Sebastián Bouzat

Dynamics of learning in coupled oscillators tutored with delayed reinforcements

In this work we analyze the solutions of a simple system of coupled phase oscillators in which the connectivity is learned dynamically. The model is inspired by the process of learning of birdsongs by oscine birds. An oscillator acts as the generator of a basic rhythm and drives slave oscillators which are responsible for different motor actions. The driving signal arrives at each driven oscillator through two different pathways. One of them is a direct pathway. The other one is a reinforcement pathway, through which the signal arrives delayed. The coupling coefficients between the driving oscillator and the slave ones evolve in time following a Hebbian-like rule. We discuss the conditions under which a driven oscillator is capable of learning to lock to the driver. The resulting phase difference and connectivity are a function of the delay of the reinforcement. Around some specific delays, the system is capable of generating dramatic changes in the phase difference between the driver and the driven systems. We discuss the dynamical mechanism responsible for this effect and possible applications of this learning scheme.

Models for microtubule cargo transport coupling the Langevin equation to stochastic stepping motor dynamics: Caring about fluctuations.

One-dimensional models coupling a Langevin equation for the cargo position to stochastic stepping dynamics for the motors constitute a relevant framework for analyzing multiple-motor microtubule transport. In this work we explore the consistence of these models focusing on the effects of the thermal noise. We study how to define consistent stepping and detachment rates for the motors as functions of the local forces acting on them in such a way that the cargo velocity and run-time match previously specified functions of the external load, which are set on the base of experimental results. We show that due to the influence of the thermal fluctuations this is not a trivial problem, even for the single-motor case. As a solution, we propose a motor stepping dynamics which considers memory on the motor force. This model leads to better results for single-motor transport than the approaches previously considered in the literature. Moreover, it gives a much better prediction for the stall force of the two-motor case, highly compatible with the experimental findings. We also analyze the fast fluctuations of the cargo position and the influence of the viscosity, comparing the proposed model to the standard one, and we show how the differences on the single-motor dynamics propagate to the multiple motor situations. Finally, we find that the one-dimensional character of the models impede an appropriate description of the fast fluctuations of the cargo position at small loads. We show how this problem can be solved by considering two-dimensional models.

Understanding the Lévy ratchets in terms of Lévy jumps

We investigate the overdamped dynamics of a particle in a spatially periodic potential with broken reflection symmetry and subject to the action of a symmetric white Levy noise. The system (referred to as the Levy ratchet) has been previously studied using both Langevin and fractional Fokker–Planck formalisms, with the main find being the existence of a preferred direction of motion toward the steepest slope of the potential, producing a non-vanishing current. In this contribution we develop a semi-analytical study combining the Fokker–Planck and Langevin formalisms to explore the role of Levy flights on the system dynamics. We analyze the departure positions of Levy jumps that take the particle out of a potential well as well as the rates and lengths of such jumps, and we study the way in which long jumps determine the non-vanishing current. We also discuss the essential difference from the Gaussian-noise case (producing no current). Finally we study the current for different potential shapes as a function of the amplitude of the potential barrier. In particular, we show that standard Levy ratchets produce a non-vanishing current in the infinite-barrier limit. This latter counterintuitive result can be easily understood in terms of the long Levy jumps and analytically demonstrated.

SURVIVAL AND EXTINCTION IN THE REPLICATOR MODEL: DYNAMICS AND STATISTICS

We study the multi-species replicator model with linear fitness and random fitness matrices of various classes. By means of numerical resolution of the replicator equations, we determine the survival probability of a species in terms of its average interaction with the rest of the system. The role of the interaction pattern of the ecosystem in defining survival and extinction probabilities is emphasized.

A counterintuitive way to speed up pedestrian and granular bottleneck flows prone to clogging: can ‘more’ escape faster?

Dense granular flows through constrictions, as well as competitive pedestrian evacuations, are hindered by a propensity to form clogs. We usesimulations of model pedestrians and experiments with granular disks to explore an original strategy to speed up these flows, which consists in including contact-averse entities in the assembly. On the basis of a minimal cellular automaton and a continuous agent-based model for pedestrian evacuation dynamics, we find that the inclusion of polite pedestrians amid a given competitive crowd fails to reduce the evacuation time when the constriction (the doorway) is acceptably large. This is not surprising, because adding agents makes the crowd larger. In contrast, when the door is so narrow that it can accommodate at most one or two agents at a time, our strategy succeeds in substantially curbing long-lived clogs and speeding up the evacuation. A similar effect is seen experimentally in a vibrated two-dimensional hopper flow with an opening narrower than 3 disk diameters. Indeed, by adding to the initial collection of neutral disks a large fraction of magnetic ones, interacting repulsively, we observe a shortening of the time intervals between successive egresses of neutral disks, as reflected by the study of their probability distribution. On a more qualitative note, our study suggests that the much discussed analogy between pedestrian flows and granular flows could be extended to some behavioural traits of individual pedestrians.