Vicenç Méndez

Vicenç Méndez
Autonomous University of Barcelona | UAB · Department of Physics

PhD in Physics

About

206
Publications
21,274
Reads
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4,342
Citations
Additional affiliations
July 2015 - August 2015
University of Cambridge
Position
  • Program participant
July 2014 - July 2014
Southern Methodist University
Position
  • Visiting Scholar of Chemistry
January 2008 - present
University of Manchester

Publications

Publications (206)
Preprint
Full-text available
We study the occupation time statistics for non-Markovian random walkers based on the formalism of the generalized master equation for the Continuous-Time Random Walk. We also explore the case when the random walker additionally undergoes a stochastic resetting dynamics. We derive and solve the backward Feynman-Kac equation to find the characterist...
Article
Full-text available
We use complex systems science to explore the emergent behavioral patterns that typify eusocial species, using collective ant foraging as a paradigmatic example. Our particular aim is to provide a methodology to quantify how the collective orchestration of foraging provides functional advantages to ant colonies. For this, we combine (i) a purpose-b...
Article
We explore the case of a group of random walkers looking for a target randomly located in space, such that the number of walkers is not constant but new ones can join the search, or those that are active can abandon it, with constant rates rb and rd, respectively. Exact analytical solutions are provided both for the fastest-first-passage time and f...
Article
We study the effect of a resetting point randomly distributed around the origin on the mean first-passage time of a Brownian searcher moving in one dimension. We compare the search efficiency with that corresponding to reset to the origin and find that the mean first-passage time of the latter can be larger or smaller than the distributed case, dep...
Article
We analyze a one-dimensional intermittent random walk on an unbounded domain in the presence of stochastic resetting. In this process, the walker alternates between local intensive search, diffusion, and rapid ballistic relocations in which it does not react to the target. We demonstrate that Poissonian resetting leads to the existence of a non-equ...
Article
Full-text available
We study the ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin- or fat-tailed distributions the normalized or non-normalized invariant density of this process. The former case corresponds to known results in the resetting literature and th...
Article
Full-text available
We study the long-time dynamics of the mean squared displacement of a random walker moving on a comb structure under the effect of stochastic resetting. We consider that the walker's motion along the backbone is diffusive and it performs short jumps separated by random resting periods along fingers. We take into account two different types of reset...
Preprint
Full-text available
We study ergodic properties of one-dimensional Brownian motion with resetting. Using generic classes of statistics of times between resets, we find respectively for thin/fat tailed distributions, the normalized/non-normalised invariant density of this process. The former case corresponds to known results in the resetting literature and the latter t...
Article
Full-text available
While approaches based on physical grounds (such as the drift-diffusion model—DDM) have been exhaustively used in psychology and neuroscience to describe perceptual decision making in humans, similar approaches to complex situations, such as sequential (tree-like) decisions, are still scarce. For such scenarios that involve a reflective prospection...
Article
Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory perspective. Parallel to the concepts from renewal theory, we introduce the conditioned backward B and forward F times b...
Article
We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time distribution between consecutive short jumps. We investigate the existence of an optimal reset rate, which minimizes t...
Preprint
Stochastic resetting can be naturally understood as a renewal process governing the evolution of an underlying stochastic process. In this work, we formally derive well-known results of diffusion with resets from a renewal theory perspective. Parallel to the concepts from renewal theory, we introduce the conditioned backward and forward times for s...
Article
Full-text available
We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. Exact results for the probability of visiting a given number of sites are derived and a practical WKB approximation to treat the nonstationary problem is developed. A mean-field version of this model, fi...
Preprint
Full-text available
We consider a walker moving in a one-dimensional interval with absorbing boundaries under the effect of Markovian resettings to the initial position. The walker's motion follows a random walk characterized by a general waiting time distribution between consecutive short jumps. We investigate the existence of an optimal reset rate, which minimizes t...
Preprint
We study a non-Markovian and nonstationary model of animal mobility incorporating both exploration and memory in the form of preferential returns. We derive exact results for the probability of visiting a given number of sites and develop a practical WKB approximation to treat the nonstationary problem. We further show that this model adequately de...
Article
Information gathering and processing can be particularly useful to enhance the efficiency of living organisms when searching or foraging under uncertain scenarios. Assuming that such situations can be conveniently modeled through random walk models, a case that has been widely explored in the physical literature is the generation of self-avoiding t...
Article
Excited random walks represent a convenient model to study food intake in a media which is progressively depleted by the walker. Trajectories in the model alternate between (i) feeding and (ii) escape (when food is missed and so it must be found again) periods, each governed by different movement rules. Here, we explore the case where the escape dy...
Preprint
Full-text available
While perceptual decision making in humans is often considered to be governed by evidence accumulator models (like drift-diffusion), mechanisms driving harder situations where prospection of future scenarios is necessary remain largely unknown. Here, experimental and computational evidence is given in favour of a mechanism in which prospection of p...
Article
We investigate the effects of Markovian resetting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power-law probability density functions. We prove the existence of a nonequilibrium stationary state and finite mean first arrival time. However, the existence of an opti...
Article
Full-text available
Emergence of collective, as well as superorganism-like, behaviour in biological populations requires the existence of rules of communication, either direct or indirect, between organisms. Because reaching an understanding of such rules at the individual level can be often difficult, approaches carried out at higher, or effective, levels of descript...
Preprint
We investigate the effects of markovian resseting events on continuous time random walks where the waiting times and the jump lengths are random variables distributed according to power law probability density functions. We prove the existence of a non-equilibrium stationary state and finite mean first arrival time. However, the existence of an opt...
Preprint
Full-text available
There is a widespread belief that the capacity of animals to orchestrate systematic/planned paths must provide a significant benefit for efficient search and exploration, so stochasticity typical of real trajectories is mostly understood as undesirable noise caused by internal or external effects. Far less is known, however, about the role that cog...
Article
Full-text available
We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the corresponding backbone and resetting from secondary fingers to the main fingers. The transient dynamics along the bac...
Preprint
Full-text available
We study a diffusion process on a three-dimensional comb under stochastic resetting. We consider three different types of resetting: global resetting from any point in the comb to the initial position, resetting from a finger to the corresponding backbone and resetting from secondary fingers to the main fingers. The transient dynamics along the bac...
Poster
Full-text available
Diffusion on a three dimensional xyz-comb is analyzed. Three different types of resetting are considered. These are: (i) global resetting to the initial position, (ii) resetting to the x-backbone, and (iii) resetting to the main y-fingers. Analyzing the probability density functions, their stationary distributions and the mean squared displacements...
Article
Full-text available
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study two generalizations of comb models and present a generic method to obtain their transport properties. The first is a continuous time random walk on a many dimensional m + n c...
Article
Full-text available
The analysis of the classical radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. A formal extension of this approach has revealed recently the existence of a universal scaling in the collective spatial patterns of pedestrians, characterized...
Preprint
Full-text available
Self-avoidance is a common mechanism to improve the efficiency of a random walker for covering a spatial domain. However, how this efficiency decreases when self-avoidance is impaired or limited by other processes has remained largely unexplored. Here we use simulations to study the case when the self-avoiding signal left by a walker both (i) satur...
Preprint
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied during the last years as particular situations within a framework of random walks with memory. We focus on (i) s...
Preprint
Full-text available
Random walks with stochastic resetting provides a treatable framework to study interesting features about central-place motion. In this work, we introduce non-instantaneous resetting as a two-state model being a combination of an exploring state where the walker moves randomly according to a propagator and a returning state where the walker perform...
Article
Random walks with stochastic resetting provides a treatable framework to study interesting features about central-place motion. In this work, we introduce noninstantaneous resetting as a two-state model being a combination of an exploring state where the walker moves randomly according to a propagator and a returning state where the walker performs...
Article
Full-text available
In this minireview we present the main results regarding the transport properties of stochastic movement with relocations to known positions. To do so, we formulate the problem in a general manner to see several cases extensively studied during the last years as particular situations within a framework of random walks with memory. We focus on (i) s...
Article
Random walks with memory usually involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the transport properties as well as on the statistics of first-passage and subsequent recurrence times through a site. A preference for revisiting sites...
Article
Full-text available
In this work, we consider stochastic movement with random resets to the origin followed by a random residence time before the motion starts again. First, we study the transport properties of the walker, i.e. we derive an expression for the mean square displacement of the overall process and study its dependence on the statistical properties of the...
Article
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with the Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean time to extinction is...
Preprint
The analysis of the radial distribution function of a system provides a possible procedure for uncovering interaction rules between individuals out of collective movement patterns. This approach from classical statistical mechanics has revealed recently the existence of a universal scaling in systems of pedestrians, provided the potential of intera...
Article
Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean-square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first-arrival time (MFAT) to a given position x may reach it in a finite time when they reset their position. In this work we study these emergi...
Preprint
Full-text available
In this work we consider a stochastic movement process with random resets to the origin followed by a random residence time there before the walker restarts its motion. First, we study the transport properties of the walker, we derive an expression for the mean square displacement of the overall process and study its dependence with the statistical...
Preprint
Full-text available
Stochastic resets have lately emerged as a mechanism capable of generating finite stationary mean square diplacement (MSD) when they are applied to diffusive random searches. Furthermore, walkers which have an infinite search time or mean first arrival time (MFAT) may become finite when they are randomly restarted. In this work we study these emerg...
Preprint
Full-text available
We study simple stochastic scenarios, based on birth-and-death Markovian processes, that describe populations with Allee effect, to account for the role of demographic stochasticity. In the mean-field deterministic limit we recover well-known deterministic evolution equations widely employed in population ecology. The mean-time to extinction is in...
Book
Full-text available
Random walks often provide the underlying mesoscopic mechanism for transport phenomena in physics, chemistry and biology. In particular, anomalous transport in branched structures has attracted considerable attention. Combs are simple caricatures of various types of natural branched structures that belong to the category of loopless graphs. The com...
Preprint
Full-text available
Random walks with memory typically involve rules where a preference for either revisiting or avoiding those sites visited in the past are introduced somehow. Such effects have a direct consequence on the statistics of first-passage and subsequent recurrence times through a site; typically, a preference for revisiting sites is expected to result in...
Article
Inspired by recent experiments on the organism Caenorhabditis elegans we present a stochastic problem to capture the adaptive dynamics of search in living beings, which involves the exploration-exploitation dilemma between remaining in a previously preferred area and relocating to new places. We assess the question of search efficiency by introduci...
Preprint
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have bee...
Article
In this work we construct individual-based models that give rise to the generalized logistic model at the mean-field deterministic level and that allow us to interpret the parameters of these models in terms of individual interactions. We also study the effect of internal fluctuations on the long-time dynamics for the different models that have bee...
Article
We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary branches may be described either by a Langevin equation or by other types of random processes. The mean square displa...
Preprint
We propose a generalized Langevin formalism to describe transport in combs and similar ramified structures. Our approach consists of a Langevin equation without drift for the motion along the backbone. The motion along the secondary branches may be described either by a Langevin equation or by other types of random processes. The mean square displa...
Article
Full-text available
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Understanding the structural complexity and the main drivers of animal search behaviour is pivotal to foraging ecology. Yet, the role of uncertainty as a generative mechanism of movement patterns is poorly understood. Novel insights from search theory suggest that organisms should collect and assess new information from the environment by producing...
Article
Full-text available
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial ker...
Preprint
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial ker...
Poster
Full-text available
We consider a generalized fractal comb model, where the intrinsic properties of the structure are described by memory and spatial kernels. It is shown that the considered model is suitable for the description of superdiffusion on a fractal comb structures. We concern with special cases of the model, which manifest a competition between long rests a...
Article
Full-text available
In the Near East, nomadic hunter-gatherer societies became sedentary farmers for the first time during the transition into the Neolithic. Sedentary life presented a risk of isolation for Neolithic groups. As fluid intergroup interactions are crucial for the sharing of information, resources and genes, Neolithic villages developed a network of conta...
Article
It is known that introducing a stochastic resetting in a random-walk process can lead to the emergence of a stationary state. Here we study this point from a general perspective through the derivation and analysis of mesoscopic (continuous-time random walk) equations for both jump and velocity models with stochastic resetting. In the case of jump m...
Article
We present a rigorous result on ultra-slow diffusion by solving a Fokker-Planck equation, which describes anomalous transport in a three dimensional (3D) comb. This 3D cylindrical comb consists of a cylinder of discs threaten on a backbone. It is shown that the ultra-slow contaminant spreading along the backbone is described by the mean squared dis...
Article
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Full-text available
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Using experimental and computational methods, we study the role of behavioural variability in activity bursts (or temporal activity patterns) for individual and collective regulation of foraging in A. senilis ants. First, foraging experiments were carried out under special conditions (low densities of ants and food and absence of external cues or s...
Article
Full-text available
L’étude des échanges d’obsidienne permet d’obtenir une meilleure connaissance des systèmes d’interaction entre les villages sédentaires au début du Néolithique au Proche-Orient. Le modèle d’échange d’obsidienne, down-the-line, a dominé pour expliquer la diffusion de l’obsidienne entre les villages néolithiques. Cependant, l’information disponible s...
Article
Full-text available
We develop non-linear integro-differential kinetic equations for proliferating Lévy walkers with birth and death processes. A hyperbolic scaling is applied to them from the onset without further long-time large scale (diffusion) approximations. The resulting Hamilton-Jacobi equations are used to determine the rate of front propagation. We found the...
Article
Full-text available
Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT) through the origin [Phys. Rev. Lett. 113, 220602 (2014)]. Here we show how actually an interesting dynamics, in...
Preprint
Recent works have explored the properties of L\'evy flights with resetting in one-dimensional domains and have reported the existence of phase transitions in the phase space of parameters which minimizes the Mean First Passage Time (MFPT) through the origin [Phys. Rev. Lett. 113, 220602 (2014)]. Here we show how actually an interesting dynamics, in...
Article
Full-text available
Combs are a simple caricature of various types of natural branched structures, which belong to the category of loopless graphs and consist of a backbone and branches. We study continuous time random walks on combs and present a generic method to obtain their transport properties. The random walk along the branches may be biased, and we account for...
Article
Full-text available
An efficient searcher needs to balance properly the tradeoff between the exploration of new spatial areas and the exploitation of nearby resources, an idea which is at the core of scale-free L\'evy search strategies. Here we study multi-scale random walks as an approximation to the scale- free case and derive the exact expressions for their mean-fi...
Article
Full-text available
In this paper, we explore the conditions that led to the origins and development of the Near Eastern Neolithic using mathematical modelling of obsidian exchange. The analysis presented expands on previous research, which established that the down-the-line model could not explain long-distance obsidian distribution across the Near East during this p...
Article
Full-text available
The Verhulst model is probably the best known macroscopic rate equation in population ecology. It depends on two parameters, the intrinsic growth rate and the carrying capacity. These parameters can be estimated for different populations and are related to the reproductive fitness and the competition for limited resources, respectively. We investig...
Article
Full-text available
We present a simple paradigm for detection of an immobile target by a space-time coupled random walker with a finite lifetime. The motion of the walker is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption of motion in the new directi...
Article
Full-text available
We present a simple paradigm for detection of an immobile target by a L\'evy walker with a finite lifetime, which we alternatively call a mortal creeper. The motion of the creeper is characterized by linear displacements at a fixed speed and exponentially distributed duration, interrupted by random changes in the direction of motion and resumption...
Conference Paper
Full-text available
Anomalous diffusion in spines • Levy walks on fractal comb • Fractional reaction-diffusion along spiny dendrites 1.4 Front propagation in combs. .
Article
We investigate the behavior of five hyperbolic reaction-diffusion equations most commonly employed to describe systems of interacting organisms or reacting particles where dispersal displays inertia. We first discuss the macroscopic or mesoscopic foundation, or lack thereof, of these reaction-transport equations. This is followed by an analysis of...
Article
Full-text available
We derive the Fokker-Planck equation for multivariable Langevin equations with cross-correlated Gaussian white noises for an arbitrary interpretation of the stochastic differential equation. We formulate the conditions when the solution of the Fokker-Planck equation does not depend on which stochastic calculus is adopted. Further, we derive an equi...
Chapter
Fluctuating phenomena are ubiquitous in nature. The reader just needs to look at the first plot from Fig. 2.1 which represents the signal X(t) as a function of time. If I would say that this represents the hourly series for the temperature of a city during a whole week you would probably believe it (and this is actually what it is). But if I would...
Chapter
The intention of this chapter is to provide a brief survey of probability theory in a very schematic way, just to present some essential concepts and results that are necessary to understand the ideas exposed throughout the rest of the book. Readers with a background in mathematical probability can skip this chapter and only revisit it occasionally...
Chapter
In the previous Chapter we have reviewed different classical models of movement and have explored how they behave in the large time asymptotic regime. The emphasis has been put in showing the working methods and characteristics of the different levels of description (macroscopic, mesoscopic and microscopic). Next we shall show how this differentiat...
Chapter
Dispersal and reproduction are fundamental elements in the life-cycle of every biological organism. As a result, if one needs to understand population evolution within timescales of the order of the individual lifespan of larger, then one needs to deal with reaction-dispersal models, where reaction is the technical term to designate birth and death...