Related papers: Diffusion in sparse networks: linear to semi-linea…
Convolutional network are the de-facto standard for analysing spatio-temporal data such as images, videos, 3D shapes, etc. Whilst some of this data is naturally dense (for instance, photos), many other data sources are inherently sparse.…
We consider diffusion processes on power-law small-world networks in different dimensions. In one dimension, we find a rich phase diagram, with different transient and recurrent phases, including a critical line with continuously varying…
We study percolation on networks, which is used as a model of the resilience of networked systems such as the Internet to attack or failure and as a simple model of the spread of disease over human contact networks. We reformulate…
A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…
We study spectral behavior of sparsely connected random networks under the random matrix framework. Sub-networks without any connection among them form a network having perfect community structure. As connections among the sub-networks are…
Normal and anomalous diffusion are ubiquitous in many complex systems [1] . Here, we define a time and space generalized diffusion equation (GDE), which uses fractional-time derivatives and transformed d-path Laplacian operators on…
This study addresses the challenge of predicting network dynamics, such as forecasting disease spread in social networks or estimating species populations in predator-prey networks. Accurate predictions in large networks are difficult due…
By means of analytical calculations and numerical simulations we study the diffusion properties in quasi-two-dimensional structures with two exciton subsystems with an exchange between them. The experimental realisation is possible in…
Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure,…
Several systems can be modeled as sets of interdependent networks where each network contains distinct nodes. Diffusion processes like the spreading of a disease or the propagation of information constitute fundamental phenomena occurring…
This paper introduces a measure of the diffusion of binary outcomes over a large, sparse network, when the diffusion is observed in two time periods. The measure captures the aggregated spillover effect of the state-switches in the initial…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
Low-dimensional dynamical systems are fruitful models for mixing in fluid and granular flows. We study a one-dimensional discontinuous dynamical system (termed "cutting and shuffling" of a line segment), and we present a comprehensive…
The random diffusion model is a continuum model for a conserved scalar density field driven by diffusive dynamics where the bare diffusion coefficient is density dependent. We generalize the model from one with a sharp wavenumber cutoff to…
We considered diffusion-driven processes on small-world networks with distance-dependent random links. The study of diffusion on such networks is motivated by transport on randomly folded polymer chains, synchronization problems in…
The spread in time of a mutation through a population is studied analytically and computationally in fully-connected networks and on spatial lattices. The time, t_*, for a favourable mutation to dominate scales with population size N as…
We study diffusion (random walks) on recursive scale-free graphs, and contrast the results to similar studies in other analytically soluble media. This allows us to identify ways in which diffusion in scale-free graphs is special. Most…
We examine the heterogeneous responses of individual nodes in sparse networks to the random removal of a fraction of edges. Using the message-passing formulation of percolation, we discover considerable variation across the network in the…
Diffusive properties of a monodisperse system of interacting particles confined to a \textit{quasi}-one-dimensional (Q1D) channel are studied using molecular dynamics (MD) simulations. We calculate numerically the mean-squared displacement…
Diffusion describes the motion of microscopic entities from regions of high concentration to regions of low concentration. In multiplex networks, flows can occur both within and across layers, and super-diffusion, a regime where the time…