Related papers: Modeling the Network Dynamics of Pulse-Coupled Neu…
To accurately represent disease spread, epidemiological models must account for the complex network topology and contact heterogeneity. Traditionally, most studies have used random heterogeneous networks, which ignore correlations between…
Synaptic plasticity is a key component of neuronal dynamics, describing the process by which the connections between neurons change in response to experiences. In this study, we extend a network model of $\theta$-neuron oscillators to…
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…
We give an intuitive though general explanation of the finite-size effect in scale-free networks in terms of the degree distribution of the starting network. This result clarifies the relevance of the starting network in the final degree…
Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…
Network modeling based on ensemble averages tacitly assumes that the networks meant to be modeled are typical in the ensemble. Previous research on network eigenvalues, which govern a range of dynamical phenomena, has shown that this is…
We study networks of noisy phase oscillators whose nodes are characterized by a random degree counting the number of its connections. Both these degrees and the natural frequencies of the oscillators are distributed according to a given…
We propose a generalization of the concept of assortativity based on the tensorial representation of multilayer networks, covering the definitions given in terms of Pearson and Spearman coefficients. Our approach can also be applied to…
In random graph models, the degree distribution of an individual node should be distinguished from the (empirical) degree distribution of the graph that records the fractions of nodes with given degree. We introduce a general framework to…
Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently…
We study the asymptotic law of a network of interacting neurons when the number of neurons becomes infinite. Given a completely connected network of firing rate neurons in which the synaptic weights are Gaussian correlated random variables,…
We study the synchronizability and the synchronization dynamics of networks of nonlinear oscillators. We investigate how the synchronization of the network is influenced by some of its topological features such as variations of the power…
Training large neural networks exposes neural scaling laws for the generalization error, which points to a universal behavior across network architectures of learning in high dimensions. It was also shown that this effect persists in the…
The micro-structure of the giant component of the Erd{\H o}s-R\'enyi network and other configuration model networks is analyzed using generating function methods. While configuration model networks are uncorrelated, the giant component…
We study a simple model for a neuron function in a collective brain system. The neural network is composed of uncorrelated random scale-free network for eliminating the degree correlation of dynamical processes. The interaction of neurons…
Delaunay triangulation can be considered as a type of complex networks. For complex networks, the degree distribution is one of the most important inherent characteristics. In this paper, we first consider the two- and three-dimensional…
We introduce a growing network model in which a new node attaches to a randomly-selected node, as well as to all ancestors of the target node. This mechanism produces a sparse, ultra-small network where the average node degree grows…
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the corresponding adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of…
Some years ago a cellular automata model was proposed to describe the evolution of the immune repertoire of B cells and antibodies based on Jerne's immune network theory and shape-space formalism. Here we investigate if the networks…
A probabilistic generative network model with $n$ nodes and $m$ overlapping layers is obtained as a superposition of $m$ mutually independent Bernoulli random graphs of varying size and strength. When $n$ and $m$ are large and of the same…