I request Founder President of Symbiosis and Chancellor of Symbiosis International University, Professor Dr. S.B. Muzumdar to kindly felicitate our Honorable Prime Minister, Srinarendra Modi ji, Professor Dr. S.B. Muzumdar, Founder President of Symbiosis and Chancellor of Symbiosis International University to kindly address the gathering. An iconic visionary 86 years young who has dedicated his entire life to the motto of Vasudev Kutumbakam, the world is one family. Srinarendra Modi ji, Honorable Prime Minister of India, Bhagat Singh Kosheri, Honorable Governor of Maharashtra, Subhash Desai, Honorable Minister of Industry, Government of Maharashtra, Devendra Ferdinandji, Leader of Opposition and a great well-wisher of Symbiosis, our Vaishyanjala Rajni Gupta, Professors, Directors, Industrialists, Council Generals who have come here and those 5000 students who have gathered specially here to see you sir and listen to you. Where I come from a small town called Harali-Buddhru in Kolhapur district, this population is just 2000 and many of them have come all the way from Harali-Buddhru just to see you and listen to you that is your popularity in rural India. It was perhaps a divine design that the Prime Minister of the country, Srinarendra Modi ji would physically bless the Golden Jubilee Celebrations of Symbiosis. Sir, you are the Prime Minister of a country where there is the largest democracy where rugviz and upanishads, Ravayan and Mahabharat were crafted, where sacred Ganga flows, where world is regarded as one family, where Buddha and Mahatma Gandhi trod and where truth triumphs. Prime Minister Srinarendra Modi ji who is loved, respected and honored all over the world has made Symbiosis campus historic and sacred by very presence. Sir, this is the historic moment to all of us and the moment of fulfillment of my life. I bow my head, I repeat I bow my head with respect and reverence for sparing your time and bless Symbiosis giving paripurthi, paripurthi to my life. Sir, more than an institution, Symbiosis is an idea. It evokes coexistence and interdependence. 50 years ago the idea germinated in my mind to promote friendship and understanding between foreign and Indian students and thereby promote international understanding. Initially a cultural center that was started in a small room in my house at Furbishan College campus eventually flowered into international university. Its motto has been Vasudraya Kutumbakam and foreign and Indian students, foreign students from 85 countries and students from almost all states of India are provided quality education. Symbiosis has also started skill universities in Indore and Pune. Symbiosis Dr. Babasar Ambedkar Museum and Memorial is recognized as one of the prominent museums of her country. Today we are celebrating golden jubilee of this golden idea. Sir, every organization has its well wishes and aapka jo slogan nahin na sir, sabka saad, sabka vikas equally applicable to organizations like Symbiosis. And therefore I acknowledge the cooperation of important individuals like then chief minister VP Naik, then education minister Madhukura Chaudhary, industrialist Yathur Sanctani and the founder members, principal S. D. Patil, James Ramlal, A. S. Andhikar, Dr. S. Stigare, Dr. S. K. Bhosle and of course my wife Sanjeevadeva. Sir, you will be inaugurated, you will be inaugurating Symbiosis Aarogidham. This university is health promoting university and Aarogidham is situated in proud place. Sir, having spent over 60 years in higher education, I take liberty to make few comments regarding medical education system in our country. Indian doctors are world class and second to none. They have magic in their fingers. India needs more doctors. But we have made medical education costly, lengthy and difficult. No wonder thousands of eligible students who are not selected in need go abroad to countries where medical education is affordable and admissions is easier. Is there a solution to the problem? Yes, provided authorities have willing to change their mindsets. National Medical Commission should evolve the age old practice of family medical family doctor and prepare a four year course which is a short course for our students. And this course should also be available to nurses by giving them a short course. Sir, for the first time in history you have made very remarkable and significant reforms in education, the ranking of university golden. Sir, for the first time in the history of education, ranking of university related autonomy to good university and path breaking national education policy. In 1897 Swami Vivekananda predicted that 21st century will be India century and India will be Jagatguru. I feel that his prediction will come through only innovative education. We should now turn to the rich heritage of ancient Indian knowledge system. We should have fusion of eastern wisdom and western dynamism. We, the Vasudeva Kutumbakam is the USP of India. We should imaginatively incorporate it in all levels of education. Our education should produce global citizen Vishwamanao. It will be the main endeavour of Symbiosis to realize the concept of Vasudeva Kutumbakam through education. Modi ji, I am now 87. I am sitting in the departure lounge of airport waiting for my flight. I do not know the timing. One thing is certain, my soul will hover over Symbiosis forever. My only prayer to God is, my only prayer to God is, my only prayer to God is, I will be reborn as a teacher to shape the destiny of students. Jai Hind, Jai Maharaj, Jai Jagat. I request the Prime Minister of India to present his Symbiosis Aarugya Dham to us. A momentous occasion as we celebrate 50 golden years of the illustrious educational journey of Symbiosis. The establishment of the Symbiosis Aarugya Dham during this golden year is indeed a very proud moment for the entire Symbiosis family. Keep the applause going please. World renowned multicultural, multilingual and multidisciplinary educational institution with a vibrant history. Symbiosis has consistently set new benchmarks in its three avatars of culture, education and health. Symbiosis truly embodies honourable Prime Minister Shrinarendra Modi's transformative vision, manifest in the country's national education policy that aims to create global citizens with Indian values, which has also been the focus of Symbiosis throughout its illustrious journey of 50 years. Inspired by the vision of our honourable Prime Minister and the untiring efforts of Dr. S. B. Mujandar, Symbiosis International University has established Symbiosis Aarugya Dham over a sprawling 70-acre campus at Loveley, announced to the world by the magnificent Symbiosis Swarna Mahotsav Dwar and ushering in a new era of holistic and integrative medicine. Symbiosis Medical College for Women, the first residential medical college for women in Maharashtra and the Symbiosis University Hospital and Research Centre are dedicated to serving humanity, especially marginalised communities in line with the motto of Ayushman Bharat. Symbiosis Aarugya Dham houses institutions dedicated to diverse disciplines such as health sciences, biological sciences, nursing, health skills, sports sciences, emotional well-being, yoga and specialised research. Symbiosis Aarugya Dham strives to provide affordable, available and accessible medical and healthcare services. The various pathies such as allopathy, homeopathy, naturopathy, yoga, ayurveda and other alternative medicines have been brought under one umbrella at Symbiosis Aarugya Dham. To take healthcare to people's doorsteps, Symbiosis International University has now commissioned a new mobile medical unit to serve as many as 23 villages in the Mulsi block, providing impetus to rural health literacy and primary healthcare. Inspired by Honourable Prime Minister Srinarendra Modi's Pradhan Mantri Grameen Digital Saksharta Abhiyan, Symbiosis International University has conceptualised and created a rural digital literacy lab to enable rural communities to unlock the power of the internet to improve their daily lives. The identity of Symbiosis International University has acquired many hues and dimensions over the decades. But the world was, is and will always be its family. Vasudhaiva Putumbhakram Mr. Sai Ji, East University's Founder-President, Professor S. B. Majumdar Ji, Principal Director, Dr. Vidya E. Rautkekar Ji, Dr. Vidya E. Rautkekar Ji, Principal Director, Dr. Vidya E. Rautkekar Symbiosis has reached its golden jubilee. How many people are involved in this journey? There is a common destiny of many people. The students who studied here adopted the vision and values of Symbiosis and recognized Symbiosis through their success. Symbiosis is the greatest contribution in this journey. I have received the opportunity to congratulate all the professors, all the students and all the alumni on this golden moment of the R.O.Gyadham Complex. For this new beginning, I wish to congratulate the entire Symbiosis family. You are a part of such an institute that is based on the idea of Vasudhaiva Putumbhakram. Symbiosis is a university where there are different courses on Vasudhaiva Putumbhakram. This is our tradition, our culture, our culture. I am happy that this tradition is still alive in our country. I have been told that in the last Symbiosis, more than 44,000 students of 85 countries study here. They share their culture, that is, the ancient heritage of India is moving forward even today. Friends, today this institution is representing the generation in front of which there are infinite opportunities. Today, our country is among the largest economies in the world. The third largest hub of the world is the start-up ecosystem in our country. Start-up India, stand-up India, make-in India and the mission of the Atmanirbhar Bharat are representing your aspirations. Today's India is innovating, improving and influencing the whole world. People living in Pune know very well that India has shown its strength in front of the whole world with the coronavirus vaccine. Now, you are also seeing the time of the Ukraine crisis, how the operation is going on and India is taking its citizens out of the war zone safely. There are many problems in the world's major countries. But, the impact of India is that we have brought thousands of weapons back to our country. Friends, your generation is lucky that it did not have to face the first defensive and dependent psychological damage. But, if this increase has come in the country, then the first credit of it goes to all of you, to our youth, to our youth. Now, as you can see, in the sectors in which the country was not even thinking about moving forward on its own feet. In those sectors, India is now on the path to becoming a global leader. For example, we have a mobile manufacturing example. A few years ago, we had a mobile manufacturing example and we did not know how many electronics we had. We had only one meaning, import it. In the world, there is a market, import it from anywhere. In the defense sector, we had been accepting that we can do something with the trust of the other country. But today, the situation has also changed, but the situation has also changed. In mobile manufacturing, India is the second largest country in the world. Seven years ago, India had only two mobile manufacturing companies. Today, more than 200 manufacturing units lie in this work. In the defense sector, India is the world's largest importer country. Today, the defense sector is becoming an exporter. Today, two big defense corridors are being built in the country, where they will become the largest manufacturing company. They will fulfill the needs of the country. Friends, in the next 75 years, we are moving forward with the new goals of a new India. Our young generation has to do the same. Today, from the software industry to the health sector, from AI and AR to automobile and EV, from quantum computing to machine learning, new models are being built in every field. In the country, geospatial systems, from drones to semiconductors, and from space technology, reforms are taking place. These reforms are not to be recorded by the government. These reforms have come with an opportunity for you. And I can say that these reforms are for you and for the young generation. Whether you are in the technical field, management field or medical field, I believe that all these opportunities are being created for you. The government in the country believes in the surrender of the youth of the country. That is why we are waiting for you in different sectors. Take advantage of these opportunities. Do not wait. You start your start-ups. The challenges of the country, the local problems, should be solved by the universities, or the minds of the young generation. Always remember that you are in a field where you set goals for your career. Similarly, you should have goals for the country. If you are in the technical field, then how can your innovations and your work be useful to the country? Can you develop such a product that will help the farmers of the village? Can students help in remote areas? Similarly, if you are in the medical field, then how can our health infrastructure be strengthened? How can quality health services be available in the villages? You can plan a new start-up together with tech friends. Similarly, the region where the symposium has started can be useful as a model for the whole country. When I am talking about health, I will also tell you that you should take care of your fitness as well. You are laughing a lot. Not now. You are joking. You are laughing a lot. And take the country to a new level. When our goals increase from personal growth to a national growth, then in the national level, the sense of belonging increases. Friends, when you are celebrating your 50th birthday at your university, then I would like to request the Symbiosis family and not just the people sitting here, I would also like to request you. Can we develop a tradition in Symbiosis that every year, a theme is dedicated to it? And whoever is here, in any field, they should be dedicated to their work for a year for a theme, that should be dedicated to it. If you agree with me now, that when you are building a Golden Jubilee, then in the next 5 years, in the next 5 years, what will be the theme of 2022? What will be the theme of 2023? What will be the theme of 2027? Can we still make a decision? And as I am telling you in one theme, it is not necessary that we should go on this theme. We should make our own decisions. But think about it. Let's take a global warming issue. Our family came to Pugra in 2022. We should focus on every aspect of global warming. We should do research on it. We should do seminars on it. We should make cartoons on it. We should write poems on it. We should write poems on it. We should make some equipment on it. That is, while doing everything else, we should take a unique job. We should take a theme. We should wake up people too. In the same way, what is our coastal area today, or we can work on the impact of climate change on the ocean. Such a theme can be that our border is for today's development. What is our last village, which is protected by our border, with the army, and with the help of the army, is still alive and alive. In a way, the generation after generation is the protection of our country. That we are in the family of the university. What can be the plan for our border development? For this, students of the university should tour that area. They should understand the problems there. They should come here and sit and chat. They should find solutions. Your university, in order to strengthen the feeling of India, the dream of Vasudev Kuttum Kambi is also there. When India is the dreamer of India. The university, in one area, and in the other, can learn a lot of languages. It will be better. You can keep in mind that when Simbarshi's language will come out of here, then in Marathi, five different languages of India, at least 100 languages, 100 words, will be remembered for sure. And in life, its use will be destroyed. The history of our independence, is so strong. You can do digital work on any aspect of this history. In the youth of the country, like the NSS, like the NCC, we can increase the number of people. This can also help the entire family. For example, water security, agriculture, technology, soil health testing, food products, storage, and natural farming. You have research, to increase awareness. There are a lot of topics. What will be the topic? I will leave it to you. But I will definitely say that the needs of the country, the solutions to the problems of the country, you choose your own issues so that we, all the young people, all the young minds, have such a big infrastructure, we give solutions to the country. And I am giving you a guarantee that you share your suggestions and experiences with the government. After working on these themes, you can send your research, your results, your ideas, your suggestions, to the Prime Minister. I am sure that when the professors here, the faculty here, the students here, will be a part of this discussion, then there will be great results. Now imagine, today you are celebrating for 50 years, when you celebrate for 75 years, and for 25 years for the country, on the 25th theme, 50,000 or 50,000 minds have worked, you will give such a big support to the country. And I understand that it will be of great benefit to the Symbiosis students. Finally, I would like to say one more thing to the students of Symbiosis. Staying in this country, you will have learned a lot from your professors, teachers, and friends. I suggest you that self-awareness, innovation and risk-breaking ability are always made strong. I hope that all of you will move forward in your life and I also believe that for 50 years you will have such an experience that you have. While doing many experiments you have reached here. You have a treasure. This treasure will also help the country.  This is my good news for you. Once again, I would like to thank you that I get many opportunities to come here. But I cannot come here. I am sure that I will get many opportunities to come here. I am very grateful to all of you for giving me the opportunity to be a part of this new generation. Thank you very much. Thank you very much. Thank you very much. Thank you very much. Thank you very much. Thank you very much.


Thank you, thank you, Mercedes, and thank you, all of you, all the organizers, Jacopo, Mateo, Silvia, for this nice and interesting workshop, because all the, all the talks are going, are being excellent. And we are learning a lot of limits of diversity in ecological communities. It's a pleasure for me being invited for you. Today I'm going to talk about how can theory explain- Jose, sorry to interrupt you. We are seeing the presenter view. Can you put it into the- Jose, how do you call it? Yeah, I know, I know. So it's kind of, sorry. Maybe if you just share your screen and then you just put it in the mode, the presentation mode. That's better. Yeah, that's better, sorry. Okay, fantastic. Sorry. But I was saying, yeah, the purpose of my talk is going to be kind of investigating a little bit of how can theory tell something about the limits of diversity in ecological communities. We have some theoretical predictions and a simplified assumption. This is kind of related to the ideas that guy put forward in his talk before. Can we make some simplifications in our models to get some hint of how diversity can be predicted under some certain settings? Well, this is kind of the first slide I used to introduce the topic as species diversity is huge. There are a lot of species reported around the world and it is assumed that 80% of the species are still undiscovered. So this huge amount of diversity needs a well-grounded theoretical explanation. This is puzzling because what theory tells us about diversity is just the opposite. All of you know this complexity stability trade off which was put forward by Robert Mayne in 1972 when he challenged the view that ecological communities are diverse, which is puzzling because we observe that ecological communities are really diverse. We have two Jacobian metrics of a locable terradynamics distributed with random interactions with a given variance and some sort of connections which tells you the linkage density and showed that using elementary random matrix theory that there is an upper bound on the diversity that the ecological community can accommodate. Our intention in doing the work that I'm going to present is try to find an explanation of why do we see this overwhelming diversity in ecological communities and what are the limits that these theoretical models can set to the number of species that we observe. Until like 10 years or 10 years before, the idea of studying stability in ecological communities was just considering the whole set of species as coexisting together. And there were a lot of studies studying the stability and the feasibility of the equilibrium points of a given dynamics, but considering the whole set of species as the assembled community. As you can imagine, the probability that this whole set of species, the pool for example, is feasible, is really negligible. So in this talk, I'm trying to change the perspective which is kind of something that has been commented in the talks before. Here I'm going to change the perspective in the sense that the species that survive that we observe in local communities are basically a selected portion of the species pool, which actually has been proved by a certain population dynamics. So the question that I'm going to try to answer in my talk is whether we can predict the distribution of the number of species that survive when we assemble the community from a pool of species that in principle interact randomly. I'm not going to make any assumption of how the interactions are, whether they are safe, whether they show patterns, we take this simplified and new model perspective that guy was commented in his talk. And yeah, this is, I'm interested in predicting the distribution of the number of species in the in the minimal setting that one can imagine. So we are going to talk about top down species assembly here, I'm going to put those pieces together and let the dynamics unfold. And I will analyze, I will discuss here to two examples. One, when the interactions are basically random, and then when you consider phylogenies to generate the interactions. So if you have questions up to this point, I cannot see the chat at this moment. Sorry. No questions for now I will let you know Jose. Fantastic method. Thank you. The first part of the of the talk is what we call the random soup problem, which is work done in collaboration with Carlos, Sir van. And Stefano Alessina from the University of Chicago. Also, Jacopo really is was a key part of this of this collaboration in when I when I was visiting the University of Chicago in 2017. Also Ken Morrison collaborated. I give you here the reference if you are interested. So the way we do we call this the random shoe problem. Well, consider the following thought experiment. Consider that you can you take a large shoe. And at some point you open all the cages. If we were to come back after like 10 years, 20 years, can we predict how many species will still coexist in the soup. In other way, this will be kind of the outcome of when at some point Noah opens his arc after after what you know the you know the story right so this is the idea. And we are considering we put this metaphor in this time because we are considered and basically random interactions. So the practical setting of the problem is that we take a basically lockable terraria dynamics with variability in principle in growth rates. Also by variability in random interest and I don't see, I don't know whether you can see my pointer. Yeah. Fantastic. And this will be the general setting. So how can we compute the average number of species that one expect to observe after the community has reached to an equilibrium. Well, we for for doing that. We have to make some assumptions. Our strong assumption is this Lyapunov diagonal stability. We assume a piece it has some of this kind of related to to the talk of the dog by guy because well we are here we're considering that the dynamics has only just one single attractor. This can be achieved by assuming that our interaction matrix. The definition of interaction of the lockable terraria dynamics is such that there exists a diagonal matrix D does such that this combination is definite negative definite right in this case. And this is not so strong because you can always satisfy this condition by letting this self regulation terms being large enough, right. Okay, if this condition is satisfied is a theorem by our own segment that it guarantees you that for every vector of rates there is a single globally stable stable equilibrium point of the dynamics. So we are in a setting that that we can characterize if we study the properties of this single equilibrium point we can characterize the the ecological community. That is totally right. So, this, this is the characteristics of the of this equilibrium point that this is, it is not invisible by the remaining in minus kind of species, right. I mean if you if you if only K species survive in the community the other species in the pool cannot invade the the equilibrium this these two conditions the feasibility of the equilibrium and then no non impossibility of the equilibrium to understand the, the size of the attractor and the distribution of the pieces that survive and which is basically what I'm interested in. So, here I mentioned this this paper by by Carlos and Stefano, where I, although I'm interested in top down assembly process by just putting all the pieces together. In this case, it is easy to see that the sequential assemble community will be would be the same. But there are many conditions in this paper I recommended you to look at to look at it that give you necessary and sufficient conditions in which top down and bottom up assembly are the same. So, our setting is interaction matrix are basically a diagonal metric matrix mean term and random part right which has kind of mean zero and vector rates are have this mean and kind of a variability. So, to characterize this saturated fixes fixed point, we just need to impose the two conditions that define the, the, the saturated point which is basically the feasibility and the non impossibility feasibility is basically that the, if we order the the the species. The one that survived here in the, in the, in the first place, the feasibility condition is basically that this sub matrix times this vector plus the vectors of rates is equal to zero so they satisfy the equilibrium condition for the non impossibility the species rates has shouldn't grow when rare when rare. So this translates in this sub matrix times this green vector plus the remaining part of the vector of rates is equal to a vector that is negative so species. The remaining species in the pool cannot invade. I'm going to speak about two cases. The first case with this within this random two problem is the case of mean zero. In this case we can calculate with very simple symmetry arguments, the distribution of the pieces that that survive. We can consider arbitrary run interactions with mean zero and arbitrary growth rates also with with means you in this case, the distribution of the species that survive is basically a binomial with probability one half. What is this? Well, first you can analyze feasibility, the feasibility properties kind of intuitive right because which is the probability that out of then you can get in a species surviving right. This is basically one over two to the end. This is kind of intuitive which is the probability that all species relay in this in this in this quadrant if I if I take this one randomly well you have basically to solve a system of two equations a linear system of two equations with two unknowns and the probability of laying in these in this quadrant is kind of intuitive to be one half or one over four right. So you can you can prove that the probability of feasibility is one over two to the end. In this case of mean zero. Similarly, by a symmetry argument you can also calculate that the probability of this equilibrium point to be is not is feasible. What is feasible is basically this, this, this probability, the probability that n minus case species cannot invade condition that case survive times the probability that these cave species are feasible. This conditional probability is basically equal to one over two to the n minus k because any sign pattern for this vector is equally likely. It is simple to see that. So multiplying this this result to the with the times the the the other the other result you get that the probability is one over two to the n times the combinatorial factor because species can can be arranged can be sorted. In this number of combinations, right. So basically we get the binomial the binomial distribution in the case of mean zero, which is kind of unrealistic from the ecological point of view. Can we say something about the case of non zero mean. Well, in this case we we just choose. We just chose the, the simplest scenario where we were able to do the calculation up to the end, which was basically considering that species rates are normally distributed. We include a randomness in growth rates, right, but we switch off the random part in the interactions, right, so we cannot consider random interactions and allow variability for growth rates. I'm not going to give to give all the all the details but we can see as in the means in our case we can calculate here the distribution of species that that survive. We have to give a hint of how the calculation proceeds basically you just take the probability distribution of the of the rates which is basically a product of product of gaze and gaussians. See, you just only have to perform this change of variables, right, change the airs into the X and into the C into the vector C, right. If you do this change of variable which is very simple then you only have to compute the probability that that this vector X has all is components positive, and this vector C has all is terms. Which is basically this, this, this thing, right. Yeah. I think we have some raised hand. Can you take the question. I was fixated on a little detail might have missed the part of what you were saying but are you a priori assuming global stability and just imposing some kind of sign structure. No, no, no, no, no, no, no, I am assuming a global stability, right. This is this is something I'm assuming in the in the dynamics, I'm assuming that matrix a satisfied this condition the X is this diagonal matrix that this combination is definitely negative, but negative definite but what I was saying about this design combination is that all the sign combinations for this vector for the C vector and the X vector are equally likely. Right, you can if you think a little bit about it, about that you do realize that all the sign combinations are equally likely. Right. So this gives you a one half times a probability of one half raised to the, to the number of elements that you have or them to the number of entries that your vector has. Okay. So then we don't necessarily know what the interaction structure looks like we're just keeping it arbitrary or just do you mean any distribution only with the with the restriction that the mini zero, basically, right. And that, and that, I mean, but how do we know that implies the global stability, other than I mean of course that condition the diagonality. You, you can, you can do some to some extent in incorporate diagonal stability by just setting the self regulation large enough in order to get this, this, this, the stability, right. Okay, so you can you can send some of the plug in into the into the dynamics. Okay. Thank you. So, yeah. So after doing this calculation which is one kind of conversion calculation, you can get an analytical prediction of the mode of the distribution. Okay. So the, which is basically related this by this by this equation to model parameters this Q star would be the, the, the fraction of species that survive. I mean the, the, the number of species that survive divided by the size of the pool. And then this is an analytical prediction that can serve as a new model to test something about coexistence in problems that can be related to to do this to the system. I show some results about the fully connected network, because we can, we can, we can kind of, once we have the prediction of the expected diversity, we can kind of complicate the model or add some ingredients to the to the new approach by, for example, considering a network structure. In the case of a window not consider network network structure, we have a very nice prediction of the number of species that survive in this case the distribution is no longer binomial, and then you can have regions where the expected number of species is very large and regions where the expected species is really, really low. Okay, but the key point here, or the idea I'm trying to transmit here is that we can find an analytical predictions that an analytical prediction that can serve for further model testing or to compare with the system. In the case that you impose some network pattern, I mean this is basically introduced introducing a connected structure and a pattern of zero entries of the of the matrix in the in the model right and we can we can do it by introducing another range of distribution, power load distribution or some bipartite or modular structure. And if we do this and compare with our analytical prediction, we have that the network has really a moderate effect in the prediction for the diversity, right. Because the full line is basically the the analytical prediction for the for the fully connected network. Okay, so maybe I can stop here because sorry. Okay, because I'm going to talk about the effect of phylogeny when I don't know if some questions on someone has something to ask. I don't see questions in the chat. If someone has a question you can raise hand or unmute yourself before we go into this next section. Jose, I think you can continue for now. Thank you. Thank you. In this in the second part I'm going to do the same stuff, something, something similar, but I'm not going to consider that interactions are fixed as in the as in the previous in the previous random soup problem. So I'm going to consider the effect of phylogeny, which will be a way to introduce variability in interactions in the model, right. So I work down in collaboration also with with Stefano and Carlos also with with Zach from all of them from from the university of Chicago and I refer you to do this, to this to this reference where you can, we can see the details of the things I'm going to summarize here. Well, the idea here is just can we say something about the limits that are imposed to diversity when you impose a phylogenetic structure in in the community or when you when interactions are inherited by kind of phylogenetic structure. So for that purpose we start with phylogenetic tree, assuming that you have a pool of five species here and, for example, you have this perfectly hierarchical tree. This gives you a correlation between the, between the species, even by the basically by the covariance matrix of the of the tree, and we formulate the interactions in terms of trades. Okay, we can see that at the, at the, at this point of the tree, each trade, and in order to calculate the tree, the trade of each species is basically a random walk on the, on the, on the leaves. This basically gives you that the vector of trades is a multivariate normal distribution whose correlation matrix of his or whose covariance matrix is basically the covariance matrix of of the tree. Okay, so if we consider L trades. We have this this G matrix, which was also mentioned by by guy in the in his talk. And we just take as a measure of the interaction between species they share overlap between the between the vector of trades. And these, these sample covariance metrics a equal to one over L G G just post as the way we are going to introduce the, the, the interactions in in our model. If the vector of trace is basically multivariate normal then the sample covariance method follows the wizard distribution, right, depending on the parameters and which is the size of the pool, L is the number of trades and Sigma is the correlation of the tree. Now, we basically do the same thing as before we do top down assembly. In this case, things are kind of simple because a is symmetric and positive definite. So this means that all the again values are positive, right. This immediately gives you a diagonal stability, we have not. We don't have to impose diagonal stability on in this case. So you can see that local terraria dynamics in this setting we are assuming that fitness difference are absent. We assume that all all species grow at the same rate in terms of this Chessonian paradigm. And we are interested in considering like competitive ability differences, right in the industries, we are a kind of switching off fitness difference in order to get the picture more tractable. So in principle, you can consider a swimming and then you have this local terraria dynamics as in the as in the case before before notice the difference in design here because this is not important. But so, since we have a global stability, we can characterize the number of existing species by feasibility and noninvasibility. We can see simply that these these mean interaction does not affect species identity identities and also basically the vector of rates rescales biomass is so we can remove them from the dynamics and then we have to down assembly and we are reaching a unique endpoint. Okay. What are my biodiversity my diversity prediction with this model. Well, first, I'm going to consider the deterministic limits. I also want to mention that this model can be also recast in terms of MacArthur consumer resource model so I'll be con other things I'm going to say here about the, the number of trades else. It can be translated in immediately immediately on on a number of resources, which could be L as well in MacArthur model. Okay. So in the deterministic in deterministic limit, we consider that the number of trades is very large compared to the size of the pool. In this case, the sample covariance tends to the covariance of the tree. It is simple to show in this case that every covariance made in this induced by a tree yields full feasibility we cannot worry about in this limit about feasibility because it is guaranteed. The, the idea is simple as I'm trying to sketch by this. Basically, if you have a tree with this with this shape, you can show that the covariance matrix of the full tree is basically this block matrix, which this Sigma one is basically the covariance matrix of the subtree and so on, plus this constant 10, which is related to the time to the split of the tree. So if this is blocks, each block is feasible then by induction you get simply that the full team would be with the feasibility. This is a very strong result. Right. So we don't, you don't have to worry about feasibility. There are also some predictions about a total biomass and the abundance distribution in order to get to get things tractable we considered the limit of a perfectly hierarchical tree and perfectly balanced tree, right. So we have predictions of the total biomass and the, and the number of the abundance distribution. For example, in the case of the total biomass, you can see that the biomass, the biomass scales basically with the square root of the number of the number of species that you can have in the tree. In order to compare with a with an empirical phylogeny, we consider here the Senna phylogenetic tree, and we see that the we basically took some samples of the tree in order to get the this increasing number and we basically observed that the, the, the empirical trees basically kind of in the middle of this perfectly hierarchical and the, and the perfectly balanced, right. But in the deterministic limit, most of the things are easily predictable. We also can ask ourselves, what is the prediction for a general result. I know, of course, going to it in to enter into into a full detail bit, but using the properties of the wizard distribution you can calculate basically expressions for the probability of feasibility on the probability of noninvasibility. And these, these are the the expression which are basically the an integral over the, the key square distribution times the probability of a multivariate distribution over a certain condition. And the probability of noninvasibility is the same and this is the probability that the given multivariate normal distribution is containing a negative orphaned. So in principle, this, this, this result give you the exact probability of feasibility and noninvasibility and in principle this can be computed numerically, right, to a certain accuracy. Also, you can show that these two probabilities are independent of each other. So the probability of being an attractor factorizes and you have the probability that the attack those has size M. Okay, so again, we can have this theoretical prediction if we consider a simple case, which is the case of a star phylogeny, the case of a star phylogeny is basically that you have a point that every species is split and no more. In this case, we can carry out all these integrations and all these stuff, and we can have a prediction for the number of species that that survive in average. This is, this is the, the relation this reminds the experimental result that Martina showed in the in the first start on Tuesday, because these gamma is basically the number of traits, or the number of resources if you think of this in in a MacArthur risk setting. And we observe that the number of resource as the number of resources increase the the average fraction of species that you observe is is an increasing function, right. Those are simulations and lines are our analytical analytical prediction. This is interesting interesting because the prediction of the competitive exclusion would be here in gamma at gamma equal equal to one when the number of resources is equal to the number of species. And our theory predicts that the expected number of species is well beyond to what classical theoretical competitive exclusion predicts. Okay. So we have fully characterized the diversity as in the other case we have regions where the diversity increases to a high level. Basically, the idea is if you increase the number of traits in the limit of infinite number of trades we see basically the deterministic limit you get full coexistence. So, so if you increase correlation between between trades, then this is opposite to to coexistence. Also, we have predictions. Maybe I don't know because we started a little bit late but if I'm correct, you don't have a lot of time left are you do you have a lot to show. I have two slides just two slides. Fantastic. Yes, I just wanted to show how the total biomass depends on the on the on the number of resources on the number of of today's we find a good agreement with simulations. And it's a decreasing function. It is because kind of the biomass splits into into it kind of divides into the set of traits that you have into the number of traits. So this is it. I hope I convinced you that under some simplifying assumptions, you can do some interesting predictions on the diversity, even in the in related to the distribution of the number of coexistence pieces, assuming top down assembly in these two meaningful situations. So these, I have studied these, these two models where I will have analyzed the variability in rates and also the variability in interaction so in this case these two approaches are kind of complimentary. We don't have a new expectation of how many species should coexist and we can use it to probe the effect of other mechanisms in coexistence so this is a basically the idea home on carrying out these all these ugly calculations. We can we can introduce, for example, in networks, patterns, for example, modularity. Not yet in the position of the non zero elements of the networks, but also introducing patterns, patterns in the in the strengths, which have in the past have been shown to strongly stabilizers or destabilize the system. And to the to the talk by by guy. It would be interesting to relax all the assumption that we impose on diagonal stability and consider multiple multiple attractors, attractors. And basically this is this is this is all I wanted to say, I want to thank all my collaborators, most of them are in this in this picture also is done here. And Jacob is not in this picture because he was precisely taking taking the photo so thank you very much for your attention I'm happy to answer any question you may have.


Hey this is Michelle Getzinger and I'm here doing the Freeport Focus at the Freeport Volunteer Fire Department and this is our Methi Hero Series. This is Jeff, he's the captain of the Volunteer Fire Department and he's going to introduce himself here. Hi my name is Jeff Lowers, I'm a 38 year member of the Freeport Volunteer Fire Department, president and captain. I've lived in Freeport all my life and we do our best to protect the community and surrounding communities. Anything of the negative happens. So Jeff tell me a little bit how the Volunteer Fire Department works. In this type of community we have limited members for the department so we do our best to train and we all have cell phones and monitors. Somebody calls 911, we respond as best we can and go and quell the situation. But how many volunteers do you have right now? Right now to answer calls volunteers are between 12 and 14. As a parallel when I joined back 38 years ago it was probably about 30-35. If somebody wanted to become a volunteer what do they need to do? Just get a hold of one of us or you can email us on our website and we will get in touch with you, do a mini background check, have an interview with you and start the process. It isn't too hard and the rewards are nice. We are very fortunate here in Freeport to have a good a good community. We do get a couple fun drives a year and we are always looking for volunteers to help with the fun drives. Virtually everybody in Freeport over the years has always been very nice to the department either coming to help with chicken barbecues or with the Halloween parades anything we are we're extremely fortunate. Chicken barbecue is the bomb. That's really about it and I appreciate the time. Thank you Jack. Sure.


Hey, Trevi, can I do a therapy session with you? Dan Herron, Dan Herron tweeted that retiring from baseball is a mental challenge more difficult than any I had in my playing days. And he was quote tweeting something about Roy Halliday and his troubles. But you're a guy that recently retired from the baseball life. And the word like institutionalized or like on the schedule and the program for all of your high school and until age 31. Did you do you have any struggles or you just found us now and you're good? I don't think people put a lot of their self worth into their work. And baseball and sports in general is one of those things that just comes to a screeching halt one day. And I was aware of that. So I wanted to prepare myself mentally for it. And I think I did like had a season in the minor leagues at the end of my career. And I don't think a lot of guys do that like I went and played like I played and like there just wasn't room for me anymore.  Yeah, and originally I didn't do that. And like when I didn't make the team with the Rangers, I just like I went to AAA for five days and I went home and I was going to be done with baseball. And I'm happy I went back and went and played for the Phillies that year. I made my way back to the big leagues for a short time for like a month or whatever it was. But I like went back to the minor leagues put myself through that. And I just I was done. Like I gave it all I gave everything I had. So I like I feel like I transitioned well because I prepared myself for it. But yeah, a lot of guys well it's weird because you know, we're very similar ages. And I'm like, just now found what my career will be. And like to think that baseball players like it ends there. Or you know, that's like it's a quick like close the book and the guy to open a new one that would be crazy hard. So I understand it. But yeah, a lot of guys don't do well with their money. They have they don't budget while they're playing. And so like the paycheck start coming. I think guys really freak out about that because they've established these lifestyles. They got bills. And they got no money coming in. So I think I've done a good job with that. Like I don't I try to live within my means and just I'm happy man. Like, I'm yeah, you guys are part of it. Definitely. I have an outlet now to be creative. And I like a few of you. Boom. Awesome. Some of you guys I don't like. Great. But that's okay. Man, it's it's it's tough watching some some players, you know, they'll lock themselves in their basement and open up cards. And it's like, Are you all right, man? Do you want to talk about it or something?


Every year, millions of visitors come to Washington, D.C. to tour the National Archives, the nation's largest storehouse of historic documents. This year marks the Constitution's 200th anniversary, and to help monitor the aging process of this document and others, like the Declaration of Independence and the Bill of Rights, the National Archives recently installed a space-age camera designed by NASA's Jet Propulsion Laboratory in Pasadena, California. The National Archives came to NASA with a request for NASA to take a look at what kind of technology could possibly be used to provide a long-term monitoring system that would allow them to have baseline information that was taken at the beginning of the monitoring period and then to be able to follow in a very detailed fashion the fate of the documents over the next 50 to 100 years. Chris Stevens' team, led by Ed Miller, designed the National Archives camera, adapting technology normally used for deep space missions. The camera images the documents by scanning, under green light, a handful of pre-designated postage stamp-size areas. In this case, a practice target is used instead of a real document. During each pass of the scanner, a million bits of digital information are collected. The system has the capability of going back year by year to the exact same spot in order to make comparative studies of the condition of the documents. In addition, a whole variety of image processing techniques can be used. In the case of the first two letters in the Constitution, the W and E of We the People, the black and white image can be color-enhanced to more easily see areas where ink has flaked off the function. There are other needs for the system according to Norville Jones of the National Archives Preservation Line. We have concern that changes do happen when documents are exhibited, that there can be fading or changes in contrast or paper can darken. And by getting a baseline reading before an item goes on exhibit and then monitoring it after exhibit and keeping records on items that are frequently requested that we'd be able to tell changes that were occurring before any serious damage had happened. The monitoring system can also be a valuable tool for determining what type of active measures to take in order to save and stabilize a document or piece of artwork. The imaging system represents a down-to-earth use of technology developed over the years for outer space probes like Voyager, which used it to capture incredible pictures of our nearby planets. Norville Jones sums up NASA's link with the past. At the time that the Constitution was created, pen and ink on parchment was about the most permanent and best that you can do. And I think now in honor of the 200th anniversary of the Constitution we're able to use what is I think now the best that you can do in terms of wrapping up new technology in order to be able to assure that the documents last not only 200 years longer but 2,000 years as long as we can imagine.


Panoramics and bite wing panoramics are not diagnostic images for interproximal decay in young kids. Here is a panoramic image of a three-year-old that was referred to my office. You can see some interproximal decay, but when we take a look here at the bite wings, we can see a completely different story. Here you can see on the bite wings two additional lesions that were not evident on the panoramic. This is why intraoral bite wings are the standard of care with kids set up post-year context. There are different technologies that are currently available to you. There are digital size zero sensors and also size zero plates. If you're a traditional office, size zero film will work as well.


In Oyo State has suspended its governorship primary, citing logistics as a challenge. The primary election was to hold at 11 am. Earlier, a governorship aspirant, Nyi Akintela, stepped aside 14 abnormalities in the composition of party delegates.