Related papers: Macroscopic coherent structures in a stochastic ne…
The distinct timescales of synaptic plasticity and neural activity dynamics play an important role in the brain's learning and memory systems. Activity-dependent plasticity reshapes neural circuit architecture, determining spontaneous and…
We study a stochastic nonlocal PDE, arising in the context of modelling spatially distributed neural activity, which is capable of sustaining stationary and moving spatially-localized ``activity bumps''. This system is known to undergo a…
Coarse timesteppers provide a bridge between microscopic / stochastic system descriptions and macroscopic tasks such as coarse stability/bifurcation computations. Exploiting this computational enabling technology, we present a framework for…
Localized persistent neural activity can encode delayed estimates of continuous variables. Common experiments require that subjects store and report the feature value (e.g., orientation) of a particular cue (e.g., oriented bar on a screen)…
We demonstrate that waves in distinct layers of a neuronal network can become phase-locked by common spatiotemporal noise. This phenomenon is studied for stationary bumps, traveling waves, and breathers. A weak noise expansion is used to…
The proposed stochastic model for pedestrian dynamics is based on existing approaches using cellular automata, combined with substantial extensions, to compensate the deficiencies resulting of the discrete grid structure. This agent motion…
We deal with the problem of bridging the gap between two scales in neuronal modeling. At the first (microscopic) scale, neurons are considered individually and their behavior described by stochastic differential equations that govern the…
Understanding the activity of large populations of neurons is difficult due to the combinatorial complexity of possible cell-cell interactions. To reduce the complexity, coarse-graining had been previously applied to experimental neural…
Understanding and predicting environmental phenomena often requires the construction of spatio-temporal statistical models, which are typically Gaussian processes. A common assumption made on Gaussian processes is that of covariance…
We introduce and analyze a class of neural network models motivated by the Drosophila central complex nervous system, designed to capture the emergence and dynamics of orientation-selective activity bumps. Starting from a biologically…
We study bifurcations in networks of integrate-and-fire neurons with stochastic spike emission, focusing on the effects of the spatial and temporal structure of the synaptic interactions. Using a deterministic mean-field approximation of…
We study the effects of noise on stationary pulse solutions (bumps) in spatially extended neural fields. The dynamics of a neural field is described by an integrodifferential equation whose integral term characterizes synaptic interactions…
The highly variable dynamics of neocortical circuits observed in vivo have been hypothesized to represent a signature of ongoing stochastic inference but stand in apparent contrast to the deterministic response of neurons measured in vitro.…
In this paper, we propose a stochastic cellular automaton model of traffic flow extending two exactly solvable stochastic models, i.e., the asymmetric simple exclusion process and the zero range process. Moreover it is regarded as a…
This thesis develops exact analytical tools to study strongly correlated stochastic systems, with a focus on extreme value statistics, gap statistics, and full counting statistics in multi-particle processes. A central contribution is the…
Many complex systems occurring in the natural or social sciences or economics are frequently described on a microscopic level, e.g., by lattice- or agent-based models. To analyze the states of such systems and their bifurcation structure on…
We propose a stochastic dynamical model of noisy neural networks with complex architectures and discuss activation of neural networks by a stimulus, pacemakers and spontaneous activity. This model has a complex phase diagram with…
Graph neural networks are often used to model interacting dynamical systems since they gracefully scale to systems with a varying and high number of agents. While there has been much progress made for deterministic interacting systems,…
Learning is based on synaptic plasticity, which affects and is driven by neural activity. Because pre- and postsynaptic spiking activity is shaped by randomness, the synaptic weights follow a stochastic process, requiring a probabilistic…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…