Waves and Oscillations in Model Neuronal Networks

In this thesis methods from nonlinear dynamical systems, pattern formation and bifurcation theory, combined with numerical simulations, are applied to three models in neuroscience. In Chapter 1 we analyze the Wilson-Cowan equations for a single self-excited population of cells with absolute refractory period. We construct the normal form for a Hopf bifurcation, and prove that by increasing the refractory period the network switches from a steady state to an oscillatory behavior. Numerical simulations indicate that for large values of refractoriness the oscillation converges to a relaxation-like pattern, the period of which we estimate. Chapter 2 brings new results for the rate model introduced by Hansel and Sompolinsky who study feature selectivity in local cortical circuits. We study their model with a more general, nonlinear sigmoid gain function, and prove that the system can exhibit different kind of patterns such as stationary states, traveling waves and standing waves. Standing waves can be obtained only if the threshold is sufficiently high and only for intermediate values of the strength of adaptation. A large adaptation strength destabilizes the pattern. Therefore the localized activity starts to propagate along the network, resulting in a traveling wave. We construct the normal form for Hopf and Takens-Bogdanov with O(2)-symmetry bifurcations and study the interactions between spatial and spatio-temporal patterns in the neural network. Numerical simulations are provided.Chapter 3 addresses several questions with regard to the traveling wave propagation in a leaky-integrate-and-fire model for a network with purely excitatory (exponentially decaying) synaptic coupling. We analyze the case when the neurons fire multiple spikes and derive a formula for the voltage. We compute in a certain parameter space, the curves that delineate the region where single-spike traveling wave solutions exist, and show that there is a region of parameter space where neurons can propagate a two-spike traveling wave

Rheology in Wood Engineering

AbstractThe system strains under external loads in a certain amount of time and under the influence of the environmental factors define the rheological behavior. Rheological phenomena depend on many factors: temperature such as air humidity or moisture content of rheological system, radiations in term of intensity, duration, type - UV, IR, X, geometry of the parts; loadings in terms of intensity, variation, duration; defects; aggressive environment; composition, material properties; combinations of these factors. Rheology science is based on the theories of the strength of materials, thermodynamics, chemistry and materials science, but in terms of application, it provides a personalized analysis or diagnosis according to the condition of the structures/systems used. Wooden constructions are subjected to various loadings on both short and long durations. The joints can be elastic (flexible) if the failure occurs gradually, or plastic, if the failure occurs suddenly. Sudden failure of joints is caused by shear as predominant load because wood does not resist at shear stresses. In order to study the rheological behavior of the wood joints with metal rods under constant load, three types of joints in terms of diameters of bolts and stiffening systems were tested. They were stressed to traction force of 500 to 900N for 200 days, in real conditions of temperature (-7°C la +30°C) and humidity (from 47.8% to 83.8%). The aim of the tests were to determine the rheological behavior of wooden joints; variation of deformations in relation to the relative humidity and temperature; rate of strain and connections in determining rheological model of wood with threaded rods. It was found that the low temperatures during winter (-7…0°C) correlated with high relative humidity led to sudden changes in strain. It was observed that the high-speed deformation had a joint with the largest diameter rod (8mm). The paper highlights the rheological analysis of joints in wooden rods in real conditions of temperature and humidity, with regards to applied tension and the determination of the creep function that characterizes these types of connections, establishing the optimum diameter rods

Dynamical characteristics common to neuronal competition models.

Shpiro A, Curtu R, Rinzel J, Rubin N. Dynamical characteristics common to neuronal competition models. J Neurophysiol 97: [462][463][464][465][466][467][468][469][470][471][472][473] 2007. First published October 25, 2006; doi:10.1152/jn.00604.2006. Models implementing neuronal competition by reciprocally inhibitory populations are widely used to characterize bistable phenomena such as binocular rivalry. We find common dynamical behavior in several models of this general type, which differ in their architecture in the form of their gain functions, and in how they implement the slow process that underlies alternating dominance. We focus on examining the effect of the input strength on the rate (and existence) of oscillations. In spite of their differences, all considered models possess similar qualitative features, some of which we report here for the first time. Experimentally, dominance durations have been reported to decrease monotonically with increasing stimulus strength (such as Levelt's "Proposition IV"). The models predict this behavior; however, they also predict that at a lower range of input strength dominance durations increase with increasing stimulus strength. The nonmonotonic dependency of duration on stimulus strength is common to both deterministic and stochastic models. We conclude that additional experimental tests of Levelt's Proposition IV are needed to reconcile models and perception. I N T R O D U C T I O N Binocular rivalry occurs when two different images are presented to the two eyes. With such ambiguous stimuli, only one of the images is perceived at any given moment, with dominance switching between the two images in a haphazard manner. The average dominance durations are typically a few seconds. Several stimulus parameters have been shown to influence the dynamical characteristics of the perceptual alternations. In particular, increasing the contrast of the rivaling images has been shown to increase the frequency of percept switching, which implies a decrease in the mean dominance times, an observation known as "Levelt's Proposition IV" Reciprocal inhibition architecture is widely used to describe binocular rivalry and bistable perception in general. The dominant side of the system exerts a strong inhibitory influence on the competing side, so that the latter is suppressed. The switching in dominance between the two sides is realized by a slow negative feedback process, such as spike-frequency adaptation or synaptic depression, that weakens the inhibition either by decreasing the activity of the dominant side or by decreasing the connectivity between the sides and allows the suppressed population to become active. These general principles have been incorporated in numerous mathematical models of binocular rivalry In addition to studying these two models as formulated, we also consider two variations of the model of We identify the parameter regimes where each model shows behavior that is consistent with Levelt's Proposition IV. In addition, we demonstrate that all the models predict previously unreported types of behavior. Using stimulation strength as the control variable, we focus on its effect on the existence and rate of oscillations. In spite of the differences in architecture and mathematical formulation of the explored models, we find substantial generalities in their behavior. In all models, for very high stimulus strengths the two populations are simultaneously active at a high level. Just below this regime is a range for stimulus strength where the behavior of the system is oscillatory, with the dominance period of each percept decreasing as stimulus strength increases, in accordance with Levelt's Proposition IV (decreasing duration, or DD behavior). However, for input strengths below this range new regimes of behavior are discovered: first, a winner-take-all (nonrivaling steady dominance) behavior appears. Next, as stimulus strength is further reduced, another range of rivalry (oscillatory) behavior appears, but this time with the dominance periods increasing with increasing input (increasing duration, or ID behavior). Finally, at very low input strengths there is again a range where the two populations are simultaneously active, this time at a low leve

An Asynchronous Solver for Differential Equations Arising from River Basin Models

Source: ICHE Conference Archive - https://mdi-de.baw.de/icheArchiv

Model-based functional neuroimaging using dynamic neural fields: An integrative cognitive neuroscience approach

A fundamental challenge in cognitive neuroscience is to develop theoretical frameworks that effectively span the gap between brain and behavior, between neuroscience and psychology. Here, we attempt to bridge this divide by formalizing an integrative cognitive neuroscience approach using dynamic field theory (DFT). We begin by providing an overview of how DFT seeks to understand the neural population dynamics that underlie cognitive processes through previous applications and comparisons to other modeling approaches. We then use previously published behavioral and neural data from a response selection Go/Nogo task as a case study for model simulations. Results from this study served as the ‘standard’ for comparisons with a model-based fMRI approach using dynamic neural fields (DNF). The tutorial explains the rationale and hypotheses involved in the process of creating the DNF architecture and fitting model parameters. Two DNF models, with similar structure and parameter sets, are then compared. Both models effectively simulated reaction times from the task as we varied the number of stimulus–response mappings and the proportion of Go trials. Next, we directly simulated hemodynamic predictions from the neural activation patterns from each model. These predictions were tested using general linear models (GLMs). Results showed that the DNF model that was created by tuning parameters to capture simultaneously trends in neural activation and behavioral data quantitatively outperformed a Standard GLM analysis of the same dataset. Further, by using the GLM results to assign functional roles to particular clusters in the brain, we illustrate how DNF models shed new light on the neural populations’ dynamics within particular brain regions. Thus, the present study illustrates how an interactive cognitive neuroscience model can be used in practice to bridge the gap between brain and behavior

26th Annual Computational Neuroscience Meeting (CNS*2017): Part 3 - Meeting Abstracts - Antwerp, Belgium. 15–20 July 2017

This work was produced as part of the activities of FAPESP Research,\ud Disseminations and Innovation Center for Neuromathematics (grant\ud 2013/07699-0, S. Paulo Research Foundation). NLK is supported by a\ud FAPESP postdoctoral fellowship (grant 2016/03855-5). ACR is partially\ud supported by a CNPq fellowship (grant 306251/2014-0)