Related papers: Macroscopic coherent structures in a stochastic ne…
In [1], we have shown that the dynamics of an interconnected population of excitatory and inhibitory spiking neurons wandering around a Bogdanov-Takens (BT)bifurcation point can generate the observed scale-free avalanches at the population…
For many complex dynamical systems, a separation of scales prevails between the (microscopic) level of description of the available model, and the (macroscopic) level at which one would like to observe and analyze the system. For this type…
Among the different computational approaches modelling the dynamics of isogenic cell populations, discrete stochastic models can describe with sufficient accuracy the evolution of small size populations. However, for a systematic and…
Time series forecasting based on deep architectures has been gaining popularity in recent years due to their ability to model complex non-linear temporal dynamics. The recurrent neural network is one such model capable of handling…
We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…
In this paper we present a general framework in which to rigorously study the effect of spatio-temporal noise on traveling waves and stationary patterns. In particular the framework can incorporate versions of the stochastic neural field…
We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a "wrapper" around a fine-scale simulator. We discuss how this approach alleviates certain…
Biological neural networks are notoriously hard to model due to their stochastic behavior and high dimensionality. We tackle this problem by constructing a dynamical model of both the expectations and covariances of the fractions of active…
We show how the Equation-Free approach for multi-scale computations can be exploited to systematically study the dynamics of neural interactions on a random regular connected graph under a pairwise representation perspective. Using an…
We obtain exact travelling wave solutions for three families of stochastic one-dimensional nonequilibrium lattice models with open boundaries. These solutions describe the diffusive motion and microscopic structure of (i) of shocks in the…
We propose a new model based on the Ising model with the aim to study synaptic plasticity phenomena in neural networks. It is today well established in biology that the synapses or connections between certain types of neurons are…
Machine learning techniques not only offer efficient tools for modelling dynamical systems from data, but can also be employed as frontline investigative instruments for the underlying physics. Nontrivial information about the original…
Continuous "bump" attractors are an established model of cortical working memory for continuous variables and can be implemented using various neuron and network models. Here, we develop a generalizable approach for the approximation of…
We address an iterative procedure that can be used to detect coarse-grained hyperbolic unstable equilibria (saddle points) of microscopic simulators when no equations at the macroscopic level are available. The scheme is based on the…
Bottom-up models of functionally relevant patterns of neural activity provide an explicit link between neuronal dynamics and computation. A prime example of functional activity pattern is hippocampal replay, which is critical for memory…
Complex coherent dynamics is present in a wide variety of neural systems. A typical example is the voltage transitions between up and down states observed in cortical areas in the brain. In this work, we study this phenomenon via a…
We implement a computer-assisted approach that, under appropriate conditions, allows the bifurcation analysis of the coarse dynamic behavior of microscopic simulators without requiring the explicit derivation of closed macroscopic equations…
Over the past few years it has been demonstrated that "coarse timesteppers" establish a link between traditional numerical analysis and microscopic/ stochastic simulation. The underlying assumption of the associated…
Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…
In this paper, we investigate the existence, uniqueness, and spectral stability of traveling waves arising from a single threshold neural field model with one spatial dimension, a Heaviside firing rate function, axonal propagation delay,…