Related papers: Initial conditions in the neural field model
Understanding the dynamical behavior of many-particle systems both in and out of equilibrium is a central issue in both statistical mechanics and complex systems theory. One question involves "nature versus nurture": given a system with a…
Currently used models of opinion formation use random initial conditions. In reality, most people in a social network, except for a small fraction of the population, are initially either unaware of, or indifferent to, the disputed issue. To…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Assessing the systemic effects of uncertainty that arises from agents' partial observation of the true states of the world is critical for understanding a wide range of scenarios. Yet, previous modeling work on agent learning and…
Recurrent neural networks (RNNs) trained on neuroscience-inspired tasks offer powerful models of brain computation. However, typical training paradigms rely on open-loop, supervised settings, whereas real-world learning unfolds in…
Phenomics is concerned with detailed description of all aspects of organisms, from their physical foundations at genetic, molecular and cellular level, to behavioural and psychological traits. Neuropsychiatric phenomics, endorsed by NIMH,…
Traditional mathematical approaches to studying analytically the dynamics of neural networks rely on the mean-field approximation, which is rigorously applicable only to networks of infinite size. However, all existing real biological…
We propose the use of recurrent neural networks for classifying phases of matter based on the dynamics of experimentally accessible observables. We demonstrate this approach by training recurrent networks on the magnetization traces of two…
Basic problems for the construction of a scenario for the Life are discussed. To study the problems in terms of dynamical systems theory, a scheme of intra-inter dynamics is presented. It consists of internal dynamics of a unit, interaction…
The integration and transmission of information in the brain are dependent on the interplay between structural and dynamical properties. Implicit in any pursuit aimed at understanding neural dynamics from appropriate sets of mathematically…
This paper explores the connection between dynamical system properties and statistical physics of ensembles of such systems. Simple models are used to give novel phase transitions; particularly for finite N particle systems with many…
We analyse the long-lasting effects of initial conditions on fluctuations in one-dimensional diffusive systems. We consider both the fluctuations of current for non-interacting diffusive particles starting from a step-like initial density…
Starting from the concept of binary interactions between pairs of particles, a kinetic framework for the description of the action potential dynamics on a neural network is proposed. It consists of two coupled levels: the description of a…
Dynamics of a chaotic spiking neuron model are being studied mathematically and experimentally. The Nonlinear Dynamic State neuron (NDS) is analysed to further understand the model and improve it. Chaos has many interesting properties such…
In a many body system, constituents interact with each other, forming a recursive pattern of interaction and giving rise to many interesting phenomena. Based upon concepts of the modern many body theory, a model for a generic many body…
Declarative approaches to process modeling are regarded as well suited for highly volatile environments as they provide a high degree of flexibility. However, problems in understanding and maintaining declarative business process models…
Quantum theory provides an extensive framework for the description of the equilibrium properties of quantum matter. Yet experiments in quantum simulators have now opened up a route towards generating quantum states beyond this equilibrium…
In recent years, the field of neuroscience has gone through rapid experimental advances and a significant increase in the use of quantitative and computational methods. This growth has created a need for clearer analyses of the theory and…
The effect of initial spin configurations on zero-temperature Glauber spin dynamics in complex networks is investigated. In a system in which the initial spins are defined by centrality measures at the vertices of a network, a variety of…
This paper is an introduction to the membrane potential equation for neurons. Its properties are described, as well as sample applications. Networks of these equations can be used for modeling neuronal systems, which also process images and…