In this topic, we are going to talk about the situational requirements for selection criteria for international assignments. In the previous topic, we had talked about the individual requirements. What are the requirements that the individual must possess to be selected for an international assignment? In this topic, we are going to talk about the situational requirements that are those requirements or those factors which are important to take into account regarding the situation. For example, what type of country that person is going to, what type of multinational it is, what type of language requirements would be there. So these are the situational requirements which are important to be taken into account while selecting a person for international assignment. So the selection criteria must take into account these situational requirements. So let's take a look what are the various different types of selection requirements. The first situational requirement for selection for an international assignment is the country or the cultural requirements. The country requirements could vary from different governmental requirements to the cultural and societal requirements of that place, including various different cultural dynamics that are over there. So the country requirements could be the work visa and permit for a desired parent country national or a third country national. So it should be important to note that whether a person would be given a visa or work permit to work in that place or not. Then work visas for spouse is also another factor which should be taken into account if that country does not give work visa to the spouse. That means that it would be a limiting factor for sending a person to that international assignment. A host country is a very important determinant. Some regions and countries are considered as hardship postings. So countries which have difficult environment, which have difficult cultures, which are torn with terrorism, which have different kinds of other problems, for example, disease epidemics. For example, in America, there are certain countries which are affected by various different diseases such as Congo virus or other type of such kind of diseases. So these areas, they are considered to be hardship areas. So the host country is a huge determinant whether a person would be interesting and willing to go to that particular location or not. So your selection criteria would be quite limited in case the country is a hardship area and people would not be ready to accept postings to that place. And therefore you need to develop such kind of packages which could provide incentives or you have to make sure you have to give them this kind of assurance that your requirements and your safety will be taken into account and what you are doing to ensure their safety and their well-being. So host country is a very important determinant, particularly in case it is a hardship country. On the other hand, if it is a country which people want to go to, then you would have a lot better pool of people who would be interesting to take up that international assignment. So this is a very important factor. Then the second type of situational requirement belongs to the multinational itself. And multinational requirements could include the mode of operation. So as we discussed in previous topics, whether it is a joint venture, whether it is a merger or an acquisition, that particular type of setting that would set the stage for what type of international assignments can you send your people to. And then what is the duration and type of assignment that you are sending your expatriates and the amount of knowledge transfer. How much knowledge do you need to transfer to the other country, that is also important. If you don't need to transfer a lot of knowledge from your parent country to the host country, then it is quite flexible. You can also hire host country nationals, but if you need to transfer a lot of knowledge from the headquarters to your host country, then you would need to hire parent country nationals for that particular post things. Alright, then language is another very important aspect. In some situations it is important. In some situations it may be less important. For example, if it is the same region, it may not be really important to take into account the language barriers. For example, if you are sending somebody from Pakistan to UK, a lot of people in Pakistan, they are very much familiar and conversant with the English language. But if you are sending somebody to Japan or somebody to Germany, German language or Japanese language is not something that Pakistani people would be really familiar with. So you may need to give them that kind of training and that kind of awareness about that particular language. Earlier language was considered to be a mechanical and manageable problem and that individual would take care of it themselves. So it was considered to be a responsibility of the individual itself. But now it is considered as a situational requirement so that the match between the person and the job that he is taking up is basically according to the language requirements of that particular position as well as that of the person. Selection tests are therefore used to select people who are appropriate and the appropriateness of the selection test is something which also determines how well you are able to select people for your international assignments. So there is a varying validity of selection tests. In different countries, they have a different type of prediction about use of these selection tests and selection is basically based on the subjective nature of these characteristics. And the subjective nature of these characteristics is actually then defined in a model of selection criteria in which there are four types of selection criteria which are defined which must be taken into account while you are selecting a person for an international assignment. So there are four selection criteria to be tested in the selection test. One is the self-oriented dimension, the degree to which an expatriate expresses an adaptive concern for self-preservation, self-enjoyment and mental hygiene. So this is a kind of tendency that a person is able to manage his own emotions, manage his own self and is able to adapt to different situations. Then second dimension is the perceptual dimension which is the expertise the expatriate possesses in accurately understanding why host nationals behave the way they do. So it is about the perception of the person that he is able to create the right perception about people who are in the host country belonging to a different culture and working in a different environment. He has the ability to perceive the way they are doing things, why they are doing it that way. For example, if they are bowing in front of you and that is happening in Japan, the person would know that this is something that is very much cultural in Japan. Then the third dimension of this selection criteria is other oriented dimension. So it is very much self-explanatory that this dimension is about orientation toward other people. So it is about the empathy. So it is the degree to which the expatriate is concerned about host nationals, coworkers and desire to affiliate with them. So it is other oriented dimension. The person is ready to affiliate, is ready to make connections, is ready to make relationships and is ready to accept that these are also equal people and what are their problems, what could be their issues and is ready to empathize with those people of the host country. And finally the fourth dimension is the cultural toughness dimension which is the mediating variable that recognizes that a culture ration is affected by the degree to which culture of host country is incongruent with that of the home country. So cultural toughness is actually the difference between the host country and the parent country. If the difference is too high, then cultural toughness is obviously something which is too high and if the difference between the host country and the parent country is low, it means that the cultural toughness is low and that means that the person who is moving from the parent country to the host country will not have to face a lot of difficulties in adjusting and understanding the other culture. But if it is a tough culture, if the cultural toughness is high, that means that the person would need to be given a lot of first of all training and then he would have to be culturally adaptive to actually understand the differences between parent country culture and the host country culture. So these are the four dimensions on which a person's ability to be selected for an international assignment would be assessed. So in this topic, we have discussed about the situational requirements of selection for an international assignment.


There will never be a time when it can be completely automated. We will absolutely need the human in the loop with judgment to make the essential connections between the user and the technology and the problem. And these are really important things to solve and I think you are exactly the kind of people who solve them. And so I think with AI people, data analytics people like you could say, I think there's a lot to be done. You can see that quantitative modeling can do a lot of good things within the intelligence domain. I hope this will make a difference and make the world just a little bit safer. We can't view analytics as a single project, it really is about a longer term investment in how we're going to use data and allowing that to transform the business, not just a discrete project that happens at every one time.


The first takeaway is that values can be inherited by descendants, but those descendants can't pass back values to their ancestors. Yep, that's a big one. Here's another takeaway. An invalid custom property value is unable to fall back to previously set cascaded value. Which is also why I really like registered custom properties, because you can set the fallback, so you don't run into that case and you foolproof your custom property systems, which are a big part of design systems. Also, just learn all about URLs and custom properties, so relative URLs are resolved to the directory they are found, which can be a remote directory. And then you already captured this takeaway, but use a fallback value when defining a custom property. That way, in case something happens, there's always a value there to be found.


Thanks a lot, Mike. Thank you, Alina, Philip, and Mike for the invitation. It is a really great honor. So this talk is based on joint work with Olexi Klurman and Yoni Teravinen. And like many other analytic number theory talks, I'm going to begin by motivating things by looking at problems about the primes that we still don't know how to solve. And a lot of those problems relate in some form or other with the nature of the sequence of primes. In particular, we'd like to know what kinds of patterns exist among them. For example, can we find infinitely many twin primes? Can we find infinitely many primes that are given by values of irreducible polynomials, like x squared plus one? And a lot of these questions explore the extent to which the multiplicative properties, so for example, primality or the number of prime factors of additively coupled integers, say M and M plus H, so for example, M M plus two or M M minus one in these two examples, must depend on one another or if they can be independent. And at least a qualitative version of a very classical conjecture of Hardy and Littlewood states that if k is greater than or equal to one, and we have an admissible tuple of distinct non-negative integers, and that just means that the integers h i don't cover all the residue classes modulo any primes, so we don't have some fixed prime factor, then infinitely often we can, there should be simultaneous prime values given by M plus h one and plus h two all the way to M plus h k. Now we don't know how to solve this type of problem at the moment. And part of the reason is because the prime number theorem tells us, among other things, that the primes are sparse, and it's difficult to study their patterns. So what we'd like to do instead is to look at some sort of avatar of the primes that say is supported on a non-sparse set that we can analyze in some way, and that gives us some fruitful information about the primes. And a classical instance of this is the label function. So this is the completely multiplicative function, which is given by a minus one to the number of prime factors of integer n, counted with multiplicity. And it's been known since Landau, in the beginning of the 20th century, that the prime number theorem is equivalent to the partial sums of the label function on average tending to zero as x goes to infinity, and that the Riemann hypothesis, which is equivalent to a statement about the size of the error term in the prime number theorem, is equivalent to a statement about the cancellation in the partial sums of the label function. So somehow the label function has some intimate connection with the primes, and so naturally, it's reasonable to think that if we want to study tuples, simultaneous prime values amongst tuples of integers, it might make sense to look at tuples of values of the label function. And in the remainder of the talk, I won't be able to say anything that will tell me anything about the prime. So for now, I'm just going to focus on the problem of analyzing these values of the label function. Okay, so for the remainder of the talk, I'm going to refer to a k tuple of pluses and minuses as a sine pattern of length k. And Chalice conjecture is a statement about precisely the values assumed by these k tuples of values of the label function. So for each k greater than or equal to one, we expect that the values lambda n plus h1 through lambda n plus hk, where these h i's are distinct non negative integer shifts, assume each of these length k sine patterns infinitely many times. And moreover, we expect that they equidistribute among these sine patterns, namely, there are two to the k sine patterns of length k. And we expect each of those sine patterns to be reproduced with frequency x over two to the k when n is an integer less than or equal to x. Now this is known for k equals one, because the prime number theorem, which is a statement about partial sums of the label function, tells us exactly that lambda then takes the value plus one and the value minus one with equal probability one half among integers up to x. But for k greater than or equal to two, we don't really know very much about this problem. But at any rate, we can interpret what Charles Conjecture says. First of all, I mentioned that these tuples should equidistribute amongst these sine patterns of length k. But the upshot of that is that we should expect that each of the values lambda n plus h1 through lambda n plus hk, these could should be statistically independent as n varies. In other words, the value taken by lambda at n plus h1 should not influence or be influenced by the values given by lambda at these other numbers n plus h2 through n plus hk for most n, at least. Okay, now there's another way to phrase Charles Conjecture, which is related to what are called correlations. So here by a correlation of arithmetic functions f1 through fk, I just mean products of the form f1 n plus h1 through fk n plus hk. And sometimes I'll call these autocorrelations if all of these functions are the same. Well, then the correlation averages of the legal function, you can you can take the sum and you can decompose it according to the different sine patterns of the legal function, a length k the legal function assumes, and thereby express this correlation average in terms of the frequencies of these sine patterns. And conversely, you can express the frequency of sine patterns using correlations. And that's because there is a very convenient identity to express the indicator function for the legal function taking either a given plus or minus one value. And if we apply that for each of the different signs that we want the legal function to assume along this tuple, then we get a sum of these sorts of products, which we can then expand into a term which is independent of n, and then a sum of correlation terms, correlation averages. And so if we expect that each of the frequencies is about x over two to the k, it would be enough to show that all these correlations are small. And so chalice conjecture in the correlation formulation is a statement that for each k, and each set of distinct shifts h1 through hk, these k-point autocorrelations vanish in the sense that these averages tend to zero as x goes to infinity. Okay, now we can interpret these these two versions of chalice conjecture as saying that a lambda of m, which depends on the prime factorization of m and therefore is manifesting some information about the multiplicative structure of n plus h1 and plus h2, 300 plus hk, this conjecture suggests that these multiplicative structures, these factorizations, for example, should be independent at some level as n varies. And so we might expect that any other function which interacts in a predictable way with products should also manifest this sort of independence. And so for example, if we take a multiplicative function, so a function that splits products whenever the factors are co-prime, should also have this sort of independence property for its various values. But of course, this depends on the function and there are many exceptions. So for example, so by the way, for most of this talk, I'm going to focus on real valued functions, although in this slide I'll refer to some complex value functions. So for example, for if f is a real Dirichlet character, modulo q, then if I shift n by q, then the function is left invariant because the function is q periodic. And more generally, if I take complex valued functions that take values in the closed unit disk, which already is u, then we have other exceptions. So of course, we have complex Dirichlet characters as well. But then also our comedian characters. So these are functions n to the i, i, t for t, a real number. And these vary slowly with n. So if n is sufficiently large, n plus 1 to the i, t, n to the i, t are very close together. So the value f of n is very similar to value f of n plus 1. These are not independent values. And more generally, if we take a product of these characters, if even if we take a function, we sort of make it slightly different, but not too different from a product of a character, a Dirichlet character and an Archimedean character, then we'll still see some coupling between these values. And so this independence between these values is not seen by these types of multiplicative functions. So there is a generalization of Chalice conjecture, which is due to Elliott, which speaks about functions that precisely don't have these sorts of obstructions that they look like twisted characters. And the way that these can be, this conjecture can be formulated is by using the pretentious distance of Granville and Saundra Rajan, which is given as follows. So if we're given two parameters, y and x, bigger than two, and we have arithmetic functions taking values in the closed unit disk, we'll look at the distance between f and g over the primes between y and x to be this sum over primes.  When we want y to be, if we want to consider all the primes up to x, we'll just write that as dfg x. And then if we take x to infinity, this is a non-negative, this is an increasing function in x. So this limit exists and we can define dfg infinity. It could be infinity, it could be finite. Now, if we replace the numerator in this definition of the distance by the maximum that it could take, which is two, then Mertens' theorem tells us that this pretentious distance is bounded above by two log x plus a constant. And all of the summands are non-negative because this real part is always less than or equal to one. So we get this set of chain of inequalities. And of course, the upper bound can be attained. I were interested more in the case where it's far from the truth, which suggests that f and g behave very similarly. So we'll say that f is pretentious if the distance between f and one of these twisted characters, the character terms in our comedian character, is bounded. So it doesn't increase with x. And we'll say it's non-pretentious otherwise. And an example of non-pretentious function is the liable function, for example. Now, as I said, for most of the talk, I'll focus on real-valued functions, in which case, non-pretentiousness is just the same as saying that f, the distance between f and any real Dirichlet character tends to infinity. And le's conjecture for real-valued functions, at least, can be stated as follows. If f is a non-pretentious real-valued multiplicative function, then all of its average autocorrelations tend to zero. Okay, in particular, if we take f to be the liable function, this recovers chalice conjecture. Okay, now this is still open for all k greater than or equal to 2. If k is equal to 1, this is sort of a generalization of pnt, the prime number theorem, which is due to piercing in this case for real-valued functions. Okay, so I want to talk about two problems related to sine patterns, and they have to do with chalice conjecture in some form or other. But in order to motivate them, let me talk about the knowledge that we currently have about sine patterns and how many are attained. And some of this is a bit weaker than what is actually proven, but I just want to give it for motivation's sake. So if we look at k between 1 and 4, and we ask, okay, how many sine patterns are attained by the tuple lambda n plus 1, by k consecutive values of the liable function, then it's known that in all of these cases, all of the sine patterns are attained infinitely often, and in fact, they're attained with some notion of density, positive upper density, certainly. If k is equal to 5, then work of tau and teravine recently has shown that there are at least 24 of these sine patterns that are attained, but as far as I know, not all of them are known to be attained.  Currently, the best result that I'm aware of is from a very deep paper of Matamaki, Rajabio, tau, teravine, and Ziegler, where they show that more than a polynomial number of sine patterns for each k are attained. But as far as I know, there are positive proportions of sine patterns. We don't know if that occurs for any large enough k. Now, if we assume some unproven hypotheses, then child's conjecture is known to hold. So, for example, if we assume that Ziegler's zeros for Dirichlet L functions real characters exist, then Chen has showed that all two of the k sine patterns do occur. But if we want to know, I mean, currently, we don't know how to prove child's conjecture unconditionally. So this motivates a problem that was stated by Duda-Hur in 2018 at an AIM meeting, which is the following. If rather than looking at the Liouville function, we look at a Liouville-like function, which is non-pretentious. Can we show that not only can all the sine patterns occur, but can we get equidistribution among the sine patterns? So in particular, can we construct a set of primes p such that the sum of the reciprocals of the primes in that set is infinite? This is what leads to non-pretentiousness, as I'll show later. Such that the Liouville function of p, that is the function minus 1 to the number of prime factors of n coming from p, counted with multiplicity, is such that all of the sine patterns of length 2 to the k are assumed by these two poles, lambda p and plus h1, through lambda p and plus hk, and in a way that's in the sort of, with the same frequency for each of them. Okay, so the Liouville function is precisely the case where p is a set of all primes. Here we're looking at possibly p not being the set of all primes, but can we still have such a function that looks like the Liouville function that does what Charles Conjecture suggested ought to? Okay, so I'm just reminding you what the definition here is. So we're going to focus on p that have relative density 0. So what that means is if we look at the number of primes in p up to x, that is proportion 0 of the primes up to x, x goes to infinity. Then with Clermann and Theravine, and we showed that for such a set that has relative density 0, but still has a sum of reciprocals that's infinite, there are such examples, then we do get this expected equidistribution among the sine patterns of length k. Now, how does it relate back to Elliott's Conjecture? This is a multiplicative function which takes real values, but it's not the Liouville function. Well, it's not difficult to show as I'll show a bit later in the talk that lambda p is non-pretentious whenever p has relative density 0 and it has the sum of reciprocals condition being unbounded. So these lambda p's that we treat in this theorem are in fact non-pretentious. And so this gives us an instance of Elliott's Conjecture folding. And as far as we're aware, this is the first deterministic example of a real value function that satisfies Elliott's Conjecture. I say deterministic because it was proven by Kluhrmann-Schreder-Benjoux that if you look at so-called random multiplicative functions, they do satisfy Elliott's Conjecture with high probability. Okay. Now, I just mentioned an example of a function that does hit all of the sine patterns with the right frequency, but we could ask on the flip side, okay, well, maybe the Liouville function doesn't hit all the sine patterns, is that possible? Or must any plus minus one value completely multiplicative function produce every sine pattern of length K? And the answer is no. So here's a very simple example. If you take the Legendre symbol mod 3 and then you modify so that that takes the value 0 at the prime 3. So if you want to correct that to get a plus minus one valued function, you can choose its value, a corresponding modified function so that the value of the function at 3 is plus or minus one. And that leads to two different functions, that leads to chi A3 tilde plus and chi 3 tilde minus. And if you look at either of these examples, and you look at the numbers 3m plus 1, 3m plus 2, 3m plus 3, and you evaluate these functions, well, this chi 3 tilde retains some amount of periodicity from the Legendre symbol. In particular, if the number is not divisible by 3, then it is genuinely equal to the Legendre symbol of that number. So chi 3 tilde plus minus of 3m plus 1 is just chi is just Legendre symbol of 1, which is plus 1. Similarly, these functions of 3m plus 2 is just Legendre symbol of 2, which is minus 1. And then this last one, which is divisible by 3, we don't necessarily know, we get a plus or a minus. But the upshot of this is that we can never get three pluses in a row. In any set of three numbers, we'll get at least one minus and at least one plus. And so we can never get three pluses, and we can never get three minuses. So those sign patterns of length three are omitted by the consecutive values of these two functions. And you can ask more generally, as the Lamers did in the 60s, for a classification of all completely multiplicative functions that omit the pattern plus plus plus plus for any k. So for each k, you get a different problem, classify the set of f such that you don't get k consecutive pluses in a row. This is what the problem is. And I think their motivation for this was because if you did study this problem, you'd be able to tell which completely multiplicative functions such as say, Legendre symbols, modular primes, give rise to a certain number of pluses in a row, and that sheds light on the number of consecutive quadratic residues you can get in a row. At any rate, Isai Schur proved in the 70s that in the case k equals three, the two examples I've given you here, chi three tilde plus, chi three tilde minus, these are the only possibilities for completely multiplicative functions that omit the sign pattern plus plus plus. So of course, you can ask this question for other sign patterns. But as I mentioned in just a moment, the sign patterns of pluses are a bit more special in a sense. So we'll just focus on that. Now Schur's argument is a bit involved and it's not very systematic. There's lots of casework. So preferably we'd like to approach these types of problems in a different way. Now Hudson considered the problem with k equals four and actually did a lot of computational work on this and claimed that there were precisely 13 functions aside from Schur's examples, because so Schur's examples say that plus plus plus number occurs. So certainly four pluses in a row can't occur for those examples. But besides those, Hudson said that for four pluses in a row, there are 13 functions that omitted. And they break down roughly into a union of two sets. This is a very non-standard way of stating this. But the point is that one set consists of modified Legendre symbols. So for primes five, seven, 11, 13 and 53, you do the same thing as I mentioned with chi three. You just change its value at the prime to plus or minus one and you get two different functions that way. And interestingly enough, the first four primes here are just the primes after three. The first four primes after three, 53 is quite different. It is what it is. If anybody has some insight as to why that should occur, I'd be happy to hear that. And then the second set T is sort of related in that it contains two of these modifications of the primitive character of mod four. And then it has another function, which is basically the completely multiplicative function that takes value plus one at all the primes other than two and takes the value minus one at the prime two. Okay. So, yeah, I mentioned plus plus plus plus is special. Also, these cases k equals three and four are special. What do I mean by special? Well, in these two results, Scherz result and this conjecture of Hudson, sorry, the Scherz result and Hudson's conjecture, we have a classification with a finite number of examples. But as soon as you take k bigger than or equal to five for plus, you know, the sign pattern of k pluses in a row, you get infinitely many functions. And currently, my PhD student each and you at Durham is looking at this problem of classifying these examples, assuming elites conjecture. So that's one thing. And then the other thing is that this pattern of pluses and four pluses in a row is special in the sense that if we replace four pluses in a row by say a pattern like plus plus minus minus, or in fact, any pattern that has two minuses in a row, that's very easy to construct infinitely many examples. So for example, if you have two minuses within a segment of length four, and you look at the function fp zero, which takes the value minus one exactly at a single prime and that prime is bigger than three, then you can only produce minus one at a single time at most, you can never get two minuses in the same length for segment. So certainly you get infinitely many examples for certain sign patterns of length four. So plus plus plus plus is special. Minus minus minus minus also, but I haven't thought about that too much. So with Alexi and Yoni, we proved that in fact, Hudson's classification is correct, and we proved in a bit of a stronger way. What we proved is that not only do functions outside of Scherz examples, and the examples in S union t produce plus plus plus plus at least once, it actually, they actually must produce them with on a set of positive upper density. So a large number of these occurrences do happen. Okay, so in the remainder of the talk, I'm going to focus on these two problems, the problem of constructing a Leuval-like function that equidistributes among sign patterns of all lengths, and then also about Hudson's conjecture, and hopefully I'll be able to shed some light on both of these problems. Okay, so in order to talk about correlations and sign patterns, these are related problems, it's worth noting, and certainly what I'll discuss in a moment is sort of extending this work, that there is a complementary result to Eliot's conjecture due to Kluhrmann, which treats the case where F is pretentious. So Eliot's conjecture suggests that the autocorrelations of a non-pretentious function vanish, what happens if F is pretentious? So it behaves like a Dirichlet character at many props. So what Kluhrmann proved in 2016 is that if you take a real value function, which is pretentious, so if the distance of F from a real character is bounded, then you can actually compute asymptotically all of the autocorrelations of that. And what those correlations, we can think of them as like global averages, these global averages factor into a product of local contributions. So we have this Euler product, which represents sort of the behavior of the values of F and chi at primes that don't divide the conductor of chi. And then we have this factor, which represents sort of the behavior of F at the primes that divide the conductor of chi. Again, there's a misprint that should not depend on chi p new because that's just zero. So ignore that. But anyway, the CF chi depends only on chi and the value of F at primes that divide you. So we have this sort of local to global type result. And the key observation, which I'll delve into a bit more in the next slide, is that if F is pretentious to a character chi, so meaning F of p looks like chi p very often, then if we look at the, then let's say assume F takes values plus or minus one, then the function capital F, which is f of n chi of n, this is basically determined by a small primes at large primes, F times chi will look roughly like one. So the values at those larger primes will not really influence the value of that. And so the correlations between these different values fn plus h1, fn plus hk, which sort of are certainly related to the correlations of F, can be analyzed using CF. Okay, so let me be a bit precise about that. So how does this work? Well, if we take the one of these correlation averages, so I haven't normalized it, but but if we take one of these correlation averages and for simplicity, I'll assume F is completely multiplicative, and I pick some parameter y between two and x, the length of the sum, then I can split each of the numbers n plus h1 through n plus hk into the product of the primes that divide it that are less than y and the product of the primes that divide it that are bigger than y, and that will give me some sort of product for n plus h1, n plus h2, n plus hk, which I can then split because of multiplicativity. And that produces then a double sum of some over the divisors of these n plus hj, where all the prime factors are less than y, and then the contribution from the remaining primes. So this inner sum is over the ns that where n plus hi is divisible by each of these dIs. And then moreover, all the primes that divide this quotient are larger than y. Now, of course, if f is varying significantly, then this is a difficult thing to estimate, mainly because we don't really know how to deal with large primes in a systematic way. And of course, large means something specific, which I'll say in a second. But here's a very simple toy case. If f of p is equal to one for all of the primes bigger than y, then all these summands are just one. And so this inner sum is precisely a cardinality. It's the number of n satisfying some congruence conditions, as well as some sort of sieve condition, namely that all the prime factors of these numbers, these quotients are bigger than y. And this is exactly what tools and sieve theory allow us to deal with. So for example, if we take y to be less than x to the epsilon, and we make sure that these conditions are not too strong, so if the dj's are not too large, then we can use the fundamental limit lemma of sieve theory to get asymptotic formula like for this. So in particular, we can estimate the correlations very well under this condition. And in some sense, this is underlying a result of Debussy and Sharpezy, which I sharpened a few years ago, which says the following, as a specific instance of this, if we take the leval function and we truncate it, meaning we take it to, we take a function lambda y, which is equal to lambda for all p less than some parameter y, and we make lambda y equal to one for all of the primes bigger than y, and y here is less than x to the epsilon, then we can actually show cancellation in the correlation sums, lambda y and lambda y and plus h, or h. The point being that if we do this sort of, we sort of go through this scheme of taking the small, the contributions from small primes away from this contribution from large primes, the large primes don't really hurt us. Okay, so you can run the same type of argument, if not just if f is equal to one on the nose for all primes bigger than y, but first of all, if f is equal to a Dirichlet character, because then you can split, you can split the sum over n into residue classes, and then you can kind of rewrite this type of argument with an extra arithmetic progression constraint on n, basically. And moreover, you don't need f to be equal to chi p on the nose, you can allow f to vary slightly away from chi p, if p is bigger than y, and you can still run similar arguments. And this is sort of underlying what Clurman's theorem is about. So in Clurman's paper, what he's effectively doing is he's taking this threshold y to be something like log x, and if f is pretentious, then because the sum of primes here, it converges, the tail gets small, and so because he can control the tail, somehow he's able to control this sum in red effectively. And so kind of the insight of what we did in our paper as one of the inputs to the main theorems that I'm talking about here is that we noticed that actually using a better sort of sitting technique, we can deal with not just pretentious functions, but also a certain class of non pretentious functions. And these are precisely the ones where f of p looks like one of these characters in some narrow window of primes, namely between x to the epsilon in x. So this improves over this narrow window log x to x. And so the analogy between Clurman's theorem and our theorem is the following. So here's the statement, if chi is a real Dirichlet character, and f is a real value to multiplicative function taking values in minus one one, which is non pretentious. So therefore the distance gets large eventually between f and chi. But also f is close to chi on the primes between x to the epsilon in x, then we can show that the correlation averages of f cancel. Okay, and we use this to solve Dudavir's question. So how does that go? So if we know that p has relative density zero in the primes, and the sum of the reciprocals of the primes in p is infinite. Well, first of all, what we can do is we can show that lambda of p, this associated variable function, so this function which is minus one exactly on the primes in p, is close to one for all for most of the primes between x to the epsilon in x. So how does that work? Well, we know because of this relative density condition that eventually the number of primes in p up to y is small compared to pi of y. And so if we look at this distance quantity, which is just a sum over primes, it's a form one minus lambda of p. But of course, lambda of p is plus one if p is not in this set capital P. So this is exactly what this distance is. Well, then we can just use partial summation to relate that to the count of primes in p. And because we know that that is small compared to pi of y, we can get some some bound on that distance. So here this integral is of size log one over epsilon. And so epsilon cubed log one over epsilon is small compared to epsilon squared. So this the distance between lambda p and one is small. And in order to apply our theorem, just to go back, we want to show that lambda p is also far away from one. So here I've been thinking of chi as being the the the trivial character. Okay, so I want to show that's the case, but I'll also show that lambda p is actually non pretentious. And because I mentioned that earlier. So how do you see that? Well, if we take any real character, we can split the distance into two parts, one part relating chi to one, and then another part relating lambda p times one with lambda p times chi. And roughly speaking, you can rewrite that in this way. So there's two contributions. There's a contribution from how close chi can be to one. And then there's a contribution from the primes in p. So if chi is a non principal character, this first sum is large basically by the prime number theorem in arithmetic progressions under the Ziegler-Bofisch theorem. And the second term here is little low of log log x because p is sparse compared to the primes. So that deals with the case of non principal characters. And if we compare lambda p to one, well, this first sum is identically zero, but the second sum is exactly two times one over p, where p is ranging inside of this capital p. And of course, by assumption, this is tending to infinity. So this is also going to infinity. And therefore, this distance of lambda p to chi is always large for any fixed chi. So that means lambda p is non pretentious. And moreover, if we take x large enough, then the distance between lambda p and one is large. As we've shown the distance between lambda p and one between x to the epsilon and x is also small. So based on our result that I mentioned before, we show that all the correlations of lambda p are small. And as I mentioned before, that tells us something about the sine patterns. So you're using the fact that all of the correlations are vanishing, we then establish equidistribution in sine patterns. Okay, so that's how we solve the problem using this new idea about how to deal with a certain sub collection of non pretentious functions. Okay, so in the remaining time, I want to talk about the second problem that I mentioned about Hudson's conjecture. And Hudson's conjecture is an example of what I like to call a rigidity problem for multiplicative functions. And what are these? In general, they are statements like the following. I want that we want to determine all multiplicative functions, they could take bounded values, real values, or they take complex values that are not bounded values. That satisfies some sort of stringent local property. So I'll give you some examples to give you a sense of that. But what I mean by a local property is that there's some relationship between f of n and its neighboring values. So f of n plus one, if the minus one, there's some sort of conspiracies between these various neighboring values. And if we can't, if we can't shift, and so there's two possibilities, either you determine all of them, because there are some, or show that there are no such functions that satisfy this local property. So here are some classical examples. Erdisch proved in the 40s that any multiplicative function, which is everywhere non-decreasing, is a polynomial. So here I should have said that this f is integer valued, if it could take complex values in which case, k doesn't actually have to be a non-negative integer, my apologies. But anyway, you can modify this, so this makes sense in all cases. Sorry, not complex value, real value. If f is real value and has this property, then it looks like a polynomial entity output.  And again, I think here I want, I'll enter the alpha, not just k, my apologies. More recently, some of these problems have come under consideration because of the relationship with correlations, which I'll talk about. So if f is a plus minus, well, plus minus one valued multiplicative function, then the partial sums of f are un, are bounded, if and only if f is periodic and its sum over its fundamental domain is zero. So this is related to the Erdisch discrepancy problem that tau, that tau resolved. So tau showed that if f is completely multiplicative, then this condition never occurs. And so Kluhrmann's got tau looked at the multiplicative cases level, Kluhrmann proved a classification for these, for those multiplicative, but not completely multiplicative functions that satisfy this. And then with Kluhrmann, a few years ago, we proved that no completely multiplicative function that takes values on the unit circle can have uniformly bounded gaps between its neighboring values. So this is an example of a stringent local condition that never occurs for any function in this class. Okay, so I mentioned correlations come into the picture. And the reason, the rough scheme of how this works is we want to analyze these local conditions about neighboring values in two steps. So the first step is to rule out non pretentious functions. And the reason why we don't expect these to occur is because if we have enough stringent, if we have a stringent property, this implies that f is not very random. And non pretentious functions in some sense are random, random in some sense. And then once we've ruled out non pretentious functions, we're in the pretentious regime where Kluhrmann's theorem is at a disposal and we can classify these pretentious examples using his theorem. So in order to be able to talk about rigidity problems, I need to tell you something about non pretentious functions and their correlations. And as I mentioned, this is a difficult area. There aren't too many results, but there are some very deep breakthroughs that do lead to some useful information. But these typically have to do either with weighted versions of correlations or correlations along a long sequence of scales. So I'll be clear about what that means in a moment. So here by a weighted version, I mean a logarithmically averaged version. So here, I'm going to use a notation, this notation to mean that I'm summing this arithmetic function A of n with the weight one over n overall integers up to x. So if A of n is bounded by one, then this sum has absolute value at most one over n summed over x, which is a size log x. So that's why we normalize this by log x. Then tau proved a result in the direction of Elliot's conjecture, at least for two point correlations, which says again, for real value functions, that if f is real valued, multiplicative and non pretentious, then all of the binary or two point logarithmically averaged correlations vanish as x goes to infinity. Now, this is not quite the same as the two point version of Elliot's conjecture, but town terrifying showed that from this, you can conclude that there is a dense sequence of scales, why such that if you look at the correlation averages along the scales and why along the scales that are not in, okay, sorry, the two ways to look at this, if you if you if you look at all the scales outside of some small set, why then the correlation averages 10 to zero along those scales. And here's small means that if you look at the the logarithmic measure of y intersected with interval one up to x, then this tends to zero. So for most scales, these averages are small. And maybe I won't talk too much about this, but the idea that that is exploited that uses this logarithmic averaging is that you can dilate these correlations by primes and suitable intervals and get some sort of in variance. And the the upshot of that is you can start with a logarithmic correlation in one variable and get some sort of average in two variables. And that average in two variables can then be estimated using some recent advances related to multiplicative functions, specifically, variants of the matamaki-ragivio theorem. I won't talk too much about that the point is that this logarithmic weight is sort of crucial here. Now in the same vein, one could ask about k point correlations where k is greater is greater than or equal to three. And in this case, there are there has also been some spectacular progress, but the hypotheses required to apply them are stronger. So what do I mean by that? These results relate to what are called strongly non pretentious functions. So these are functions again real value functions, such that for real for each fixed real character chi, the distance between g and chi is close to as large as it can be. So it's bounded from below by a constant times log log y. If you recall this distance is at most two log log y. So it's of that size. Well, then talent turbine improved. Two results in separate papers, but they're related. If you assume as given k real value functions that are multiplicative, such that the product of f1 through fk is strongly non pretentious, not just individually, but their product, then the logarithmic average k point correlation average of f1 through fk vanishes as x goes to infinity. And moreover, by a similar sort of approach as they did for the two point correlation, there is a dense sequence of scales on which the usual correlation averages 10 to zero. Here the notion of density is slightly different. I won't go into it. But the point is that at most scales, these correlations are small. Again, if the product of these functions has a stronger non pretentiousness condition. Now, in spite of the fact they're stronger conditions, this is still useful. So for example, if you take f1 through fk to just be the livable function, then if k is odd, lambda to the k is just the same as lambda, because plus minus one values are invariant under odd powers. And it's not too difficult to show that lambda is strongly non pretentious. Again, using the properties of Dirichlet L functions. And so for example, they were able to show some results about sine patterns. Namely, they were able to get logarithmic equidistribution for the various sine patterns of length three. And again, the reason is because there's some relationship between counting the sine patterns and correlations, and they could basically show that all of the correlations of the livable function are small, either with this theorem or with tau's theorem or with the prime numbers. Now the drawback of this result is that of course, if we want to use it in a rigidity problem, and we want to show that using correlation data, non pretentious functions can't satisfy the condition, well this is not going to work sufficiently well for us, because it only deals with a certain sub collection of non pretentious functions. So we'd like to plug up that whole by being able to treat other non pretentious functions as well. And so we do that by noticing that, okay, what has been treated in previous theorems, I mentioned Cloramans theorem is about pretentious functions. So here I'm looking at plus minus one value multiplicative functions. So Cloramans result says if f is close to a real character, then we can actually compute the correlations. And on the extreme opposite side of the spectrum, if f, and look at k odd, if f is very far away from every Dirichlet character, then we can show that all of the correlations vanish. But there's some intermediate range. There's an intermediate range of non pretentious functions, where there are characters chi, where the distance of f to chi is not is smaller than any constant multiple of log log x, when x is large enough. So we'll call these moderately non pretentious, they're not strongly non pretentious, but they are non pretentious. Okay, and the interesting point about these moderately non pretentious functions, which links them back to this theorem I mentioned previously, about f being close to a character in the range x to the epsilon to x, is that for most, so for many scales, a moderately non pretentious function will look like a character in that way. So if we look at what this statement means, if we take y large enough, then the sum over here one minus fp chi p over p, its sum up to y is small compared to log log y, which, and we can decompose that sum roughly speaking into segments of the form x to the epsilon up to x for various x's, so these x's look like basically y to the epsilon j for various j's. And it's not difficult to show using say Markov's inequality that there are many scales, there are many of these j's where this sum here is smaller than epsilon, which means that there are many scales where we have this required closeness condition between f and a character. And because f is non pretentious, we know that f is far away from that character if we look at overall primes. So this puts us into the position where we can apply our correlation theorem and deduce that those correlations are small, at least at many different scales, these generic scales I'm referring to. Okay, so based on that, what we are able to conclude is that if f is a plus minus one value moderately non pretentious function, these are the examples that we'll consider in the sequel, then for many scales, you don't really need to read this, but the point is that there's some sense in which we have a dense sequence of scales along which these correlation averages tend to zero. Okay, now what does this have to do with Hudson's conjecture? So recall that in Hudson's conjecture, we have a rigidity problem, which is that we want to classify all the plus minus one valued completely multiplicative functions that don't take plus, plus, plus, plus as consecutive values. So we can relate that to correlations in the usual way that I've mentioned already a couple of times, which is that we can take the product of one plus f of n plus j, that's equal to two or zero, depending on whether f of n plus j is one or minus one. And if we never get four pluses in a row, then this product will always be zero, because at least one of these numbers f of n plus j is equal to minus one. So we have the left hand side is equal to zero, and we can expand this into correlations, we get a main term and then a sum of correlations. So if we know how to deal with the correlations for non-pretentious functions, we can rule out the possibility that a non-pretentious function does this. That's what we want to do. And of course that is what we want to do in this case, because Hudson's classification, his list of examples are precisely just characters modified at one prime, so they really are pretentious examples. And so we want to show that the only examples possible are indeed pretentious. And so to show that they're non-pretentious, we'll get a contradiction by showing that either these different correlation averages vanish, meaning are a little low of x, or they are sufficiently small. And I'll show you what that means in just a moment. So we can get rid of a couple of examples right away, a couple of cases, sorry, for these different correlations right away. If k is equal to one, then this is just an average f of n plus j. And we know by Viercing's theorem I mentioned earlier that these are small, if f is non-pretentious. And if k is equal to two, then we know that at almost all scales, by work of Taylor and Theravine, and all of these averages are small as well. Now of course, there is some issue about, okay, almost all scales, maybe that depends on which choice of correlations we have. It turns out it doesn't, it depends only on the functions involved, at least in this instance. There's a way to keep track of the sequences and make sure that all the subsequences in question are consistent. Okay, so what's left over using these two results is we need to deal with the four-point correlation and all of the three-point correlations, at least on most scales. So these are the scales that Theravine and Theravine's result deal with. Okay, I misprinted this, it should be two. Okay, so for the four-point correlation, we can't actually deal with that directly. We can't show that it vanishes, but what we can do is we can show that it's smaller than one. And the way we do this is by using the fact that if we take this correlation f of n plus one up to f of n plus four, and we shift n by n plus one, that product retains three of the same factors, f of n plus two, f of n plus three, and f of n plus four. So we can take our sum, our original correlation sum, we can sum it twice. And what that leads to roughly is just the sum of the product f of n plus one through f of n plus four, f of n plus two through f of n plus five. We can factor out three of those factors and use a triangle inequality. And what we're left with is this sum. And this sum has some n's which are equal to two or zero, depending on whether f of n plus one is not equal to f of n plus five or it is, they are equal to f of n plus five. So we get two here. And again, we can track this condition about equality using correlations. In particular, this event is supposed to have density one half. So that gets rid of that too. We get a main term and a correlation term, which we know is going to vanish along the substance. So we get that we can control this, we can control, we get an upper bound by a half, which means that the only thing left to do in order to rule out non-pretentious functions is to deal with the K equals three case, which now if we input what we know that the correlation average for the four point correlation is less than a half, less than a half, then what we have as a lower bound for the three point correlation contribution is at least a half times x, roughly. Okay, so that leads to the three point case. Now, as I mentioned before, if f and therefore f cubed, which is the same function, is strongly non-pretentious, then we know that along subsequences, tau and teravine improve that these are small. Well, there's that leaves open the possibility that f is non-pretentious, but not strongly non-pretentious, but these are exactly these moderately non-pretentious examples that our theorems are about. And so if we apply our results, then we can show that all of these three point correlations are also small along a subsequence. And as I mentioned, we can, it turns out that we can choose a common subsequence that works to make sure that all of these different conditions about vanishing occur along the same subsequence, which leads to this contradiction for non-pretentious functions, that we get this lower bound condition for the three point correlations, but then actually also, oops, this should be little, that's right, but also that we get an upper bound, which is like little over one along a subsequence. Okay, I don't think I have much time left, but if you're interested, I can talk about during the question period about the pretentious case. Thank you very much for listening.


This is Think Tech Hawaii, Community Matters here. It is noon on Thursday, folks, downtown Honolulu, Ted Raulston here, and for those who manage their life based on our show, as you know, this is the show where the drone leads on Think Tech. We bring subjects and experts and people who have questions on the show and talk about the themes, the topics, the issues that are riding high in the world of drones these days. On our show, the very progenitor of the whole idea of the show, Jay Fidel. Jay, I just want to make sure you can follow the script, right? What script? There is no script. Read the teleprompter if you need. Okay. All right. Okay. So we got Jay back on, and actually this started, you and I together probably four years ago. Yeah. This began upstairs here in the building. Yeah. Downstairs. Was it downstairs? Yeah. Well, actually, yeah. Well, it was upstairs where the panel discussion was. This is one of my favorite stories. Go ahead and do your favorite story. This program, a luncheon program with the Hawaii Venture Capital Association in the Plaza Club upstairs. That's right. Upstairs. Right. Right. And you, of course, were an aficionado in drones. We included you on the panel, and after the show was over, you and I spoke. And the idea is how could we perpetuate that discussion? How could we keep it going? How could we make drones ubiquitous in Hawaii, you know, associate drones in Hawaii together going forward? Or not. If that's appropriate. Get the right thing. Right? Yeah. And you said, you know, can we use your studio to meet? I said, of course. Come meet. Bring your friends. And you met. You didn't have a show. You just met. And then one day, a show. Why don't we do a show also? Let's do a show on drones regular. And that was like, hmm, what? Four years ago? It had to be four years ago. Yeah. By now.  It's been great. Well, I've really enjoyed it. It's an opportunity to bring a lot of these complex issues to bear and look at them from different perspectives. And especially right now, we're getting ready for the 2018 legislative session.  It was enabling legislation. It was protective. It was supportive. And we got to fix that. Well, as an example, we can develop that kind of theming right here on this show because we bring people together and ask questions and talk about what we need to do to make it work in the future. Now, you probably have a question or two if I'm in history. Last time you and I were together was probably about a year ago, you know, and I had lots of questions for you then about the status of drones, both from a technological point of view and also a legal and political point of view in Hawaii. And I want to follow up on that. And in that sequence, so you have a drone on the table. I think you always carry them around like I carry my keys in my wallet. I thought it was going to be a true believer. Yeah. And it looks very high tech. My observation is the propellers seem to be a little bigger. It looks lighter, smaller, more high efficiency. And the controller, I don't know what you call this, a controller or whatever. Looks like it has a lot more functionality than the earlier ones. And so, you know, I suspect that there's been a lot of development in drones such as you and I could go to a store and buy. I don't know about the military side of things, but the general flow of technology seems to be way higher than it was even a year ago. Am I right? I think you're quite right. Things are moving fast in the half life of a new design, maybe two years in the industry, placed by something that's got superior capability. But that really brings up an interesting point. Here in Hawaii, we have a lot of interest in STEM. A lot of the kids are involved in STEM programs in the high schools and into college and such. And that's where this really has a chance to grow fast is in that when you get the young kids involved and the schools involved. And because this is a small miniaturization, you mentioned that already, the things are getting smaller and getting more reliable. This is the kind of business that could actually take root and exist in Hawaii because you don't need a big factory. You need 2,000 square feet, 5,000 square feet, something like that, and you can do a lot in that. What about the cameras? Have the cameras evolved? Well, that's another interesting question. The future of this game is not so much in what you might call the mule aspect. The thing that aviates and has props on it and carries the payload. It's the payload itself that matters. And beyond the payload, it's the analytics you can apply to which you collect the software that you can collect from the payload to get all kinds of information that we don't have today to support infrastructure, public safety, law enforcement, environment and such. And those again, sensors and payloads are really small. On this guy here, the cameras are maybe half a cubic inch in terms of total volume. That's it.  There's more than one. And it pulls it right down to a screen like that. More than one camera. What's that? This free on this guy. Oh, my goodness. And of course, the payloads that add another three. So the sensors are getting miniaturized and getting much more rugged and reliable. And that's, again, even smaller than the system itself. And that's a perfect business orientation for Hawaii. The University of Hawaii makes micro-sats, cube-sats with small sensors on them. So we're already in that game. And somehow we have to go forward in the world of sensors, payloads and analytics software as a theme within Hawaii Aerospace. Well, cameras have to be one of the most important things. And before we get to the question of using cameras like this on video production, like we do. Such as ThinkTech? Yeah, such as ThinkTech. Because it's very relevant. Let's talk about disaster management. Let's talk about using drones to observe and see what happened after some disaster or another. Remember, you had one fellow on from UH, from the Department of Geography, a lot. Chuck DeVaney, right? Chuck DeVaney. Hello, Chuck. Shout out to Chuck. He went to, hi, Chuck. Always a good guy. And he went to the mainland, I think. But he had a lot of involvement in developing drones for disaster management. So how has that evolved? How has he evolved? Well, that's Chuck's doing very well. He's in Las Vegas at this point in time as a young child and new family and all, and working in the business as he had been here in Hawaii. And that's on our point. Places on the mainland do have some advantage because they have large aerospace manufacturing associated with them, as such as we don't have here. So we have an advantage in it, we're small, and we have capability at the university. The disadvantage we have is we don't have an ingrained aerospace culture to work with them. So we have to go develop that. And that's what Chuck has done on the mainland. In any case, the world of disaster management, disaster preparation, and that sort of thing that you're referring to has actually moved forward more in the legislative enablement side, perhaps, and in the technology side. The technology is pretty much what it has been, is cameras and analysis capability. But the question is getting that capability to collect information associated with the disaster scene in the hands of the right people to make decisions. I think we're slowly gravitating towards the perspective that the incident command system, the ICS, part of the national incident management system, NIMS, NIMS, ICS, to go together. That's the framework for how all disaster management occurs. And what we've got to do is find a way to inject this capability within that existing structure, which has legal definitions and that has protections and such from a liability perspective. And we have to operate within that framework. So in the case of UAS or drones, and by the way, this station and this program have a rule about no monologues. So if you hear anybody doing a monologue, you can shut them down by asking them. No, I'm interested. Okay, good. The monologue just got shut down. Sometimes monologues are okay. Not often, but sometimes. You heard that both, okay, from the boss. So anyway, working within the incident command system, which means having training, having qualifications, having certifications as the case may be, like anybody in disaster management is an important aspect. And understanding how information flows within the incident command system so that the right information is delivered at the right time is something we have to construct in terms of workflows. And then that leaves us something on the monologue continuation here that to me is really interesting. If we start depending on systems like this in disaster operations, say the Marco Polo Fire down here, if we start depending on these things, then they have to be robust and reliable enough. Are they? Not necessarily. To handle all the conditions that would come at them in that kind of a situation. Well, it's clear that, you know, for disaster, you don't want to put human life at risk. For example, I saw something recently about the nuclear meltdown in Fukushima. And they were using drones to see the damage, using drones to try to figure out what to do. And it's actually worse than they thought because of what they found out from the sensors on the drones. You certainly don't want to use human life, put human life at risk for that. And more and more, I think, you know, we will see drones as a primary function of drones to do that. And I'm pushing aside, you know, battlefield applications, but disaster management. So it's really interesting.  How about right after lunch? I'll just work on my lunch to develop drones like that, you know, that would be robust, quote, whatever robust means in order to deal with any kind of disaster management at maybe greater distance than this can handle. What would you do? How would you use that development money? What kind of new, robust drone would you design? A program for, did you say a million or a billion? I said a billion. A billion. I thought that's what you said. It could be no... Yeah. Essentially no budget. Go for it. I think we could work that out. I would make myself the king or something like that and make you the emperor. Yeah. And we'll work... I'll put that up and down below that, but seriously, there's a structured process called Systems Engineering at the University of Hawaii. It's under the VIP or Virtual Integrated Program construct, which allows a really complex problem like you just outlined to be then decomposed down into the pieces that have to be addressed. In the case of disaster management, if you wanted to have full robustness, full reliability and full trust in the system, now we first, perhaps, look at the weather conditions under which we're going to operate. In Hawaii, we're looking at, say, 40-knot winds, a lot of turbulence, and we're looking at rain and salt water, and we're looking at thick, moist air. So we have a bunch of things that the environment makes us deal with. Have to write those down. Okay. How are we going to handle the winds? Well, we're going to handle winds by a lot of performance margins, which means we're going to have to have a lot of radar climb or other extra performance available in order to compensate for the wind turbulence. It means we're going to have to have a rapid response command and control system to keep this thing stable during turbulent conditions. Yeah, this reminds me of a video I saw just a few days ago, maybe of the MIT newsletter, about not drones, but robots, the new models of robots, they're smaller, they're much more compact, they're stronger, they're faster, they're more agile, and that they're walking along, I use the word walking, I think, visibly, and you push them like that. They get right back up, and this is the same kind of thing with the drones, so a gust comes and pushes it all across the field, and it knows enough to get back where it was and stay there, and this is the kind of resilience I think you're talking about when you use the word robust. Yeah, I think so, because if the fire department starts depending on these, you can't say, well, I can't fly it today because it's too turbulent or too windy, or in downtown Honolulu, where you have a lot of what they call signal bounce on the GPS signal and such, and I don't have a good GPS signal, I can't fly it because I haven't got a good GPS, well, we've got to get around that, we have to have a DGPS or some other means of replacing that function. How about range? Range, that's range and endurance kind of go together in this game, and that requires user input from what the user's perspective might be in terms of what's needed in the open range. Well, I mean maximum range, I mean, we're not talking about a situation where the FAA says, and I think that's going to be old anyway, since you have to have a line of sight. You must be able to see it. That's got to go away, that's ridiculous. We're talking about disaster management, which could be 10 miles away, where this drone has to fly longer distances and stay in the air for a long time to do any real payload. And I guess the question I put to you is, is the direction going that we go out 10 miles, we survey the area, we send the signal, the data back, and it's interpreted back home on one of these, maybe, or a computer that draws the signal from this controller, and then we let the drone fail. We let it drop or explode or whatever it wants to do, drop in the water, because we don't care, it's disposable, right? Or do we want to build it so robust that it can go to 10 miles, send the data back, and then return to base? Which one is going to prevail? And that's, there's probably going to be both answers, because at the very low end where you can afford to throw it away at $500 or $1,000 a pop, perhaps that's acceptable. Once it hits, say, $10,000 or $20,000 in terms of value, it's going to be something you're going to have to get back, because at that point in time, you're truly depending on it, and you can't not perform the mission. But let's talk about how we might take your, the challenge you raised here, how are we going to define, from a Hawaii perspective, the robustness, the reliability, the performance, the range, how we would think about that, as an exercise for all of us here in Honolulu. Let's take that on after we get back from our first break. This is Think Tech Hawaii, raising public awareness. We have this crazy thing going on today. I was just walking by and all these DJs and producers are set up all around the city. I just walked by and I said, what's happening, guys? They told me they were making music. I do musical talent and then sat down and kind of... And for our faithful viewers, we're back here on the eighth floor of the Pioneer Plaza building downtown Honolulu Think Tech Studios. Ted Rolston here with our show, Where the Drone Leads. And the very originator of this show, the person we can hold accountable for all of us in the last four years, J. Fidel. The power of accountability. So we were talking before the break about how to take, how to think about requirements in the first place. And I hadn't finished that piece of the monologue. And then the question you brought up over the break was, how do we think about this as it applies to Hawaii? How are disasters in Hawaii? So let's try the two of them. Back on the issue of systems engineering and the VIP process. We have to take all the issues you mentioned, whether endurance, reliability, sensor analysis, sensor, weight and payload. Those are each individual items that contribute to the mission at the end of the day. What we have to do is determine the connectivity between that and the transfer function between that little piece of the game and the mission. And the more critical and the more important from a timeliness perspective have to work on them first. You work on the things that are hard first and you work on the things that are easy or gonna be coming to you anyway in time. You decompose the problem into the individual pieces, generate the solutions and then start composing the solution up the chain. You're not using a pronoun, who does this? Oh, there's teams at UH that are really good at this. The UH has again a good program called VIP under water guys involved, Zach Trumbull, Wayne Charoma and that bunch and got a lot of students who are really good at this because we too much focus on one thing, electrical or mechanical or ceramic or something but they all have to come together and play in the solution. So it's a solution that matters not so much the individual pieces. Well, what you're talking about is if it was an academic experiment in the engineering school, but I should be able to go out and buy a drone. I should be able to go out and buy a drone, get a license, we haven't talked about that yet and I should be able to fly it up alongside the Marco Polo during the fire, after the fire, survey what's happening, what has happened, what is happening right now today and get a snapshot without a helicopter at $1,500 an hour and it will and I should be able to do that, I suppose as a government, a government certainly should be able to do that, the fire department, the city, the state, anyone, emergency management guys and for that matter, and I put this question to you, why can't I just do that myself? Say for the press, say for the media, say for ThinkTech. Why can't I do that? Why can't I go down to a shop or image or wherever I go and buy one of these guys? I mean, somebody is selling them and be confident enough that it will work even in the back draft of a fire. Okay, and that's the situation that we face today and there's many aspects of what you just brought up in terms of what the problem statement is. The things you can buy today were designed to somebody's specification of what the needs were. In general, is to generate commercial sales or something like that. And it may not have considered the back draft, it may not have considered the high turbulence, it may not have considered the fact that there's a lot of smoke in the air or that we have salt water wet hands when we change batteries. So there's certain designs might have considered that and that's what you would have to search out to find them. Unlikely to find all that in an existing solution today, which is why we go back to the point of having a set of requirements written for something that's gonna work every day, come hell or high water and... In the rain. In the rain, right. And in the case of the Marco Polo or any other structure fire we have around here, there's other things that have to be addressed as well, obviously. Well, there's people's rights of privacy which can be suspended under certain times, but still there's issues of privacy. People down below who are at risk if the thing falls out of the sky. Well, there's that risk which you have to mitigate. All risks have to be identified and then mitigated. That's the way this thing works. So in the case of the people on the ground protecting them, the rules are clear, you gotta be, you can't fly over people. And what that means is whatever failure modes this thing might have, how it might come apart, how it might fail, wherever it might distribute itself under a fault or a set of faults. That perimeter, nobody can be inside because if it did, if those events did occur you would actually hurt them. Now you've had a number of guests on this show in the past year who are in the business. They find places to buy them. And I went to the National Association of Broadcasters program as I did last year in April of this year and I saw incredible offerings for the broadcast industry of drones this size and smaller and bigger and all the sizes in between doing all kinds of things but especially camera work. And I say to myself, industry is really putting some money into this. But the guests you brought in, the young fellows who are entrepreneurs here in Hawaii who are trying to actually make a living renting or using drones to take video whether it be after a disaster or just for making movies or something else. I would expect that crowd, that industry crowd. Now you talk about the School of Engineering but I would expect that crowd to be working with the School of Engineering and determining all the parameters that you're talking about so that this is regular, this is de rigueur that it happens automatically in every case and we always consider these risks and problems and operational issues and so forth but it doesn't sound like we've gotten there yet. Well I think that we have a really robust business community here. We have Mike Elliott and drone services in Hawaii. We have Greg O'Olufua coming up with his systems which are more at the enterprise level and we've got very strong roots in the ground that are growing in that direction. All of them are tied with the current manufactured systems and in terms of serving our more stringent requirements we still have a ways to go to get that but we're actually doing that. Last like two weeks ago we had a gathering of 80 people from the public service sector in the UH Stadium and had a session on that very subject. How do we generate requirements from the police to fire the environmental people? How do we pull those requirements together? And it's a slow process because you don't think about, you don't think about requirements for your car. You don't think about requirements in a technical sense and we both buy things. We go to whatever Costco or Best Buy hasn't buy it but the intelligent buyer who creates his structured needs and then gets some serve, that's kind of how the military operates. So we have a military perspective which generates extremely expensive systems that are very competent and we have the commercial electronics industry which deals with a broader base of less. And not necessarily so robust. Right, because they're dealing with a whole different. Well people are not gonna put that much money into it. So we did that. It's a toy for them, yeah. What's that? It's a toy. So a lot of people go down to shop or image what have you or right away to Amazon. So the question is? This is not professional stuff, it's a toy. The question is where's that break point between what's a toy, what's an entertainment, or something you can depend on for business. We could talk about that at some point in time. Now I know we don't have a few minutes left here but you mentioned earlier. Yes, we do have rules on this show. We have a hard start and stop time and monologues and all that stuff. He's doing pretty well I think. Monologues, right. No, you can do high marks. Anyway, and for the whole show it's a great show. But one of the side effects of the show is that you actually consider legislation, bills and policies and you advance them in the state legislature. Absolutely. And for that matter a city council. So I just, you made a comment before about how you were developing a legislative agenda. And I think before we shut the show down here you should say what it is, what you hope to achieve and why and what kind of bills will be pending. Sure, we'd like to do three things. I think and I'm speaking for myself now but I would say this to anybody who wanted to hear it. We've got to get a very straightforward and simple to understand enabling legislation so to speak that allows the police and the fire and the public safety to use with proper controls these systems going forward but also prevents against nuisance or malicious effects that could harm them. For example in a Marco Polo if they're flying down there and somebody shows up with his own drone someone's got to give, you can't have both. So we have to have a control mechanism for those who are uninformed or unlicensed. You know the last week an airliner on the mainland was brought down because of a drone. I did not know that. They had to make an emergency landing because the drone was in the way they were concerned that it would bust up the engine. It's really horrible and there needs to be regulation and sanctions for anybody who does that. And that's part of the confusion. That's coming at the federal level. So we don't want to have any state preemption of emerging federal rules. The federal rules are forever changing and not there yet. So it's like a standoff. Then we have to have state orientation in terms of privacy protection and landowner issues and such. And then we probably need a professional component in here as well. If you're gonna be a surveyor or you're gonna be a disaster management guy you probably have to obey some stipulated set of capabilities. So we have like three different levels of enabling legislation. Some of the legislation some is not. This is not the first time either. You've been doing this as a pattern for the last few years. So I don't mean to take any credit for this myself. We're just gonna try to stabilize it. Who's the champion in this particular area in the legislation? There's probably half a dozen I think. They're right. Good champion. And getting them together beforehand if we can do that without getting a violation of the Sunshine Law and that sort of thing was what we have to go do. So we'll take that on. So the last question I would put to you when we're running out of time. We are over time. We are over time. You know the guy who runs this place? What? Can you make a deal with the guy who runs this place? Yeah, I'll talk to him. You'll talk to him. I'll talk to him right now. So the big thing is developing an industry here. And I know there were companies making fixed wing drones back a few years ago. Williams Aerospace comes to mind that went out of business. And I wonder if we, and we have a special dispensation from the FAA we're allied in a special region with Alaska, as I recall. That's correct. So my question to you is how are we doing in that? Are we really advancing on that initiative? Are we taking advantage of that opportunity? Are we developing an industry? Absolutely, you're referring to the hookup between Alaska, Hawaii, Oregon, now including Kansas and Mississippi called the Penn Pacific Unmanned Air Systems Test Range which is managed out of the Applied Research Lab at UH on behalf of D-Bed. And that structure is moving forward in terms of integrating across the university the capabilities to use that, the test range. We've got arrangements with the university's own properties as well as the Isle of Ani, for example, as test ranges. And we've got three customers lined up that are wanting to use the range for testing. So it's moving not as fast as it might, but it's moving. Well, let me say that this show is really important in it. And I was never so convinced as when the United States Federal District Court asked you to come down and do a panel program on drones to educate the federal judges. That was something. And that really puts you on the map. I really enjoyed that. And we'll do it again anytime. And please make sure they don't cut the last three minutes off the show. You know the guy who cuts here, so. Yeah, I'll say something. You can talk to him. Okay, Jay Fidel, thanks so much for coming on. Okay, see ya.