[Seminario] INVITACIÓN DOBLE SESIÓN Seminario Conjunto Núcleo MESCD/ Modelamiento Escolástico MARTES 27 DE NOVIEMBRE A CONTAR DE LAS 15:30 HRS.
Maria Ines Rivera
mrivera en dim.uchile.cl
Lun Nov 26 09:36:50 -03 2018
Estimados Académicos y Alumnos,
Se les invita para este martes 27 de noviembre a acontar de las 15:30
hrs, a 2 sesiones del *Seminario Conjunto Núcleo MESCD/ Modelamiento
Escolástico*, este seminario se realizará en la sala de seminarios John
Vob Neumann CMM, ubicada en la torre norte, piso 7 de Beauchef 851.
*
Seminario Conjunto Núcleo MESCD/ Modelamiento Escolástico*
*Primera sesión:*
**
*15:30-16:30 hrs *
*Expositor:*
*Rodrigo Cofré (CIMFAV* Universidad de Valparaiso*)*
*Titulo:*
*Collective behavior of spiking neuronal networks and other biological
systems inferred from the Maximum Entropy Principle.*
*Abstract: *
**Our sensations, thoughts, and memories emerge from interactions among
many neurons. Physicists have long hoped that the emergent collective
activity of populations of neurons could be described using the ideas
and methods of statistical mechanics. Among the many ideas rooted in
statistical physics that have been suggested to characterize the
collective activity in the brain, perhaps the most intriguing is the
idea of self-organized criticality [1]. While it is still unclear which
biological mechanisms are behind the collective behavior, the idea that
biological systems poise themselves at or near a critical point remains
tantalizing. In the past few years, new experimental techniques have
made it possible to build statistical mechanics models of biological
systems directly from experimental recordings, allowing researchers to
determine whether these ideas work in their models. In this talk, I will
review the surprising successes of the maximum entropy approach in the
field of spike train statistics [2,3,4] and some progress we have made
to generalize and better characterize results obtained from this
approach. In particular, I will discuss the surprising fact that the
statistical models that emerge from the experimental spike train
statistics seem to be poised at a critical point in their parameter
space [5], which suggests that there may be some deeper theoretical
principle behind this collective behavior [1].
[1] T. Mora and W. Bialek, Are biological systems poised at
criticality?, J. Stat. Phys, 144(2), 2011.
[2] E. Schneidman, M.J. Berry II, and R. Segev and W. Bialek, Weak
pairwise correlations imply string correlated network states in a neural
population, Nature, 440, 2006.
[3] R. Cofré and C. Maldonado, Information Entropy Production of Maximum
Entropy Markov Chains from Spike Trains, Entropy 20(34), 2018.
[4] R. Cofré and C. Maldonado, F. Rosas, Large Deviations Properties of
Maximum Entropy Markov Chains from Spike Trains, Entropy 20(8), 573, 2018.
[5] I. Mastromatteo and M. Marsili, On the criticality of inferred
models, Journal of Statistical Mechanics: Theory and Experiment, 2011.
*Segunda sesión*
*16:30-17:30 hrs. ***
**
*Expositor:*
*Hector Olivero (CIMFAV **Universidad de Valparaiso)*
*Titulo:*
*Synchronization of stochastic mean field networks of Hodgkin-Huxley
neurons with noisy channels.*
*Abstract:*
**In this work we are interested in a mathematical model for the
collective behavior of a fully connected network of finitely many
neurons when their number or when time go to infinity. We assume that
every neuron follows a stochastic version of the Hodgkin-Huxley model,
and that pairs of neurons interact through both electrical and chemical
synapses, the global connectivity being of mean field type. When
the leak conductance is strictly positive, we prove that if
the initial voltages are uniformly bounded and if the electrical
interaction between neurons is strong enough, then, uniformly in the
number of neurons, the whole system synchronizes exponentially fast as
time goes to infinity, up to some error controlled by (and
vanishing with) the channels noise level. Moreover, we prove that if
the random initial condition is exchangeable, on every bounded time
interval the propagation of chaos property for this system
holds (regardless of the interaction intensities). Combining these
results, we deduce that the nonlinear McKean-Vlasov equation describing
an infinite network of such neurons concentrates, as times goes to
infinity, around the dynamics of a single Hodgkin-Huxley neuron with
neurotransmitter channels. Our results are illustrated and
complemented with numerical simulations. Joint work with Mireille Bossy
and Joaquín Fontbona.
Martes 27 de Noviembre a contar de las 15:30 hrs, en la sala de
Seminarios John Von Neumann CMM, Beauchef 851, Torre Norte, Piso 7.
Esperando contar con su presencia, les saluda,
Ma. Inés Rivera
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