Related papers: Thermalization of isolated harmonic networks under…
Kinetics of a balanced network of neurons with a sparse grid of synaptic links is well representable by the stochastic dynamics of a generic neuron subject to an effective shot noise. The rate of delta-pulses of the noise is determined…
The dynamical behavior of networked systems is expected to reflect the features of their coupling structure. Yet, symmetry-broken solutions often occur in symmetrically coupled networks. An example is provided by the so-called solitary…
Characterizing the in uence of network properties on the global emerging behavior of interacting elements constitutes a central question in many areas, from physical to social sciences. In this article we study a primary model of disordered…
Randomly coupled Ising spins constitute the classical model of collective phenomena in disordered systems, with applications covering ferromagnetism, combinatorial optimization, protein folding, stock market dynamics, and social dynamics.…
We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…
The time elapsed model describes the firing activity of an homogeneous assembly of neurons thanks to the distribution of times elapsed since the last discharge. It gives a mathematical description of the probability density of neurons…
Simple binary-state coordination models are widely used to study collective socio-economic phenomena such as the spread of innovations or the adoption of products on social networks. The common trait of these systems is the occurrence of…
We demonstrate that solitary states can be widely observed for networks of coupled oscillators with local, non-local and global couplings, and they preserve in both thermodynamic and Hamiltonian limits. We show that depending on units' and…
In this paper, a detailed analysis on normal modes of the linearized Hermite collision operator is presented, which follows from linearizing spin Boltzmann equation for massive fermions proposed in \cite{Weickgenannt:2021cuo} with the…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
We consider how to connect a set of disjoint networks to optimize the performance of the resulting composite network. We quantify this performance by the coherence of the composite network, which is defined by an $H_2$ norm of the system.…
We design several examples of constrained, symmetric quantum circuit dynamics that generate non-equilibrium steady states. The qubit networks maintain local memory of the initial conditions and display inhomogeneous subsystem dynamics over…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
We discuss the scaling of the interaction energy with particle numbers for a harmonically trapped two-species mixture at thermal equilibrium experiencing interactions of arbitrary strength and range. In the limit of long-range interactions…
The synchronous dynamics and the stationary states of a recurrent attractor neural network model with competing synapses between symmetric sequence processing and Hebbian pattern reconstruction is studied in this work allowing for the…
We study binary coordination games over graphs under log-linear learning when neighbor actions are conveyed through explicit noisy communication links. Each edge is modeled as either a binary symmetric channel (BSC) or a binary erasure…
Networks of coupled neural systems represent an important class of models in computational neuroscience. In some applications it is required that equilibrium points in these networks remain stable under parameter variations. Here we present…
We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of…
We investigate the properties of the thermodynamic limit in a general bipartite spin network with pairwise interactions. This is done by integrating one of the the spin groups, to transform the bipartite problem into a single group problem…
This paper presents a framework for designing a class of distributed, asynchronous optimization algorithms, realized as signal processing architectures utilizing various conservation principles. The architectures are specifically based on…