7,520 research outputs found
Towards the Modeling of Neuronal Firing by Gaussian Processes
This paper focuses on the outline of some computational methods for the
approximate solution of the integral equations for the neuronal firing
probability density and an algorithm for the generation of sample-paths in
order to construct histograms estimating the firing densities. Our results
originate from the study of non-Markov stationary Gaussian neuronal models with
the aim to determine the neuron's firing probability density function. A
parallel algorithm has been implemented in order to simulate large numbers of
sample paths of Gaussian processes characterized by damped oscillatory
covariances in the presence of time dependent boundaries. The analysis based on
the simulation procedure provides an alternative research tool when closed-form
results or analytic evaluation of the neuronal firing densities are not
available.Comment: 10 pages, 3 figures, to be published in Scientiae Mathematicae
Japonica
Oscillatory phase transition and pulse propagation in noisy integrate-and-fire neurons
We study non-locally coupled noisy integrate-and-fire neurons with the
Fokker-Planck equation. A propagating pulse state and a wavy state appear as a
phase transition from an asynchronous state. We also find a solution in which
traveling pulses are emitted periodically from a pacemaker region.Comment: 9 pages, 4 figure
Lyapunov functions for a non-linear model of the X-ray bursting of the microquasar GRS 1915+105
This paper introduces a biparametric family of Lyapunov functions for a
non-linear mathematical model based on the FitzHugh-Nagumo equations able to
reproduce some main features of the X-ray bursting behaviour exhibited by the
microquasar GRS 1915+105. These functions are useful to investigate the
properties of equilibrium points and allow us to demonstrate a theorem on the
global stability. The transition between bursting and stable behaviour is also
analyzed.Comment: Published on International Journal of Non-Linear Mechanics, vol. 88,
pp. 142-14
On Myosin II dynamics in the presence of external loads
We address the controversial hot question concerning the validity of the
loose coupling versus the lever-arm theories in the actomyosin dynamics by
re-interpreting and extending the phenomenological washboard potential model
proposed by some of us in a previous paper. In this new model a Brownian motion
harnessing thermal energy is assumed to co-exist with the deterministic swing
of the lever-arm, to yield an excellent fit of the set of data obtained by some
of us on the sliding of Myosin II heads on immobilized actin filaments under
various load conditions. Our theoretical arguments are complemented by accurate
numerical simulations, and the robustness of the model is tested via different
choices of parameters and potential profiles.Comment: 6 figures, 8 tables, to appear on Biosystem
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