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Recently developed neural network-based wave function methods are capable of achieving state-of-the-art results for finding the ground state in real space. In this work, a neural network-based method is used to compute excited states. We…
An adaptive network model using SIS epidemic propagation with link-type dependent link activation and deletion is considered. Bifurcation analysis of the pairwise ODE approximation and the network-based stochastic simulation is carried out,…
This work deals with the stationary analysis of two-dimensional partially homogeneous nearest-neighbour random walks. Such type of random walks are characterized by the fact that the one-step transition probabilities are functions of the…
Although conditional branching between possible behavioural states is a hallmark of intelligent behavior, very little is known about the neuronal mechanisms that support this processing. In a step toward solving this problem we demonstrate…
We explore the cooperative behaviour and phase transitions of interacting networks by studying a simplified model consisting of Ising spins placed on the nodes of two coupled Erd\"os-R\'enyi random graphs. We derive analytical expressions…
We study the phenomenological model of ensemble of two FitzHugh-Nagumo neuron-like elements with symmetric excitatory couplings. The main advantage of proposed model is the new approach to model of coupling which is implemented by smooth…
This paper studies the dynamics of a network of diffusively-coupled bistable systems. Under mild conditions and without requiring smoothness of the vector field, we analyze the network dynamics and show that the solutions converge globally…
Genetic regulatory networks are usually modeled by systems of coupled differential equations and by finite state models, better known as logical networks, are also used. In this paper we consider a class of models of regulatory networks…
Many biological neuronal networks exhibit highly variable spiking activity. Balanced networks offer a parsimonious model of this variability. In balanced networks, strong excitatory synaptic inputs are canceled by strong inhibitory inputs…
We studied, both analytically and numerically, complex excitable networks, in which connections are time dependent and some of the nodes remain silent at each time step. More specifically, (a) there is a heterogenous distribution of…
We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral…
We present extensive experiments training and testing hidden units in deep networks that emit only a predefined, static, number of discretized values. These units provide benefits in real-world deployment in systems in which memory and/or…
We study the collective dynamics of strongly diffusively coupled excitable elements on small random tree networks. Stochastic external inputs are applied to the leaves causing large spiking events. Those events propagate along the tree…
Stochastic reaction networks are mathematical models frequently used in, but not limited to, biochemistry. These models are continuous-time Markov chains whose transition rates depend on certain parameters called rate constants, which…
The dynamics of noise-resilient Boolean networks with majority functions and diverse topologies is investigated. A wide class of possible topological configurations is parametrized as a stochastic blockmodel. For this class of networks, the…
Mixed positive and negative feedback loops are often found in biological systems which support oscillations. In this work we consider a prototype of such systems, which has been recently found at the core of many genetic circuits showing…
We study a model for a statistical network formed by interactions between its nodes and links. Each node can be in one of two states (Ising spin up or down) and the node-link interaction facilitates linking between the like nodes. For high…
While most models of randomly connected networks assume nodes with simple dynamics, nodes in realistic highly connected networks, such as neurons in the brain, exhibit intrinsic dynamics over multiple timescales. We analyze how the…
The response of the Hodgkin-Huxley neuronal model subjected to stochastic uncorrelated spike trains originating from a large number of inhibitory and excitatory post-synaptic potentials is analyzed in detail. The model is examined in its…
Models of simple excitable dynamics on graphs are an efficient framework for studying the interplay between network topology and dynamics. This subject is a topic of practical relevance to diverse fields, ranging from neuroscience to…