相关论文: Time walkers and spatial dynamics of ageing inform…

Many natural and artificial networks evolve in time. Nodes and connections appear and disappear at various timescales, and their dynamics has profound consequences for any processes in which they are involved. The first empirical analysis…

Locally activated random walks are defined as random processes, whose dynamical parameters are modified upon visits to given activation sites. Such dynamics naturally emerge in living systems as varied as immune and cancer cells interacting…

Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously…

In this paper, we explore the reduction of functionality in a complex system as a consequence of cumulative random damage and imperfect reparation, a phenomenon modeled as a dynamical process on networks. We analyze the global…

We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying…

Aging refers to the property of two-time correlation functions to decay very slowly on (at least) two time scales. This phenomenon has gained recent attention due to experimental observations of the history dependent relaxation behavior in…

The versatility of renewal theory is owed to its abstract formulation. Renewals can be interpreted as steps of a random walk, switching events in two-state models, domain crossings of a random motion, etc. We here discuss a renewal process…

We propose the Temporal Walk Centrality, which quantifies the importance of a node by measuring its ability to obtain and distribute information in a temporal network. In contrast to the widely-used betweenness centrality, we assume that…

We present a model for a random walk with memory, phenomenologically inspired in a biological system. The walker has the capacity to remember the time of the last visit to each site and the step taken from there. This memory affects the…

We study a family of weighted random walks on complete graphs. These `democratic walks' turn out to be explicitly solvable, and we find the hierarchy window for which the characteristic time scale saturates the so-called fast scrambling…

Random walks find applications in many areas of science and are the heart of essential network analytic tools. When defined on temporal networks, even basic random walk models may exhibit a rich spectrum of behaviours, due to the…

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…

Many human social phenomena, such as cooperation, the growth of settlements, traffic dynamics and pedestrian movement, appear to be accessible to mathematical descriptions that invoke self-organization. Here we develop a model of pedestrian…

The evolution of many dynamical systems that describe relationships or interactions between objects can be effectively modeled by temporal networks, which are typically represented as a sequence of static network snapshots. In this paper,…

Random walks are powerful tools to analyze spatial-temporal patterns produced by living organisms ranging from cells to humans. At the same time, it is evident that these patterns are not completely random but are results of a convolution…

The random walk process underlies the description of a large number of real world phenomena. Here we provide the study of random walk processes in time varying networks in the regime of time-scale mixing; i.e. when the network connectivity…

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…

Active walker models have proved to be extremely effective in understanding the evolution of a large class of systems in biology like ant trail formation and pedestrian trails. We propose a simple model of a random walker which modifies its…

We study a one-dimensional random walk with memory in which the step lengths to the left and to the right evolve at each step in order to reduce the wandering of the walker. The feedback is quite efficient and lead to a non-diffusive walk.…

Virtually all real-world networks are dynamical entities. In social networks, the propensity of nodes to engage in social interactions (activity) and their chances to be selected by active nodes (attractiveness) are heterogeneously…