 We thought about when did we meet last time and it came out that the first time when we met, it was 1994 in Madrid, then in 1996 here in Vienna and then in 2005 in Paris. And all that meetings, all these meetings were the meetings of the foundations of information science. The community which is already based also on systems thinking, on complexity thinking, on cybernetics thinking and so on. And so we meet you for the fourth time. And so Peter Jaggi is the Henry R. Bruce Professor at the Center for Complex Systems Studies at the Kalanasu College in Kalanasu in Michigan. But he is also the leader, the head of the Budapest Complex Systems Computational Neuroscience Group of the Wittner Research Center for Physics of the Hungarian Academy of Sciences in Budapest. And he will give a lecture, as we already heard in the morning, from Luigi and Charlie who passed away last year. And he will make another lecture on that along with the development of biology and how systems thinking came into biology. So please Peter, it's your turn. For that kind of invitation, so this is a memorial lecture for Luigi and Charlie who was their influential for the series of conferences. This is from Robert Travis Wittler, I had the pleasure of meeting at the first European meeting on Cybernetics and Systems Research in Vienna in 1972. Then he organized the Chair Symposium on Bio-Cybernetics and Theoretical Biology. It was such a success that I invited Luigi to organize a Chair Symposium also at the next meeting in 1974 and then again at order following biennial meetings until 2010 and I met him for the last time. The Symposium organized by him usually attracted the largest number of contributors with high quality presentations. So that is the reason that we found EMS CSR 12 lecture. Thank you very much. I made some correspondence with Tonya Ricciardi, which is docker and some of his colleagues to give some details about his life, his contribution to bio-cybernetics, some of also to the development of the field. This is what you see here. This is Robert and I said about him as a co-enter, but I don't. He was very serious with all of I's Luigi, then his friend and colleagues working in bio-cybernetics is Francesco Benfilio and then the ladies, the students, former students of Luigi, became professors of mathematics. Laura Sacevotano in Turin, Maria Noghiere in Salerno. These guys here is Dan Troncoe from Cal State at Pomona, a strong influence in the system. He was a wonderful, passionate worker. Dan Troncoe from Cal State, Pomona just going into retirement. We did not identify him because he had different opinions. So probably in 1988 or 1982, that was a meeting here. So what I will do today. So Luigi lived, worked in Naples. He spent seven years in Chicago, but I understood that he simply did it. That was so cold for him. But the first time that he managed to get a job in Italy, well back. That's still a very influential period also in Chicago. There is a conference that he organized in Salerno. Bagnometamantis is a wonderful book emerged from this conference. Then he organized many symposia here at Sorge Vino. Just mentioned one here, a typical here in Vienna. A little bit about neurons and neural networks. He's really interested in stochastic models of signal neural activities, little bit about networks. He's also a population model, population dynamics. Then he organized a series of conferences about biological computation. So just a little bit about this. So he was born, died in the influence of political resuvio. And yet in Japan he's a post-doc. Hiromi Shingo now, professor of mathematics at Hiroshima University. And he's a professor of epidemiology at Spiti. He's also a former professor of Latin History in Italy. So he's a student of a former Italian professor. And he's a very good student of classical questions applying to geological projects in the לכty world. Actually, I told our students this correspondence, which was, I'm fairly surprised at them, these people that he obtained an Italian role in champion medicine. Then he was 17. The story of, the story of herself is a dedicated mathematician now, a mathematician. And this is a wedding photo of the physicist Tili Konadakava, and here are the two wedding photos. This is Edoardo Paenielo, one of the sons of Italian cybernetic, very famous Italian mathematician working with information. This is Edoardo de Luca. So, why do I show? Paenielo, Edoardo Paenielo, influential painter, in the first volume of the Journal of Theoretical Biology, that was about the sinking machines and thought processes, basically he unified the background of his application to the neural activities and the happy and learning applications. So, Edoardo himself, he wrote about Paenielo, who died in the night of his sleep. So, Paenielo wrote cybernetics from Italy, partially motivated by Enrico Ferri. In 1954, he supported a series of seminars in computers, and Norbert Wiener, of course, one of our heroes, came to Italy to give a series of lectures in law. So, Paenielo would take a quick interview, one and two more. This has been one and two in October, and I will mention soon, a specialist in psychiatry and mostly neural anatomy, and could join the Institute of Theoretical Physics, a real organization, by the Italian National Research Council, the G&R. It promises that the Institute of Theoretical Physics of the Navy's University, so that is already a physicist, a mathematician, an embroiderer, a neural anatomist, and so that was something, okay, let's focus our attention to the mathematical description of the brain activity, which was the prospect of the program of Macau. So, it was the beginning of the very repetition that Scuggi wrote for Neapolatia Research in Physics, Mathematics, and Psychiatrics, which, on the other hand, was the founding director of the Institute of Theoretical and the National Research Council. So, write about it. It's a little correspondence in which our friends, such as the Venturio, suggested me also to speak a little about writing like, which I must say, oh. So, write about it was in the early 1960s, in Naples, which I was working with, for example, and then he was the director of the Department of Structural and Function of Natural Nermets at the Max Planck Institute of Yolovisheky Berber, taken to Mingen. And this research was mainly based on combination of neuroanatomic in brain theory and statistical approach to cortical structures and cerebral cortex and cerebellar cortex. Quantitative anatomical studies, most of mom's, human cortical structures, orientation specifically in the visual cortex of primates, connected with psychophysical studies of humans, neurological theory of language. Futuraries are, you know, these are very important people about point of error in 1962. That was in the Journal of Comparative Neurology and an important journal for the morphologists. So this is a new term, we have a lot in practice, but here, quite contrary to this approach, the cyber-analytical program, Metcow, Pitz, Wiener, Neumann, that is, you don't see now in morphological journals. Here is an other name, Laurea, in 1963. I will mention this name again. Keith, Keith Isaac. So a mathematical approach. Covered in the first paper by Gucci Road, this was it was published in the Kibernach, Kibernach was the predecessor of the bio-analytical cyber-analytical program for some distribution functions for non-linear switching elements with finite dead time. Then, step time in that year, in Cayenne Law School, had a mathematician under the rule of so reverberations and control of neural network. So that was the probabilistic description of asymptotic theorems. So that time we had the mecca of this model and we also had a little more. And then there was a question, deterministic and hot news, deterministic and stochastic models, describing single neural network. Francesco Mantiglia, retired recently from the Institute of Ecumenitica, and which are, we published in 1997, probabilistic models. Determining the input-output relationship in formalizing. So that was the first spirit in the early 1960s, early 70s to find out the conceptual frameworks of neural networks. Next is Luci Gatt, assistant professor in the committee of mathematical biology, the University of Chicago. And one of his student, former student, he doesn't look now as a student or called, just retired from the Oriental State University and attended many of his meetings. From most of the field he served as a stochastic resonance. He was a stochastic resonance in neural systems in the last years. But that's it. He didn't look now as a student. So how was Chicago called in the words of Paul Caldwell? So Luci came to Chicago in 1969 as assistant professor of mathematical biology. At that time, the University of Chicago organized this committee. It was a famous committee on mathematical biology founded by Plashevsky. There was personal stories behind him. So he was being expanded and was expected to work in the department of theoretical biology. Luci was among a group of young new assistant professors who went on to distinguish very well. Art of Winfrey, Stuart Kaufman, and Henry Slotkin. Then Jack Cowell, who is very well known in the Neurodiac and is one of the leaders of Cowell. But he became the director of the Committee on Mathematical Biology. That means, which is a gluing tone before he moved to Harvard. There was a recent wiki moods who were already well known, such as rice or corn. Many visitors might argue that Cowell himself was a very tone, cayenne-like. So at that time, Neural Nets were a hot topic. That was, thus, a little earlier in the Percepton, the Minsky-Bappert Percepton that apparently killed Neural Network research for 50 years. That callup who had invented Neural Nets 75 years earlier was still active. He had a number of students working in that area. That's my colleague for instance. Stuart Kaufman had recently shown that related Boolean models, so that was which became the famous N.K. model, could also be used to describe genetics extensive. Since Slotkin had heard of Neural Nets with cayenne-like in Del Nuka, it seemed natural that Neural Nets would be used to describe my thesis of Neural Nets. My thesis showed that techniques from linear algebra would be used to study Neural Nets if they were considered as polynomials to the finite fields, rather than as a linear threshold device. Linear threshold device, binary linear. That was there, to really look out at Neural Nets. So Paul different with his thesis in 70 from the Chicago look. I have it up, but also important to be personally to look at Neural Nets and then also about the finite field of the finite fields. I'm a learner, I'm a historian. In Monterey, for many years, I'm a Swiss in North Carolina. So they fought a very, very, very influential and strong group. So Chicago was just caught which he went back Italy first, then in Salerno, he also had a Japanese vibe but also had strong connections in Japan to spend year in Osaka. So there was a fitness conference with just half of the people what I mentioned. So what were the key concepts? Sort of something yourself. Robert Rosell. Robert Rosell was a very influential controversial personal growth introduced concept of interdisciplinary systems. So that time he was thinking about fit format control. Herman Hakel from Stuttgart founded the Synergetics in the early 70s. So that time he was already more or less a stimulus science. So he spoke as many times later also that mathematical methods of synergetics and how to apply to self-organizing systems are involved in different leads about the mathematics of excitation and volunteer the bright-tempered himself. That was already the beginning when he outlined the theory of cerebral cortex in the book with Anash Shus, the University of Tokyo before he moved to Rikken. So that was a mathematical theory of self-organizing systems. My friend from Lulapesh learned a lot about information processing in neural networks. He studied physiology from that time. That time Czechoslovakia became a sign of human visual perception as recognition. And he started at his former students, nobile, not as such a doctor. That was about population models of the class or differences of the class. So finally that time the class was bordering gross processes. So that was it. The feelings were active and the book reflected very much confidence for the big success. So Lujci organized this series Symposium on Biosyvernetics and Mathematical Biology. First time I attended in 1984. That was the first time I had the chance to see Lujci and a few international leaders. And also that was a very good place to send students to give their first international presentations. And just to start with all of them, I only went to students here and strongly hope that the next time more and more students don't have to try to be critical of the whole movement of Symposiums I wear like this. So where are the students? So in 89 just like also just not kind of topics but in this meeting so more ideas about visual movement discrimination one group a formerly answer to that now in many cases self-organization through visual system formality that's still in the style of Ayanello and he is a lot of people who noted Lujci Richardi in 1960s and 38 years later speaking here about new dynamic model for time processing temporary neural processes and of course neural oscillators for the whole copy it is integration, fire, oscillation the difference just so I wanted to show you just to give back a little flavor of 14 years now pre-vator pre-systems competing corporations and genetics was becoming so more and more gene-location biochemical clocks for the first processing time problem that is a key problem in stochastic URAB hotels and there was a paper from Ciorina from Rostov informational aspects of biocide benefits so just I wanted to tell something a little bit science so single cell models so the original mechalloc is neural, it's a binary device, it's a neuron computation here we have the input though and with that weight in some of the input is larger than threshold than the neuron generates a signal it's not an being in silence actually the network LNABOS showed how formal neural network can use long cycles and got the whole E-M-C-S-F E-M-C-S-F are a word in 1984 of course other type of neurons would be defined is the linear neuron it's also the sound of the weight input and then the model features some of the combination of the threshold devices and the linear so now just 60 years ago how should we not have to formulate it at the end of this of course before the formulation of the what should we have to model many things could already know so mechalloc consciously decided not to put these formal model physiological details because he wanted to grasp the logical basis of the process so then after having the patch clamp voltage clamp the voltage clamp has been enhanced and it was possible to measure the transport processes through the memory so the stimulus comes from sodium of that signal so like ions so there was a detailed mathematical model the original version was a four-dimensional combination coordinate with the spatial variation was suppressed by using very clever experiment called a splice-camp clever experiment so the four-dimensional model is an equation for the propagation of the membrane potential and there are gate invariables for the sodium and potassium generally it is a four-dimensional equation and in 1952 Poczkin and Huxley using electro-mechanical calculations were able to integrate with good field and nice simulations so they were able to sort their patients and every mid-parameter studies and some sensitivity analysis so basically that was the formal biophysical botanist so now that we have the general description of the ionic flow for the cell membrane for the membrane potential so this was a four-dimensional equation still computers were in the elementary form so it was good to make some approximative solutions and so what to do of course two-dimensional is much less than four and the paper is two-dimensional it was possible to make geometrical analysis fits you in 55 and then a rumor the early 60s generated a two-dimensional approach of the four-dimensional equation by separating the time scales for rapid and slow variables and assuming that there is an algebraic constraint that was not a systematic reduction but it worked well and some variables substituted by the statistician so now we have a slow variables and fast variables and then it was possible to make mathematical calculations to apply bifurcation thoroughly to show how the equilibrium solutions can bifurcate to their periodic behavior which was very important what kind of inputs are able to elicit periodic responses from the neurons so everything happened so what I told so far that the deterministic model does originally Charlie was most interested in stochastic model and actually that was the reflection of the pressure of the cookie when the neurons fire us then we exceed and then what the studies came out in the beginning of the book having 500 citations also that was published in the series lecture notes in biomethmatics the most important book series that time in biomethmatics so the diffusion processes and related topics in biology they were actualizing it was 1977 so what is behind there was a classical deep traversed in a modern world let's see the random models for the spike activity of the singly neurons the biophysical journal is 64 so the membrane potential was considered as a bronion process stochastic process more or less a diffusion process and the corresponding stochastic differential stochastic differential application to start this model and then of course there is a question for that to find out the transition time when the trajectory intersect that threshold so that was the starting point for the stochastic singly cell models to summarize the results of the diffusion models of singly neuron activity in a book edited by Francesco Venteria from a school that was organized in CACI in 1992 so basically it was necessary to stochastic models are specified in the diffusion processes by the these two coefficients E1 and E2 and in the classical the classical bronion process this is a linear process this is state dependent linear state and there is a non-stationary version of the the one problem is the first passage time so when the voltage and particular place of the neuron reaches a threshold then an action potential is generated so many point processes in biology have similar origins and called first passage times so they occur when some underlying process first reaches a critical level of threshold even for simple models in a simple and one-dimensional stochastic differential equations there were very few analytical results so simulations and heuristic approximation methods several different types of behaviors were identified the main current research activities are part of the development of these approximation methods actually some results came from which is student and Tachwell no one likes it so when the Tachwell is a random variable and the first time an X hits the Y which is not a moving barrier not a constant and they cut into the distributions so just some hints about several other important papers and co-workers which involved with his students Anielo Petr Lansky from Prague who is a very important colleague of mine Sato, Osapla a couple of other well-cycled papers and also they are managed to the first test of time programming in this division process in biology so they constantly do stochastic progress so that is so far I spoke about single neurons but of course people are interested in networks and also there is a big fashion about neural networks are organized deterministically or what is the role of chance and stochasticity my own mentor we are the center of this year at the paper he speculated about specificity versus first we should tell randomness of safety in Europe quasi-randomness in Portugal connectivity and we played about this problem with neural connectivity deterministic randomness in the mid-eighties this is a picture from just 20 years ago in Calcutta he is Michael Arby one of the most famous he considers himself as a mathematician he himself was a student of metal and this is from the center of the university and by center he was a mathematician he had a paper written by Rémy Rémy is a very well known mathematician in the world of networks he was a random person randomness so do you know your Erdogan number he is a random person one, two, three I am going to read some before this and I will tell you a little bit really so about network organization so the nervous system of this the elegance forced probably a small world network the mammalian cerebral cortex is not purely deterministic not that you do that not that you don't twenty five years ago I said I get old bad but I know that we have ten on ten neurons ten on fourteen synopses still if you arbitrarily choose two networks in the cortex I am not able to measure I believe it might be not more than three, five synopses between them so the distance of two everything is surprising is small so now this network theory is strongly influenced neural network theory and this concept is anatomical connectivity functional connectivity and effective connectivity anatomical connectivity we are able to identify the synopses there is a correlation between spatially remote neurophysiological events but still there is a functional connectivity and effective connectivity I don't believe I got the details so graph theory influenced very much now because of the neural network researchers we have these characteristics past lengths the clustering coefficients so the characteristic past lengths is given by the global mean or the finite length in some cases the median can provide better estimate the clustering coefficients so how closely whether or not my friends are also friends of each other the clustering coefficient load is calculated as the number of existing connections between the nodes meters divided by all the possible connections and this is not the technical talks I don't go into the details but basically the application of graph theory positive question a smaller network a smaller network is a type of mathematical graph in which most nodes are not lasers of one another but most nodes can be reached every other by a small number of cogs of steps it is a purely regular it is a purely random graph and then it is a somewhat artificial algorithm and a smaller network I give value to the edges from the regular graphs that is not something as the ontogenics works some is asking from our old group in Budapest and in the project he defined some concept and compared them some monkeys visual up to cortex to generate a small world graph and there was some deviation of course there are different type of networks one type of network where the elements are nodes and the connections are synods functional connections or when the nodes are brain regions so this is not a micro network this is a macro network it works many others so sketches are the top illusory structural connectivity these are basically fight that pass phase functional connectivity correlations effective connectivity this is some kind of information flow among four different brain regions these are the corresponding connectivity matrices binary structural connections here symmetrical mutual information non-symmetric transparent there are so many anthropic concepts these are so network theory and application for brain this is something that people do a few words about population dynamics what is your life so theoretical biology basically people from 1797 when exponential drops and this forecast the end of world by overpopulation and the more mathematical approach the branching process is headed has been introduced as early as 1873 by Galton and Watson and still they are an important area of that probability theory so roots here because this friend died very early in his early which is Renato Capocelli in Salerno is a diffusion model for population growth in random environment I mentioned the theoretical population by 1874 now a recent people know the birth death or specific catastrophes we used to go with the chance to do a little bit of that in Salerno this is a little bit Capocelli in Salerno during the years which are dispensed in Salerno so this is all a little a few minutes about the biopromky things that was in 19 that was in just 10 years ago in San Luigi it was a 60 Saac, Marinaro the very famous metameticism he done working on the bronin in Luigi but I wasn't there so talk a little bit he done another biopromky which was found years ago he spoke about the scientific first of Wiener and Levy after bronin bronin and motion was specialized in scientific research object by Robert Bronn in 1827 and then many scientists started the motion and so Wiener and Levy started bronin and motion metametics and that is he appreciated their words and would like to know that these are very important words in the sound of the biopromky this is Luigi this is already known so that is the last picture that I found actually there was something that I see Luigi with front speaker in Linz and I think this is a story personally I would like to send to Luigi very much to help I have family and I got many help to prepare this lecture I told it to Shadi and then a warm welcome called in French Luigi