[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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