Random walks with stochastic resetting in complex networks: A discrete-time approach.

We consider a discrete-time Markovian random walk with resets on a connected undirected network. The resets, in which the walker is relocated to randomly chosen nodes, are governed by an independent discrete-time renewal process. Some nodes of the network are target nodes, and we focus on the statistics of first hitting of these nodes.

Random walks with long-range memory on networks.

We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way such that the most visited nodes have proportionally a higher probability to be chosen for revisit. The occupation probability can be expressed as a sum over the eigenmodes of the standard random walk matrix of the network, where the amplitudes slowly decay as power-laws at large times, instead of exponentially.

Antifragility of stochastic transport on networks with damage.

A system is called antifragile when damage acts as a constructive element improving the performance of a global function. In this paper, we analyze the emergence of antifragility in the movement of random walkers on networks with modular structures or communities. The random walker hops considering the capacity of transport of each link, whereas the links are susceptible to random damage that accumulates over time.

Stochastic Compartment Model with Mortality and Its Application to Epidemic Spreading in Complex Networks.

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási-Albert (BA), Erdös-Rényi (ER), and Watts-Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health.

Dissimilarity between synchronization processes on networks.

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a metric on a hypertorus, allowing us to compare the phases of coupled oscillators. In the first part, this formalism is implemented to examine systems of networked identical phase oscillators that evolve with the Kuramoto model.