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Departamento de Matematica

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Charlas 2006

Viernes 15 de Septiembre, 16hs: Marisa Toschi (Universidad Nacional de La Plata)

Título: Estimaciones a priori con pesos para soluciones del Laplaciano.

Martes 4 de Abril, 14hs: Horacio Rotstein (Boston University)

Título:A dynamical systems approach to the study of rhythmic subthreshold neural activity.

Abstract: The study of rhythmic activity in various areas of the brain has been the object of many experimental and theoretical investigations. This talk concerns rhythmic oscillatory activity at theta frequencies (8 - 12 Hz) in the medial entorhinal cortex (MEC), which is the interface between the neocortex and the hippocampus, and plays an important role in some forms of learning and memory. Stellate cells (SCs), the main cell type in MEC layer II, display complex mixed-mode oscillatory (MMO) patterns (at theta frequencies) in which both subthreshold oscillations (STOs) and spikes coexist. These experimental results have been reproduced, via simulations, using biophysical models of SCs. These models consist of a multiscale system of nonlinear, high-dimensional, ordinary differential equations describing the evolution of voltage and other biophysical variables. A quantitative investigation, beyond simulations, on how the interaction between the participating SC's currents creates time scales that allow the cell to fire at theta frequencies has been difficult, mainly due to the complexity of the models and the lack of appropriate tools to deal with them. In this talk we answer some of the relevant mechanistic questions. We show that, during the interspike interval (ISI) where STOs are generated, the SC seven-dimensional model can be reduced to a three-dimensional one, with two well differentiated time scales. Using dynamical systems arguments we provide a mechanism for generations of STOs.  This mechanism is based on a ``canard structure'', in which relevant trajectories stay close to repelling manifolds for a significant interval of time. We also show that the transition from subthreshold oscillatory activity to spiking (``canard explosion'') is controlled in the ISI by the same structure. A similar mechanism is invoked to explain why noise increases the robustness of the STO regime.

Viernes 7 de Abril, 11hs. Martin Stynes (National University of Ireland)

Título: Convection-diffusion problems and their numerical solution.

Lunes 10 de Abril, 15hs.Uri Ascher University of British Columbia – Canada)

Título: Level set regularization for highly ill-posed distributed parameter estimation problems.

Martes 11 de Abril, 14hs: Rafael Orive (Consejo Superior de Investigaciones Científicas España)

Título: Ondas de Bloch y aplicaciones.

Martes 9 de Mayo, 14hs: Bruno Canuto (FCEN - UBA)

Título: Algunas observaciones sobre el problema de Serrin .

Martes 6 de Junio, 14hs: Federico Tournier (IAM - CONICET)

Título: Técnicas para la desigualdad de Harnack.

Abstract: Introducción a la desigualdad de Harnack para ecuaciones en forma de no divergencia. Técnicas para su demostración y generalización para otro tipo de ecuaciones.

Lunes 17 de Julio, 14hs. Jesús Hernández Alonso (UAM - España)

Título:Soluciones positivas para problemas elípticos singulares.

Jueves 30 de Agosto, 14hs. Antonio Degasperis (Universita' di Roma "La Sapienza")

Título: Novel soliton dynamics in systems of coupled nonlinear wave equations.

Abstract: Multi-component fields modeling the propagation of nonlinear waves may display a rich phenomenology of soliton dynamics. Several integrable systems of coupled wave equations are constructed and discussed to show novel features of soliton behaviors. In particular boomerons of the 3-wave resonant interaction equations are shown to describe decay and excitation processes.

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Last modified 2010-04-15 12:13 PM

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