Integration of continuous-time dynamics in a spiking neural network simulator

Contemporary modeling approaches to the dynamics of neural networks consider two main classes of models: biologically grounded spiking neurons and functionally inspired rate-based units. The unified simulation framework presented here supports the combination of the two for multi-scale modeling approaches, the quantitative validation of mean-field approaches by spiking network simulations, and an increase in reliability by usage of the same simulation code and the same network model specifications for both model classes. While most efficient spiking simulations rely on the communication of discrete events, rate models require time-continuous interactions between neurons. Exploiting the conceptual similarity to the inclusion of gap junctions in spiking network simulations, we arrive at a reference implementation of instantaneous and delayed interactions between rate-based models in a spiking network simulator. The separation of rate dynamics from the general connection and communication infrastructure ensures flexibility of the framework. We further demonstrate the broad applicability of the framework by considering various examples from the literature ranging from random networks to neural field models. The study provides the prerequisite for interactions between rate-based and spiking models in a joint simulation

Fine Scale Simulation of Fractured Reservoirs: Applications and Comparison

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Dynamic Reconstruction of Complex Planar Objects on Irregular Isothetic Grids

International audienceThe vectorization of discrete regular images has been widely developed in many image processing and synthesis applications, where images are considered as a regular static data. Regardless of final application, we have proposed in [14] a reconstruction algorithm of planar graphical elements on irregular isothetic grids. In this paper, we present a dynamic version of this algorithm to control the reconstruction. Indeed, we handle local refinements to update efficiently our complete shape representation. We also illustrate an application of our contribution for interactive approximation of implicit curves by lines, controlling the topology of the reconstruction

An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum

Motivated by recent experimental studies, we derive and analyze a twodimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a model of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The model equations for the poroelastic medium are obtained from continuum force-balance equations that include the relevant mechanical fields and an incompressibility relation for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stresses. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a chemomechanical feedback. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.Comment: Additional supplemental material is supplie

Travelling waves in a model of quasi-active dendrites with active spines

Dendrites, the major components of neurons, have many different types of branching structures and are involved in receiving and integrating thousands of synaptic inputs from other neurons. Dendritic spines with excitable channels can be present in large densities on the dendrites of many cells. The recently proposed Spike-Diffuse-Spike (SDS) model that is described by a system of point hot-spots (with an integrate-and-fire process) embedded throughout a passive tree has been shown to provide a reasonable caricature of a dendritic tree with supra-threshold dynamics. Interestingly, real dendrites equipped with voltage-gated ion channels can exhibit not only supra-threshold responses, but also sub-threshold dynamics. This sub-threshold resonant-like oscillatory behaviour has already been shown to be adequately described by a quasi-active membrane. In this paper we introduce a mathematical model of a branched dendritic tree based upon a generalisation of the SDS model where the active spines are assumed to be distributed along a quasi-active dendritic structure. We demonstrate how solitary and periodic travelling wave solutions can be constructed for both continuous and discrete spine distributions. In both cases the speed of such waves is calculated as a function of system parameters. We also illustrate that the model can be naturally generalised to an arbitrary branched dendritic geometry whilst remaining computationally simple. The spatio-temporal patterns of neuronal activity are shown to be significantly influenced by the properties of the quasi-active membrane. Active (sub- and supra-threshold) properties of dendrites are known to vary considerably among cell types and animal species, and this theoretical framework can be used in studying the combined role of complex dendritic morphologies and active conductances in rich neuronal dynamics

Interest rate models with Markov chains

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Modeling interest rate dynamics: an infinite-dimensional approach

We present a family of models for the term structure of interest rates which describe the interest rate curve as a stochastic process in a Hilbert space. We start by decomposing the deformations of the term structure into the variations of the short rate, the long rate and the fluctuations of the curve around its average shape. This fluctuation is then described as a solution of a stochastic evolution equation in an infinite dimensional space. In the case where deformations are local in maturity, this equation reduces to a stochastic PDE, of which we give the simplest example. We discuss the properties of the solutions and show that they capture in a parsimonious manner the essential features of yield curve dynamics: imperfect correlation between maturities, mean reversion of interest rates and the structure of principal components of term structure deformations. Finally, we discuss calibration issues and show that the model parameters have a natural interpretation in terms of empirically observed quantities.Comment: Keywords: interest rates, stochastic PDE, term structure models, stochastic processes in Hilbert space. Other related works may be retrieved on http://www.eleves.ens.fr:8080/home/cont/papers.htm

Network Plasticity as Bayesian Inference

General results from statistical learning theory suggest to understand not only brain computations, but also brain plasticity as probabilistic inference. But a model for that has been missing. We propose that inherently stochastic features of synaptic plasticity and spine motility enable cortical networks of neurons to carry out probabilistic inference by sampling from a posterior distribution of network configurations. This model provides a viable alternative to existing models that propose convergence of parameters to maximum likelihood values. It explains how priors on weight distributions and connection probabilities can be merged optimally with learned experience, how cortical networks can generalize learned information so well to novel experiences, and how they can compensate continuously for unforeseen disturbances of the network. The resulting new theory of network plasticity explains from a functional perspective a number of experimental data on stochastic aspects of synaptic plasticity that previously appeared to be quite puzzling.Comment: 33 pages, 5 figures, the supplement is available on the author's web page http://www.igi.tugraz.at/kappe