 So it's a distinct honor to be here, and I am delighted to be here to have the opportunity to participate in an inclusive event which has been really a transformative program at the National Science Foundation, and I check in my time, so I still haven't started just in case. So it is sort of a complicated task to figure out what exactly you're going to have to say. I want to say a few things. I know this is an emphasis in data science. Now my visit to Brown is co-supported by the Data Science Initiative. I don't know what they thought about doing that, the way I was chosen to, but so I have to talk about data, so I already did, right? So let me see if I can go with this. All right, so first, you know, there are at least two ways of doing science that you should be aware. It's not just as Senior Google, and he will tell you. But there is a third way of doing science, and I think it was better highlighted by a New York Times op-ed article by my former colleague Steve Strogett, and in fact he just wrote a book about calculus that the white calculus, I forgot what exactly it was called, but it says anything that he writes is worth reading, and it has some excellent interviews so you want to see them. And what he talked about that is the two defining events that took place exactly in, I think, 1953, and those were the discovery of the chemical structure of DNA by Watson and Crick, but also the invention of the computer experiment. We're not talking about simulating a partial differential equation or anything like that, but the use of the computer as an exploratory tool and with this, a third way of doing science. And then over the last couple of decades, a fourth way of doing science has come up, and that has to do with data science, which is how to develop these ways of analyzing data that comes massive amounts of data, and how can we actually explore and search for patterns among these data, and what can we say about this. So just to remind you, Enrique Farmapas and Hulam, essentially they did, this is a simplified version, this is not what they did, but let's suppose that you have a bunch of oscillators and they are connected, and then you are very smart, you have won a Nobel Prize, you are one of the founders of computer science, you are an extraordinary mathematician, and you say, ooh, I know what's going on. So that's what this guy said, and then they make some predictions, and then somebody had the bright idea, let's put it on a computer, and they put it, and they realized that they were totally wrong, that they have no idea what was going on, and that was the birth of the computer experiment by these individuals. If you see at the advances with the Human Genome Project and all the advances that have been in the social sciences, none of that could have happened with the great advances that have taken place in computer science, not only in the development of hardware, but also in the development of hardware. A few years ago I visited Orange National Laboratory, I can't correct the word national yet, but and then I looked, so somebody took me to see what it was, the fastest computer at the time, and then I took a picture with Titan at the time, I was very happy, the fastest computer, and about ten days later China announced a faster computer, and I think now we have the fastest computer for the next two hours or something like that, but this is just the advances that take place. Data science provides some really dramatic challenges, because we generate data velocity all the time, in fact we do it over our cell phone all the time, we do it with streaming this presentation, so the amount of data that is generated is immense, and then the question is, since you have also tremendous volume, that's another challenge, where you put it, the velocity, where you place it, so these are some of the challenges, and also in addition to the fact that all the data that we generate is on different formats, that's what diversity is called about, and therefore how to be able to use all these data that comes from different different formats, from different different purposes, how can we actually make use of all that, so there is a lot of challenges associated with data science. One of my areas, and more importantly, is essentially epidemiology, mathematical epidemiology, and it's interesting to see who developed mathematical epidemiology and why, and most of them were physicians. Now I think that we have somewhat forgotten what is the connection between science and physicians, and I think a lot of the medical pre-college med programs in fact make it almost impossible for many of them to become curious about science, about evolution, and everything, but that wasn't so in the past. So Daniel Bernoulli, who comes from my family, a prestigious mathematician, was also a physician, Euler was also a physician, mathematicians don't like to say these kinds of things, but bringing them out of the closet, Sir Ronald Ross was a physician, and then Anderson MacKendrick, and Kermak, one was a physician and the other was a mathematical statistician, and I get confused, and I won't remember, but between then they developed the field of mathematical biology. The most important work really is the one for Sir Ronald Ross in 1911. He wins the Nobel Prize for his work on Malaria, and then one of the challenges that he has to do is now that I know the transmission process of malaria. How can I use that information, not only to take care, better care of my patients, but how can I use that information to ameliorate the impact of malaria in my community, in cities, in the whole world? That's the challenge, right? That's a predecessor of what data science is about, right? Exactly. How can we use information at low levels of organization, and how can you use that information and those patents to understand patents at larger levels of organization and how you can change that? He had won the Nobel Prize, so he said, all we have to do is there is this tipping point, he didn't call it that way, and if you bring the mosquitoes below some level, then that would really make a huge difference, and they didn't believe him, so then he writes on mathematical equations and then they believe him, okay? So that's the power of mathematics, so probably a good scientist had a good idea of what had to happen, and then he does, and he writes these deterministic equations where the terms actually make sense, which is different from the statistics. So you see, for example, that M over N is the host vector ratio, which should be important, right? You have a trillion mosquitoes per person, you are more likely to get beaten, that you have only five, okay? So this is information that we have there, and then he talks about probably the most important process that taken science and is to differentiate when you go from no growth to growth, and of course then the most important function of mathematics is the exponential function, and what does exponential function mean? It means that you have a pattern of growth, or in terms of processes, for example, of infection, that means that if I infect more than one person in this room before I leave, and I just travel from Providence, then I will have generated an epidemic, but if I infect only half a person, then that won't happen, right? So that's the general idea, that's the basic reproductive number, so if it is greater than one for mosquitoes and for humans, then the mosquitoes will generate secondary cases on the mosquitoes via human, and the human will generate secondary cases on the humans via the mosquitoes. So that's the general idea, and just to, and essentially these ideas were used by Sir Ronald Ross, and I think it's important to analyze why was his holistic perspective. This is, it is interested in the public good, after he made these scientific discoveries, can malaria be controlled at various levels of organization? And this represents a challenge of scales, he understands how the transmission process takes from human to vectors and vice versa, how can you use that information to understand the patterns of spread of malaria at a high level of organizations? Do I have to incorporate every bite of every mosquito on every person, or do I use less information to do that? The mathematics help, yes, identifying thresholds, right? Also the prestige of mathematics play a role here. And finally, can we use these models to study other phenomena? Does the abstraction of mathematics, can mathematics be useful to address other types of problems? And of course, that's the case. And in order to, to, to explain you what they did, I'll use the simplest possible model, which now I'm happy because that's not taught also, and sometimes in calculus courses, certainly in differential equations courses. And this is the simple model of epidemics, which is the SIR model susceptible to infected and recovered. And in this case, we have three classes susceptible to people that don't have the disease. Then you have infected individuals. And they come into infections because they interact with infected humans. Here in this model, they interact at random. This is a simplified model. And then eventually they recover after some time the infection doesn't last a lifetime. So this could be a case of one outbreak of influenza. This case, there is no births and deaths. So this time scale is short. So you see how all the elements associated with what is mathematics are used for are clearly delineated when you postulate a model, because you have to be very precise and clear about the assumptions that you make. And then you write those differential equations. And the only nonlinearity here is S I over N, which is that the susceptibles, you know, might be infected depending on the proportion of susceptibles of infected individuals, which is I over N. And then you make some magic. You say, what happens at the beginning when almost nobody has the infection when S is equal to N? So you cancel the S and the N. In applied mathematics, you can do everything. And then you write this equation, D I D T is beta I minus gamma I. And then bingo, that's the most important differential equation that you have. The only one that you need to know how to solve. And then the solution is the exponential function. And you see beta I minus gamma is greater than zero. You have exponential growth or the beta divided by gamma is greater than one. You have exponential growth. And that's what is called precisely the basic reproductive number. So essentially beta is the transmission rate and one over gamma is the time that you are infected, the window of opportunity to you to pass the disease. And if that's greater than one, then you get exponential growth. And you have an epidemic. So this is basic. This is what happens almost any physical phenomena. For example, what is the transition point from boiling water to steam from ice water to regular water? I mean, these are transition points that take place. And there is a tipping point there. And in these cases, when you go from not growth or for an exponential decay to not growth and then to exponential growth. It has been used to study gonorrhea, for example. And some of the way gonorrhea gets treated today is the work of Herbert Headcott, which applied mathematician, Kenneth Cook, which played both teams. And James York, which is a person that introduced the word chaos, a very personal and dynamical systems. And the changes that they made about gonorrhea had transformed the way that we treat gonorrhea. And then you have people like Ed Kaplan at Yale, which also used these ideas of roles to study the dynamics of the needles, to study needle exchange programs on HIV, the needles were the vectors, the humans were the humans. And then there are needle exchange programs. So there is dynamic in the needle, there is dynamic on the humans. And he studied this to figure out if needle exchange programs actually work and reduce in HIV. All these ideas generated by the work of Ross. Now there is epidemics in complex communities. And we will talk about the case of Episemes. This is Sara Del Valle. She participated in my summer program. And I will talk briefly about that afterwards. And she came with me when she was a graduate student. She was at Iowa. She had worked in my program. And he says, I know you're going to be Ulaanba Scholar and Osalamus. Can I come with you? And I said, sure. In fact, one of the practices that I make every time I visit some place, I take students. I don't go to spend a considerable amount of time at a place without taking the students. So at Brown I have right now one grad student and two postdocs in residence and I bring in two more. And then including two U.S. Latinas that are coming to the program. It's very important. I was at MIT and I took again three U.S. Latinas to that, including Camila Young-Quest as a postdoc that visited when we was at MIT. And so forth I was at SAMHC and again we took six or seven graduate students. So this is very important. And let me tell you, they changed the dynamics of the place. They changed the dynamics of the interactions and they changed also the understanding of what underrepresented groups can do. So Sharad El-Bagi got involved in a study that was created before. It was a PCIMS, which is like SIMS series. Creating this series in this case was to reorganize series so that they could save energy. But now they also used to study epidemics. And the example that I have here is has been highly developed by, particularly by Steve Eubank. And they involved a million and a half people running around 180,000 buildings and then tried to understand how these parts of movement might affect the part of the spread over a single day. This is important because unless you are in a college campus, at midnight most people are at home sleeping so there is not much movement and afterwards the movement starts to stack. So you don't have a fixed network, you don't have a scale free network, you don't have any of those networks, you have a real network and that network changes over time. So this is an example of, I guess Alicia commented to the conference before there was sunlight and everything else to be sure that everything was going to work out. And then we studied all those parts, we started by activity, we started by social activities and we study all these kinds of networks, they are dynamic networks, they don't scale free networks, they change over time and so forth. So we published a paper by that and also Steve Eubank has applied this to the study of epidemics and behavior in the left. You have an epidemic of influenza where everybody continues to say hi to each other, give Biden kisses, whatever they have to do to go on online, on the other side they say no there's an influenza epidemic, this is the strong arm of Pelosi that says I have a call, I just read that today, did you expect that? And then you see that you have more cases where people are friendly, less cases where people are not friendly. So this is the best, so this is the best case against friendliness. Okay, but you see the epidemic curve is just a typical curve, it's a very complex of interactions but the epidemic curve is very simple, it will use simple statistical analysis and fit curve, we can do a perfect fit, but use a simple model, it doesn't tell us anything unless we interact the complex patterns of spread and what are the critical points of this network. So we have to be careful also about that, so making use of a whole lot of data and not just the aggregated patterns is very, very critical and that science has played a role on that. Here is the same epidemics, but a study over the whole United States, I believe 300 million people were moving around and again people have studied these patterns of spread and understood essentially. So you can imagine the amount of data that you have, how do you sample this amount of data to do some statistical approach to have some understanding of what's going on, what are the most important places of transmission and so forth and you know, so this requires new algorithms, new ways of thinking, new ways of doing science. Okay, so let me go back to the tipping point and the tipping point is according to Merriam-Webster dictionary, which I have never seen, but I saw it on the Mr. Google, the critical point in a situation, process or system beyond which a significant and often unstoppable effect or chain takes place. That's one definition. Mr. Google says the point at which a series of small changes or incidents becomes significant enough to cause a larger more important change. All right, Malcolm Gladwell became famous for this. It's a Canadian journalist that writes beautiful, he doesn't quite understand no linear process, but he changed, he changed, I think he had a tremendous positive impact by talking about tipping point, but the tipping point is that magic moment when an idea, trend or social behavior, that one sounds like a political speech, right, crosses a threshold, tips and express like wildfire. Just as a single sick person can start a flu epidemic, so too can small, but precisely targeted, precisely that's the key part, right, push, cause a fashion trend, the popularity of a new product or a dropping crime. So this is and he has made millions of understanding exponential growth. So guys, this is your chance. Okay, and now that's used everywhere, right, at tipping point in education, at tipping point this, at tipping point that now has become now part of the common and essentially the question is why high school students can't quite understand exponential growth, because probably they don't use these ideas to explain exponential growth. They probably just write the question and digraph and things like that. So this is an area. Now what happens in an epidemic, see, so what you have is, in this case, tipping point is being beyond one, initially you have exponential growth, eventually you start running out of people to infect, so it saturates and you have a limit, and this is the curve. And if you are below the tipping point, then nothing takes off. So this is the typical epidemic pattern that you see, it's called a transcritical bifurcation. What happens when you have social processes, like drug addiction, etc., and some complicated transmission processes when you have multiple modes of transmission in the spread of diseases. You don't get that. You don't get this standard. Certainly you are above one, you are always going to get an outbreak. Certainly. In this case, the outbreak is actually a lot faster than exponential. But what you see here is in that wide, wide region, that if you have enough people that arrive there, that are infected, they can generate growth even below the tipping point. In addition, most of the practices that people use to control the diseases is to bring, right, is to bring the process from exponential growth to exponential decay. It's not even the process so that the parameters that operate in the process now operate below exponential growth. But we see, in this case, that that's not possible unless you go well beyond the wide line. So controlling a disease, controlling any kind of behavior becomes a lot more complicated. That's why social processes like drug addiction or others, they are resilient communities that are very difficult to change, right, because they get structured in such a way that the process of conversion is continuous at all times. There are many, many layers that we operate, many non-linear times that operate that generate these kinds of curves. I'm going to use this to talk a little bit about meritocracy. And meritocracy and social justice is important. See, the promises of our democracy cannot be fulfilled selectively. Therefore, a social justice educational model that does not account for the following factors, is not a social justice model. Initial conditions, family background, quality of school, access and resources. And you can see the recent scandal with people buying themselves into colleges makes this incredibly evident, right? Yet many people talk about, tell people that we actually do live in meritocracy. A model that does not eliminate the deleterious impact of preconceived notions of ability and talent that are pretty disempowered those with a history of exclusion. A model that asks us to wait until care through education is perfect. Of course, they don't have the children in those schools. And it must be put out of commission as no family, white, yellow, brown, or blue, I forgot green, can possibly have said the sacrifice of a single generation delays in access are simply unacceptable. A system where inequality is pervasive cannot be called meritocracy. And I think this is very important that this gets stressed over and over and over. And I think if this recent scandal tells us and in addition to all the legacy admissions, it just proves conclusively, conclusively that we live in any kind of model except a meritocracy. True, there are some schools that are doing a marvelous job but that's not the rule. That's the exception. So I'm going to tell you a model that or how we should do this and hopefully we can apply to this. These models can also be used to create communities of mentor people, resilient people. This is about mentorship. So at one point I call this the Richard Tapia model. Okay, we can call it any way you want today. And essentially, we have susceptibles. So that's people that don't understand the importance and value of studying mathematical epidemiology, right? So we put in a community that they talk about this all day. And there are some people that are key, they semi-convinced the people say, yeah, epidemiology is cool. But sometimes they say, well, maybe not so. But they have some impact on you. And you have the brainwash. Okay, the people that say, no, this is absolutely. But if you live in a community that interacts like that, right, you have second order effects, second two modes of transmission. And if you do that, right, do you get a situation where conversions are generated by a typical mentor obeying the basic model? If R0 is greater than one, you have a mentor community. Otherwise not. We get that. And you can see in this case, these believers, these exes. And the answer is no, you get this. You get this. You get faster growth. You get a community. And you get a community that there is very difficult to destroy. This is the this is the power of collaborative learning. This is the power of having communities that interact. This is the power of clearing opportunities for global communication and learning. This is the power of these communities. And this is what we have developed on the Mathematical and Theoretical Biology Institute. They started in 1966, 1996, where essentially we have a model, but we have a common language. Students select the questions so that we don't have the answers. We cannot look at the back of the book. So students realize very quickly that they are smarter than most, not all of the faculty, and that that's not too hard to accomplish. And then they realize that when we are put in a situation where we don't know what to do, we could be called all sorts of things that we should not be called because we should be respectful, but that often takes place in the classroom when they want to discourage people about the ability to learn something. But that happens there. And we have done this. And out of that, the first paper of women asked this question about bulimia. They published the first paper on the dynamics of bulimia in 2003. They have, and they even made a model of this, this resilient community right talk, that was appeared in discrete and continuous dynamical systems B. And there is a lot of proof that in fact that's what we create. So for the ones that think that this is just a nonsense actually, there is mathematical proofs that talk about that. We have written lots of articles about that, more about writing about that. I think that there is a volume in a book where we wrote also something about that. This is the first group of students that participated. And what you see is a lot of people, for example, in the bottom you see Erika Camacho, the first student admitted to the theoretical, to mathematical and theoretical biology institute. Now she's my colleague and she just won a Paesmana Award. You see the late George Casella sitting in the first row. One of the big drivers of Bayesian statistics, which is critical to the study of data science. And you see many others. A lot of those people that are there are mathematicians that now have positions on the right side, Jorge Velázquez Hernandez, who was my post doc and later on, the first biologist to become the president of the Association of Mathematics in Mexico. They must not have enough mathematicians. So rightly so they chose a biologist, right? And so forth. Anyway, this is the, when I went to Los Alamos, I took all these students and all of them have tremendous career. They have Erika Camacho. She was my post doc for some time then. She's now, as I said, Paesmana Award winner. She's Daniel Professor Ariel Sintron. He's Associate Professor of Eastern Tennessee University. Gerardo Chaval is the chair of Epidemiology at Georgia State. Steve Wilkos is my colleague at Arizona State. Fabio Sanchez likes to travel. He's, so he's a Daniel Professor at Costa Rica. Miriam Nuno, Daniel Professor at UC Davis. Karen Rios-Osto, Full Professor at University of Puerto Rico and Macau. David Murillo, I think he's now is VP with American Express. So here are some. This is Sara Del Valle. I talk about this. Kevin Flores, Professor at North Carolina State of Individualized Medicine. Johnny Guzman. He's a Daniel Professor at Brown. Maybe that's what they invited me, okay? It helps to have good students, right? And then you have Brisa Sanchez, University of Texas El Paso, Full Professor at Michigan. Now she has a Center at Drexel University that she just started. Here is again Miriam Nuno. She's a Daniel Professor at UC Davis. And she crossed the U.S. Mexico Desert at age 15, right? And her contributions to our community and our society have been immense, immense. You have Daniel Romero. I met him when he was chief manager at Wendy's at age 19. I asked him, how much do you pay? I pay you the same and you become a full-time student of math. It took me 10 minutes to figure a guy that this was good in math. 10 minutes. No SAT, no ACT, nothing to me. And now he's a Professor. He began to just let a diverse student in Arizona State. And he wanted to study with me. And I said, no. And he asked me, aren't you good enough, Carlos? And I said, you are correct. I'm not good enough. You have to go to... You have to really get out of Arizona and try another one. So he... So we made an agreement. You try several universities. If you like one, you stay there. You know, I'll sacrifice myself and take a really good student. Eventually, he went to Cornell where he graduated. Now he's Assistant Professor at the University of Michigan. Emilia Huerta Sanchez, the woman that wrote the paper of Bulimia. Now she's my colleague at Brown. Another reason why I was invited. Now I have two votes. Okay. And then Gerardo Chaguel. He is now again Chair of Epidemiology at Georgia State, Karen Riosoto, which she was about to get married in Puerto Rico. And her husband to be said, you can leave Puerto Rico. And she said goodbye. Now she has a beautiful family. And you have Ryan Hernandez. He was at UC San Francisco. Now he took a position on McGill. So we're in bed in Canada. And then Daniel Riosdoria. He always wanted to go in business. He wanted to be at Disney. He is there. Another Peruvian, Carlos Torres. He is now Vice President of JP Morgan. He picked me up with a $200,000 card the other day. Indirect effects. We have managed to establish the Blackwell Tapia Award that has been done. All these winners we have in some sense facilitated the knowledge of the great people that our communities have created like David Blackwell and Richard Tapia. We have won awards and we have written lots of books. And thank you.