Preparatory School for StatPhys 2019

### July 1-5, 2019

#### São Paulo, Brazil

#### ICTP-SAIFR/IFT-UNESP

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This school will introduce graduate students and young researchers to a set of tools and concepts that underlie many of the works being performed in modern Statistical Physics. **The school is thought to operate as a preparation for Stat. Phys.**; therefore it consists of three main activities: a set of three courses taught by three lecturers, a set of discussion sessions where the abstracts of the conference will be discussed. The students will be tutored in how to select the posters to visit in a consistent way with their research interests, prepare for discussing with the authors, and framing the selected works within a larger body of research. Finally, one of the members of the Steering committee of Stat. Phys. (Maxi San Miguel) will present two lectures on the recent history of Statistical physics and its perspectives.

Much of the present work in modern statistical mechanics deals with study of collective behavior emerging from the interaction of nonlinear, out of equilibrium units, whose individual dynamics is described by a body of qualitative tools known as “nonlinear dynamics”. For this reason, one of the courses presents an introduction to nonlinear dynamics, with special emphasis on the study of large networks of coupled oscillators and excitable systems.

The second course deals with how to approach the problem of modeling these systems where many agents interact in out of equilibrium conditions. The construction of observable quantities, the formulation and validation of models and the study of their dependence with control parameters will be investigated in the framework of a variety of problems, ranging from epidemiology to neural dynamics.

### Announcement

### Online application is now closed

**Organizers:**

- Pablo Balenzuela (University of Buenos Aires, Argentina)
- Mauro Copelli (UFPE, Brazil)
- Gabriel Mindlin (University of Buenos Aires, Argentina)

## Registration

## Lecturers

**1.Courses**

I. *Introduction to nonlinear dynamics* – **Gabriel B. Mindlin** (University of Buenos Aires, Argentina)

Much of the present work in modern statistical mechanics deals with study of collective behavior emerging from the interaction of nonlinear, out of equilibrium units, whose individual dynamics is described by a body of qualitative tools known as “nonlinear dynamics”. In this course we present

1. The elements of the description of a nonlinear system (attractors, limit cycles, trajectories, invariant manifolds)

2 The reduction of a problem to its normal form, and the study of paradigmatic bifurcations

3. Time series data arising from nonlinear systems

4. The dynamics of averaged quantities from many nonlinear, out of equilibrium units: synchronization

II. *Multi-agent models in complex networks* – **Pablo Balenzuela** (University of Buenos Aires, Argentina)

This course provides an introduction to the use of Statistical Physics tools for the analysis and understanding of multi-agent systems. Most systems in this realm are composed by elements (generically termed agents) that do not act in isolation and are inhomogeneous. As a result of their interaction, complex behavior is usually observed at a macroscopic scale and the systems operate usually in out-ofequilibrium conditions. Therefore, advanced techniques from Statistical Mechanics are suited for understanding some of their properties. The objectives of the course are to allow the students to

understand the modeling approach taken to uncover the mechanisms behind large-scale phenomena and assimilate its underlying difficulties, limitations and strengths. Special emphasis will be given at the interpretation of the parameters included in the models. The course will be organized in four classes comprising the following topics:

1 – Introduction to generic properties of Agent-bases models and Complex Networks

2 – Neuronal models: Phase transitions in the Greenberg-Hastings model

3 – Epidemic compartmental models: SIR – SIRS. 4 – Opinion formation models: Voter and Axelrod model

III. *Criticality, with applications to neuroscience* – **Mauro Copelli** (UFPE, Brazil)

Since the seminal work of Hodgkin & Huxley unveiled the essential biophysical mechanisms of single neurons in the 1950s, a major challenge in Neuroscience has been to understand how neurons operate *collectively* in order for the brain to work “properly”. But what does “properly” mean? In a naïve line of reasoning, one could imagine neurons that were connected so that their collective behavior is essentially chaotic: such a brain would probably fail to make any orderly sense of the stimuli arriving from its surroundings. In the opposite extreme, neurons that collectively behave in a very orderly fashion might also face difficulties, possibly being dynamically too rigid to account for a rich, varying environment. This led to a conjecture that the brain as a high-dimensional dynamical system might be operating somewhere in between these two qualitatively different

behaviors, more precisely near a second-order phase transition. According to the theory of critical phenomena in Statistical Physics, at this critical point a number of nontrivial statistical properties emerge, such as long-range time and spatial correlations, diverging susceptibility etc. When transposed to models of neuronal networks, some of these properties have been interpreted as functionally beneficial to a putative critical brain. Research in this field gained a lot of momentum in 2003, when Beggs & Plenz experimentally detected power-law distributed neuronal avalanches in vitro. Since then, other nontrivial statistical signatures have been revealed in neurophysiological data at different spatial and temporal scales, including both anesthetized and non-anesthetized animals, thus strengthening the connections with the criticality conjecture. In this series of four classes, I will explore the strength and limitations of this theoretical framework in light of experimental results. More generally, I will highlight the need of theoretical developments in Neuroscience, which offers theoretical physicists a fertile ground for interdisciplinary research.

**2. Special Lectures **

* Physical limits to biological function *–

**William Bialek**(Princeton, USA)

On a dark night, our eyes can count single photons. The quietest sounds we can hear move the eardrum but less than the diameter of an atom. Bacteria navigate chemical gradients so reliably that they must be counting almost every molecule that arrive at their surface. These and many other example suggest that evolution has pushed biological systems close to the physical limits on performance. Importantly, this notion of observation can be turned into a principles from which we can derive the behaviors of these systems, and in some cases make more detailed predictions about mechanism. I’ll present examples of these ideas, showing how we can now connect these general (and sometimes abstract) physical principles to real data on particular systems.

* Statistical physics for real biological networks *–

**William Bialek**(Princeton, USA)

Life is more than the sum of its parts, and some of the phenomena that we find most fascinating emerge from interactions among hundreds or thousands of elements. Examples range from protein structure to neural networks to flocks of birds. Recent experimental developments give us much more quantitative and complete data on these systems. I’ll discuss approaches to building statistical physics models that can connect with these data, in surprising detail. These models are sufficiently accurate that we can take them seriously and ask where real systems are in phase diagram of possible systems. I’ll also describe approaches to the analysis of data on these systems that are inspired by the renormalization group. Recent data on large populations of neurons show striking evidence of scaling, suggesting that these complex systems are described by some nontrivial fixed point.

*Statistical physics: state of the art (I and II)* – **Maxi San Miguel** (IFISC, Spain)

The lectures will describe the history of complex systems, the importance of simple models in the description of complex phenomena, and recent applications of tools and concepts from statistical physics to fields including sociology and economy

## Program

School Program: it will be available in June 2019

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## Additional Information

**Visa information:** Nationals from several countries in Latin America and Europe are exempt from tourist visa. Nationals from Australia, Canada, Japan and USA can apply for an e-visa through VSF Global. Please check here which nationals need a tourist visa to enter Brazil.

**Hotel recommendation: **http://www.ictp-saifr.org/hotel-recommendations-2. Participants and Speakers whose accommodation will be provided by the institute will stay at The Universe Flat.

**How to reach the Institute:** The workshop will be held at ICTP South American Institute, located at IFT-UNESP, which is across the street from a major bus and subway terminal (Terminal Barra Funda). The address which is closer to the entrance of the IFT-UNESP building is R. Jornalista Aloysio Biondi, 120 – Barra Funda, São Paulo. The easiest way to reach us is by subway or bus, please find instructions here.

**Yellow fever vaccination** is recommended for travellers going to Brazil. Note that the vaccine needs to be taken at least ten days before the trip to be effective. Information: https://wwwnc.