Scale-free foraging patterns are widespread among animals. These may be the outcome of an optimal searching strategy to find scarce, randomly distributed resources, but a less explored alternative is that this behaviour result from interaction animals with particular distribution resources. We introduce simple model where individual primates follow mental maps and choose their displacements according maximum efficiency criterion, in spatially disordered environment containing many trees...

Strongly non-Markovian random walks offer a promising modeling framework for understanding animal and human mobility, yet, few analytical results are available these processes. Here we solve exactly model with long range memory where walker intermittently revisits previously visited sites according to reinforced rule. The emergence of frequently locations generates very slow diffusion, logarithmic in time, whereas the probability density tends Gaussian. This scaling form does not emerge from...

We study the problem of a target search by Brownian particle subject to stochastic resetting pair sites. The mean time is minimized an optimal rate which does not vary smoothly, in contrast with well-known single site case, but exhibits discontinuous transition as position one varied while keeping initial fixed, or vice versa. discontinuity vanishes at "liquid-gas" critical point space. This exists provided that relative weight m further comprised interval [2.9028...,8.5603...]. When random...

Thanks to recent technological advances, it is now possible track with an unprecedented precision and for long periods of time the movement patterns many living organisms in their habitat. The increasing amount data available on single trajectories offers possibility understanding how animals move testing basic models. Random walks have represented main description micro-organisms also been useful understand foraging behaviour large animals. Nevertheless, most vertebrates, particular humans...

Bacterial colonies often exhibit complex spatio-temporal organization. This collective behavior is affected by a multitude of factors ranging from the properties individual cells (shape, motility, membrane structure) to chemotaxis and other means cell-cell communication. One important but overlooked mechanisms organization direct mechanical contact among in dense such as biofilms. While natural habitats all these different act concert, one can use laboratory cell cultures study certain...

We solve an adaptive search model where a random walker or L\'evy flight stochastically resets to previously visited sites on $d$-dimensional lattice containing one trapping site. Because of reinforcement, phase transition occurs when the resetting rate crosses threshold above which nondiffusive stationary states emerge, localized around inhomogeneity. The depends strength and walker's return probability in memoryless case. belongs same class as self-consistent theory Anderson localization....

We study random walks with stochastic resetting to the initial position on arbitrary networks. obtain stationary probability distribution as well mean and global first passage times, which allow us characterize effect of capacity a walker reach particular target or explore finite network. apply results rings, Cayley trees, complex Our formalism holds for undirected networks can be implemented from spectral properties walk without resetting, providing tool analyze search efficiency in...

Abstract We study the non-equilibrium steady states (NESS) and first passage properties of a Brownian particle with position X subject to an external confining potential form V ( ) = μ | |, that is switched on off stochastically. Applying intermittently generates physically realistic diffusion process stochastic resetting toward origin, topic which has recently attracted considerable interest in variety theoretical contexts but remained challenging implement lab experiments. The present...

The transport of particles through channels is paramount importance in physics, chemistry, and surface science due to its broad real world applications. Much insight can be gained by observing the transition paths a particle channel collecting statistics on lifetimes or escape probabilities from channel. In this paper, we consider diffusive narrow conical Brownian subject intermittent dynamics, namely, stochastic resetting. As such, resetting brings back desired location where it resumes...

We study the diffusive transport of Markovian random walks on arbitrary networks with stochastic resetting to multiple nodes. deduce analytical expressions for stationary occupation probability and mean global first passage times. This general approach allows us characterize effect capacity walk strategies reach a particular target or explore network. Our formalism holds ergodic can be implemented from spectral properties without resetting, providing tool analyze efficiency search apply...

The study of diffusion with preferential returns to places visited in the past has attracted increased attention recent years. In these highly non-Markov processes, a standard diffusive particle intermittently resets at given rate previously positions. At each reset, position be revisited is randomly chosen probability proportional accumulated amount time spent by that position. These revisits typically generate very slow diffusion, logarithmic time, but still Gaussian distribution late...

Principles of self-organization play an increasingly central role in models human activity. Notably, individual displacements exhibit strongly recurrent patterns that are characterized by scaling laws and can be mechanistically modelled as self-attracting walks. Recurrence is not, however, unique to displacements. Here we report the mobility wild capuchin monkeys not random walks, they recurrence properties similar those cell phone users, suggesting spatial cognition mechanisms shared with...

Modern developments in microscopy and image processing are revolutionizing areas of physics, chemistry, biology as nanoscale objects can be tracked with unprecedented accuracy. The goal single-particle tracking is to determine the interaction between particle its environment. price paid for having a direct visualization single consequent lack statistics. Here we address optimal way extract diffusion constants from trajectories pure Brownian motion. It shown that maximum likelihood estimator...

Many attempts to relate animal foraging patterns landscape heterogeneity are focused on the analysis of foragers movements. Resource detection in space and time not commonly studied, yet they tightly coupled properties add relevant information behavior. By exploring simple models unpredictable environments we show that distribution intervals between detected prey (detection statistics) is mostly determined by spatial structure field essentially distinct from predator displacement statistics....

Motivated by studies on the recurrent properties of animal and human mobility, we introduce a path-dependent random-walk model with long-range memory for which not only mean-square displacement (MSD) but also propagator can be obtained exactly in asymptotic limit. The consists random walker lattice, which, at constant rate, stochastically relocates site occupied some earlier time. This time past is chosen randomly according to kernel, whose temporal decay varied via an exponent parameter. In...

Groups of animals (including humans) may show flexible grouping patterns, in which temporary aggregations or subgroups come together and split, changing composition over short temporal scales, (i.e. fission fusion). A high degree fission–fusion dynamics constrain the regulation social relationships, introducing uncertainty interactions between group members. Here we use Shannon's entropy to quantify predictability subgroup for three species known differ way their split time: spider monkeys (...

Abstract During a random search, resetting the searcher’s position from time to starting point often reduces mean completion of process. Although many different models have been studied over past ten years, only few can be physically implemented. Here we study theoretically protocol that realised experimentally and which exhibits unusual optimization properties. A Brownian particle is subject an arbitrary confining potential v ( x ) switched on off intermittently at fixed rates. Motion...

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

Abstract We study the relaxation of a diffusive particle confined in an arbitrary external potential and subject to non-Markovian resetting protocol. With constant rate r , previous time τ between initial present t is chosen from given probability distribution <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mi>K</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>τ</mml:mi> <mml:mo>,</mml:mo> <mml:mi>t</mml:mi> stretchy="false">)</mml:mo>...

Resetting plays a pivotal role in optimizing the completion time of complex first passage processes with single or multiple outcomes/exit possibilities. While it is well established that coefficient variation -- statistical dispersion defined as ratio fluctuations over mean must be larger than unity for resetting to beneficial any outcome averaged all possibilities, same can not said while conditioned on particular outcome. The purpose this letter derive universal condition which reveals two...

Abstract We present several arguments for the preeminence of social interactions in determining and giving shape to societies. In our view, a society can emerge from interaction relationship patterns without need establishing an priori limit on who actually belongs it. Markers group identity are one element among many that allow societies persist.