Uncertainty propagation in neuronal dynamical systems

One of the most notorious characteristics of neuronal electrical activity is its variability, whose origin is not just instrumentation noise, but mainly the intrinsically stochastic nature of neural computations. Neuronal models based on deterministic differential equations cannot account for such variability, but they can be extended to do so by incorporating random components. However, the computational cost of this strategy and the storage requirements grow exponentially with the number of stochastic parameters, quickly exceeding the capacities of current supercomputers. This issue is critical in Neurodynamics, where mechanistic interpretation of large, complex, nonlinear systems is essential. In this paper we present accurate and computationally efficient methods to introduce and analyse variability in neurodynamic models depending on multiple uncertain parameters. Their use is illustrated with relevant example

Sine-Gordon field theory for the calculatión of universal finite size corrections in the free energy of Coulomb systems at the Debye-Hückel regime

Magíster en FísicaMaestrí

Mecánica estadística, topología y el sonido del tambor

Se analizan los sistemas de Coulomb -salmueras y plasmas- desde puntos de vista micro y macroscópic

Mecánica estadística, tipología y el sonido del tambor

Discute algunas propiedades de estos sistemas (moléculas y átomos), en particular propiedades que dependen de su forma, o más precisamente de su tipología, lo cual nos permitirá encontrar una relación interesante entre estos sistemas, tan comunes en nuestras vidad, con conceptos metemáticos que podrían parecer lejanos a nuestra realida

Uncertainty propagation in nerve impulses through the action potential mechanism

We investigate the propagation of probabilistic uncertainty through the action potential mechanism in nerve cells. Using the Hodgkin-Huxley (H-H) model and Stochastic Collocation on Sparse Grids, we obtain an accurate probabilistic interpretation of the deterministic dynamics of the transmembrane potential and gating variables. Using Sobol indices, out of the eleven uncertain parameters in the H-H model, we unravel two main uncertainty sources, which account for more than 90\% of the fluctuations in neuronal responses, and have a direct biophysical interpretation. We discuss how this interesting feature of the H-H model allows one to reduce greatly the probabilistic degrees of freedom in uncertainty quantification analyses, saving CPU time in numerical simulations, and opening possibilities for probabilistic generalisation of other deterministic models of great importance in physiology and mathematical neuroscience