Adaptation and fatigue model for neuron networks and large time asymptotics in a nonlinear fragmentation equation.

Motivated by a model for neural networks with adaptation and fatigue, we study a conservative fragmentation equation that describes the density probability of neurons with an elapsed time s after its last discharge. In the linear setting, we extend an argument by Laurençot and Perthame to prove exponential decay to the steady state. This extension allows us to handle coefficients that have a large variation rather than constant coefficients.

Reproduction cost reduces demographic stochasticity and enhances inter-individual compatibility.

A population׳s survival depends on its ability to adapt to constraints impinging upon it. As such, adaptation is at the heart of an increasing number of theoretical models. In this paper, we propose a bottom-up evolutionary model to explore the relationship between individual evolutionary dynamics and population-level survival.

Evolution of aging: individual life history trade-offs and population heterogeneity account for mortality patterns across species.

A broad range of mortality patterns has been documented across species, some even including decreasing mortality over age. Whether there exist a common denominator to explain both similarities and differences in these mortality patterns remains an open question. The disposable soma theory, an evolutionary theory of aging, proposes that universal intracellular trade-offs between maintenance/lifespan and reproduction would drive aging across species.

Commuter mobility and the spread of infectious diseases: application to influenza in France.

Commuting data is increasingly used to describe population mobility in epidemic models. However, there is little evidence that the spatial spread of observed epidemics agrees with commuting. Here, using data from 25 epidemics for influenza-like illness in France (ILI) as seen by the Sentinelles network, we show that commuting volume is highly correlated with the spread of ILI.

Synchronization in random balanced networks.

Characterizing the influence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered neuronal networks with excitatory-inhibitory structure and balance constraints. We show how the interplay between structure and disorder in the connectivity leads to a universal transition from trivial to synchronized stationary or periodic states.