Seminars

There is an avalanche of new data on activity in neural networks and the biological brain, revealing the collective dynamics of vast numbers of neurons. In principle, these collective dynamics can be of almost arbitrarily high dimension, with many independent degrees of freedom — and this may reflect powerful capacities for general computing or information. In practice, neural datasets reveal a range of outcomes, including collective dynamics of much lower dimension — and this may reflect other desiderata for neural codes. For what networks does each case occur? We begin by exploring bottom-up mechanistic ideas that link tractable statistical properties of network connectivity with the dimension of the activity that they produce. We then cover “top-down” ideas that describe how features of connectivity and dynamics that impact dimension arise as networks learn to perform fundamental computational tasks.

After more than 4 million deaths worldwide, the ongoing vaccination to conquer the COVID-19 disease is now competing with the emergence of increasingly contagious mutations, repeatedly supplanting earlier strains. Following the near-absence of historical examples of the long-time evolution of infectious diseases under similar circumstances, models are crucial to exemplify possible scenarios. Accordingly, in the present work we systematically generalize the popular susceptible-infected-recovered model to account for mutations leading to repeatedly occurring new strains, which we coarse grain based on tools from statistical mechanics to derive a model predicting the most likely outcomes. The model predicts that mutations can induce a super exponential growth of infection numbers at early times, which self-amplify to giant infection waves which are caused by a positive feedback loop between infection numbers and mutations and lead to a simultaneous infection of the majority of the population. At later stages -- if vaccination progresses too slowly -- mutations can interrupt an ongoing decrease of infection numbers and can cause infection revivals which occur as single waves or even as whole wave trains featuring alternative periods of decreasing and increasing infection numbers. Our results might be useful for discussions regarding the importance of a release of vaccine-patents to reduce the risk of mutation-induced infection revivals but also to coordinate the release of measures following a downwards trend of infection numbers.

How can neural networks exhibit persistent activity on time scales much larger than allowed by cellular properties? We address this question in the context of larval zebrafish, a model vertebrate that is accessible to brain-scale neuronal recording and high-throughput behavioral studies. We study in particular the dynamics of a bilaterally distributed circuit, the so-called ARTR, including hundreds neurons. ARTR exhibits slow antiphasic alternations between its left and right subpopulations, which can be modulated by the water temperature, and drive the coordinated orientation of swim bouts, thus organizing the fish spatial exploration. To elucidate the mechanism leading to the slow self-oscillation, we train a network graphical model (Ising) on neural recordings. Sampling the inferred model allows us to generate synthetic oscillatory activity, whose features correctly capture the observed dynamics. A mean-field analysis of the inferred model reveals the existence several phases; activated crossing of the barriers in between those phases controls the long time scales present in the network oscillations. We show in particular how the barrier heights and the nature of the phases vary with the water temperature.