Related papers: Dissipative Avalanche Regimes Driven by Memory-Bia…
Interactive programming environments are powerful tools for promoting innovative network thinking, teaching science of complexity, and exploring emergent phenomena. This paper reports on our recent development of the deterministic random…
We propose dynamic scaling in temporal networks with heterogeneous activities and memory, and provide a comprehensive picture for the dynamic topologies of such networks, in terms of the modified activity-driven network model [H. Kim…
We study discrete-time random walks on networks subject to a time-dependent stochastic resetting, where the walker either hops randomly between neighboring nodes with a probability $1-\phi(a)$, or is reset to a given node with a…
A self-repelling random walk of a token on a graph is one in which at each step, the token moves to a neighbor that has been visited least often (with ties broken randomly). The properties of self-repelling random walks have been analyzed…
We study a class of non-reversible, continuous-time random walks in random environments on $\mathbb{Z}^d$ that admit a cycle representation with finite cycle length. The law of the transition rates, taking values in $[0, \infty)$, is…
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…
Regime shifts in biology, ecology, and other complex systems are often interpreted through stability landscapes and early warning signals that implicitly assume dynamics without memory effects. Yet many real systems exhibit these effects,…
The observation of apparent power-laws in neuronal systems has led to the suggestion that the brain is at, or close to, a critical state and may be a self-organised critical system. Within the framework of self-organised criticality a…
We consider the correlations and the hydrodynamic description of random walkers with a general finite memory moving on a $d$ dimensional hypercubic lattice. We derive a drift-diffusion equation and identify a memory-dependent critical…
In recent years, several experiments highlighted a new type of diffusion anomaly, which was called Brownian yet non-Gaussian diffusion. In systems displaying this behavior, the mean squared displacement of the diffusing particles grows…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
Avalanches of electrochemical activity in brain networks have been empirically reported to obey scale-invariant behavior --characterized by power-law distributions up to some upper cut-off-- both in vitro and in vivo. Elucidating whether…
Anomalous diffusion processes, in particular superdiffusive ones, are known to be efficient strategies for searching and navigation by animals and also in human mobility. One way to create such regimes are L\'evy flights, where the walkers…
This work focuses on quantitative representation of transport in systems with quenched disorder. Explicit mapping of the quenched trap model to continuous time random walk is presented. Linear temporal transformation: $t\to…
A random walk is a basic stochastic process on graphs and a key primitive in the design of distributed algorithms. One of the most important features of random walks is that, under mild conditions, they converge to a stationary distribution…
We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. We deduce analytical expressions for the stationary occupation probability and for the mean and global first…
Pathways of diffusion observed in real-world systems often require stochastic processes going beyond first-order Markov models, as implicitly assumed in network theory. In this work, we focus on second-order Markov models, and derive an…
We study diffusion on a multilayer network where the contact dynamics between the nodes is governed by a random process and where the waiting time distribution differs for edges from different layers. We study the impact on a random walk of…
We consider random walks on dynamical networks where edges appear and disappear during finite time intervals. The process is grounded on three independent stochastic processes determining the walker's waiting-time, the up-time and down-time…
Directed complex network of two-state model neurons linked by synapses which can be blocked or activated stochastically in time undergoes phase transition between the quiescent phase with zero activity and the active one with persistent…