11 citations · 54 across the 12 of their papers we have counts for
13 papers
Estimating neural connection strengths from firing intervals
Maren Bråthen Kristoffersen, Bjørn Fredrik Nielsen, Susanne Solem
We propose and analyse a procedure for using a standard activity-based neuron network model and firing data to compute the effective connection strengths between neurons in a netwo…
Well-posedness and stability of a stochastic neural field in the form of a partial differential equation
José Antonio Carrillo, Pierre Roux, Susanne Solem
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 trav…
A Convergent Numerical Algorithm for -Dissipative Solutions of the Hunter-Saxton Equation
Thomas Christiansen, Katrin Grunert, Anders Nordli +1
A convergent numerical method for -dissipative solutions of the Hunter-Saxton equation is derived. The method is based on applying a tailor-made projection operator to the initi…
Noise-driven bifurcations in a nonlinear Fokker-Planck system describing stochastic neural fields
José A. Carrillo, Pierre Roux, Susanne Solem
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential…
The mean field limit of stochastic differential equation systems modelling grid cells
José A. Carrillo, Andrea Clini, Susanne Solem
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…
Noise-driven bifurcations in a neural field system modelling networks of grid cells
Jose A. Carrillo, Helge Holden, Susanne Solem
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…
Analysis and simulation of a modified cardiac cell model givesaccurate predictions of the dynamics of the original one
André H. Erhardt, Susanne Solem
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 mean…
On complex dynamics in a Purkinje and a ventricular cardiac cell model
André H. Erhardt, Susanne Solem
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…
Numerical conservative solutions of the Hunter--Saxton equation
Katrin Grunert, Anders Nordli, Susanne Solem
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…
The optimal convergence rate of monotone schemes for conservation laws in the Wasserstein distance
Adrian Montgomery Ruf, Espen Sande, Susanne Solem
In 1994, Nessyahu, Tadmor and Tassa studied convergence rates of monotone finite volume approximations of conservation laws. For compactly supported, $\Lip^+$-bounded initial data…
Convergence rates of the front tracking method for conservation laws in the Wasserstein distances
Susanne Solem
We prove that front tracking approximations to entropy solutions of scalar conservation laws with convex fluxes converge at a rate of in the 1-Wasserstein distance . As…
A second-order numerical method for the aggregation equations
José A. Carrillo, Ulrik Skre Fjordholm, Susanne Solem
Inspired by so-called TVD limiter-based second-order schemes for hyperbolic conservation laws, we develop a second-order accurate numerical method for multi-dimensional aggregation…
Second-order convergence of monotone schemes for conservation laws
Ulrik S. Fjordholm, Susanne Solem
We prove that a class of monotone, \emph{-contractive} schemes for scalar conservation laws converge at a rate of in the Wasserstein distance (-distance), whenever…