Program

Michael Benzaquen

Large endogenous fluctuations in financial and economic systems

In financial markets, empirical data reveals that most of the volatility is of endogenous nature, in contrast with standard economic theory which places greater weight on external factors. Past price trends weaken the liquidity flow and increase volatility, possibly leading to liquidity crises. Using a physics-inspired order book model, one can show that there exists a second order phase transition between a stable regime to an unstable regime as feedback increases. If relevant for the real markets, such a phase transition scenario requires the system to sit below, but very close to the instability threshold (self-organised criticality). An alternative scenario shows occasional ‘activated’ liquidity crises, without having to be poised at the edge of instability. At the macroeconomic scale, the same puzzle exists: aggregate fluctuations seem too large to be explained by fundamentals. Despite their inability to cope with recent crises and various subsequent calls to "Rebuild Macroeconomics", Dynamics Stochastic General equilibrium (DSGE) models are still at the forefront of monetary policy around the world. Such models rely on the figment of representative agents, abolishing the possibility of genuine collective effects induced by heterogeneities and interactions. Allowing feedback of past aggregate consumption on the sentiment of individual households paves the way for a class of more realistic models that allow for large output swings induced by relatively minor variations in economic conditions and amplified by interactions. Several important conceptual messages follow, as the de facto impossibility to price extreme risks and the potential of narrative engineering, which may be an efficient depression-prevention policy tool whenever confidence collapse is looming.

Beatriz Seoane

Statistical Physics of Energy-Based generative models

Energy-based models (EBMs) are powerful generative machine learning models that are able to encode the complex distribution of a dataset in the Gibbs-Boltzmann distribution of a model energy function. This means that, if properly trained, they can be used to synthesize new samples that resemble those of the dataset as closely as possible, but also that this energy function can be used to "learn" something about the building mechanisms of the dataset under study. Indeed, EBMs can be considered a powerful modeling tool for arbitrary data if one were able to map complex energy functions defined in a neural network into spin-interaction Hamiltonians that can be explored using standard statistical physics tools. Such an approach has long been used in physics for inverse Ising problems. The goal now is to extend this approach to more complex energy functions that can encode all higher order correlations in complex data. While this program is very encouraging, training good EBMs is particularly challenging, mainly because they rely on long Monte Carlo sampling processes to estimate the log-likelihood gradient. In my talk, I will present some results on the interpretability of shallow EBMs and discuss how computational statistical physics is a valuable tool for understanding and improving the training of EBMs.

Andrea Di Gioacchino

How virus-host interactions shape nucleotide usage in genomes:

a view from statistical physics

Most of the human genome does not code for proteins, but it is statistically different from a random string of nucleotides sampled from a uniform distribution. Similarly, viruses adapt the way they code for their proteins in a host-specific fashion, and scrambling their genome, while keeping fixed the proteins they code for, can severely hinder their infection capabilities. These two observations bring to the same question, that is what are the relevant drivers shaping the nucleotide usage in genomes. I will show how statistical physics paired with inference methods can shed light on this fundamental question, and I will present a set of relevant applications of this framework, including the search in the human genome of potential targets that can be exploited to strengthen the effect of immunotherapy for cancer and the analysis of the adaptation of viruses to a new host after a host switch.

Silvia Grigolon

Understanding the mechanics of coordinated tissue movements in zebrafish gastrulation

Embryo morphogenesis relies on highly coordinated movements of different tissues as well as cell differentiation and patterning. However, remarkably little is known about how tissues coordinate their movements to shape the embryo and whether and how dynamic changes in signalling and tissue rheology affect tissue morphogenesis. In zebrafish embryogenesis, coordinated tissue movements first become apparent during "doming," when the blastoderm begins to spread over the yolk sac, a process involving coordinated epithelial surface cell layer expansion and deep cell intercalations. In this talk, I will first present how using a combination of active-gel theory and experiments (performed by Dr. Hitoshi Morita, Yamanashi University, Japan) shows that active surface cell expansion represents the key process coordinating tissue movements during doming. I will then talk about the analysis of the intrinsic mechanical properties of the blastoderm at the onset of doming and how, by the aid of a simpler toy model and experiments (performed by Dr. Nicoletta Petridou, IST Austria), blastoderm movement relies on a rapid, pronounced and spatially patterned tissue fluidisation which is found to be linked to local activation of non-canonical Wnt signalling mediating cell cohesion.

Matthieu Barbier

A stroll between statistical physics and many-species ecosystems

The ecology of many-species systems is something of an outlier on the interface between biology and statistical physics. Many facets of life have already been found to resonate with physics-inspired concepts such as collective behaviors (in neurons or flocks), criticality, and so on. As we go up to entire ecosystems, however, there is no consensus on the existence of any collective dynamics or similar phenomena. Yet, more and more statistical physicists have recently been getting involved with ecological questions, and empirical data availability has also improved dramatically. Through several examples, I will try to explain some of the fundamental questions of theoretical ecology, current barriers to progress, and what physics-inspired approaches can bring to the table.

Bruno Loureiro

Dimension-free limits of stochastic gradient descent for two-layers neural networks

Stochastic gradient descent and its variants are the workhorse of modern machine learning models. Despite its current (and successful) use for optimising non-convex problems associated with the training of heavily overparametrised models, most of our theoretical understanding is bound to the context of convex problems. In this talk, I will discuss some recent progress in understanding the SGD dynamics of perhaps one of the simplest non-convex problems: two-layers neural networks. In particular, I will discuss different regimes (classical, high-dimensional and overparametrised)  where one can derive a set of low-dimensional “state evolution” equations describing the evolution of the sufficient statistics for the weights. Finally, I discuss some interesting behaviour associated to each regime, and the connections to other descriptions such as the mean-field limit.

Ulisse Ferrari

Collective behavior in neuronal networks: Maximum Entropy Principle in Neuroscience

The Maximum Entropy principle is an inference framework that allows for finding the discrete Boltzmann distribution that reproduces at best the empirical statistics of a chosen dataset.  In this talk I will present some applications of this strategy to the spiking activity of real neurons recorded during experiments, either in the retina or in the cortex. At first I will build the framework and explain how we can solve the inference problem by taking advantage of our stat. phys. knowledge of spin systems. Then I will discuss an application of this method to the prefrontal cortex of behaving rats and how it allows for identifying cell assemblies that undergo memory reply. I will then show how maximum entropy models account well for the system collective behaviour when the input stimuli have short-ranged correlations, but fail for inputs with long-ranged ones.  This happens, for example, in the cortex during sleep, or in the retina for full-field visual stimuli. In the latter case, to solve this issue we apply a previously developed framework that, in addition to network effects, accounts for external stimuli that drive the system in time. In this case, the inferred model is not anymore a disordered Ising model, but it takes the form of a random field Ising model with short-ranged ferromagnetic couplings, and disordered magnetic fields.

Xiaowen Chen

Learning the collective dynamics in social mice with statistical inference

Social interactions are a crucial aspect of behavior in human society and many animal species. Nonetheless, it is often difficult to distinguish the effect of interactions from independent animal behavior (e.g. non-Markovian dynamics, response to environmental cues, etc.). I will address this question in social mice, where we infer statistical physics models for the collective dynamics for groups of mice, housed and location-tracked over multiple days in a controlled yet ecologically-relevant environment. We reproduce the distribution for the co-localization patterns using pairwise maximum entropy models. The inferred interaction strength is biologically meaningful, and can be used to characterize sociability for different mice strains. Moreover, these models can distinguish the effect of change of prefrontal cortex plasticity due to social-impairment drugs, and useful to study autism in the mice model. The equilibrium dynamics on the resulting model can successfully predict the transition rates, but not the waiting time distribution. Inspired by the observed long-tailed waiting time distributions in the mice, we have developed a novel inference method that can tune the dynamics while keeping the steady state distribution fixed. Constructed through a non-Markovian fluctuation-dissipation theorem, this new inference method, termed the "generalized Glauber dynamics", addresses an important question in statistical inference, for which I will derive the expression, demonstrate its power, and show how to infer the model using examples of Ising and Potts spins. Finally, we will apply the generalized Glauber dynamics to the social mice data, and show how memory is important in collective animal behavior.