Zobrazeno 1 - 10
of 83
pro vyhledávání: '"Solem, Susanne"'
We propose and analyze a procedure for using a standard activity-based neuron network model and firing data to compute the effective connection strengths between neurons in a network. We assume a Heaviside response function, that the external inputs
Externí odkaz:
http://arxiv.org/abs/2409.07241
A system of partial differential equations representing stochastic neural fields was recently proposed with the aim of modelling the activity of noisy grid cells when a mammal travels through physical space. The system was rigorously derived from a s
Externí odkaz:
http://arxiv.org/abs/2307.08077
Publikováno v:
J. Sci. Comput. 99, 44 (2024)
A convergent numerical method for $\alpha$-dissipative solutions of the Hunter--Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initial data, and then solving exactly using the generalized method o
Externí odkaz:
http://arxiv.org/abs/2303.08763
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established. The resul
Externí odkaz:
http://arxiv.org/abs/2205.11968
Several differential equation models have been proposed to explain the formation of patterns characteristic of the grid cell network. Understanding the robustness of these patterns with respect to noise is one of the key open questions in computation
Externí odkaz:
http://arxiv.org/abs/2112.06213
The activity generated by an ensemble of neurons is affected by various noise sources. It is a well-recognised challenge to understand the effects of noise on the stability of such networks. We demonstrate that the patterns of activity generated by n
Externí odkaz:
http://arxiv.org/abs/2109.07936
Autor:
Erhardt, André H., Solem, Susanne
The 19-dimensional TP06 cardiac muscle cell model is reduced to a 17-dimensional version, which satisfies the required conditions for performing an analysis of its dynamics by means of bifurcation theory. The reformulated model is shown to be a good
Externí odkaz:
http://arxiv.org/abs/2105.05544
Publikováno v:
In Journal de mathématiques pures et appliquées
Autor:
Erhardt, André H., Solem, Susanne
Cardiac muscle cells can exhibit complex patterns including irregular behaviour such as chaos or (chaotic) early afterdepolarisations (EADs), which can lead to sudden cardiac death. Suitable mathematical models and their analysis help to predict the
Externí odkaz:
http://arxiv.org/abs/2005.07070
Publikováno v:
BIT Numerical Mathematics, vol. 61, p. 441-471, 2021
In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order
Externí odkaz:
http://arxiv.org/abs/2005.03882