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Many ant species employ distributed population density estimation in applications ranging from quorum sensing [Pra05], to task allocation [Gor99], to appraisal of enemy colony strength [Ada90]. It has been shown that ants estimate density…
Daily, are reported systems in nature that present anomalous diffusion phenomena due to irregularities of medium, traps or reactions process. In this scenario, the diffusion with traps or localised--reactions emerge through various…
We consider a random walk model in a one-dimensional environment, formed by several zones of finite width with the fixed transition probabilities. It is also assumed that the transitions to the left and right neighboring points have unequal…
The analysis of contagion-diffusion processes in metapopulations is a powerful theoretical tool to study how mobility influences the spread of communicable diseases. Nevertheless, many metapopulation approaches use indistinguishable agents…
We study the evolution of a random walker on a conservative dynamic random environment composed of independent particles performing simple symmetric random walks, generalizing results of [16] to higher dimensions and more general transition…
The standard diffusive spreading, characterized by a Gaussian distribution with mean square displacement that grows linearly with time, can break down, for instance, under the presence of correlations and heterogeneity. In this work, we…
Physical contacts result in the spread of various phenomena such as viruses, gossips, ideas, packages and marketing pamphlets across a population. The spread depends on how people move and co-locate with each other, or their mobility…
Exploiting multi-dimensional quantum walks as feasible platforms for quantum computation and quantum simulation is attracting constantly growing attention from a broad experimental physics community. Here, we propose a two-dimensional…
We are studying the motion of a random walker in two and three dimensional continuum with uniformly distributed jump-length. This is different from conventional Lavy flight. In 2D and 3D continuum, a random walker can move in any direction,…
We study an agent-based model of animals marking their territory and evading adversarial territory in one dimension, with respect to the distribution of the size of the resulting territories. In particular, we use sophisticated sampling…
We consider random walkers that deform the medium as they move, enabling a faster motion in regions which have been recently visited. This induces an effective attraction between walkers mediated by the medium, which can be regarded as a…
The behaviour of colony-based marine predators is the focus of much research globally. Large telemetry and tracking data sets have been collected for this group of animals, and are accompanied by many theoretical studies of optimal foraging…
The emulation of wireless nodes spatial position is a practice used by deployment engineers and network planners to analyze the characteristics of a network. In particular, nodes geolocation will directly impact factors such as…
A theory of the spread of epidemics is formulated on the basis of pairwise interactions in a dilute system of random walkers (infected and susceptible animals) moving in n dimensions. The motion of an animal pair is taken to obey a…
We introduce and study a metapopulation model of random walkers interacting at the nodes of a complex network. The model integrates random relocation moves over the links of the network with local interactions depending on the node…
Random walks are basic diffusion processes on networks and have applications in, for example, searching, navigation, ranking, and community detection. Recent recognition of the importance of temporal aspects on networks spurred studies of…
Random Walks in Cooling Random Environments (RWCRE) is a model of random walks in dynamic random environments where the environment is frozen between a fixed sequence of times (called the cooling map) where it is resampled. Naturally the…
A trophallaxis inspired model for distributed transport between randomly interacting agents Trophallaxis, the regurgitation and mouth to mouth transfer of liquid food between members of eusocial insect societies, is an important process…
We develop a framework for designing density-dependent stochastic resetting protocols to regulate distributions of random walkers on networks. Resetting mechanisms that depend on local densities induce correlations in otherwise…
Random walks are ubiquitous in the sciences, and they are interesting from both theoretical and practical perspectives. They are one of the most fundamental types of stochastic processes; can be used to model numerous phenomena, including…