Related papers: Differentiating the L\'evy walk from a composite c…
Organizing a few webpages from social media websites into popular topics is one of the key steps to understand trends on web. Discovering popular topics from web faces a sea of noise webpages which never evolve into popular topics. In this…
Levy walk (LW) process has been used as a simple model for describing anomalous diffusion in which the mean squared displacement of the walker grows non-linearly with time in contrast to the diffusive motion described by simple random walks…
We study memory based random walk models to understand diffusive motion in crowded heterogeneous environment. The models considered are non-Markovian as the current move of the random walk models is determined by randomly selecting a move…
A range of video modeling tasks, from optical flow to multiple object tracking, share the same fundamental challenge: establishing space-time correspondence. Yet, approaches that dominate each space differ. We take a step towards bridging…
In the last twenty years network science has proven its strength in modelling many real-world interacting systems as generic agents, the nodes, connected by pairwise edges. Yet, in many relevant cases, interactions are not pairwise but…
We investigate searching efficiency of different kinds of random walk on complex networks which rely on local information and one-step memory. For the studied navigation strategies we obtained theoretical and numerical values for the graph…
GPS technology is currently easily accessible to researchers, and many animal movement datasets are available. Two of the main features that a model which describes an animal's path can possess are directional persistence and attraction to…
We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on a $d$-dimensional lattice containing one trapping site. Due to reinforcement, a phase transition occurs when the…
We prove results for random walks in dynamic random environments which do not require the strong uniform mixing assumptions present in the literature. We focus on the "environment seen from the walker"-process and in particular its…
It is recognised now that a variety of real-life phenomena ranging from diffuson of cold atoms to motion of humans exhibit dispersal faster than normal diffusion. L\'evy walks is a model that excelled in describing such superdiffusive…
The two dominant approaches for the analysis of species-habitat associations in animals have been shown to reach divergent conclusions. Models fitted from the viewpoint of an individual (step selection functions), once scaled up, do not…
We carry out a comparative study on the problem for a walker searching on several typical complex networks. The search efficiency is evaluated for various strategies. Having no knowledge of the global properties of the underlying networks…
Optimal random foraging strategy has gained increasing concentrations. It is shown that L\'evy flight is more efficient compared with the Brownian motion when the targets are sparse. However, standard L\'evy flight generally cannot be…
A biological competition model where the individuals of the same species perform a two-dimensional Markovian continuous-time random walk and undergo reproduction and death is studied. The competition is introduced through the assumption…
Mathematical models of motility are often based on random-walk descriptions of discrete individuals that can move according to certain rules. It is usually the case that large masses concentrated in small regions of space have a great…
Anomalous random walks having long-range jumps are a critical branch of dynamical processes on networks, which can model a number of search and transport processes. However, traditional measurements based on mean first passage time are not…
This paper investigates whether two independent Elephant Random Walks (ERWs) on $\mathbb{Z}$, each with a different memory parameter, can meet infinitely often, extending the work of Roy, Takei, and Tanemura. We also study the asymptotic…
A particle subject to successive, random displacements is said to execute a random walk (in position or some other coordinate). The mathematical properties of random walks have been very thoroughly investigated, and the model is used in…
Many real-world systems, from social networks to protein-protein interactions and species distributions, exhibit overlapping flow-based communities that reflect their functional organisation. However, reliably identifying such overlapping…
The excursion set approach uses the statistics of the density field smoothed on a wide range of scales, to gain insight into a number of interesting processes in nonlinear structure formation, such as cluster assembly, merging and…