idea. So it's a subset of fn, right. And their f is your field and this variety is basically the set of all zeros of polynomial. Okay. So despite strong, we can say that we can say the following every F, every polynomial in the ring of polynomial that vanishes at every point of the variety, long to the idea. So if you have a representation of the points in the variety, and you can check evaluate the polynomial, the input polynomial F on those points, and for all of them you get zero, then you can say the polynomial f belongs to the variety. Okay. So, for instance, if the ideal is generated by one, basically the ideal is the entire set of them. And the entire ring of polynomials, then the variety is empty. So basically all the polynomials are inside the ring of polynomial, which is obvious, right. So I have put this radical condition in brackets. So in order to, there are some technicalities here. So in order to be able to apply this strong knowledge to us, we need the ideal to be radical, whatever that means. But we will see the way that we construct the ideals for CSP problem. They automatically be radical, so we can apply this strong. Okay. And yeah, so we have these two theorems, which are, we can strong knowledge to them, but and is a basically what I said is basically the intuition of these two. So let's see an example of some combinatorial ideal. For example, let's say I want to two color a triangle. So I have this triangle, X, Y, Z. And I want to two color the vertices of this triangle. Okay. And the colors that I have are zero one, let's say. So first of all, this vertex X, it can have only two colors. Right. So I have this polynomial equation, which says okay X times X minus one is zero. So forcing X to be zero or one. And for simplicity, let's say you are working in real numbers. Right. So we have the same polynomial equation for why which forces the image of why to be zero or one. And the same thing for Z. All right. And now we have set of constraints, which says basically, well, I want different color for for the edges screen. So adjacent vertices get different colors. All right. So I need to encode this using polynomial. So I have this polynomial which says X plus Y minus one equals zero. So because I have this edge X, Y, then I want them to have different colors. The same thing for Y VH. So I want them to have different colors. And the last edge is X and Z and X. So now I have this domain constraints, basically, domain polynomials and this edge constraints. Now we can say this graph is too colorable. If and only if the polynomial system that I explained here has a solution. Okay, if you find that's fine assignment for this polynomial, then you have a two colorable. You have a two color. But we know that the graph is not too color. All right, let me continue and okay, let me rephrase this problem in terms of ideal membership problem. So first I generate this ideal, which contains all the polynomials from the previous slide at his generators. Okay, then the graph from the previous slide has a has no two coloring. And only if one belongs to the ideal, basically the variety of the ideal is empty. Well, we can say that you can see that you can express one using this polynomial. And yeah, so one is in the ideal, which implies the variety is an empty set. So there you go. No two color. All right. So let's see some application. So this ideal membership problem is like has been a start for a long time like between mathematicians and what they have done quite amazing job. But recently we have. So this ideal membership problem has some applications in computer science for CS people right. So for instance, this ideal membership problem can be can be used as a proof. But as we saw in the case of two coloring. You can formulate your problem, such that it witnessed that an instant has no solution. Okay, as we did it before what we, what we do is we include our problems through some polynomial. And then check if one belongs to the ideal. If one is in the ideal then no solution. If otherwise, there is a solution. And in the more in more strong, then we want to find these proofs that are witnessing that one is in the ideal. Okay. So basically this nourishment of the proof and in the proof complexity, people are interested in the size of the smallest proof that you can find basically. The size constraint could be like a degree constraint or maybe number of number of monomials that you want to use. All right. So let's see another application of this ideal membership problem. Sort of in terms of optimization. So let's say we want to minimize this polynomial are of x1 to xn subject to some polynomial constant. These constraints are as follows. P1 of x1 to xn is called zero and up here. So an SOS, some of the square certificate of a lower bound for this polynomial. So let's say we want to prove that this polynomial certified that this polynomial are is at least data. So what do we do? We write this R minus data as a sum of a square polynomial. This is always positive because is the sum of a square polynomial. And then the idea membership part. So this part is zero for an assignment be satisfied all this system of polynomial. So this term is zero. And this term is always positive. So the whole thing witnesses that R is at least data. Okay. And while the degree of this sum of the square certificate is basically maximum degree of this guy that you have here and maximum degree of this guy you have here. All right. So this way we can prove like non negativity. We can define non negativity of a polynomial. So let's say we have the set of polynomial and before P1 to PL. And then we say this polynomial as the sum of a square proof of non negativity from P. If we can have this equality. So the same as before, this term is always positive because we have some of the square. And this term is always zero. So the whole thing is positive. So we have a proof of non negativity of that. So, while the main appeal of this as well as proof systems or basically the source certificate of non negativity is that we can with the existence of a degree D as well as certificate can be can be sort of formulated as a visibility of semi defended program. So this inside the semi defended program you have this monomials if you have a bounded degree. You have this monomials and then you are trying to find coefficients for this one. And if you have one degree the number of monomials that you have to consider is bounded. So then you have a like bounded size semi definite program and you try to find the coefficients. Right. So this common misconception that if you have some of the square, which is of low degree. If you know the existence of a low degree sum of square then you can find it basically as so as is degree automatically. Right. So, yeah. As I said it means like if you have a low degree so attribution, then you can find it. So this STP can be solved efficiently. Right. But it turns out this is not the case. And basically the sum of the sum of the squares are not degree automatically. And this is due to all down in 2017. It came up with a country example is that this is not the case and we need some extra condition for us to be automatically. And those extra conditions are that not only we need this low degree condition, we also need to have some bound on the coefficients of the polynomial that we are using. So that's where the ellipse of method is going to stop the city. Right. So in terms of these conditions that we are looking for can be can be satisfied provided that the IMP part of the problem is polynomial time solving. So if you can solve the IMP part. Then you can get the automatable SOS proofs. Right. And this is due to rubber band run by in 2017. All right. So we have seen some application we saw the definition and example and some applications. Now let's go to the IMP problems coming from CSP. All right. So in CSP, we have this instance P, and which is the instance of CSP of a where a is a relational structure with some basis. Let's say we denoted by T basically domain zero to R minus one. And then in the variables, let's say they are x12 xn. And we have some set of constraints. And each constraint has a set of positive set of variables and sort of the relation and coming from this relational structure. So now let's say we want to encode this problem in terms of ideal membership problem. So for every constraint that we have in the instance, we introduce a polynomial f sub C, which is on those variables inside the constraint I want to x, I want to xik and the zeros of this polynomial are exactly the samples from R. So sort of what we did in in the two in two coloring example, right? Furthermore, for every variable we introduce this domain polynomial, right? So I want every variable to get the value from this set. So we have a polynomial of degree R, which which forces this x i to get a value from this set. So as soon as we have these polynomials, we put these polynomials together and generate an ideal. So put all these polynomials together and it gives us an ideal which corresponds to this instance of CSPA. Okay. All right. So ideal membership with respect to a relational structure. Let me define the problem. So input is a CSP instance P of CSPA where a is a relational structure with some variables x1 to xn and we have this input polynomial f. So we construct the corresponding ideal to the instance IP. And the question is whether this f belongs to this ideal. Okay. And well, also find proof that it's possible. And we have a like sort of a easier version of this problem where we enforce the degree we bound the degree of input. So this polynomial f, we say, okay, let's let it have at most degree at most D. This problem is denoted by ideal membership of the. Okay. All right. Well, remember at the beginning of talk when I was talking about this new list of stuff, I was saying, okay, we need the idea to be radical to be able to apply this new knowledge that's right. So, since we we are adding all these domain polynomial, then the idea we are generating is always radical. So, you're good in that sense, we can apply this knowledge to them. So, since we have the equivalent formulation of ideal membership problem, right? Okay. So in this equivalent equivalent formulation, again, we have this instance P of CSPA is a relational structure with some variables, and this polynomial, which is coming from ring of polynomial. And now the question is, is every solution of this instance, the CSP is a zero of f. Okay. And if every solution of this CSP instance is a zero of f, so basically you take this solution, you plug it into f and evaluate f in on that solution. If you get a zero for all of them, then you can say f belongs to the idea. Right. So, here it's somehow motivating to work with this variety instead of like working with those group members, right? And in CSP we like this variety, right? We are more comfortable with this variety. So, as a corollary, if this ideal membership is co-emptive, is in co-emptive, meaning that you can verify the no instance. I give you a solution to my CSP, plug it in in the polynomial and it gives you non-zero, which is a no. So you can verify this no instance in polynomial type. So, imp is co-emptive, isn't co-emptive, right? All right. So some research questions. So the first question is that we have this relational structure A, and can we construct Grobner bases for any instance of this ideal membership problem? So let's say P is an instance of CSPA. So can you find the Grobner bases for IP, the ideal of corresponding to that CSP instance? The second question, so if we have this one, if we construct Grobner bases, we can solve the search version, obviously the decision version. The second question is that for which relational structure, we have a small knowledge that is approved of the fact that f belongs to the ideal. Okay. This is another question. For which relational structure, the problem IMPA or IMP sub-DA, a restricted version, is polynomial times all of them. Okay. So now we are slowly getting to the, studying the geometry and basically the operations of these relational structures. All sort of polymorphism. All right. So let's see what we know so far. So in the Boolean case, we have dichotomy, which classifies all the cases. And it is as follows. It's almost the same as the shepherds dichotomy. So let me get to the details. So in 2019, Monaldo, most importantly, he started to study this problem in a way that CSP people like. So I study basically the properties of this relational structure. And he proved the following. So if A has a majority polymorphism, then IMP of A is polytyped. Okay. So while in Boolean, when we have majority polymorphism, basically the instances are two settings. Right. And the proof was that a Gromner basis of this instance, if we have majority polymorphism, they have degree at most two, and they have good coefficients. Right. So what we do, we enumerate over all this degree to polynomial. Right. And we have, and we have the, we have our Gromner basis. Okay. And we have our majority, majority polymorphism. And the second result is as follows, if we have a semi-latid polymorphism, then IMP sub D of A is polynomial time for any D. So just note that in the majority case, we don't have any degree restriction on the input. But in the semi-latid case, we have this degree restriction. All right. So this is the proof idea. So when we have semi-latid polymorphism for this over Boolean, then the instances are anti or anti-homestead or homestead. Like depending if you have max or me. So then it turns out the Gromner basis includes only binomial polynomial. So polynomials, including only two monomials. And then they have good coefficient. All right. So if you have this bounded degree, if you have this bound on the degree of input polynomial, then you can enumerate over all these binomial polynomial and get your Gromner basis in time into the D. Okay. That's why we have this degree restriction for in the semi-latid case. Now the other remaining case is the affine case. So basically, the result is due to most Raleigh and Bharati. And they say if we have a fine polymorphism, if we have an affine polymorphism, then the IMP again we have this degree restriction on the input is polynomial time for any D. All right. So in this case, if you have a fine polymorphism, it means the instance is a linear equation, Mach 2. Oh, sorry. It's Mach 2 instance. And then, so this case in my opinion was like the most difficult case. And so basically we have these linear equations, Mach 2, then we need to lift them to have polynomials over real. The first thing is not always polynomial times is not always efficient to do it in polynomial time. So we need to come up with some tricks. Right. I'm going to skip the details. So it's like more tedious than the other cases. And on the hardness result, so unlike the shepherd's day, if we have this constant operations or basically this constant relation, the problem is going to be complete. So IMP 2 of A is going to be complete. And the reason that we have these two here, because we only have two constant zero and one in Boolean. If you want to have a polynomial that represents both of them, sort of speaking, then you need to stick with two here. Okay. All right. So this was what we know about these Boolean case. Now we are interested in to like have a higher level look at the problem and see if we want to extend results to higher domain. Or if we can, like, follow these tools that have been developed in CSP for the dichotomaterials and use them here for this ideal membership problem. Okay, well, let's start with something easy. We wanted to we want to check if we can expand the relational structure that we have by console. Okay, does does that change the complexity of problem or not. So let's AC denote the structure a where with the you know the structure a with some added constant relation. All right. All right. So we have this theorem which says, okay, if you add this constant relation doesn't change the complexity of the problem. Basically, I am P of AC is pull time reducible to I am P of a with a blow up in the degree. And this blow up in the degree is coming from the fact that we are trying to encode this constant relation with polynomial. So it increases the degree of the input polynomial. Yeah. Now, another simple observation is that. So, since we know that one is in the ideal if and only he has no solution, then we can say the following that whenever the CSP of CSP of AC is empty, complete, then we get a comfy, comfy, complete version of ideal membership problem. So if your CSP is difficult to solve then I am P is also difficult. So let's talk about something more advanced like pp interpretability. So this notion of pp interpretability is basically what tells us that if we if we can use this algebra instead of relational structures. So can we just talk about algebra and the operations into the relational structures or not. We say this structure a pp interpret structure be if the base set and the predicates of p can be p to define a don't bother about the definition is completely vague. Just so this pp is shorter for primitive positive. So basically you can express whatever you have in be using these relational structure that you have in a. So it turns out that if you have this pp interpretability, then the problems are reducible to each other right. So if a pp interpret p, then ideal membership of ideal membership of ship of be is for the time reduced to the ideal membership of a weather some blow up in the degree. Okay. So this blow up is because this a and B might might have like different domain. Right, so as so since we have this pp interpretability result and this means we can use algebra. So we can replace this relational structure put it aside and talk about algebra and its operations. So I am P of algebra a denotes the clock, the class of problem IPP, where B is the final language invariant under the operation of this answer. All right, let me just let me walk you through this walk you through an example right. So let's consider similarities. And we want to. We want to reduce the problem or similarities of over a domain of three elements to the bulletin case. Okay, so let's say a as base 012, and it's invariant on the semi lettuce operation of this algebra. Let's say the same lettuce operation is the following, which we have where we have a global maximum. And that's basically zero is less than two and one is less than two. And we don't have anything between zero and one. So it's not conservative. All right. The maximum zero zero and one is two. Okay, now consider this Boolean algebra P, and we have this instance. Carefully be, and we want to reduce this problem. And in the, in the algebra B we have gained the semi lettuce point, semi lettuce operation, which says, okay, zero is less than one. All right. So let's do the reduction. We use I am P of a to ampere. Okay. So, there is this result in like a universal algebra with that if you have semi lettuce polymorphism then your algebra is a sub algebra of this Boolean algebra to some power. Okay, so basically we have this mapping, which stands zero. The domain of a was zero one two, and the domain of the was zero one. So we send zero zero one, one to one zero and two, one natural way. So now, we need to first transfer and transform an instance of CSPA into an instance of CSP and we know how to do it. So we replace. So let's say we have this instance P of CSPA, and we want to construct this instance P star of the SPP. So we replace every variable X with a pair of variable X one and two. So this, this is because we have this. So here in this, in this algebra, we have zero one and one two and one more. So for every variable, we need two variables. Right. All right. So and in every country, we replace the value a for X with GA for X one and X two. Okay. Now, and for the domain constraint for every X, we add this constant, which says X one and two has to take one of these values. So the solutions of P are in one to one correspondence with solutions of P star. Okay. Now, since we have these instances P and P star, we can construct the corresponding ideals. And now we need to change the input ideal input polynomial. Okay. So the mapping G that I talked about, we can always interpolate it with the polynomial of a constant degree, right. And the same holds for G inverse, we can interpolate this G inverse mapping by polynomial. So in this case, polynomial is simple. So it takes X one and X two and gives you X one plus X one and X two. Okay. So now the reduction is as follows, we have this instance P, we convert it to instance P star from the Boolean algebra. And then we convert this polynomial input polynomial F to input polynomial F star. And how do we do that? Well, simply we replace every current of X with G inverse of X one and X two. Okay. Now, we have this demo which says, okay, if F is in the ideal of P, so F is in the ideal of P, if and only if F star is in the ideal of P star. Okay, there we go. We have our reduction, right. But so this reduction works quite well in terms of decision version. But in terms of search version, we don't know what's going on, right. So let's say I have defined a proof where F star is in the ideal of P star, so basically proof like this. But can we recover a proof for F being inside P ideal of P? This is something interesting that we don't know yet. Well, in terms of more polynomial cases. So as I thought, as I said, we have these similarities for every domain. But still we have this restriction on the degree. And our results follows like by these results from universal algebra and the one time response in Boolean. Then we have that the imp of dual discriminator. The imp of majority operation is poly time. So just remember for in the Boolean case we have the imp of majority is polynomial time but in Boolean case the only majority polymorphism or operation that we have is dual discriminators. All right. So now we consider this dual discriminator for any fixed domain. And it turns out the problem is poly time. So, well, some of the proof ideas, basically we have this geometric result about the dual discriminators, basically the variety of these dual discriminators. Then, while we have three types of constraints, if we have dual discriminator and it turns out this unigame constraint or this permutation constraint cause a lot of trouble to construct group. So what we do we preprocess the instance, get rid of this unigame constraints and then we get a group number basis after that. It's easier to get a group number basis after that. Right. And once again, we don't have this degree restriction for that dual discriminators. Or another case which is like the most difficult one is that so for Boolean we have this polynomial time. Now we want to consider that P where P is a prime. So I am PT that P is for the time solvable. And here again we construct this group number basis for these sort of reconstruct this truncated group number basis each where we only go up to degree T when we are constructing this group number. It's a long proof and yeah, so I think we can talk about it after the talk if someone is interested. Let me finish up with some open questions. Well, obviously, what are the more, what are more polynomial cases. Then the second interesting question is, what is the connection that this problem IP has to some standards to be taken. For instance, consistency. Well, we know that this local consistency stuff. Basically thing and our consistency solve all these all these bounded degree CSB straight, but why cannot we have something like this for the IMP. Or basically, it's consistency. What does it mean in terms of IP? That's the third interesting question would be like proof recovery. Just as I told you in terms of semi lattices, we can have this reduction, which works beautifully in terms of decision version. But in terms of proof recovery, you don't know what is going on there. And then we saw this low degree restriction, for instance, for semi lattices we have this degree restriction, but for majorities we don't have it. So why do they correspond to right. So by the way, if you want to have dual discriminators for on ternary domain, and if you want that like full grown up basis, then you don't have degree two, you have to go to degree three. So there's something interesting going on there. And the last thing that I didn't talk much about it. This is this like book burgers algorithm. This is just that this general algorithm to construct growth in a basis. So this algorithm uses this notion of as polynomial. Well, if you're interested, we can talk about later but it's really interesting to see what the polynomial corresponds to in terms of. So somehow in the dual discriminator case, if we do this preprocessing and get rid of this unique game concept, unique game constraint, then we don't need to compute this is polynomial anymore. So this book burgers algorithm becomes polynomial. Yeah, so thank you for listening and please ask questions if you have any. Thank you for a very nice talk. Yeah. There are questions comments. This is Peter. Question. Yeah. So I'm not sure I caught that correctly. Do you know for general imps if you have a majority polymorphism, whether that's tractable then. What do you mean, general. I think for if, if the bullying case. Oh, yeah. Okay. I think I understand your question for bigger domains. Right. So for general majority, we don't know anything yet. So, yeah, so this dual discriminator is sort of a special type of majority operations right. So we know everything for this dual discriminator, but for majority we don't know, like beyond bullying what is going on, we don't know. And it's like a super interesting because we have this boundary degree restriction for the semi lattices. We don't have this in bullying case. But we don't have this such a restriction for majority. Well, but no, never mind, because majority is in bullying case is just dual discriminator. Yeah, so to answer your question we don't know anything. Yeah. More questions. Yeah, so if I may just like, do you know anything on top of these like some concrete examples what I mean is this say this three element to some lattice or say product of two z twos or Z four. Right, so that's a really interesting question. Well, we can get the. Actually, this is what we are working on. So this, we can get the sort of multi sorted PSP. We can have like a result for multi sorted PSP. And in like in terms of. So basically the next step beyond this linear equation, but P is basically linear equations in a billion groups right when we have this fundamental theorem of a billion groups or we can write it as a direct sum of direct sum of these P groups. So, and over there we need this multiplication that's two times that's two right. So, for the decision version. It seems we can do it. Right, but for the search version, we don't know. So even like, not just Z two square but Z four is do it also all a billion groups. Yeah, but decision version. So there is a like really other pointer. Yeah, the decision version seems to be okay. Hopefully even a billion groups. But as far as I understand this multi sorted stuff should work well. Each, each variable has its own domain and then in the construction of these ideals, we shouldn't face any major problem, but some more questions. Okay, okay. It's maybe hard to answer but so this ideal membership is harder in general than the CSP problem. So somehow what does it tell us the tractability of I am. Does it tell us something more in terms of CSP, I mean, can you formulate, you know, if you can solve MP, then you can do this and this is your CSP instances not only decide but you know something. So, well, I guess I know what you mean so this basically this imp is a sort of generalization so this. So if you want to do refutation, refutation of CSP instances is basically membership of one in the ideal. Right. So but in the in the like general setting we don't so the input polynomial doesn't have to be one it can be of any degree. In that sense is more general than CSP. And did it answer your question or I know this. So, so it's more general but whether you if you can solve the general problem, does it give us anything about the CSP, you know, which you can formulate in terms of CSP that somehow not only you can decide instances but you can do this and this. Honestly, I don't know. So, well, honestly, like, I don't know anything about that because so. Well, we don't know even what is this consistency mean in terms of ideal membership problem right. So, well, I don't know. Probably it means something but we are far from knowing that you think. Yeah, so last chance for questions. Maybe I have another one then. So when you when you got the tractability result for IMP was it always by using criminal basis or did you have any alternative approach. Right. So, well, it depends if you want to work in for the search version or the decision. So, as I said for the decision version, you don't need to compute the scrub the basis. Not necessarily needed. So what you can do is just for the decision version you find the satisfying assignment to your instance, which is a non zero of the input. If you find such a satisfying assignment, then you're done. You can say the polynomial is not in the idea without using any growth basis. But for the search version. Unfortunately, we don't know any other approaches, other than growing the basis. Right. So, it's so that it comes to how do you do this polynomial division. If you don't have grobner basis, then it's not building a, maybe, I don't know, maybe there are some other notions of good basis, other than grobner basis, but I'm not aware of them. Yeah, so just in summary for the decision version, you can get around with the grobner basis. But for the version. For the search version, you mean you want to kind of nullstellensatz proof. Yeah, so in the search version, like you said, okay, F is in the ideal. So prove it, give me a bit more. Okay, I give you this time, which is some of this polynomial. There you go. This is your equality.


We're here now with Sarah Mayhew from Canada or Canadian as some of the folks here like to say and Sarah thanks for joining us. Thanks for having me. So which Tam is this for you? This is my second Tam. Okay and what do you like so far about it? What do you like most about Tam I should ask? My favorite part of Tam is people. I like coming here and meeting everyone. I come from a remote town. There's not a lot of fellow skeptics around so I really like seeing people, mingling, meeting new people and you know seeing friends that I usually only see in cyberspace. That's funny I'm surprised you don't have a Canadian accent at all. That is a lie I have total Canadian accent. Now tell us a little bit about your books. You've got a really interesting to the manga books and you've actually won international awards for that right? Yes Secret of Sorcerers was my first manga graphic novel. It won the International Anime and Manga Festival award back in 2005. I don't have one of those awards. And my newest series is Legend of the Star. It's available mostly digitally via you know iBooks, Kindle, basically all the major e-retailers and I recently signed a book deal to do a educational skeptics book with a science textbook publisher. Great is that going to be also manga style or is that more of a textbook? No it's going to be what they have are the series of textbooks that are comic books. So they have a story but they'll teach you about like statistics or relativity or astronomy but it's a comic book sort of comic book hybrid comic textbook. So trying to make textbooks a little bit more interesting basically? Yeah yeah so I thought that was right up my alley and I gave them sort of a little book proposal about it and so sort of a manga guide to skepticism. It should be fun. Okay great we'll be looking forward to that. Thank you. We'll enjoy the rest of your weekend and thank you for joining us here. Thanks.


What's up everybody, Jason here for jaspyscasebreak.com. Another wax party promo break. Just follow up guys. 2022 tops five star baseball eight box case break pickings number 47. Now I'm only saying this in the video just so people don't get confused, but I think if I'm not correct, if I'm not mistaken, I think there was a number 47 already. So I don't know if that was just a discrepancy between Nick or Joe or what, but I believe if you look at our break schedule with our wax party invite breaks, it looks like we did a five star team round number 47 where Carl got a spot in that. Now I don't think the whole break was part of the, the wax party was just a team random. So obviously this was going to be the first full break part of it. So the next one that I posted up is number 49. I'm just skipping a number because I believe technically this should be 48. But again, this is 47. You're not going to find 48 in the store. This should be 48, but it just was retyped as 47. So it separated already. Anyway, it's in that other break was a couple of days ago. So just wanted to clarify that so I don't want people to think they're confused and thinking that they're not in it and I was in this break and I should have got this. But like I said, this is 47 in the title, but it should be 48. But you guys are good. Just wanted to just clarify that. Now here's everybody in the break and last but not the rich got the Marinus. Took a shot at the wax party shadow. Well, yeah, man, I appreciate that. I mean, look, there's still plenty of breaks that we're going to be posting up throughout the next few weeks. And I think it'll probably take a little over a month. So I think the way we're going, we should be done with this by maybe the end of June. So should be some fun stuff guys. Alrighty guys, here we go guys. Our first one we have is a Ronnie Dawson for the Cincinnati Reds, which is going to Ed.  And then we have a beautiful jumbo patch autograph for the Tampa Bay Rays that is seven out of 10. And that is Brandon Lau. That's pretty sweet right there. There you go. So Rays, that's Ryan. We have a Jackson Reets for the Milwaukee Brewers going to DeWine. And how about that, a Derek Jeter for the Yankees. 10 out of 15. Yankees, Ryan also got the Yankees. And there you go, buddy. Back to back hits there. Very nice. All right, we got Aaron Ashby. And then we have one of those Contamers Penmanships. So Brewers again, that's going to go to DeWine. And we have a Brian DeLaCruz to 25, six out of 25. All right, that's Miami. Marlon's going to DeWine. We have Patrick Misega for the Metz. Metz is Greg. And how about a little NOMA, Garcia Para for the Red Sox going to Russell. All right, here we go, next one. And that is at a 75, Curtis Terry for the Twins. And then we have a Greg Maddox for the Cubbies. Cubbies going to Tyler. And of course, Minnesota Twins. Twins is DeWine. Then we have Tony Sancilan for the Reds again. And how about an Ichiro, very nice. What a nice case. Seattle Mariners, so not a Julio, but hey, rich. Last but not the Mojo Mariners. Still walking away with a nice on-card Ichiro. And then Reds is Ed. All right, we have a Chas McCormick. And then out of 10, Dave Winfield, Minnesota Twins. Two out of 10. So Minnesota Twins, that is DeWine again. And then Houston Astros is Greg. Down to the last box. Some feels really light. Oh, this one felt light. Might still be too hard. All right, we got a Rodolfo Castro for the Pirates. Wow, and a cut autograph, how about that? One of one, Pee Wee Reese. That is awesome, what a case. Nice one there for the Dodgers going to David. There you go, man. So like I said, guys, you know, just because we haven't been seeing silver or gold ink cards out of our cases, doesn't mean the cases aren't really good. Still managed to get a couple nice autos, and then about to cut autograph Pee Wee Reese. Very nice. And then a Pirates hit here for Jeremy Port. Awesome, guys, I'd love to run this back. This was a very nice case. Then we have a couple more in the store. And like I said, I got a Pee Wee Reese cut. Dave Winfield a 10, Ichiro, and then early on here, we did get that Derek Jeter a 15 with that Brownie Lyle patch autograph. So appreciate it, folks. Thank you guys so much. Now, again, if you did go hit this, unfortunately, it does happen in a break like this, and there's only about 16 hits total in a case. But this is a promo break, so you have an opportunity to win a Wax Party promo spot. So let's gather the names here, put them in a randomizer, and customer name at number one, after four and a two, six times, gets a Wax Party promo invite. Four and a two, six times. One, two, three, four, five, six. Six times, four, two, six, and Nestor. Not sure if I called your name, but hey, you did get to win that Wax Party promo spot, man. Congratulations, buddy. So there you go. Winner there, number 14. Still plenty more to go, guys. We have to fill up 200 Wax Party invites or give away 200 Wax Party invites, and then we can give away all of those boxes. So yeah, check out the website, see the details inside. It's over $100,000 in Wax, and some of them are cases, multiple boxes, tons of different stuff, guys. Appreciate it, everybody. Jaspy's Case Breaks.com.


Hi friends, welcome back to my channel and welcome if you're new here, my name is Jen I'm a certified weight loss and nutrition coach and today is Saturday So it is another grocery haul day I have a great grocery haul lots of new finds or new to me finds pretty good-sized haul today from both Walmart and Trader Joe so if you're excited for another grocery haul give this video a thumbs up It really helps out my channel kind of lets YouTube know that you like to see these types of videos And of course if you're new to my channel, or you're not yet subscribed, please make sure that you do hit the subscribe button I am this close to my 30,000 subscriber goal by the end of the year So it'd mean the world to me if you could make sure that you're subscribed Thank you so so much in advance Also, make sure you're checking out that description box down below where you're going to find my nutrition coaching website I do offer personalized macro and calorie calculation Specific to you. It's really important to know where you should fall every day Calories macros so that you can be as successful as possible on your healthy lifestyle journey You're also going to find 30 and 60 minute coaching sessions on my website. So take advantage of that Let me help you reach your goals, especially moving into the new year You're also going to find links and discount codes to all of my very favorite things and of course my Facebook group So head on over and join us there I have tons and tons of fun stuff coming your way really exciting stuff in the new year So definitely take a moment and check out that description box.  So let's jump in So here's this week's grocery haul. I shopped at both Walmart and Trader Joe's I have some fun new or new to me at least food finds that I'm really excited to share with you guys Plus a few fun things for Christmas and a really fun vlog miss video coming your way a little bit later this month So let's jump into this week's grocery haul before we do. This is currently happening She is the weirdest dog back to the grocery haul first. I picked up some pineapple bubbly This was on sale at Walmart and then there was actually another dollar off So it was just over $2 for an eight pack Which is a really good deal and then of course a restock of diet coke for Troy I did buy the stone fire non-crisps again. These are so good. I feel like every time I go to Walmart I have to pick these up. We're still working on that layer law Terafina dip from Costco And these are really good in there These are the garlic and cheese and you get a lot of these crackers for the points much more than if you bought the Trader Joe's version of the non-crisps So I do prefer the stone fire These are for Troy to little Knudsen cottage cheese doubles. These have the blueberry and the cottage cheese I don't know how bad they are in points. They're only a hundred and ten calories But I thought that this would be a good healthy snack for him And then new to me are these mini croissants from Thomas. He's playing mini croissants are so cute Look at the size of those and you can have three of them for 180 calories So I figured the points wouldn't be too bad, but of course they'll be here on the screen I thought this would be nice paired with some eggs Maybe some sausage for breakfast and then I also picked up the King's Hawaiian rolls This is for meal prep. You are not going to want to miss this week's meal prep because first of all We're using King's Hawaiian rolls and I just have some good stuff coming your way for meal prep So I picked those up. There was a lot of great deals on meat So I went ahead and stocked up one pound of 96 percent extra lean ground beef And then there was a couple of good deals on chicken These are just boneless skinless chicken breast and then chicken at tenders and they were all on sale So I'm just going to toss them in my freezer. They'll keep really well in there You can't pass it up when they're marked down Of course, I picked up another pack of the Sam's Choice chicken apple sausage whenever they're in stock I get them these freeze really really well So if you can score these in your area go ahead and pop them in the freezer They freeze great and then I needed some diced ham for a meal prep recipe Of course, I grabbed my organic happy eggs. These are my favorite eggs ever and they are such a great deal at Walmart We needed some sliced cheese So this is the great value mild cheddar cheese and then also a restock of the light shredded cheese from Trader Joe's for a vlog miss video, I'm going to be filming how I make and decorate my Famous sugar cookies. They are the cookies my entire family asks for every single year. They are absolutely incredible I will be filming the entire thing and sharing the recipe and I'll be filming that this next week So I bought everything I need number one starting with some fun new sprinkles These are a little crushed up candy canes and I'm also going to use these in a second Christmas recipe coming your way during vlogmas. So these are really cute makes it easy They're already crushed up and then in the clearance section of Walmart I saw this Starbucks peppermint mocha coffee I have heard that this is incredible and you guys know that I love peppermint anything So I grabbed it just to have it on hand to try it. It was $4 and 75 cents I don't know if these are new to Trader Joe's or if I've just never seen them But I love beets especially in my salad. So this is just cut beets in vinaigrette I had to grab it because I'm planning on having some salads for lunch this next week And then I did pick up a very small Squeezable light mayonnaise for Troy's lunches We are almost out of the primal kitchen mayo and I don't go to Costco for another week or two for my big stock Up so this will get us through and then for the cookies. I needed or I think I need food coloring I wasn't 100% sure but I didn't want to start the recipe and not have any food coloring And then I need almond extract actually for a couple of different recipes Like I said, I have some really fun Christmas baking recipes coming your way big bag of the Applegate chicken and maple breakfast sausage I've been liking having eggs and sausage for breakfast and I've been having the chicken apple But I really wanted breakfast sausage this whole bag was 999 Which is a great deal for Applegate farms and I think I will have that with eggs and Many croissants so I picked that up in the freezer section if you have it in your Walmart It's actually a killer deal because the small boxes are about four dollars and this is a 1.25 pound bag for 999 and then in the back here I wanted to show this to you guys because I was actually Pretty excited when I saw this at Walmart. So I have a real estate client closing on a house. She's a younger girl She's a single mom. It's her first house here in the next couple of weeks and her daughter loves Barbies So I want to show you this line of Barbies and I don't know if this is new, but I'm loving it These are the Barbie fashionistas and I don't know if you can tell but she's not a skinny mini Barbie Like back in the day when I was a kid She is a normal size woman Barbie and I love that and then on the back It's very awesome because it is a very diverse collection of Barbies You can see there's even some in a wheelchair, which is awesome There's African-American Barbies Asian Barbies just all different cultures men and women and I absolutely Positively love it. I think it's great We are being inclusive with Barbie instead of just the skinny mini version that I had as a kid So I picked this up for her five dollars at Walmart great deal for my salads. I wanted somebody in the pepper rings I haven't had these in a while and whenever I go to Subway I always get these on my sandwich. So I decided this would be great for sandwiches Salads and then for a recipe. I needed poppy seeds actually I think for a couple of recipes and this was only two dollars and fifty cents at Walmart And then I was going to get the Campbell's healthy request cream of mushroom soup They literally had all of their soups picked over so I don't know what that's all about But all I could find is this fat-free great value version Not a big fan of fat-free food, but it was the only thing I could find so I grabbed it And then also in the clearance section with the coffee is this can of corn just for 86 cents There's nothing wrong with it. It's not even dented. So I grabbed that big huge ginormous pack of paper plates 999 for 300 plates great deal And then lastly in the clearance section. I saw this menagerie to a limelight Pinot Grigio Three little bottles of wine for three dollars. So I grabbed this for Christmas I thought that it would just be great to have chilled as an option on Christmas eve or Christmas day And then Troy loves the I can't believe it's not butter. So the big tub at walmart is the best deal The small tub is about four dollars. This big tub is six dollars. So I grabbed that for him And then bread for his sandwiches next week He actually goes back to work after his medical procedure and he is having tuna fish sandwiches So some sourdough bread I also did a restock on queso for him for me and also for Christmas to go with those fun Trader Joe's shaped chips that I bought And then I was all out of cheese for salads and like I mentioned I wanted salads this next week So I went ahead and picked up some feta and then of course I just grabbed another container of the mini peppermint meringues before they are gone at Trader Joe's I love these and I finally found the lilies peppermint baking chips So of course I had to pick one of those up. I found these at walmart not in the baking aisle But instead these were in the center with all of the holiday baking things someone's at our house So everyone in this house is freaking out. So anyways, these were in the center aisle And then for my cookies one of my little secrets Believe it or not is I use the bitty crocker rich and creamy frosting. I use the cream cheese And the vanilla so I picked up one vanilla and two cream cheese I mix those together and that is the frosting I use for my cookies and everyone thinks I make it homemade They love it. They rave about it. It's a great shortcut like me. I'm not very good at making frosting So if you're like me, this is a great substitution and it is incredible on the sugar cookies I also restocked my almond milk. I was completely out and I love this almond milk It's really good and it's only one point for an entire cup and 30 calories Of course kombucha. They had the big bottle of gingerade at walmart for seven dollars This is the equivalent of three bottles. Each bottle is about three dollars So you actually save a couple dollars by buying the big bottle And of course before it's gone at trader joe's a couple more bottles of my favorite fall addition with the apple turmeric carrot and spices These are three dollars a piece at trader joe's flour for my cookies. Unfortunately, they didn't have any organic flour This was the best version that I could find so I picked that up And then it's been a minute since I've had poppables. I've been loving pedos as you guys know I still love pedos. I'm just waiting for my order to come in I do have a link down below for 20 off pedos. Try them you guys. They're amazing But I picked up poppables because I've been wanting chips and these are sea salt and vinegar I actually don't think I've ever tried this flavor. So I'm pretty excited Let me know down in the comments if you've had this sea salt and vinegar and if you liked it yogurt pretzels for tori's lunch He loves these and I have not bought these in a while So I'm going to bag these up and they will be part of his lunch this next week And then potatoes.  I need potatoes for several recipes this next week Everything else I have is produce. So a couple of oranges. This is for a breakfast recipe for meal prep I'm seriously so excited for my meal prep So stay tuned at the end of this video for my meal plan and my meal prep some broccoli for a recipe Some more organic raspberries because these were actually really good this last week Cranberries for my meal prep. So you can get an idea. We'll be doing something cranberry Carrots because I was completely out and I need these for two dinner recipes And then a restock of my favorite organic sweet onions again for several recipes this next week So that's it my friends. That is this week's grocery haul. So let's jump into meal plan and meal prep So here's this week's meal plan. This is the week of 12 12 through 12 18 By the end of this week, we are literally six days from christmas. That completely blows my mind But this week I have some great meals planned Of course today saturday isn't out to dinner support a local business frozen pizza whatever we decide to do Tomorrow, I'll be making a slow cooker scalloped ham and potatoes kind of that winter comfort food You will see this recipe in next week's what I eat today. So stay tuned for that Monday is a chicken and rice casserole one of my very favorite recipes Tuesday is always a leftover night because it's a jazzy size night Wednesday, I'm doing spaghetti and meatballs good old-fashioned spaghetti and meatballs Thursday is cheese burger soup I've really been wanting soup with the cold weather So I try to incorporate a healthy low point low calorie soup recipe every week And this week is cheeseburger soup and then friday we'll do leftovers Only because we'll generally have quite a bit left over from the meals earlier in the week And for meal breakfast week, which I am so excited about breakfast is a cranberry orange loaf So this is kind of a sweet breakfast. I'm going to pair this though with something savory Maybe some sausage or some eggs as well as some additional fruit, but I can't wait for this recipe It screams the holidays lunch is ham and cheese sliders using those Hawaiian rolls This is just kind of a decadent what I think about when I think of unhealthy, but I'm making it healthy So I'm excited for that and then for dessert. I'm actually making a berry almond shortbread Cookie, which I'm excited for this too just to have these little small sweet treats on hand for the next week So that is meal prep. So stay tuned on monday for all of these recipes Thank you for joining me on another weekly WW grocery haul I hope that I gave you some good food inspiration found some new things that you can pick up the next time that you do your grocery shopping Definitely stay tuned for meal prep on monday. It's going to be a fantastic one I may be showing some of these recipes in videos upcoming as well So definitely stay tuned and with that make sure that you are subscribed again Help me reach my goal by the end of the year and turn your bell on so you are notified whenever I upload grocery hauls Or recipe videos So definitely make sure that you're subscribed if you enjoyed today's video Please give it a thumbs up It means a lot to me and really really helps out my channel And don't forget about that description box with my nutrition coaching my facebook group and links and discounts to my Favorite things. Thank you guys again so much for watching happy saturday happy vlogmas And i'll see you in tomorrow's video. Bye


by order of the Overseer Council. This file is subject to Level 4 classification. Level 4 clearance required. SCP-008, Level 4, Secret. Containment Class Euclid. Disruption Class Ecchi. Risk Class Danger. SCP-008 samples are Class 5 extreme biological hazards. They are to be handled with extreme care. If any SCP Foundation research facility with samples of SCP-008 suffers a containment breach, incineration and irradiation measures may be undertaken to contain the anomaly. Description. SCP-008 is a complex prion, samples of which are stored by the SCP Foundation. Traits of the SCP-008 prion include 100% infectiousness, 100% lethality, transmission through fluids, not airborne or waterborne. Symptoms of SCP-008 infection include Flu-like symptoms with high fever and mental processing issues in later stages. Come on set approximate 20 hours after first symptoms appear. A period of cellular necrosis which comes to resemble rot. Tissue which survives this necrosis becomes exceptionally durable. Metabolism may decrease to low levels, so subjects can survive without nutrition. Subject will wake from coma at this stage. Cognition is low and erratic. Subject is limited to basic physical actions. Subject will seek out uninfected humans and attempt to consume them. In short, SCP-008 infects subjects and converts them into zombies. Containment breach. Samples of SCP-008 were recently released in several cities across Earth. Approximately 1 million subjects have been infected by SCP-008. These cities are facing a pandemic level outbreak of SCP-008. The SCP Foundation is working with local authorities to contain SCP-008. The SCP Foundation will lock down areas of the city with SCP-008 zombies. And the area will be destroyed. Despite the civilian casualties this will cause, it is the only way to ensure that SCP-008 does not spread. A suitable cover story will be given to the public. SCP Foundation staff will be given their orders soon. Thank you for your cooperation. Secure. Contain. Protect.


Aloha! Welcome to the Savvy Chick Show on Think Tech Hawaii. I'm your host, Chantel Seville. Now, this is actually my last week for a little while because, well, I'm kind of due next weekend. So lucky I made the show today because it's a pretty exciting one and I'm so excited about our guest. You might not know who it is, but it's Honolulu Fashion Week here in Hawaii. And who better to have on the show than Kini Zamora, the Hawaiian fashion designer himself. He's an all-star from Project Runway and the CEO of Kini Zamora, the brand. So let's welcome Kini. Thank you so much for coming on the show today. Of course. Thank you for having me. Oh my gosh. Baby, stay in there. Are you okay in there? We have a show this week. Okay. Hope you don't have it on here. This is what I'm hoping for. I know. Kind of me, maybe. Maybe not. Just stop the camera if that happens. It's been such a pleasure being here on the Think Tech Hawaiian to have the last guest for a little while being yourself. This is going to be fun. So we're going to have a lot of fun today. For those of you watching, we'll show during the show. We might take one caller with a special question for Kini. So we'll put up that phone number throughout the show. And if you're the lucky one, you can ask him a question. So yeah, it's all about fashion. So tell us, you are doing the runway show this weekend. Yes, I do. I have a fashion show on Saturday, November 12th at 2 p.m. for Honolulu Fashion Week. And it's partnered with Reach the Runway with Honolulu Magazine. We put on a show. Honolulu Magazine actually does Honolulu Fashion Week every year. And it's the runway show. It's our third year doing it. And it's an amazing event to bring out fashion enthusiasts here in Hawaii. And it's grown so much since then.  Yes. So you've done a runway show all three years? Yeah, I've done a runway show three years. So just looking back at what we've done, it's kind of crazy. This has been how fast the fashion industry in Hawaii has grown. And just knowing that three years in, we're still going strong. It's pretty special, though. I think that you had a lot to do with bringing some attention to it, being with your history and whatnot, which we will get into shortly. Yes. But what does it mean to you to be a part of the Hawaii Fashion Week or Honolulu Fashion Week? Being a part of Honolulu Fashion Week, I think it's huge. It's a lot of weight on my shoulders. But then again, it's great to have that energy to put behind the fashion industry here in Hawaii and to help it grow and mold and just to be behind it at a young age, I guess, here in Hawaii. And just show people that there is fashionable creative people here in Hawaii. And that was my whole thing going through Project Runway, was showing people that there is creative people here. We don't wear Moomoo's, we don't do that. I mean, there is that culture, you know what I mean? And that's where we come from. But there is other things that happen here. We do have elaborate couture outfits that we create. And we don't live in Moomoo's every day. We do it on Fridays. And we know how to create different styles. Yeah, on Fridays.  Exactly. I think that that's, you know, from being, I guess, grown up in Canada, and Australia now being here, you just see such a beautiful island. Of course. And just like so much soul and depth. I think perhaps that's what shows through your creations. Of course, yeah. What's the latest collection you have coming up on the... So we have, we're creating our Spring Summer 2017 collection. And that was inspired by actually a traveling couple going to a destination. We are in a resort state. So I wanted to bring back the brand to a resort state. So a lot of the pieces that you'll see is from, is inspired by Hawaii. Things that we can use here. Things that you can pair with other collections of mine. And things that you can use on the beach, transforms into a cocktail event into an evening event. So I really wanted to make a lot of pieces more versatile. And things that you can use throughout the whole day. That's so good. Because when you get something, like whatever I buy, if I buy a dress, you can kind of wear it and everyone just knows that dress. Exactly. Whereas if you have versatile pieces, you can continuously reinvent your outfit and pair them with other things from your collection or someone else's. Totally. And just create your own style. And I think that's really important too. Yes, of course. So I like it. Very good. Now something that's really important to me, another reason I really wanted to have you on the show, is Reach the Runway. Yes. Can you tell us about your involvement in Reach the Runway and what it's about and what it means to you really? So Reach the Runway is a great opportunity. Stacy and Lenny last year, they had partnered up with a bunch of amazing young creative kids that wanted to learn the industry in fashion, photography, hair and makeup, graphics. And they had a great course for them to learn all of these things behind the scenes. And this year they had an amazing course as well too and they put together an amazing team to help out with that as well. And it's just great for Hawaii to offer that to these young kids. I didn't have that one growing up and I didn't have anyone to really nurture me through that. The only thing I had was my aunt who taught me how to sew and she basically was the one who taught me fashion. And then just going through whatever I knew and watching television and looking at magazines. So I think the kids are very fortunate to have this opportunity to network with industry people at this level. It's so incredible. These girls and some boys are in grade six and they're able to network with a project runway all-star. And for a person like myself, I'm all about I like connecting. Networking is not as much the word I like as connecting because you just got to connect. But you're going to connect with like-minded people. So whether you're in your 30s or you're 12, if you have a similar interest, I mean there's connection there and that can really get you far.  And they're working with not only me, but they're working with other celebrity stylists here and makeup people, photographers as well. And what they're doing is they're connecting with themselves as well too. They're actually growing a team at this young age and they're growing themselves. You know what I mean? Like they're befriending themselves at this young age and they're going to grow up with each other. That is very good. They're befriending themselves. Everyone, befriend yourself. That's a great quote. Keeney's a more happy friend yourself. Befriend yourself, yeah. It's so true though because in society, I mean everyone's judging and this and that. And when you have a focus and you have like, they say you're vibe attracts your tribes. You've got to focus. You've got to vibe. You've got something you're working on. You don't care what anyone's saying about you. Oh, you're this. You're that. You're, you know, you can't run. I don't care. I've got my thing I'm doing. I'm on my purpose. Exactly. So, I mean, yeah. And they're building their own team together. With me, when I build my team, it's a team of hair and makeup, stylists, photographers. It's a team. It's everyone together working as a creative engine, I guess. And that's what they're building right now at this young age. And that's great that they get to put that together now and work at it at what, 10 or 13 years old.  And I'm 32 years old and they're 13. So they get to start at this age. I imagine what they can achieve by the time they're like, all right. Because I actually watched an interview or read something about when you were saying it's all about letting the people that you collaborate with as you're saying your stylist or your makeup artist to really, you know, nurture their own creative talent and give them some guidelines but also open. Yes. So whenever I do that, I give them an inspiration. It's all about the feeling and inspiration of what my collection is all about. And then I offer it to them. I don't tell them I want the hair and makeup to look like this. The photography I want it to be like this. It's all about getting them in the vibe and getting them excited about, here's my inspiration. This is what I thought about this season. And then they come to me and get excited as well too. I want people to get excited at how I do about my collection and then they give me back their excitement about, I think we should do this for hair and makeup. Or I think we should do photography and lookbook like this or a campaign like this. I think when you open up the creative juices into, I mean, a big bowl, I think it's a lot better that way. And you don't put people in a one track mind like I want it to look like this. I think you put people in a box in that way and you want people to be more creative if you tell them an inspiration and you let them go free with it. And with Savvy Shakes, we're all about living our dreams and just really going out and pursuing things that inspire us like you're doing your perfect living example. And it seems like everyone around you is also doing what they love. Do you think it's possible for people to really live what their talent and dream is? Yes. I'm one person to say that I guess I came from rags to riches. I grew up with a family that had basically nothing. My mother and father, Tireman and my mom worked at a bank and I had to pay myself through college. I worked my way through college myself. Knowing that fashion was going to be my career, I had to really figure out what I was going to do to get me through and what I was going to do after college to make it a career. Was I going to make it my business at the end and what I needed to do? It's drive determination. It's that sacrifice that you have to do at a young age to really fulfill your career at the end and really find out what you really love to do. How old were you when you realized and your auntie gave the sewing machine or was teaching you? How old were you at that time? Was fashion something you've always known that you've loved? I think so. My mom always told me. She said I started sketching at eight. Oh, so it started with sketching? It started sketching, yeah. I always wonder how designers, like, did they start sewing? Did they start sketching? But I guess everyone's different. Yeah, so it started sketching and she said whenever it came around Christmas time or my birthday, I always used to ask for pens and artsy stuff. And then my aunt had a sewing class with me and my cousins at 10 years old. And by the second class, I was the only one there that was sewing. And that's when I realized that I could create stuff, a 3D image. And basically what I did was that it was about 14 or 15 years old where I sketched something out and my aunt helped me create it. And I could realize in that moment, it was old enough where I could press print on my brain and I could show people what was going on in my mind, creatively. So it was a great opportunity for me to show people what was going on. That's a big challenge for a creative person to be able to actually articulate that in a way that other people can understand. There are so many different creative professions. And I find that a lot of times creative people get stuck because they can't express that. Like it's here, don't you understand? And unless they're with other creative people, it can be challenging to get that out. Exactly. And so you got yourself through college. What did you study in college? I studied fashion technology in college here in Honolulu Community College to just further my education and just to see the world. I guess I packed up right after college here and I went to FIT in New York and I stayed there for about a year and a half just to see New York.  I got accepted to the college and I was like, okay, I'm going to go. Here you go. And I didn't know where I was staying. Figured it out and it was something that I really wanted to do and just go for it. And I did. And it's something that's the drive that I wanted. I wanted to be a fashion designer. I knew this is all I knew. Like did you have a vision of runway and everything when you were young, is that what you sort of saw for yourself?  I did. That's all I saw myself doing was just creating clothes and designing. That's basically what I saw. My future is being. It's kind of cliche to say that, but I didn't see myself doing anything else. I was just doing that. Yeah. And so getting to New York, were you surprised about what is, you know, where are we? What is this? It was kind of like a concrete jungle shock to me when I first got there. It was like, oh my God. Yeah. Like, oh my God, I didn't realize what I was getting myself into. But then I just had to get the hang of it. It was kind of fake it till you make it. And that's what I did. Made it and kind of, I didn't know where I was staying. I had no place to stay. Aunt's friend kind of lend me a couch until I could afford to get a place. And then I had to travel from Jersey to school in the city. And it was just, You just made it happen. Made it happen. Exactly. We've got so much to talk about in the next segment, so I'm very excited. But I did also watch something that you'd said about where you get your creative inspiration, like how you clear your mind and then just go for it. Can you just give me a little insight on what that's all about? So whenever I get inspiration or inspired, I always have to clear my mind by, I go to the beach a lot. And to do that, I just really go to the beach alone. I go out at six or seven o'clock in the morning and just look out in the ocean and just kind of appreciate what's around us. Sometimes we forget what's around us and forget how beautiful the land that we live in. And we kind of forget that we live here. And I do that sometimes because I'm so busy with my life and what the business that I'm in. So I take that time and I sit and I just relax and kind of clear my mind and think about things and then it kind of puts me in a mood and a vibe and that clears me for my inspiration for my next collection. And it can be totally different, I guess. You can literally reinvent yourself from collection to collection just from clearing your mind. Just from clearing my mind. And as I'm clearing my mind, these little bits and pieces will pop into my mind. This will just resonate and stick in my mind and that will just stay. And I'll just go and put it on an inspiration board. Stay tuned because we want to be inspired more by Kinies and more. This has been amazing. Thanks for tuning in to the Savvy Chick Show on Think Tech Hawaii and we'll see you in a minute. Hello, my name is Crystal. Let me tell you my talk show, I'm all about health. It's healthy to talk about sex. It's healthy to talk about things that people don't talk about. It's healthy to discuss things that you think are unhealthy because you need to talk about it. So I welcome you to watch Quok Talk and engage in some provocative discussions on things that do relate to healthy issues and have a well-balanced attitude in life. Join me. Hey, how you doing? Welcome to Abachi Talk. My name is Andrew Lening. I'm your co-host and we have a nice program here every Friday at 1 o'clock on Think Tech Studios where we talk about technology and we have a little bit of fun with it. So join us if you can. Thanks. Aloha. Hello, I'm Marianne Sasaki. Welcome to Think Tech Hawaii where some of the most interesting conversations with Honolulu go on. I have a show on Wednesdays from one to two called Life in the Law where we discuss legal issues, politics, governmental topics, and a whole host of issues. I hope you'll join me. Aloha, welcome back to the Savvy Chick Show on Think Tech Hawaii. We are celebrating Honolulu Fashion Week this week and it's very exciting. We have an all-star project one-way participant guest here who is Kaini Sabar. But I'm so excited. I want to hear all about his project runaway experience and I know you do too because, I mean, what girl who loves fashion doesn't want to be on something like that. But before we get to there, I want to know how he got there. So let's go back. You told us that ever since you're young you love fashion. You're sewing with your auntie.  So that's very inspiring. So where did you go after that? After that, I came back home actually, figured out that the amazing thing was going through college. I figured out that the college there taught me everything that Honolulu Community College has already taught me. When I figured that out, it was amazed because Honolulu and Hawaii was teaching the things that New York was teaching and it was kind of at that same level. So it was great to find that out. And then when I got back home, I figured out, I was trying to figure out what I was going to do was I was going to start my business. Then at that point I was taking in a little custom clients here and there and I was working at PacSun. I was working at a retail store as a manager there. And throughout that whole retail career I wanted to figure out all the aspects of being a manager and owning my own business. So you do that you wanted to have a business. Is that always an intention? Yeah. So I wanted to know how... I knew I was going to have a retail store. So how was I going to run a retail store? Better to be a store manager and know the whole thing of how to run one. So I knew I learned visuals really fast, sales managing, how to manage employees and how to do that whole thing just from working there. And that's what I took all those tools, worked there for about two years. And after I basically got out of that world, I put my foot down and I was like, I'm going to just take that leap of faith and start my business. So were you actually still creating while you were working at the store there?  But learning. Because I think often people, we want to just go do what we do. But it does help to go work for someone else and learn a business perhaps and have that hands-on experience with a lot of customers as long as you're outlating your creativity.  So it was just balancing both of it at the same time, trying to. Trying to. Trying to balance both of it. Trying to being the key word. But it's really what you got to do when you're pursuing something you love. Exactly. A lot of energy needs to be put in that. And then once one thing, when the designing started to overtake my day job, that's when I realized, okay, I can't do this anymore. So that's when I kind of put my foot down and I was like, I need to take this leap of faith and start my business. And did you just start as Keeney Zamora straight away? Yeah, that's when I started as that. And then I just went straight into it as my full-time job and got more clients and I just kind of relied on that. And what kind of fashion were you doing at that time? It was a lot of custom stuff. So I was doing pageants and proms and bridal stuff. So it was a lot of just people coming to me for these individual pieces. And then I had to realize what I was going to do to make my bread and butter, I guess. So I started a Hawaii collection, stuff that people in Hawaii usually wear. And at that point, I was kind of stuck. So it brings me to how am I going to let other people know of my brand, of who I am and whatnot. So of course, Project Runway has always been in my mind. I watched Keeney Zamora for seasons. Tell us all about the experience. Yes. So I tried out, when I first moved to New York, I tried out for, I think it was the first or second season and then a couple of times after that. And that's always been in my mind. So during that time where I quit my job and going into starting my business, I was like, okay, I guess I can try it out again. And I believe it was at my, that was my fifth time trying. Fifth time. Fifth time. Five. Five guys. So if you try one, so it doesn't work, five. Yes. Some people try 500, you know. That's awesome. There's people that tried out six times. So just the fact that you just keep going back. I mean, that's what I think in society, often we don't realize, oh, it didn't work. Okay. It must not be for me. I'm going to go this way. It's like, no, if it's meant for you, you just keep like, hello. Can I come in yet? Hi. Remember me, the island boy? Yeah. And for me it was, I took every time that I went back, it was a critique and I learned from it. It was everything that they taught me. And every little bit that they told me I needed to fix, I fixed. And I tried and I always thought in my mind, of course it was, why aren't you choosing me? And then it was the, okay, I'm really listening to that. That's the reason why they're not choosing me. So the fifth time it went really far. I went down to, I think them calling me, asking me if I wanted to be under the gun. And I was like, of course, it's a TV show, I'll do it. It's more pressed for me and people to see my work and see what we have exposure. It was free exposure, that's what I thought. And then it was the denial letter. It was the casting that I didn't make. And then I was like, oh my gosh, this is a lot. It was like, all right, what do I do? It put me down, but then I was just like, no, let me just try my business. And it was just like full force with my business, even stronger. And then they had emailed me one more time and it was like, we have all your information. You basically don't need to come to LA because you have everything. And but if you do want to come, here's your interview date with Tim Gunn and blah, blah, blah. So I was like, oh, I have time. I'll just come, whatever. I kind of just threw my hands up and I was like, here's what I have. You're going to take me for what it is. It is what it is. And I basically did it like that. And I went in there with an attitude kind of like, here's my collection. I stand by it. This is me. And they loved it. They took it and was like, yes, we want you on the show. And I kind of stood back and I was like, OK, what did I do this time? That was kind of different. And then the casting was different this year for regular runways because they flew us out to New York. Everything happened so fast. It was literally, I got the email. And then a week later, I was flying to LA. They told me, yes, I got the casting. I got still finalists. And then a week after that, I was flown out to New York to do a live taping of them choosing the finalists and the cast for it. I flew there on a Monday, got there on Tuesday. They filmed on Wednesday, announced the cast, and I got casted for it. And I flew back on Thursday. The email doesn't say we're leaving in a week to be filmed for six weeks. So everything happened within two months. And now this is during summer. And I was like, oh my gosh, this is happening really, really quick. And I have to be ready for this.  No project runaway. No project runaway. So what am I going to do? I'm like, I have my business. Now I have project runaway. I'm going to be gone for six weeks. So what am I going to do? And this is just a great opportunity. So it was just like everything kind of happened really fast. To being flown to New York in production, everything gets taken away. Your phone, computer, you're totally disconnected from everything. Wow. You don't even get a call home. You don't even know anything that's going on. You're basically shadowed from one place to another. So you don't even know if you're kidding. You would miss election. You wouldn't even know who won. So you don't even know anything that's going on. And throughout the whole process, you're just at all in kind of standing back. Like, am I really being filmed right now? All the time. So you're being filmed pretty much all the time? Pretty much you're woken up at 5.30 in the morning to be filmed till 12 o'clock at night. Wow. Being that I was on till I was the third runner up, so I was third finalist. You are, I was there for the long haul. I was there for the whole time. So it was like, oh my gosh, I'm exhausted and drained, not just physically, but mentally, because your inspiration just kind of gets drained. And you don't have time to prep during that two weeks of, okay, what am I going to do for the next six weeks? But you're collecting, by the way, look amazing. That is so, that was pretty awesome. And it was just, it was like that. It was just like, here's your challenge after challenge. Everyone sees a television show for a week and we think that you guys think we have to, we have a week to work on these things. We literally have every other day. Wow. And it's about eight hour days of work. It's not a full 12 hour day. We wake up at 5, we sit around for another two hours, get a challenge, shop for another half an hour, sketch for half an hour in the work room for eight hours, and then we're back in the runway the next day. And what are the, what are the, like the mentors and judges and everything like, is that, is that pretty, a pretty important part? They are. I think a lot of people see it on television as, they're being mean and cruel, but the thing is they're in the industry. They know what to expect. They have been there before. So taking their critique is really important for us as designers and we really have to listen to them because they've been there. I think it's honest opinion. Tim, everyone always asks me if Tim is really how he is. He is exactly how he is on television. He's the nicest person ever. He really gives your, his honest opinion about your collection, your pieces that you make, and he's a great mentor. Heidi's really fun on stage. She's so goofy all the time. Super, super cool. Nina is great with her feedback because she's a magazine editor. She knows what people and consumers who are looking at the magazine will be seeing. So we have to trust her judgment. And Zach, of course, knows construction. So he knows what pieces should be made like or made to be built. So of course we're going to be critiques on that. And so all of that that you've taken from them, is that now what you've put together to show us at Honolulu Fashion Week? Of course, yeah. I think that's what I've done throughout my whole career now is I'm thinking of all of those things, is putting together that stuff. And just bringing your Hawaiian spirit to all these different... Yes, knowing what I did throughout the show and then bringing it here to Hawaii and letting people know what we can do here. And just hearing the judges critique in my mind whenever I'm creating a collection is doing that. And putting it throughout my... I mean, they don't have... I don't have judges sitting at my studio telling me, here's my critique about your collection. So I have to put it in my mind, what would this person think about that person? Yeah. And what would Tim say about this and blah, blah, blah. So I have to really think about it myself and what these judges will think of on my own. And it's kind of scary to think, you know? But now you're on both sides. You're actually... I've got just a couple of things before we wrap up. But you're actually like a mentor yourself now. So what's your advice to young girls with big dreams? My advice, my big advice that I love to give people or young creative people is to be creative to who you are. Don't worry about the followers and don't worry about if people will like what you do. Just stick to your creative personality and how creative you are. The followers will come after when they find out how creative you are. That's just my big advice. It's being authentic, really. Exactly. For all of those of you watching who are in Honolulu, do not miss this show. Yes. Don't miss my show. So all the proceeds go to Reach the Runway as well. Reach the Runway. Yes. I mean, that's fantastic. And I don't know if there's still tickets for tonight. For the ball tonight? Do you know if there's still tickets available? Yes, there is. There are still tickets tonight. So you can go onto the website. I believe it's reachtherunway.com. There's a few tickets left over. So come out to the ball tonight and then our show as well on Saturday. It's November 12th. There you go. At 2 o'clock. Yeah, perfect. Now you can't miss it. No excuses. No excuses at all. It's right there. So 2 o'clock on Saturday. We're going to be covering that as well. Very excited. The Savvy Chick show will be there. Yes. Capturing you on the runway. So we'll get to see what it's all about. I'm excited. Yeah, I'm excited. Thank you so much for coming down to the studio because it's a crazy week for you. Yes. I'm excited that you've seen this lot of things. So thank you.