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Se analizan las condiciones bajo las cuales un modelo de aprendizaje no lineal (modelo beta) con dos operadores y reforzamiento no contingente simple es una sub(super)martingala en el supuesto de que todas las respuestas sean reforzadas, generalizándose al caso de ausencia de reforzamiento.Las condiciones establecidas, que nos conducen a 23 casos posibles, permiten analizar exhaustivamente el comportamiento asintótico del modelo y compararlo con la clasificación de Norman.
Finite-size fluctuations in coevolutionary dynamics arise in models of biological as well as of social and economic systems. This brief tutorial review surveys a systematic approach starting from a stochastic process discrete both in time and state. The limit N → ∞ of an infinite population can be considered explicitly, generally leading to a replicator-type equation in zero order, and to a Fokker-Planck-type equation in first order in 1/√N. Consequences and relations to some previous approaches...
Understanding the evolution of individuals which live in a structured and fluctuating environment is of central importance in mathematical population genetics. Here we outline some of the mathematical challenges arising from modelling structured populations, primarily focussing on the interplay between forwards in time models for the evolution of the population and backwards in time models for the genealogical trees relating individuals in a sample from that population. In addition to classical...
We analyze a stochastic neuronal network model which corresponds to an all-to-all network
of discretized integrate-and-fire neurons where the synapses are failure-prone. This
network exhibits different phases of behavior corresponding to synchrony and asynchrony,
and we show that this is due to the limiting mean-field system possessing multiple
attractors. We also show that this mean-field limit exhibits a first-order phase
transition as a function...
In the wine AOC system, the regulation of quantities performed by the
professional
organizations is aimed to smooth the variations of the quality of the
wine due to the
variations in the climate that affect the quality of the grapes.
Nevertheless, this regulation
could be damaging to the consumers due to the price increase resulting
from the reduction of
the quantities sold on the market. We propose a stochastic control
model and a simulation tool
able to measure the effects of this mechanism...
We investigate the optimal alignment of two
independent random sequences of length n. We provide
a polynomial lower bound for the probability of the optimal alignment
to be macroscopically non-unique. We furthermore establish
a connection between the transversal fluctuation and
macroscopic non-uniqueness.
We prove a new sufficient condition for the asymptotic stability of Markov operators acting on measures. This criterion is applied to iterated function systems.
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