OK, happy to start it. So today my topic is about the old Chinese reconstruction of the monstrosities, shi, shi, and si. These three words that, according to traditional commentaries that they are synonyms, but there are lots of issues surrounding these three. I think that since Chinese has been a monolithic language for quite a while, and then the writing system sort of also reinforces it somehow, that we are easily into believing that the Chinese texts convey only meaning. And we sometimes neglect that the sound that goes with every word, that's something that's important, too. So I think Baxter and Sagao Spook mentioned that how useful the new old Chinese reconstruction intends for reading texts, reading especially those pedographic texts written in pedographs. And I actually also think that when it comes to interpreting Chinese grammar, that knowing the sound is also important. The modern Chinese, modern Mandarin, negative Mei, for example, might not have been derived from verb, like some suggested, but from phonologically reduced the form of Wu as Pan Wu proposed. So having the phonological knowledge, in my opinion, is important when it comes to deciphering Chinese syntax. Saying that, I feel a little guilty that I cannot give you a very beautiful solution to the things that I'm about to say. Rather that I happily came here with lots of my questions and those things that bothered me and troubled me, make me puzzled and can't sleep at night, then I would like to come here and actually get helped by so many excellent specialists in Chinese phonology and related fields. So I see that if you could help me for these sets of demonstrators that I work on. More precisely, I like the idea that the OC reconstruction assumption that the old Chinese reconstruction should maximally reveal the linguistic history of the items that we are reconstructing. And when it comes to these three words, I think that what concerns this graphic or telegraphing connections among them and possible etymological and morphological connections. Speaking of etymological and morphological relation, Puli Black had a study on the morphology of Chinese demonstrative pronouns in classical Chinese. And the first quote that he identified are the cognates on the divas in the, I don't know how to pronounce it correctly again, corresponds to Chinese Zhi and this Li corresponds to Chinese Shi. Because of this, it really gave me confidence that I probably was right that by writing Shi and Zhi as dental, because as you know, the middle Chinese is the palatose that the default or Chinese source is dental. And that's what I thought. And seeing this Tibetan cognates that it makes me believe that what I think is right. But Puli Black doesn't think that this kind of dietic contrast between the Tibetan demonstratives applied to Chinese. He rather thinks that this is something independently developed in Tibetan. But in any case, I think writing something in English that makes us wonder about what kind of phonetic value that we should give. Because if you were writing in Chinese that I don't really have to give a pronunciation to Zhi or Shi or Zi or whatever I could just write. And so that was the question that I had. So when I did my dissertation, I asked around and made sure that the dental is the right form. So I'm obsessed with this because of the things that I'm about to say later. But in any case, Puli Black also noted that this Zi and Zi, which is this, and Shi and Shi, the status in the demonstrative system is a little bit tricky. But that's a little bit for the timing. But this too says that it's easy for you to see that they have this alternation between the Zhi Hu Zhe and Zhi group, and the other Yi Zhi group. So the Zhi Fu and Zhi group. So he thinks that this Zi, which is the one on the right, is the right from Zi in the same way as Shi, the right from Shi. And the Shi is, according to him, morphologically related to but stronger and more independent because of the power that is belonging to his category of the more extrovert one so that he has more independence. No, the introvert one so that he has more independence. But in any case, this study is done based on classical Chinese. And what I would like to explore is what it is like in the text that now received the text or more precisely in the Orca bone inscriptions and the Brown's inscriptions. And first, if we look at the Shuo Wen's interpretation of these three graphs, this is the Xiao Zhan poems, that the Shi Sheng lost Zhi as Chu to come out or to go, and Shi as Zhi, and Zi as to stop. And the graphic interpretation is that the Zhi is the pictograph that's depicting the brass overgrowing out of the ground. And Shi consists of two. It is Cong, X, Y, and that means that he... I mean, we think that Shi Sheng thinks that they are the Hui in the category and has these two semantic particles that combine together to give the meaning of the character. And the same thing with Zi. You have to combine to stop and be. And be he thinks that the means to put against each other. By looking at the small Xiao Zhan poem, that we don't see much similarity among these three. But somehow that we can see that the top part of this tree at the bottom part of here and left part of here looks kind of similar, but not exactly. But if we go into the bone graphs, which is around the 14th to 11th century BC, the earliest graph for Zhi consists of a foot. And with a very exaggerated... Do you call that thumb? The big toe. Anyway, so that's the finger of the foot. And so going... It seems like meaning to go, but not so nice examples of the meaning to go is found in bone inscriptions. But in any case, we have this food radical... The food component in the bones, but in the bronze, which is the Western Joe after 11th century BC. And it seems that the what Xi Shan said about this Zhi, like grass growing out, growing, seems to be relevant here, that the right side looks like a plant branching out. So we see that this corruption of this foot shape in the bronze graphs. And I can give you a very, very brief history about what happened to Zhi from the bone inscriptions to the bronze inscriptions based on Jean-Marie's study. It's similar to just called others so that I don't have to exist. I have some similar theory, but it's easier that we can find something here. So in the Xiang or Koubo inscriptions, Zhi contrasts with Zi. It is problematic that it is kind of hard to find a very strong evidence that indicating Zhi is non... I mean, indicating any type of dietic interpretation of Zhi because it's just used metaphorically, referring to something that you mentioned before. And in that usage, like we can think about English word that or this. If you use this or that, referring to things that I just said or referring to something I just mentioned, and then it doesn't matter if this or that, either way, either one can be used. So it is not a very strong indication about that. So that's why it became very controversial about what indeed is the dietic value of this Zhi. But in any case, according to Jean-Marie's study, that he finds that normally when Zi is used, it refers to the space or time occupied by the speaker. And even in the aneuphoric use, Zhi refers to the space or time that the speaker does not occupy. Based on this, mainly based on this, that he thinks that Zhi is non-proxima. But he argues that during the Western Joe, this Zhi has become neutral in terms of dietic contrast. So it's not approximate or not approximate anymore, according to him. And Zhi evolved into two directions, depending on the syntactic context. It was at a nominal position that it evolved towards a third-person foreigner, which the process, according to Jean-Marie, that completed at the spring and autumn period. And at the other context between two nouns, that the Zhi evolved into an attribute-marking particle. So in any case, you don't have to remember all this history, but a very key change took place in the Western Joe, that the Zhi became neutral in terms of dietic contrast. So that I have these questions regarding what I have said. So although Xu Zheng's interpretation of Zhi does not fit the bone graphs, it seems acceptable based on Brown's graphs. And remember that Xu Zheng used this Chu, the word Chu. That's something that when I was reading the new book, the New York's Construction of Old Chinese, that is done now for me, is that this Chu has this T pre-initial plus K. And it's used to glass Zhi, so Zhi is Chu Ye. So is there any significance in this glass? But of course, for the rhyme part, we can tell for sure that it doesn't match a Zhi, but why is this Chu deliberately chosen to glass Zhi? This is something I thought. Also that we also find that the construction of the food components co-occur with the time that when Zhi lost its dietic contrast. So does the, are they somehow related to the same kind of reason? And also the last, this graphic change, does it, there's some kind of sound change behind it from Malaysia to West Indoe, especially this shape of food, which is this the, we constructed before Chinese. If we can interpret that over like the branching out or like growing out grass or branches, does it refer to this word Zhi like to branch or to branch out? And in that case, that we get this vowel E, okay? But it's just speculation and some, those things that bothered me. And then anyway, I'll go on. So that's, we remember that the, in the Xiao Zhuang form, the small seal form Shi is analyzed as consist of Zhi and Zheng. But if you look at the paragraphs, you can see from Gommings with the bronze and the seal or bamboo forms that the Shi originally actually also has this food part. And then with this spoon shape component. And it is Guo Mo Ruo who said that the top part is the spoon or ladle. And then it's the primary graph for the word Zhi. And if we look at this sound, Shi and Zhi, and they do match quite well. But another thing that I actually noticed is something, this is the excursion but it doesn't lead any well but I just think that it's kind of very interesting to bring up if you have some kind of knowledge about pre-classical Chinese text. That is, you notice that some of the forms that, why are some of the just simple that this kind of handle of the spoon is quite simple across. But some has some like fork-like shape. So something like this. And if you sort of bend this part somehow and you count the components, something looks like a zi, something looks like zi, and then you have this fork-like shape. And you get somehow look like shi, the small silver form of shi. So it's the what we know that in those pre-classical texts that some scholars would attribute to the time of Western Zhou and there is a demonstrative written as Shi, exactly the time Shi. So, and this form is actually regarded as an earlier form of Shi. But if this is true that they actually are not quite like this earlier and later type of relationship. Also, we look at the Pyramid History of Shi. And the Shi, the graph that is specially designed specially for the word time, it was not attested until the warring state period. Before that, according to two studies done by Takashima in 2006, the graph for日 represent 2000. One is Sunday and the other one is Shi. So, if you want to write the word Shi, you use the graph日. So that means that the graph, this Shi graph was created much later than Shi. Although that's written in received text, that Shi is identified as an earlier form. But the graph that actually assigned to this Shi, identified as Shi, it's not really the Shi. So it's kind of a little bizarre to have this. But it's just an expression we can come back to Shi. If you're interested that maybe we can talk after later. Okay, anyway, there's something also remarkable is the graphic presentation of Shi during the warring state period that in two Zhongshan Brazis that dated to the warring state period as Shi, is written six times as Shi, the plan Shi. And mostly in the phrase of Shi, but not all the time. And in the manuscripts, this Shi and this plan Shi, they are also found as the phonetic loans for each other. So according to the reconstruction in the Bachelor of Arts New Book, and this Shi should be reconstructed and then so it poses the question. Has prioritization taken place at least in some words during the warring state period or the initial of the plan Shi still was keeping this pre-initial during that time. Anyway, so what I was trying to say is that it does no strong evidence, but there seems to be some little bit hints about whether we give a little bit, we include some kind of viewer elements in the reconstruction of Shi or Shi. We mentioned that it seems that from Shang to Zhou that the graph changed from representing, I mean depicting food to depicting some kind of like branching out. And then Xu Sheng lives the grass, Chu Ye for Shi. And also we have this Shi, we written as the clan Shi with the viewer. So this is why that I was really obsessed with whether I'm happy with just write it as the and which makes me really comfortable because then you have this Tibetan cognate or that you have something that makes us think that is the contact with the core which actually is originally started me, I started thinking about this because Meizu Lin had, I forgot the week here, but very long time ago had an article about the Zhi Ran Qi and he reconstructed the Zhi with Ge Xiang and had provided some evidence that but some of them are not that, I think not that strong, but he later gave up this morphological relation between Zhu and Qi because it seems that Qi, it's kind of hard to establish its pronominal usage at the earlier period. But I think Takashima had a paper in press that actually he also had the, he and the Nibbison had the articles of thinking about actually Qi is both model and pronominal so that if this kind of morphological process is going on between Zhi and Qi and Zhi actually has this kind of K-table thing. I cannot sort things out but I'm just providing you with what I found and hopefully that you can sort of help me to just maybe dismiss it or you know, so be happy and sleep well or I can really do something different. Another thing that I found quite entertaining is if you look at the graph of Zhi, this is the bone graph, this is the brown step, he also has this foot and the right side is the, this is B. In the bones, the graphs for person and graphs for spoon, it's kind of hard to distinguish, kind of all mixed. But in any case, look at the brown step and you will see that it's like this stuff, the side view of this spoon. And if this is true, and you will see that the Shi having a component that's the front view of a spoon and then Zhi has the side view of a spoon and this one has Zhi and that one has Zhi too. So I don't know why it is just an accidental similarity or it has some deeper reason. I haven't sorted it out, but I just thought it's interesting. But we can actually look at, further look at this graph in connection with Zhi, the spoon. The common interpretation, actually follow the Zhuowen jiezi by Xu Sheng, is Xu Sheng said, Bi Yi actually had two meanings, thank you. One is to, it's similar with this Bi put against each other, and it's also the things that used to scoop rice. And so in this meaning, it's also called Si. So, Blimey Tai's commentary says that this graph of Bi represent two words, first to compare and the other one, the spoon. And he said that only the second one meaning survived and the other one died out. And this Chi is not attested. In so-called the Jin, those classic texts. According to those Zhuowen scholars studied out, this is one of them, I won't read, said that it's, the earliest mentioning of this graph is in my name. And he says that, so they, the scholars claim that this is the name that the graph was created during the Han dynasty because that they, this is Han person, Han people's way of calling spoon. And I think, I didn't call it here, but there's a commentary to Han Zhu saying like this big foreign, so the Northerners call Bi as Shi in case, in one way's opinion that the Bi and the Zhi have the same similar sounds, Yi Sheng Chu Zhuang, and because the sound changed and then this Shi was added to indicate the sound because this is Han, so I just put the little Han reconstruction by Shi's work there. So, you see that the, it seems, it seems this Bi, if this means spoon, represent the word spoon, is not read as Bi, or it should be something that's similar to Shi, which, I mean, sounding like Shi during the Han dynasty, but something similar in earlier time. And in addition to Chi, we mentioned Si, right, so it's also called Si. And in the short list entry of Si, the Xu Sheng mentioned that Li, Li Ji, and so he basically is saying like in the Mi Ji, we don't have Bi, we have Si, and this is Cong Mu and Si Sheng, so Si is the phonetic. So does it mean that the Bi should be read in the sound of Si, which is the Zhi, the Fat Zhi, Ryan Bluth, and the Baxter, and some of our reconstructed with this slur, okay. And also that this is sometimes that we find, we less commonly find that this obviously not matching sound, but Bi, and Zhi, Bi, and Ni, that these two Bi are identified as phonetic in these two words by Xu Sheng. So does it mean that this Bi graph represent, can represent the Si represent some kind of Fat Zhi, that sound, and so I have no answer for that. But for the meaning, or for the words that the graphs represent and I can show you that the earliest chime, this graph existed in the earliest extent, in the oracles, and Zhang Yu Jing actually identified this one as a conjunction, thus, but many others don't take Zi as a function word here, but rather a kind of like a sacrifice here, which also makes sense. And so the main karma interpretations here as the type of sacrifice which scholars often do and they don't know what that word means. No, no, no. Anyway, then Zi definitely represents some kind of problem now in Western Joe Grants, because you can see that this person made the Father Xing or some vessel, and also he occurs as the emblem. It is in the early spring and autumn period that we found the earliest example of the use of Zi as this, as a demonstrative, and so that's the early spring and autumn period. So the karma claim between Zi and Zi that is Zi is the earlier form, and Zi is the later form, and the sound change that is involved in this change is not well studied, but at least we know that the Brahms' interpretations indicate that the Zi started to show up around the spring and autumn period, and the function and meaning stay similar to Zi, and in the Shijing and we can see that Zi occurs only 14 times, maybe in the Da'ai and Zhou's Dong section, whereas Zi occurred 86 times, and in the Shaoshu, which seems more conservative, Zi occurred 60 times and Zi only three times. So we can see, I have a question here that why was the graph formally used to represent the proper now adopted before representing approximate demonstratives around this time? So is there a particular reason that it's chosen? And also that as we have mentioned that the Puli Bank also noted that this time of alternation between these two sets. So if we look at the overall history of these three things, three words, during the Western Zhou, Zi became mutually in terms of distance contrast, Shi emerged as the sometimes emphatic and aphoric pronoun. So this used to assist the king, so use this, this use is there, so there is a proposing of the object. And this is the earliest use that tends to be for Shi. And as we noted that the generally, according that Zi continued to evolve towards the third person pronoun and the triple view marker during the three and author. And it is in this time that the Shi increased its use as the emphatic and aphoric pronoun and one instance of Shi used as a determiner. So Shi plus a noun is found and the most likely is so-called exphoric and that means like I'm just, it is in the physical existence of the situation and you pointed to this or that instead of an aphoric use in the piece that best dated to the late spring and autumn period and around this time spring and autumn also emerged as a proximal demonstrant. So my actual hypothesis is that the Shi actually emerged as some kind of alimony for Zi at the particular syntactic position which we have, I have some interpretation but we don't have to mention it, we can just say it's some special syntactic positions. And the time that when Shi appeared to the time that the Zi appeared, there is a gap of a couple hundred years, no, a few hundred years. And so it's kind of, I think it's very likely that they are derived in the same process instead that probably this Zi changed to Zi is trying to match the sound of Shi by analogy. And also during this time Shi started to acquire the syntactic function. And the further, my further hypothesis is probably this proximal made through two different processes that they compete for that slot of proximate pronoun this in Chinese language from that point on and then probably this one, this one, one and then give our job if you think about the pronunciation too. And this is a myth that hasn't been solved in the Chinese syntax, the history of syntax that which form gives the modern Chinese job and there are many Zhi or something but Zhi phonetically, Zhi doesn't, the Zhi-Hu-Zhe-Yu-Zhi doesn't work well but if you think about Shi in terms of graphic formation and in terms of sound Shi is a quite good candidate to give job in Chinese. Anyway, the last thing I want to mention that is we see that this food radical in all these three so this might be just accidental but if it's not, what was the function of this food? Is he trying to indicate some kind of phonetic value but we see that the phonetic value seems to be not, not, not, not like compatible? Is it some kind of semantic indicator that they are somehow all related to some at least a pronominal kind of usage? So that's something that I haven't decided but that's all that I'm presenting today. Thank you.


that I'd like to introduce the next lecturer. So it's my pleasure to introduce Mercedes Pascual. Mercedes is a professor in the Ecology and Evolutionary Department of the University of Chicago and an external faculty of the Santa Fe Institute. Her research focuses on modeling and theory of the Ecology and Evolution of Infection Diseases, combining, in my opinion, a unique way, highly conceptual theoretical question with highly applied ones. And today is giving the first lecture on the Ecology and Evolutionary Dynamics in host pathogen systems and data set. So Mercedes, thank you very much for being virtually with us. Yes, what can I do? Here I am. OK, thank you. Let me share the screen. OK, let me just, OK. I see Jacopo here in my screen. It works well. Yes, I don't see myself. That's better. OK, so yeah, thank you, Jacopo, and Matteo, and also Simon, and the organizers. So I will give this first lecture. And then I change a little bit my program. The third lecture will not be on this interplay of Ecology and Evolution. And I'll mention a little bit more about that at the end. So but today, I'd like to follow up from what all you have heard about communities and talk about assembly and coexistence, but no longer in the context of species, but pathogen strains within a population and their interaction with a host. So this will concern the interplay of ecology and evolution in host pathogen systems. And it will also be about assembly when we consider ecological interactions, but now as a function of explicit traits. And finally, there is a conceptual connection to what you heard yesterday from Jonathan on stabilizing competitions and success and I would like to emphasize frequency-dependent selection. My real goal is to set the stage for what I want to tell you tomorrow about our work, rather than so anyhow, this is intended as background to tell you really about what I will call hyperdiverse systems in next lecture. So oops, why is it that I can't go forward? Jacopo? I don't know. Try to... Let me try again. Okay, good. Ah, thanks. So let me start with a quote from Simon, of all people Simon Levine. This is from his paper on complex adaptive systems, where he wrote the fundamental problems in the study of any... Why is it now that the fundamental problems in the study of any complex system are understanding what maintains diversity and how the existence of diversity affects system dynamics? And he mentions it is these three features, heterogeneity and its maintenance, frequency dependence and modularity that complicate the picture and that will occupy most of my attention today. So I will basically be telling you about frequency-dependent interactions and frequency-dependent selection, as you will see. And when we talk about, of course, diversity in ecology, we almost have two large camps. One that emphasizes the sort of glissonian view that Stefano told about you, about that emphasizes stochastic assembly and demography, the processes, the birth death processes of extinction, immigration. And, of course, we have there the neutral theory of Steve Hubbell. In the other camp, we have approaches, perhaps traditionally more based on deterministic systems, but not necessarily that emphasize interactions, ecological interactions. And I have here specific ecological interactions that were differences between the species really matter. And, of course, this is very different from neutral theory where we basically have an equivalence of species in these kind of birth death processes. We heard from Jonathan yesterday about the many hypotheses, the many possible mechanisms and explanations for coexistence that lie here. And, of course, one of them involves this limiting similarity through niche partitioning character displacement, et cetera. And I like now to get back to this picture you saw yesterday to emphasize that besides help us organize these different mechanisms, they also tell us about the different traits that underlie these interactions. In the axis that was called niche differences, the traits really confer, as we heard, an advantage to the rare, but also disadvantage to the common. So this is the axis where we have frequency-dependent interactions, frequency-dependent selection when we start looking from the perspective of evolution. The other axis, which was called yesterday, fitness differences really relates to traits that confer absolute fixed advantages. And what I will talk about today will lie on the x-axis here. So I will consider that the strains vary only in their frequencies dynamically, but not really on the y-axis. And, of course, the realm of the y-axis for pathogens concerns the reproductive number r0. So really there we have this, of course, the exclusion of the pathogen with the lower r0. And there are mathematical studies of those kinds of interactions. Now, you can tell me why am I talking here about competition, perhaps it's obvious to some of you. I like to remind everybody, and especially those that are not interested in pathogens, but like ecology, that infectious diseases are consumer resource systems. They are essentially natural oscillators where the infections are the consumers and the resource are the hosts. And when we do not consider any strain differences in the typical susceptible infected recover system where individuals acquire immunity and that removes them from the pool of resources, we have essentially this generalized competition for the resources. When we have specific, when we have now specific immunity, we will have something more interesting. And, of course, the traits that matter here are the variant surface antigens, the molecules that the immune system recognizes. So one advantage of thinking about competition between strains is that we really know what are the traits we should be looking at. So what are the traits that underlie competition for hosts? And this is an example in influenza, in this diagram where we have, of course, the well-known lycoproteins that are on the surface of the cell, in particular hemagglutinin, and this variable protein is the major antigen of influenza. There is a second. So when we hear about H2N2, H1N1, we are referring to the big types of these, essentially the big classification of the subtypes of influenza. Now, you see here to the right, H3N2, and a typical tree of the seasonal influenza, H3N2, where the colors, essentially, well, this is, of course, a tree from the genetic sequences, but what you see with the colors here are the different clusters corresponding to different phenotypes. So these are seen by the immune system as distinct, and this can be really tested with assays, and so we know that there are these clusters. Now, what is interesting about this tree and has led to a lot of interesting theory is not the high diversity, the opposite, the limiting diversity at any given time. So you have here a dynamics of replacement with short branches, and it has puzzled people, why is it that given this very fast evolution of the virus in theory, we don't have the branches persist, why don't we have much more diversity of H3N2 globally? This led to interesting theory and essentially to a field, not by itself, not just that question that was introduced by Brian Grenfell and others in terms of its name, phylo-dynamics, where we look at essentially the influence of population dynamics on the structure of the trees and then how does the structure feedback onto the population dynamics? I like to briefly mention in passing two well-known papers in this area just to emphasize that there are studies that have relied on computational models that track both genotype and phenotype, essentially the genetic sequences of the viruses and then how they map to the phenotype, essentially to the traits I'm talking about, this antigenic variation on the surface of the viruses. And this is one paper by Neil Ferguson and others in Nature, where essentially they noted that of course the trees tend to be extremely explosive in terms of diversity and it is not easy to get these short branches. The explanation they provided for the short branches was that of short term, what they call strain-transcending immunity. So this is not, this is generalized immunity if you get infected by any strain, you are protected, you are no longer a resource and therefore this is a generalized competition that works in this regard. An alternative explanation was provided by Katya Cole and well, I'm in this paper too. And this was a paper that relied on this idea of a complex genotype phenotype map, the idea that we know that in flu, although the genotype varies with time in a continuous way, the phenotypic change of the virus is punctuated. So this is an observation, empirical observation from a paper by Derek Smith and colleagues, but what Katya proposes in this paper is essentially an interesting genotype phenotype map that I will not describe in detail, but I want to mention because this returns later where essentially, and this map is implemented with the idea of neutral networks and this was sketch here in a commentary on the paper where essentially the nodes of these networks of these networks are sequences, the different colors correspond to sequences that map to different antigens and you see that mutation moves you around, that's innovation, so you can move around and not change color in a sense. Once you change color, you have a great advantage so you have a selective sweep, then you explore again this new one and you go on and on. She showed, we showed in this paper that essentially this continuous mapping between the genetic distance and the phenotypic one allow you to have this limited effect on diversity. But again, these are complex systems very complex systems that rely on knowing something about the genotype to phenotype map and the computational models implement these ideas in some complex code. But I like to get back to simpler models after this somewhat brief introduction, but because before phylo dynamics, there was a large field I'm going to call strain theory that look at the competition of strains and for hosts and questions of diversity. And here I will mention the work of Suna Tragupta and focus on work now that does not consider the genotype at all, but focuses directly on the traits that is the antigenic identity of the pathogens. And it's interesting in this sort of seminal paper by Suna Tragupta and Day to see that they were motivated by malaria and the question of malaria in very endemic regions and the question of if there is such high transmission and people get infected so much, will it ever be possible to control malaria to vaccination? So we can return to these questions tomorrow when we get to malaria, because that's truly a very hyper diverse system. Now, the early models, I should say there is, as I said, a large literature and I'll provide at the end of this talk some references for those of you who are interested. There are a series of more analytical studies on the dynamics, analyzing moles with multiple strains. But I like to focus here on moles that in particular consider combinations of traits. So phenotypes that are essentially combinatorial in nature, right? Because we don't have, so this is not like, okay, strain I, strain J, right? The identity of the strains will emerge from a pool of variation and from a combination of traits. And I think that is important and I'll return to that tomorrow to give you a sense for why. And here we can choose to go with a discrete or a continuous space and I'm going to start with a discrete trade space. So you have to visualize here the representation as a pathogen having a set of I'm going to call them sites or loci. Each of those represents an antigen. You may find in the literature the word epitope, that's the part of the molecule that the immune system recognizes. And for each of these antigens, we have a finite number of possible variants as represented. So essentially a strain is a combination of these variants. So for example, we may have three epitopes or three antigens, one with three variants, another with four, another with five and then a strain is a combination. These are not linked, they are not physically linked but we will see that they can become dynamically linked. So one of the possible outcomes if you write models for these kinds of systems and here I have sketched the simplest possible case of well, essentially two antigens with two variants each. So there are four possibilities and what happens under some parameter regimes is that of course, as you let the model go, the ones that have some overlap will be selected against because they are at the disadvantage and the model goes towards this state that is this discordant state in which there is no overlap between the coexisting types. So we have hosts now that are immune to Y and B so they can get infected by this virus XA and the other way around. And I have this here just to let you see that essentially the niches that have emerged are these groups of hosts with different histories with different memories. And so it is these different groups of hosts that are the niches that emerge from this frequency dependent, essentially advantage of the rare disadvantage of the common. And you can see here that this depends strongly on the intensity of competition. We will see the equations in a moment if there is very weak effect of cross immunity. So if I'm infected by another kind, my memory does not influence what happens next. Of course, there is no strong structure. At the limit of very strong immune selection we get this emergence of niches with this stable discrete strain structure of the strains that have limited overlap. Now, when we write these equations, I have borrowed, I want to show you a little bit the equations that Gupta and colleagues wrote just to show some equations. And I also like the way they simplify the notation of the system by defining the state variables in a particular way. I have also borrowed this from a methodological paper they wrote after they had proposed all these ideas because this comes from, this comes a company with an R package that embeds some C code. And this is called Mantis. If you like to write and play with these kinds of things you can go to this paper and download that code. But what you can see here is that we have in this two by two systems, the state variables, the Zs here, Zax, is the proportion of the population that has seen, has been infected and has memory to strain Ax. More interesting is the definition of the variable Y, sorry, W in which you basically take the union with all those other essentially memories, right, that have some overlap with Ax so that either have A or X. And you do that for every pathogen there is a typo here in the blue this should be Bx, not Ax, but you see the picture. So just to show you that this simplifies greatly the notation because now for a given, of course there would be additional equations for other types, but you can see here in particular the equation for Y, which is the infected. Sorry, Jacopo, if I'm not mistaken the sort of typical epidemiological moles have been shown, right, by Marino, right? Yes, yes, Marino has discussed that. He has gone further, obviously further but here you can see, we have Z, W and this you can see how easily we can now write the equation for the infections, which this Y are the infected and you can see that we have okay beta, the transmission rate, then the infected with Ax, but now we have these two kinds of susceptibles, the one minus W have never seen Ax so they are fully susceptible while the W's minus those that have full protection have a reduction in their susceptibility, this is the cross immunity and this parameter gamma has the intensity, is the intensity of the competition or this cross immunity because you can see essentially if gamma is one, right, you basically any exposure will protect you completely even if you haven't seen both types, if you just have seen one of the types. So in this initial paper, one of the initial papers in science by Sunetra and colleagues, you can see here that gamma, if you look at the bifurcation diagram on the bottom, that of course this intensity of competition or cross immunity gamma is very important to the dynamical regime you see. Of course, if gamma is weak enough, you see no strain structure, if you move to the right, completely to the right, we get to this, what they call a discordant set, which is like the sort of complete limit, no overlap between the essentially, the steady state here. And then in the middle, we have the either periodic or chaotic cycles with some replacement. And this picture is a little busy, but just to emphasize those transitions, if you look in the center for one of these variable Ws, the bifurcation diagram, moving from the left to the right, you get essentially a steady state with everybody there. You go to these more cyclic or chaotic dynamics and finally completely to the right, one of the discordant sets. Of course, there are multiple discordant sets and which one you reach will depend on the, where you start and as we will see the history of this. Now, I provided before some explanations for the limited diversity of influenza, H3N2. And in a paper in PNAS 2006, this model that I just show you was revisited as an explanation, an alternative explanations to the one I gave you, essentially this limited set of possible strains, would lead under some parameters in this cyclic or more chaotic regime to something resembling influenza. Now, that's when we got together with Suna Tragupta in reaction to that paper, because when you look at those models in particular, in the deterministic version, obviously there is no stochastic extinction, but more important in these models, there was no explicit evolution. And by that I mean, there was of course, the change in frequencies, and you can call that evolution, but there was no explicit mutation, there was no explicit innovation. So we started with all the pool of variation in the system and what happened was that, of course, the abundances, the relative proportions went up and down when you have the discordant sets, you basically get some dominant coexisting ones, but in the fluctuating regime, you can always be rescued from these low levels, right? Nothing goes completely extinct. So we wanted to see what happens when we essentially take these models and really look at evolution. And again, there is a literature, an analytical literature and I'll get to that later, but here we don't want to separate the time scales of evolution and ecology or evolution and epidemiology because, well, essentially for these pathogens, that separation does not necessarily apply. So we will be talking about mutation and I should remind you that since we don't want to track genotypes and we don't want to deal with genotype phenotype maps, we are going to basically go, call mutation, a phenotypic change. So I may go from one epitope to another variant of this epitope in the pool of possible variation, but we are not going to track genotype. And this does not preclude us from looking at the tree. We will have individual basemoles, stochastic individual basemoles, where we can track the infection history of each host in time. And because we do that and the risk of infection then given a contact will depend on your immune history, whether you are protected, how much cross immunity you have, we can in fact, we don't need to reconstruct the genealogy in the way trees are built because since we know the whole history, we can sample it and basically we know the parent of any virus. So we can construct the tree computationally as we go along. So in that sense, we don't really need to track the genotype. So this was done in this paper by Zindor and colleagues. It was also done in a paper by Trevor Bedford. I'll show you in a moment. I'm just to give you a few more details about this here on the right. As I said, we can follow the tree. So we can also measure diversity, genetic diversity, for example, by going back from two viruses back to a common ancestor and the time to the common ancestor is a measure of that genetic diversity. On the ecological side, rather than having this cross immunity given just that you have seen one of the epitopes, we mold that a bit differently. We said the risk of infection will depend on the fraction of the epitopes. So the fraction of these traits you have seen before. And of course, here you see that a parameter sigma as we move sigma down here, the intensity of competition. So how important it is to have seen a certain fraction goes up. I did place down here a quantity that tells you whether we are seeing some positive or negative selection in the system. We adapted an index from McDonnell-Crogman to look at selection. Here, we basically count or compute the mutation rates on the trunk of the tree compared to the rate of mutations on the side branches. So the side branches are those that will go extinct. As you see here in black, from the end of the simulation, you can trace back the trunk. Those are the ones that have become fixed in the system. And so this ratio will give you, essentially when it is bigger than one, we have positive selection. When it is below one, you have negative selection of mutations. So the main result I want to show you is here. Remember that perhaps I was not clear enough in the work before, in the purely ecological work without explicit mutation, the parameter that was very important for the bifurcation diagrams was the intensity of competition. Here, I want to show you the effect of the speed of evolution of the mutation rate on the emergent structure and shape of the tree. So we start on the left by comparison with essentially the completely neutral case where there are no antigenic mutations. So we still get the tree, but all are equivalent. So this is the neutral tree. As we move to the right with mutation a bit higher, in this particular example, we see this regime of positive selection with the index I just described clearly above one. And this short branch is a short diversity, genetic diversity. This is the flu-like regime, the H3N2 regime. Now if we move to the right, and now the antigenic mutation is even faster, we get a more interesting situation, at least if you are interesting in diversity. I have to say I have cut the tree here just for the purpose of the figure. These purple and orange branches joined in the past. So they are two coexisting set of branches. So you see what we would call these discordance sets where now mutations may come in but get selected against because essentially the niches in the host have been established at least temporarily by these coexisting types. So we see here that these different dynamical regimes are very influenced by the speed of evolution and that to achieve the coexistence of discordance trains. So the emergence of niches in this system, evolution needs to be fast enough to explore trade space. And for this essentially, yes, equivolutionary dynamics to assemble niches with limiting similarity. That may be a bit counter-intuitive. If we go a little bit faster, or I mean, if we go faster, of course at some point we lose the pattern we are going to have essentially just a random pattern with variation on top of the tree. Oops, did I write on my slides or did you write on my slides, Jacopo? I'm not sure, but now I don't see the error. I just was wondering if you are interfering. So I will stop in a moment to see if there are temporary questions, but I wanted to mention that all this does not depend on of course having a discrete space.  I mean, here in the paper by Zinder, you will find an application to flu where we simulate with the tropics, the northern hemisphere, the southern hemisphere. So we try to see whether we can get the flu-like dynamics with realistic parameters. But we consider essentially five epitopes and each has a certain number of variants. So there is a limited space and that limited space has been emphasized in the past. I like to show you that in continuous straight space with this no limit to the different types, you can get essentially the same dynamics. This continuous straight space has a very strong empirical connection motivated by the very elegant work of Derek Smith and colleagues looking at data on the virus. And what you see here on the right is really what is called an antigenic map. So you can look at distances in a map that tells you how similar these viruses are. This is not like just an imaginary space. This is derived from data. We have for these viruses and this has been used for a long time to produce vaccines. Essentially, you can test one virus against another for how much cross-protection it gives you. There are these immuno-assays than in ferrets that allow you from those tables then to define a distance. And the very interesting idea of Derek Smith was to define that distance from those tables and then ask how many dimensions do we need to describe H3 and 2 influenza? And they found that you need a few dimensions with two dominant ones. And you can see in this plot that there is indeed one dominant one that corresponds to this tree with very short branches, right? And you are moving from 68 on the top down with a little bit of fluctuation in a second dimension but it's very one dimensional corresponding to this limiting diversity of flu. In this model, so this is a model by, let's see if I have, I'll have the reference later by Trevor Bedford when he was in my lab with Rambo and myself. This model now lives in a continuous and dimensional space. Here I'm going to start with two dimensions and now a phenotype is just a vector in that space. So we can look at what happens in this kind of representation. Importantly, the mutation here is where the trick of this model comes in a sense. So the mutation occurs at the rate. This is a stochastic model. It's an individual based model as before. And when a mutation occurs, then the phenotype, you choose the direction at random but the size of the mutation was chosen from a gamma distribution. And this was based on some empirical data. The idea of a gamma distribution comes here from the important, the parameters we chose. Most of these steps are going to be small but eventually you'll have a bigger step. And this is essentially a phenomenological representation of what Katya Cole did with this, with this genotype phenotype map represented here in this simpler way. So that is essential. And I like to just show you that this implementation recovers all the characteristics of flu. We have it here with northern hemisphere, southern hemisphere and the tropics because there is differences in reality in those parts of the world. And of course, the virus travels around. You can see the replacement dynamics. You can see the short branches of the tree and on the right in B, you see the two antigenic dimensions. The virus moves predominantly in one direction. And in the bottom, we just added the noise of the size that is typical of these kinds of measurements. But that's more or less what we should see. You can ask yourself, did it matter that we started in two dimensions? It doesn't seem to matter if you run this mall and you start, for example, with 10 dimensions, what emerges for the flu-like parameters of H2N2 is also just this one, largely one-dimensional trajectory shown here by showing the principal components of this antigenic space, where you see that, for example, PC1 against PC2, you are moving in time to the right, essentially, mostly along one dimension. And you see that, well, anyhow, in other projections. So these dynamics did not depend strongly on assuming two dimensions. Now, before I ask whether there are questions, for this part of the talk, I'd like to refer you, for those of you who are interested, to this paper by Trevor Bedford and colleagues in Nature, which followed, and which shows these actually are trees from data. So they are very interesting empirical trees. And I want to show you that, of course, as usual, the connection between these structure and dynamics, there are many, well, there are other factors that matter besides the speed of evolution and the intensity of the cross-protection. Here, we have the observed trees, we've reconstructed from sequences for H2N2, now you are familiar with it, except the colors here have to do with their geographical location. You have H1N1, another subtype within influenza A, and then two types of the influenza B that are less prevalent. And you see that the trees vary. A very interesting thing here is that H1N1 and the other flu viruses are known to evolve. Genetically, they mutate as fast, but phenotypically, they are not capable of changing as much. So the traits that matter to competition in H1N1 are not changing as rapidly as H3N2. What this paper then proposes is that, of course, then these changes, essentially, what is happening is that you are reducing the overall, the general pool of cost, right, faster for H1N1 because the virus is not moving away fast enough and therefore you are moving more towards what I would call neutral dynamics, but in a way that interacts here with the geography because the new types are coming from mostly from East Asia, South Asia, Southeast Asia. And so what you have is this new, in the mold that is presented in this paper, you also have this more detailed immigration patterns. And to show you the complexity of this, if essentially you are reducing overall susceptibles more, you are reducing the age of infection towards children farther and the children travel less. So you are having this interaction of travel, age of infection and intensity of competition. I mentioned that because there is a parallel work in phylo dynamics that really goes into inference. And when you hear about community phylogenetics and all the efforts to use community patterns in species, to say something about the underlying forces that are at play, I would like you to have a pitch for essentially inference. So you may have your hypothesis, but you may have to connect your molds to the data, the machinery for doing that in viruses where we have sequences and phenotypes as a function of time exist. And there is a lot of interesting work at this interface with statistics. So just to show you that here the demography, the competition and the speed of evolution are interacting to shape the trees. So what inference we can make, what explanations we have for the trees and what do they tell us in terms of how to intervene, how is it maybe to control the evolutionary drift of the virus, all of that requires this sort of going back and forth with the data. Okay, I'm going to take a break here for questions. Yes, there is one question by Miguel Rodriguez. Yes, this is really interesting in the models. For example, in the neutral tree that you show from the cinder paper, what is the source of the oscillations? What causes the rate of infections to oscillate? Yeah, this is an interesting question. And here, what is the source for, we have seasonal transmission in this model. Now, and I assume this is what is causing it here because it's very regular, but I would say that we would also have in these neutral models because of the equivalence, because of the complete equivalence, we would have also the possibility of cycling because you are basically eating up the susceptibles and having to wait for those to be replenished by births. So in the typical, if you take the paradigmatic studies of nonlinear dynamics in disease, you have of course a tendency of disease systems to oscillate. That tendency is essentially a damp cycle going to equilibrium. And then when it interacts with seasonality, you can get more complex patterns because you have two cycles interacting. So we could have even in the neutral case, in fact, measles, measles which has been studied and is the sort of more, as I said, paradigmatic studies of what we understand in epidemiology, measles is largely neutral because measles is a virus and this is why the vaccine works so well. Measles mutates but it cannot change antigenically. It cannot effectively change antigenically. So it's mutating but it's neutral because once you are infected, so essentially every virus is competing, it's a form of generalized competition that is neutral. So it's interesting to think about those parallels just because if I'm a host, I got measles or I got vaccinated, I'm removed. I'm no longer a resource. Right, and in the paper later on, when you simulate these dynamics and show that you can reconstruct the similar dynamics from the real data, in those simulations, are you imposing that seasonal? Yes, they are, yes. And I have not gone enough into those details in some simulations like here we have, I have to remember here, here we have seasonality in this paper. We also have a figure with the three, the simpler geographic structure, right? The tropics where there is, because the very interesting thing is that seasonality influences persistence. So away from the tropics, the seasonality is stronger. And for example, persistence in the northern hemisphere or the temporary regions is not high. And so essentially a lot of the persistence is in the tropics and there is also a typical movement from the north to the south. And so there is the very interesting, there has been a lot of inferential work on looking at the origin. Where is the trunk? So essentially where is the trunk of these trees in the world, right? Because that tells you the ones that the mutations that eventually become fixed, where do they come from? And it's very interesting to see where is the trunk, where do these mutants, these effective mutants come from? Thank you. So you can see the trunk right in the different places. And yeah, it's kind of interesting. There is another question from Gabriel. Yeah, I was wondering about the result you showed for the high dimensional phenotype. I was wondering, so is it because of the specific way that flu works that you're assuming that there's immunity towards past strains that it's always 1D? Like why can't we see like limit cycles, oscillations? Very interesting, yeah, good question. There is a nice picture, Trevor, but for this magnificent work. In fact, I should point you to all to the page he has. His websites, he has developed something called Next Flu which monitors on real time, does predictions of the next virus on real time and so on. So he has a picture of that landscape, that evolutionary landscape in this paper and you see exactly what you said. What happens is that the virus, there is this sort of wave of immunity behind it and it sort of has to move forward. But it's interesting if in this mall, and this is a toy mall, of course, if you mutate a bit faster, not that much faster, you will bifurcate and you will have coexisting, you know, the regime I showed you before in which you don't get replacements but you get coexistence of types. And so probably, of course, reality always has a mixture of hypotheses. And so there is a generalized immunity that was proposed, the generalized immunity that was proposed by Neil Ferguson as the original mechanism that gives you the short branches is also probably at play helping with this, preventing those bifurcations, right? And in this mall, you can get it, but of course you have to have the speed of evolution. Otherwise the system will bifurcate and will find niches and coexistence and then you get this coexisting regime. But what about the oscillations? Can you ever get like the immunity chasing the virus? Yeah, this is a very interesting question because in this paper that I like to go back here, sorry, here at the bottom I like to point you to, in this paper by Riker and colleagues in PNAS, they did propose that this mall, essentially this mall from strain theory that Sunetra had proposed earlier was an explanation for flu. And that's this discrete mall where you have this essentially a limited number of combinatory possibilities. And so in theory, what you should see at some point is the system cycling back, which has never been seen for H3N2. So of course in their paper, they argued that some interesting, there are some interesting issues about how we get the data from the assays, these immuno assays and which virus we test against past viruses, right? And whether we have seen, there is a question, have we long enough in time to see the cycles or are we sampling in the right way to see the cycles? I would say most people will feel more comfortable. I don't know where reality is. I don't think that this limited pool of variation is an important hypothesis for explaining the patterns. Now, how, whether an assumption of a completely infinite space like here is reasonable, it's hard to tell. So far, so far we have not seen any of these viruses we turn in a cyclic fashion. Yeah, interesting. Great, I don't see any other question, so. Do I have time, 10 more minutes? Yes. Yes, people must be very tired after this long day, but let me do this because I, yeah, I like to do this. So before I go on, I wanted to just stop here for a moment and point out again for those of you who are really tired of now listening to about, I mean, this lecture about strains, but there are very strong conceptual analogies to what we would see in ecological systems if we start essentially modeling this frequency dependent competition. Essentially along the Chesson axis of niche differences. And this was done in this paper. I'd like to direct you to this paper by Schaefer and Van Ness in PNAS where they have a niche axis. It's a one-dimensional niche axis. This is essentially a version of the MacArthur and Levine's model, but with evolution. So you have time running down and you start with these pieces that can mutate and are competing as a function of distance. And the only thing I like to notice at the end is that what persists in this discordant state here is these clusters, these clusters. So these are species and they are not one species at the distance of another species. It is these clusters of similar species away from another cluster of similar species. Very similar to the model I just showed you in continuous space for flu except that this one was done in one dimension. These communities do not talk to each other. I'll mention tomorrow further, well, sorry Thursday, some further analogies. Here I wanted to leave you with an example. We'll do this quickly off another virus because you can say, well, flu motivated all this work but is there evidence for the discordant regime in nature? Essentially the emergence of these kinds of niches. In the work by Gupta, Caroline Bacchi and so on, they talk about the meningococcus virus. You will see some empirical evidence. I like to mention here these other viruses. This is a rotavirus, the main cause of diarrheal disease in children and mortality due to diarrheal disease worldwide. This is a virus with, it's a double standard RNA virus. It has on the surface on this sort of nice picture that they drew here. We have two types, two main, two or three but let's say two main determine and molecules that determine the G types and then the P types. So those are different parts of the capsule of the virus. And I like to show you that if you look at here the genealogy of the G types, you'll see this coexistence. This is the global data set that exists for this segment. Essentially the segment is the segment that encodes the G type. If you do these trees, you find these coexistence that goes back to very, very, very long time. And if you look at the population dynamics, you also see coexistence here on the right, on the top with some fluctuations. And of course some new types that are coming like the green because this virus is of zoonotic origin and we get new viruses that come from animals into humans and introduce. So we have not just mutation but we have novelty through immigration. And I just like to point out that we have, we did an individual based model with three of these proteins just to mention that now the risk of infection again depends on distance but we have two components here in this formula. One is generalized. So if you have been infected before you are protected and that is believed to be the strongest protection against these virus. We added some specific protection with the Sigma specific depending on the fraction of these three types you have seen before. And this specific immunity is much believed to be much weaker in this virus. Now, this virus is messy because I said you get immigration but you also get reassortment. So these segments you get essentially recombination in these viruses, it's called reassortment. So you get this genetic mixing. So can you get any structure in the presence of this kind of genetic mixing that is essentially you, it's a force against this, just the simple lineages through mutation. I just want to tell you that in all of these, you see here an example where there is no reassortment the colors, I'm just stacking up the abundance of the different viruses in colors. The colors represent a different combination, a different strain, the red strain invaded and you see that we on the bottom, we are basically look at the number of shared segments.  If you get reassortment, of course you will get only partial discordance but this force, this frequency dependent competition is still leaving a strong signature of partial discordance. And I like to show you this wonderful, there is not enough data for these virus, there is nothing compared to flu but I wanted to show you this because I think it's an incredible pattern possibly of niches in nature. If you take the global data set that exists and take, you map it to the percentage of samples here on the left that have a certain G and a certain T type. So the red colors are the most abundant, the blue, the least abundance. You see that we have a lot of G1, P8, some G2, P4. So it looks like there is not that much overlap between these domain and things but you can say, well, maybe, maybe this is just because of their frequencies and it has nothing to do with a force acting like a negative frequency dependent selection. So on the right, I'll show you what is the probability of essentially is if you look at what you would expect from the frequencies, the global frequencies of the corresponding Gs and Ps, do you have a positive or a negative deviation and how significant it is? You can do this with randomizations, you can also do it with certain statistical tests here with randomizations in red. In red, we have the very, the sort of the deviations that are positive, right, that under P value and you see that of course we have much, we have much more G1, P8 and G2, P4 than we expect at random but more interestingly, some of the later arrivals like G6 or G12, they have come in and of course there is a lot here on the left of them associated with P8 because there is a lot of P8 around but if you look at the deviations, they are deviating positively towards places that were not occupied by these dominant types. So there is somehow this movement of the system to limit similarity. Maybe I could end there or I can show you a little bit more but I don't want to, you know, maybe I can end there. How am I doing with type? Maybe I'll go to the conclusion. So we are five minutes past. Yeah, so let me just conclude. I just wanted to show you that because it is a nice picture of this discordant state possibly in nature. And this makes the point that we can get these non-overlapping repertoires, in this case, even with weak cross immunity and that this frequency dependent selection can remain this effect of what we would call niche differences sense to Chesson but in a context of evolution can remain apparent despite this mixing by reassortment and despite immigration. Of course, depending on the relative strength here of these processes. So under these data shows patterns consistent with niche partitioning, this emergent niche partitioning but what are we missing? And I like to get to that tomorrow. I will not touch much on functional differences or barriers to reassortment essentially how does this access interact with the other access in Chesson which is a very interesting idea. But we haven't explored a lot. How do we compare the patterns to what we expect under neutrality which is a very important question. And because, and I have been talking about limiting diversity. I really want to talk about diversity and I want to talk about hyper diversity. So tomorrow I will present a system where the diversity of the pool of variation is so large that you will say, well, there can be any structure here and I hope to surprise you by showing you that we may be in a regime that is the complete opposite of neutrality and where specific interactions are incredibly important and are seen in the patterns we see in nature and that to see those patterns because we have recombination we are going to use not trees but networks. And networks will allow us to look at the structure that emerges from the underlying processes. So this is where I'm going to go tomorrow to hyper diverse systems. Hopefully connecting with the more analytical work that Daniel Fisher will show us. I think there are some conceptual connections to that and here are some papers for those of you who may be interested in some more mathematical aspects of competition between strains and in particular at the end some attempts to use population genetics to explain the patterns I just show you for flu. Thank you very much. Thanks a lot Mercedes for the very nice lecture. So we have a few more minutes for questions. If any, please use the raise hand feature. Okay, I don't see any. So otherwise, I mean, we will be back with Mercedes tomorrow, right? Yes, I don't have the program. No, I think Thursday. On Thursday, yes. I don't have the program. Yeah, I should say Jacob for the third lecture will not be anymore on diversity or whatever because as we discussed, since yes, this was about quantitative approaches in ecology. I like to talk a little bit about climate urbanization and vector-borne diseases. So different aspects from diversity which of course that fits more with what other people have been talking but I like to go a little bit there. Yes, absolutely. But to say that if there are more questions there will be, if question arises there will be time to answer them and this video will be available on YouTube. So you can really watch it.


Hi, we're now ready to move on to linear theory lesson 8. Now in our last lesson we dealt with perfect intervals that is fourths, fifths and octaves. Now in this lesson we're going to deal with our major and minor intervals. So let's get right to work and we'll do a little quick review on the perfect intervals and then get right to the new material for today. We will just review that our perfect intervals came from the major scale. So let's go ahead and go back to this major scale. I know I keep coming back to it, but it really is the foundation for all of this theory. And we have our good old whole, whole, half, whole, whole, half. There's our major scale. And we said that the distance between the first and the fourth note of the scale was a perfect fourth. The distance from the first to the fifth note of the scale was a perfect fifth. And the distance from the first to the eighth note of the scale is a perfect octave. All of that is definitely true. Now we're going to move on to the seconds, the thirds, the sixths and the sevenths. Now they're very similar, but let's take a look at how they work. We're going to list these out here. First of all, the interval that grows from the major scale is the major interval. So a major second is the number of half steps that grow from the first to the second note of the major scale. In other words, a major second is two semitones. Now here's where it gets a little different than our perfect intervals. A minor second that's used with a lower case too is one semitone smaller or one semitone from a note to the next. However, we can go a couple of more steps. We already know about diminished intervals from the perfect side, but we also have a diminished second. And it in fact is one half step smaller than a minor second or in this case is zero half steps or zero semitones. We also have an augmented second and it's one larger than a major. It is three semitones. Let's see if we can give an example of each of these and clarify this just a little bit farther. And I think I am going to go ahead and rewrite that major scale and its intervals. Three, four, five, six, seven, eight. Here's our whole, whole, half, whole, whole, whole, and half. So let's see. We said we had a major second which grows from that interval of the first and second notes of the major scale. Major second is two semitones, so like the distance from C to D would be a major second. And if we just go to our piano keyboard, we can take a look at a C right here and a D right here and say, okay, it's one, two half steps, definitely a major second. Okay? So C to D would be a major second. Now, a minor second might be something like C sharp to D or C to D flat. Again, think of a minor interval as being a little bit smaller than a major. How do we make that happen? Well, we either make the lower of the two notes higher to compress that interval, or the higher of the two notes a little lower to compress the interval. Okay? So a minor second would be one of those. A diminished second is one smaller than that. So what would we have? Well, a C sharp to D flat would be considered zero semitones or a diminished second. Okay? So that's how we come up with that old zero semitones. As weird as that looks, that's how it works. And then, finally, an augmented second is three semitones and it would be something like C to D sharp, stretching that interval out, or C flat to D is another way to do it. And if we take a look at that, there's C flat to D. Let's go to this and we will take a look and let's find our C flat, which would be right here, one half step lower than C, and here's our D. So we have one, two, three semitones. There it is. C flat to D is an augmented second. Right? Let's move on to the next one. That is thirds. Okay? Now in our thirds, back to our scale, whole half, whole, whole, whole half. I know I spend a lot of time doing that, but trust me, it makes everything easier. Thirds, same deal. A major third grows from the first three notes of the scale or four semitones. Okay? So I bet you can figure this out. Then if a major third is four semitones, then a minor third is how many? Three semitones. A diminished third is how many? Two semitones. And an augmented third is five semitones. And again, if you're thinking you might be going, okay, wait, five semitones is also a perfect fourth, which is which? Well, it's very simple. It comes down to the letter names. If we have a C to E sharp, well, then that, and let's go to our keyboard. C to E has to be a third because there's just a D in there. That's a second. That's a third. So from C to E sharp is one, two, three, four, five semitones. Okay? Or an augmented third. Whereas if it were called C to F, that would be called a perfect fourth. So hopefully you're starting to really get a feel for that and how it works. Okay? So there are thirds. Major third is four semitones. Minor third is three semitones. Diminished third is two. And an augmented third is five. Now let's go to sixths. Sixths. Again, we're going to start with the major interval on sixths. A major sixth, again, grows right from the major scale. So we have two, four, five, seven, nine. A major sixth is nine semitones. So it follows suit that a minor sixth would be eight. A diminished sixth would be seven. And an augmented sixth would be ten. Okay? Same deal. You figure out the interval first and then count the semitones. Okay? And I think we can go right on to sevenths. And again, we'll get our major scale up here. One, two, three, four, five, six, seven, eight. Whole, whole, half. Whole, whole, whole, half. And now a seventh would be two plus two plus one, five, plus two, seven, plus two, nine, plus two, eleven. So a major seventh equals eleven semitones. A minor seventh. Everyone should be getting this by now. Ten semitones. A diminished seventh should be nine semitones. And an augmented seventh is twelve semitones. Hopefully that's all really making sense to you at this point. Okay? Now let's just do a little bit of this in a way that we can start to figure some stuff out. If I give you, let's say, the note F, and I ask you to find a minor seventh above F, what should that process be? Well, the first part of the process is to determine the note letter name. Okay? Now you can do that by just counting letters or on the staff. From our lesson two lessons ago, we ought to be able to just say, okay, then I know that's a seventh above F. That's an E. Okay? Then I asked for a minor seventh. That's ten semitones. So we'll go here. Here is our F, okay? And we want the E that's going to work. We need to count ten semitones. So one, two, three, four, five, six, seven, eight, nine, ten. A major seventh would be eleven semitones. Major seventh is eleven semitones. I asked for a minor seventh or ten semitones. So here's the spot we want to be. That happens to be E flat. So I'm back up here. That E would be E flat, and we've identified a minor seventh at that point. Okay? And we can do that for all of them. But first, we're going to identify the note name or the general. Then we're going to determine the specific name, and that's going to be major, minor, diminished, augmented, or perfect of each and every interval. Okay? Now it's time for you to go on to the assignment. Get working on this concept, and there's several different things that you can look at to make sure that you understand major and minor intervals and how they work. Good luck.


Two talks. So since we encourage people to ask a question during the talk, so when you raise the hand, also say the word question.  And the first speaker is Eugene Matsuda. And the title of the talk, Myaranda Quantization and Half-Integer Thermal Quantum Whole Effect in a Kitai spin liquid. Thank you very much. So first of all, I'd like to thank the organizer inviting this workshop. So today, I'd like to talk about Myaranda fermions and quantum whole phenomena in quantum magnet. This main player of this work is Kasahara, Onishi, and Ma, and Sugii, in the middle of Tokyo. And the work has been done in collaboration with Takashi Baichi's group. And the single crystals has been grown by Tanaka's group, Tokyo Institute of Technology. And Nassu and Motome gave us many important theoretical suggestions. In my talk, I'd like to start with explaining the Kitai quantum spin liquid quite briefly. Then I talk about detecting Myaranda fermions in insulating magnet. Then I talk about Kitai candidate material, alpha-routinium shield 3. After that, I'll focus on thermal whole effect in alpha-routinium shield 3. In particular, I'll address the issue of half-integer quantized thermal whole conductance and topological phase transition. The Kitai interaction is a bond dependent, ising like interactions. And each bond favors different directions of x, y, and z, x, y, and z. Then the spins cannot satisfy the three different configurations simultaneously, leading to exchange frustrations. In 2D honeycomb lattice and 3D hyper honeycomb lattice, exactly solvable quantum spin liquid grand state appears. In Kitai model, spins can be represented in terms of four Myaranda fermions, a particle is its own antiparticles under this constraint. In Kitai model, this bracket operator commutes with total Hamiltonian. And because WP square is unity, the WP can be taken as plus minus 1. In the grand state, the old bracket takes a value of plus 1. The excited state is a minus 1 state, which is called G2 flux bisome. The Kitai spin rigid has very short spin correlation lengths. But actually, this state is orthogonal to this state. Then the spin correlation length is similar to Bratz spacing. Then the quantum spin rigid state with extremely short spin correlation length appears in the Kitai model. There are two types of Kitai quantum spin rigid state, depending on the anisotropy of J1, Jx, Jy, Jz. The very anisotropic case, the gap spin rigid, appears. And when the small anisotropy, the gap spin rigid with 2D deluxe cone appears. Then today, I'd like to discuss in this region. Two types of excitations in the quantum spin rigid due to the fractionation of quantum spins, namely the Italian and localised minor fermions, G2 flux bisome. At a very high temperature, larger than the Kitai of interactions, system is a parabenetic regime. On the other hand, at a very low temperature regime, system is a quantum spin rigid with deluxe dispersions. And only the Italian and the minor fermions are moving in the bulk. In the intermediate temperature range, the G2 flux are excited and interact with the Italian and the minor fermions. Together, let me discuss how to detect the minor fermions in these initiating magnets. In the absence of magnetic field, as I mentioned, minor fermi-metal state with deluxe cone dispersion appears in the bulk. The magnetic field opens up the gap. And topologically, a non-trivial state with the channel number of unity appears in the bulk. And so this is different from the, in this sense, this state is very different from the graphene. Because in graphene, if you have a magnetic field, the gap does not open. And as a result, the chiral edge current of gap-less neutral minor fermions appears at the edge of the sample. Then how to detect this chiral minor edge current? Because the minor fermions cannot carry the heat, but can carry the heat. The thermal hole effect is a very powerful probe to detect this chiral minor edge current. So let me compare the system with the chiral quantum magnet with two-dimensional electron gas, which shows the quantum hole effect. I would like to remind you, in quantum hole effect, two-dimensional conductivity sigma xy is quantized in the unit of e square over h. In the integer quantum hole effect, nu is 1, 2, 3. And edge current carried by electrons. In the fractional quantum hole effect, the nu is 1, 3, 2, 5. And the denominator is usually odd number. And in this case, the edge current carried by fractional recharged quasi-particles. Also, it is less known that in the quantum hole state, thermal hole conductance is also quantized. Actually, the two-dimensional thermal hole conductance, couple xy 2D divided by temperature, is quantized in units of this quantity. So q is the central charge and n equal 1, 2, 3.  This is recently reported by Weitzman group. Then let me discuss a case for a quantum spin rigid. In the Kitei quantum spin rigid, the edge current of the neutral Mylar fermion carries the heat. Because our degree of freedom of Mylarna is half of the conventional fermion, and q is 1 half, namely the non-Aberian enions. So in this case, two-dimensional thermal hole conductance divided by temperature takes half value of this quantity. So namely, half-integer thermal quantum hole effect is expected. In other words, if we observe this half-integer thermal quantum hole effect, this provides the direct evidence of Mylarna particle. So let me introduce the thermal hole effect quite briefly. The thermal hole effect is a? I'm sorry, I don't understand. Do you have the Z2 field applied in your akitaev model? In 2D electron gas quantum hole effect, you apply magnetic field. And in akitaev spin rigid, what plays the role of the magnetic? It is because we apply the magnetic field, perpendicular to the plane. Adjust magnetic field? Yeah, we apply the magnetic field. But it does not act on the Mylarna fermions the same way as magnetic field acts on ordinary fermions. If we apply the magnetic field to the akitaev spin rigid, the gap opens in the bulk. But at the edge, the gapless state appears. They are similar to the quantum hole effect. But in zero field, there is no gap.  And it is a transverse response in the applied current and magnetic field. Let me discuss the further we are measuring. The further we can measure is the Jx and the temperature gradient around the x-axis and y-axis. And using these relations, we determine kappa xx and kappa xy. The far as important is that in contrast to kappa xx, kappa xy does not contain the phonon contribution. Then the kappa xy only contains the spin contributions. Then we have some advantage to measure kappa xy. So let me discuss the akitaev candidate material, alphardenium CL3. The akitaev type interactions arise from partially filled T2G levels in the presence of strongly spin omitted coupling. Then the J equal 1 half motor insulator appears. The material, honeycomb lattice, with 90-degree bound bond by H shared octahedral, can host the akitaev systems, as suggested by Jack Allen and Kalyurin. Actually, in this case, the super exchange pass from this one and this one cancels. Then we can obtain the akitaev interaction. With the recently strongly spin omitted coupled, J equal 1 half motor insulator, alphardenium CL3, has emerged as a prime candidate for hosting a properly approximate akitaev quantum spin rigid. So today I discuss this material. Actually, in this material, the first principle calculation shows that akitaev interaction has dominance. But actually, this material contains the Heisenberg term, but it's very small. But the off-diagonal term, but it's comparable or smaller than the akitaev interaction. Then this material has significant akitaev time. However, because of the non-kitaev interactions, anti-fermented order with zigzag spin structure appears at T equal 7.5 Kelvin. So this model is often discussed by K gamma model. So let me show you some signature of the akitaev spin rigid. The broad magnetic continuum observed by Ravan scattering indicates the presence of ferrebenic, not bosonic excitations up to very high temperature. Moreover, the EN-sq neutrons scattering show that the magnetic continuum appears. This is an experimental result of this simulation. The magnetic continuum appears below the temperature characterized by kitaev interactions. So these results reflect the proximity to the kitaev model. Now let me discuss the thermal whole effect in alpha-alternium CL3. We first measure the thermal conductivity. Actually, thermal conductivity has been measured by many groups here. The thermal conductivity decreases and shows a sharp increase at the nail temperature. And then decrease. We observe the clear anomaly at the nail temperatures. But we need to be careful to study this material. Because in this material, above the nail temperature, the thermal anomaly often appears. For example, mainly the 14 Kelvin due to the stacking fault. So as I discussed later, this stacking fault is a very important rule for the quantum thermal whole conductance, so that we carefully select the sample which does not show the 14 Kelvin anomaly due to the stacking fault. Actually, before the experiment, we carefully selected the sample which shows no anomaly at 14 Kelvin. But this is not enough, because the sample is very easy to bend. So if you bend the sample, the stacking fault is easy to be introduced inside the crystal. And once you introduce the stacking fault inside the crystal, you cannot remove it. Then to check it, after the measurement, we always measure the multisurcerability and the special key and confirm the stacking fault was not introduced by the measurement. And also, we selected high quality single crystal which shows a large couple of x-axis. This is the temperature dependence of the thermal whole effect divided by temperature or two different crystals. We applied the magnetic field perpendicular to the frame. Again, the thermal whole response is very tiny compared to the longitudinal response. It's 0.1% of the longitudinal response. Then special care was taken to measure couple x-y. So we have done the following method to check our result. So we measured two different crystals, shaft 1 and shaft 2, sample 1 and sample 2, by different setup. One sample was measured by our university, Kyoto University. The other sample was measured in University of Tokyo, ISSP. So with different kind of summator, so we used Sanox 1070 and ISSP used Sanox 1050. And in this measurement, calibration of the summator in magnetic field is crucial. Then both summators are calibrated by different method. We calibrated the summator by capacitance method and ISSP calibrated the summator by, I forget it. Maybe the cancellation coil method. And most importantly, the data was analyzed by different persons, female and male. So as far as this figure, we observed the same behavior in sample 1 and sample 2. So we have confidence on the result. Then the finite couple x-y appears, below 70 Kelvin, nearly 70 Kelvin, which corresponds to Kitter-Fm interaction. This indicates couple x-y detects excitations inherent to the skewered state. This is consistent with the numerical result. And that is the absolute value of couple x-y of this material is called this behavior. Yeah, yeah, yeah, yeah. So the red points indicate the maximum around between 60 and 70 K. And the blue just goes slowly. Can you comment this? This is the error bar. Because as I mentioned, the sum of response is very tiny. Then at high temperature, we have the blue error bar. So we repeated many times in these regions, but still we have some error bars like this one. But below 50 Kelvin error bars are just like this. So the absolute value of couple x-y of this material is really large. It's one or two thousand magnitude larger than other materials, like the Triangular and Kagome and the Paracolar lattice. So with decreasing temperature, couple x-y divided by temperature increase and show the maximum and then decrease. Yeah, I probably miss it, but why does the conductivity changes sign twice, right? I mean, at low temperature, it is negative and it is negative again at the higher temperature. Is it? Yes, why is it changing sign? That's an interesting question, but at least now that we don't have any explanation, why is it changing? But what is important is at low temperature, it goes to zero. And then at low temperature, it changes sign. And even at very low temperature, they have some finite couple x-y, but it's negative. But I think that this comes from the summer gel-synx-molier interaction. Gel-synx-molier interaction of this material is the order of five Kelvin. Then if we take into account the gel-synx-molier interaction, we can observe the couple x-y even in the order of state. But again, we don't have the satisfactory explanation for this behavior. Okay, then the, so in this figure, the right figure represents a couple x-y, two-dimensional summer-hole conductance divided by temperature, which is plotted in the unit of this one. So one half corresponds to the half quantization. So unfortunately, the couple x-y is, okay, the couple x-y reaches close to the half of the quantized value, but the quantization is not attained. This is because the low temperature properties are masked by finite order. Then we could not observe the half quantized summer-hole conductance in this geometry. So we almost gave up the experiment. So we are in the dead end. But we can escape this problem by the following method. Actually, in this material, if we apply the magnetic field parallel to AB plane, the net order is strongly suppressed. And at nearly seven or eight Tesla, net temperature goes to zero. Actually, this shows the in-earth-neutron scattering result. So in this regions, above the, in zero field, the magnetic continuance is observed. But in this regions, the speed wave-like excitation is observed. But in this regions, again the continuance of excitation is observed here. And this is the gap, okay. So this indicates the magnetic continuance at high energy above H star perpendicular. So indicating the appearance of angel-spin-legged state above H star, namely in this regions. Then we measure the summer-hole conductance in tilted magnetic field. So in this case, the magnetic field parallel component separates the antifreeze order and phase transition is tuned by H parallel. But the summer-hole response is induced by perpendicular component, H perpendicular. So we have done this measurement. Together, I skipped the detailed argument, but this is a phase diagram in tilted magnetic field. So cross is a phase diagram in parallel field. And these are the data for 60 degree. This is a TN at 60, 60 degree agree well with that for parallel field case. And the vanishes at the same H parallel. And the 45 degree case, slightly reduced. But anyway, these indicates the quasi-2D nature of magnetic properties. Actually, this is a van der Waals coupled compound. Together, this is a field of dependence of a couple of xy divided by temperature. So in this region, the system is in the anti-parametric order here. But once entering the spinic heat state, summer conductivity simply increase. So in these regions, the couple of xy divided by temperature shows a plot of behavior here. And this is the right figure. Again, two-dimensional couple of xy divided by temperature is plotted in the units of these quantities. Vijay, I have a question. So in this plot for couple of xy, you have only one point which is negative. And before you were showing the whole tail which was negative couple of xy. Is it just how we can understand this? Because you see that for very small field, the first two points show positive. But actually, that data, we apply the magnetic field of 14 Tesla. Then the resolution is very good. But in this case, the magnetic field applied is only two or three Tesla. So resolution is not so good compared to the previous data. But it shows the negative. If you take the, so in these regions, as you see, the two-dimensional couple of xy over T is nearly half quantized. Actually, in these regions, we take the data many times and the data is quite reproducible. And that means the quantum, whole plateau appears in the quantum speed limit state. And the value is half of this value, namely the half of the quantized value of the quantum whole effect is observed. So again, this is half of the that expected integer quantum whole effect. So this is our temperature dependence of the thermal whole conductance for the 60 degree with tilted angle. In this case of 4.9 Kelvin and 3.7 Kelvin. So in all temperatures, we observe the plateau behavior which is quantized nearly half of the quantized value. Unfortunately, we could not go down to below this temperature because below this temperature, the thermal response is become very tiny. So the error increase. And at the high temperature, the deviation from the quantized value is observed. And at 15 Kelvin, we never observed the plateau like behavior. So we also measure the different angle. At 45 degree, we again observe the half quantized thermal whole conductance at all temperatures. Interestingly, at 60 degree, we observed some enhancement enhancement from the plateau value. But at 45 degree, we never observed such a behavior. Actually the origin of such enhancement is unknown. But in both case, in the case, the thermal whole conductance suddenly go to zero at high temperatures. So I would like to emphasize. So as I mentioned, this is a response of the insulator. So this thermal whole conductance arise from the response of neutral quasi particle. The second point is the plateau indicates the topological protectant. Degree of freedom is half of conventional of elements because one half quantized. So these are the, provide the evidence of the Mylana-Phermium. So let me discuss the temperature dependence of plateau behavior at this point. Here the temperature dependence of couple x over t, and here's the counter value. The half integer thermal whole conductance is preserved nearly up to five Kelvin. Above five Kelvin, up term of couple x over t is observed. And this is a high temperature regime. So it increase and show the peak at 20 Kelvin, then decrease and burnish nearly 60 Kelvin. So in the conventional quantum whole system, the quantum whole plateau is observed at very low temperatures, usually the very 100 millimeter Kelvin. But in this case, the concentration preserved up to five Kelvin. This indicates the Mylana gap is very large. So this is the NMR result. The NMR one over T1T has been measured four group. And the three groups observe the similar result. And three groups report in the region we observe the plateau, the large gap nearly 30 Kelvin is reported. On the hand, these group show the gap less. But if you believe this result, this is consistent with the plateau up to five Kelvin. Recently the neutron scattering experiment also shows a gap of 10 Kelvin. Okay, the next important question is what is the origin of up term of couple x over t from the quantized value, this one. Actually there are two theories has been proposed. First one is the phonon by Atchim Rosch. And in this case, couple xy increase as a function of t squared. And recently the Young-Goomers group Kaisto also claims that this enhancement come from the delocalized bisons due to the presence of next to the nearest neighbor interactions. Unfortunately our experimental result cannot check which is correct because of the resolution. Okay, another important point is the effect of the phonon. So recently the Atchim Rosch and Valence proposed the effect of the phonon. They proposed a similar theory. The according to their theory, the thermal hole conductance quantized when the phonon and H current are equally summarized. On the hand at very low temperature when the phonon become ballistic the decoupling of phonon and H occurs. So in this case, we never expect a quantized thermal hole conductance. But at t called zero we can expect a thermal hole conductance. So unfortunately we could not check it because we cannot go down to very low temperatures. But anyway this are consistent with our experiment. Okay, let me discuss the sample dependence. Until now we measured four crystals. There are sample one, two, three and now sample three is now we are measuring. So I did not show this later. And sample one and two which shows a very large kappa xx we observe the plateau. But we also measure the sample with low quality, the sharp sharp three crystal. In this crystal we observe the large anomaly at 14 Kelvin is stuck in fault.  Also the some kind of plateau behavior is observed. Okay, let me discuss the topological phase transitions. Okay, so I summarized the data as there are three regions. In these regions kappa xy is very small and in these regions half integer plateau appears. And in these regions parallel edge current of neutral parallel element flowing at the edge. And in these regions kappa xy suddenly goes to zero. And in these regions the topological phase transition to force the ferromagnetic space for a new contact of the state. The name is anyway this topological phase transition point located in these regions. But actually there are recently there are a special key to show the clear anomaly at this point. So this indicates the suggest the presence of contact critical point which I skipped the kappa xy color plot. Okay. One minute, one minute. Okay, the recently minor edge current has been observed fractional quantum hole effect. The half integer thermal hole conductance of the five half state appears in the fractional quantum hole effect. But question, but the point is the origin of five half state in fractional quantum hole effect is controversial. And also the minor edge current induced by a proximal effect has been also reported in quantum anomalous hole insulator superconducting hybrid systems. So as they observe the half integer of sigma xx, not xy, longitudinal effect conductance. But soon after this experiment, different interpretations other than minor has been proposed. So this effect is still controversial. Okay, this is a summary of my talk. Thank you very much. Thanks a lot for very nice talk.


The US and China are embroiled in a rumbling trade war. But where does that leave Europe? Beijing's long-term economic strategy passes through the Belt and Road Initiative. This trillion-euro project is bringing China closer to Europe, through the development of ports, railways and pipelines for oil and gas. Chinese money is pouring into Europe in almost every sector. Yet at the same time, the European Commission views China as a systemic rival. So how did China gain control of key infrastructure such as the Port of Piraeus or the electricity grid in Portugal? And how do European businessmen, politicians and workers see China's growing influence? As a threat or as a blessing? Has Beijing's expansion affected Europe's stance regarding human rights in China? And how will China's plans for a new trade route via the melting Arctic impact the climate crisis? For three months, Investigate Europe's reporters travelled the continent, from Valencia in Spain to the Arctic port of Quirkinus. What we found was not always what you might expect.