1,720,990 research outputs found
Self-diffusion in a two-dimensional system of colliding vertical sticks
No full textWe consider a system of N horizontal lines where colliding vertical sticks are placed initially according to an equilibrium prescription; they move parallel to the lines and collide; the collisions take place between sticks of the same line and of the adjacent ones. The asymptotic behavior of a tagged stick is diffusive, and the self-diffusion constant is inversely proportional to N
Fluctuations of the empirical entropies of a chain of infinite order
No full textThis paper addresses the question of the fluctuations of the empirical entropy of a chain
of infinite order. We assume that the chain takes values on a finite alphabet and loses mem-
ory exponentially fast. We consider two possible definitions for the empirical entropy, both
based on the empirical distribution of cylinders with length c log n, where n is the size of the
sample and c is a suitable constant. The first one is the conditional entropy of the empirical
distribution, given a past with length growing logarithmically with the size of the sample. The
second one is the rescaled entropy of the empirical distribution of the cylinders of size growing
logarithmically with the size of the sample. We prove a central limit theorem for the first one.
We also prove that the second one does not have Gaussian fluctuations. This solves a problem
formulated in Iosifescu (1965)
LARGE-DENSITY FLUCTUATIONS FOR THE ONE-DIMENSIONAL SUPERCRITICAL CONTACT PROCESS RID G-5544-2010
No full text
Hydrodynamic limit for interacting neurons
No full textThis paper studies the hydrodynamic limit of a stochastic process describing the time evolution of a system with neurons with
mean-field interactions produced both by chemical and by electrical
synapses. This system can be informally described as follows. Each
neuron spikes randomly following a point process with rate depending
on its membrane potential. At its spiking time, the membrane
potential of the spiking neuron is reset to the value
and, simultaneously, the membrane potentials of
the other neurons are increased by an amount of {\sl
energy} . This mimics the effect of chemical
synapses. Additionally, the effect of electrical synapses is
represented by a deterministic drift of all the membrane potentials
towards the average value of the system.
We show that, as the system size diverges, the distribution of membrane potentials becomes deterministic and is described by a
limit density which obeys a non linear PDE which is a conservation law of hyperbolic type
Estimating the interaction graph of stochastic neuronal dynamics by observing only pairs of neurons
Full text linkWe address the questions of identifying pairs of interacting neurons from the observation of their spiking activity. The neuronal network is modeled by a system of interacting point processes with memory of variable length. The influence of a neuron on another can be either excitatory or inhibitory. To identify the existence and the nature of an interaction we propose an algorithm based only on the observation of joint activity of the two neurons in successive time slots. This reduces the amount of computation and storage required to run the algorithm, thereby making the algorithm suitable for the analysis of real neuronal data sets. We obtain computable upper bounds for the probabilities of false positive and false negative detection. As a corollary we prove the consistency of the identification algorithm
Kalikov - type decomposition for multicolor infinite range particle systems
No full textWe consider a particle system on Zd with real state space and interactions
of infinite range. Assuming that the rate of change is continuous we obtain a
Kalikow-type decomposition of the infinite range change rates as a mixture of
finite range change rates. Furthermore, if a high noise condition holds, as an
application of this decomposition, we design a feasible perfect simulation algorithm
to sample from the stationary process. Finally, the perfect simulation
scheme allows us to forge an algorithm to obtain an explicit construction of
a coupling attaining Ornstein’s ̄ d-distance for two ordered Ising probability
measures
Informe que rinde el Visitador Joseph de Galves a D. Antonio Bucareli del estado en que se encuentran las provincias de Nueva España. (Méxi-co, 1771).
No full textInforme que rinde el Visitador Joseph de Galves a D. Antonio Bucareli del estado en que se encuentran las provincias de Nueva España. (Méxi-co, 1771)
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