Related papers: Fractal transit networks: self-avoiding walks and …
Random walks constitute a fundamental mechanism for many dynamics taking place on complex networks. Besides, as a more realistic description of our society, multiplex networks have been receiving a growing interest, as well as the dynamical…
The behaviour of complex networks under failure or attack depends strongly on the specific scenario. Of special interest are scale-free networks, which are usually seen as robust under random failure but appear to be especially vulnerable…
Scale-invariant spatial or temporal patterns and L\'evy flight motion have been observed in a large variety of biological systems. It has been argued that animals in general might perform L\'evy flight motion with power law distribution of…
Traffic fluctuation has so far been studied on unweighted networks. However many real traffic systems are better represented as weighted networks, where nodes and links are assigned a weight value representing their physical properties such…
Fractal behavior and long-range dependence have been observed in tele-traffic measurement and characterization. In this paper we show results of application of the fractal analysis to internet traffic via various methods. Our result…
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight…
L\'evy flights and L\'evy walks serve as two paradigms of random walks resembling common features but also bearing fundamental differences. One of the main dissimilarities are discontinuity versus continuity of their trajectories and…
Motivated by developments in renewable energy and smart grids, we formulate a stylized mathematical model of a transport network with stochastic load fluctuations. Using an affine control rule, we explore the trade-off between the number of…
L\'evy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of L\'evy glasses allows to study L\'evy flights in controlled way…
This paper investigates L\'evy walks with random velocities, extending classical models beyond constant speed assumptions. We derive scaling limits, demonstrating that diffusion depends on interplay between heavy-tailed duration and…
We experimentally investigate the transmission of light by dense atomic vapor. The light propagating in dense atomic vapor can be modeled as a L\'evy flight random walk. For such system, the step-length distribution can be modeled as…
The L\'evy walk, a type of random walk characterized by linear step lengths that follow a power-law distribution, is observed in the migratory behaviors of various organisms, ranging from bacteria to humans. Notably, L\'evy walks with power…
Recent studies have shown that the spatial structures of animal displacements and local-scale human motion follow L\'{e}vy flights. Whether transnational human activity (THA) also exhibits such a pattern has however not been thoroughly…
Many studies on animal and human movement patterns report the existence of scaling laws and power-law distributions. Whereas a number of random walk models have been proposed to explain observations, in many situations individuals actually…
The L\'evy-Lorentz gas describes the motion of a particle on the real line in the presence of a random array of scattering points, whose distances between neighboring points are heavy-tailed i.i.d. random variables with finite mean. The…
In the literature, scaling laws for wireless mobile networks have been characterized under various models of node mobility and several assumptions on how communication occurs between nodes. To improve the realism in the analysis of scaling…
When light travels through strongly scattering media with optical gain, the synergy between diffusive transport and stimulated emission can lead to lasing action. Below the threshold pump power, the emission spectrum is smooth and…
Metro networks serve as good examples of traffic systems for understanding the relations between geometric structures and transport properties.We study and compare 28 world major metro networks in terms of the Wasserstein distance, the key…
We present a novel method for analysing socio-spatial segregation in cities by considering constraints imposed by transportation networks. Using a multilayered network approach, we model the interaction probabilities of socio-economic…
Delay-capacity tradeoffs for mobile networks have been analyzed through a number of research work. However, L\'{e}vy mobility known to closely capture human movement patterns has not been adopted in such work. Understanding the…