arXiv subjects

Alejandro P. Riascos

Publications and source records attributed to Alejandro P. Riascos.

At least 19 recordsLinked to original sources

arXiv2026

Dissimilarity measures for generalized Lotka-Volterra systems on networks

In this paper, we introduce a general framework to quantify dissimilarities between generalized Lotka-Volterra dynamical processes, ranging from classical predator-prey systems to multispecies communities interacting on networks. The proposed measures capture both transient and stationary dynamics, allowing systematic comparisons across systems with varying interaction parameters, network weights, or topologies. Our analysis shows that even subtle structural changes can lead to markedly distinct outcomes: in two-species systems, interaction strength and initial conditions strongly affect divergence, while in small directed networks, differences that are invisible at the adjacency-matrix level produce divergent dynamics. In modular networks, the fraction and distribution of negative interactions control the transition from stable to unstable dynamics, with localized perturbations within cliques yielding different global outcomes than distributed ones. Beyond structural variations, the framework also applies when modified processes follow distinct nonlinear equations, demonstrating its versatility. Taken together, these results highlight that dynamical dissimilarity measures provide a powerful tool to analyze robustness, detect structural sensitivity, and predict instabilities in nonlinear systems. More broadly, this approach supports the comparative analysis of biological systems, where complex interaction networks and nonlinear dynamics are central to stability and resilience.

cond-mat.stat-mech↗

arXiv2026

On discrete-time arrival processes and related random motions

We consider three kinds of discrete-time arrival processes: transient, intermediate and recurrent, characterized by a finite, possibly finite and infinite number of events, respectively. In this framework, we study renewal processes which are externally stopped at an independent stopping time which may be defective or non-defective. For defective stopping time, the resulting arrival process is of intermediate nature. For non-defective stopping time, the resulting arrival process is transient, i.e. stopped almost surely. For these processes we obtain finite time and asymptotic properties. Particular attention is devoted to the class of transient renewal processes, that is, renewal processes with defective interarrival times. Among these, we consider two examples: The "Defective Bernoulli Process" and the "Defective Sibuya Process". We validate some analytical results using Monte Carlo simulations. We apply these results to biased and unbiased random walks on the $d$-dimensional infinite lattice and as a special case on the two-dimensional triangular lattice. We study the spatial propagator of the walker and its large time asymptotics. In particular, we observe the emergence of a superdiffusive (ballistic) behavior in the case of biased walks. For geometrically distributed stopping times, the propagator converges to a stationary non-equilibrium steady state (NESS), which is universal in the sense that it is independent of the stopped process. In dimension one, for both light- and heavy-tailed step distributions, the NESS has an integral representation involving alpha-stable distributions.

math.PR↗

arXiv2026

Encounter times of random walkers with simultaneous resetting on networks

In this work, we study the dynamics of multiple random walkers on networks subject to a simultaneous resetting protocol, whereby all walkers are synchronously returned to their respective initial nodes. For this collective Markovian process, we derive exact analytical expressions for the mean first-encounter time, defined as the average time required for all walkers to meet for the first time at a given node. These results are formulated in terms of the eigenvalues and eigenvectors of the transition matrices governing the dynamics without resetting, providing a clear spectral interpretation of the impact of resetting on encounter processes. We further establish a general criterion for finite networks that determines when the introduction of a nonzero resetting probability reduces the mean first-encounter time and leads to an optimal resetting strategy. The theoretical predictions are illustrated through numerical results on regular and heterogeneous networks, for encounters involving two or more walkers, and for combinations of local and nonlocal dynamics. Our findings demonstrate that simultaneous resetting can significantly reduce encounter times for specific target nodes and initial conditions, while becoming ineffective for highly exploratory dynamics or distant targets. A comparison with independent resetting shows that simultaneous resetting is more efficient in homogeneous networks, whereas independent resetting can outperform it in heterogeneous structures, thereby revealing a trade-off between synchronization and exploration. The framework provides a unified approach to collective search and encounter problems on networks with resetting.

cond-mat.stat-mech↗

arXiv2026

From motifs to Lévy flights: Modeling urban mobility in Bogotá's public transport system

In this paper, we study two years of access card validation records from Bogotá's multimodal public transport system, comprising over 2.3 billion trips across bus rapid transit, feeder buses, dual-service buses, and an aerial cable network. From user trajectories constructed exclusively from access records, we derive motifs that reveal recurrent mobility patterns extending beyond simple two-location visits. This approach enables the construction of an integrated origin-destination (OD) matrix covering 2,828 urban zones. Similarity analysis using the Jensen-Shannon divergence confirms the temporal stability of mobility structures across semesters, despite infrastructure changes and fare policy adjustments. From the obtained OD matrices, we derive transition probabilities between zones and uncover a robust power-law relationship with geographical distance, consistent with Lévy flight dynamics. We validate our model using Monte Carlo simulations showing that reproduces both local and long-range displacements, with similar scaling exponents across time. These findings demonstrate that Bogotá's public transport mobility can be effectively modeled through Lévy processes, providing a novel framework for analyzing complex transportation systems based solely on user access records.

physics.soc-ph↗

arXiv2025

Evanescent random walker on networks: Hitting times, budget renewal, and survival dynamics

We consider a mortal random walker evolving with discrete time on a network, where transitions follow a degree-biased Markovian navigation strategy. The walker starts with a random initial budget $T_1 \in \mathbb{N}$ and must maintain a strictly positive budget to remain alive. Each step incurs a unit cost, decrementing the budget by one; the walker perishes (is ruined) upon depletion of the budget. However, when the walker reaches designated target nodes, the budget is renewed by an independent and identically distributed (IID) copy of its initial value. The degree bias is tuned to either favor or disfavor visits to these target nodes. Our model exhibits connections with stochastic resetting. The evolution of the budget can be interpreted as a deterministic drift on the integer line toward negative values, where the walker is intermittently reset to positive IID random positions and dies at the first hit of the origin. The first part of the paper focuses on the target-hitting statistics of an immortal Markovian walker. We analyze the \textit{target hitting counting process} (THCP) for an arbitrary set of target nodes. Within this framework, the second part of the paper addresses the dynamics of the evanescent walker. We derive analytical results for arbitrary configurations of target nodes, including the evanescent propagator matrix, the survival probability, the mean residence time on a set of nodes during the walker's lifetime, and the expected lifetime itself. Additionally, we compute the expected number of target hits (i.e., budget renewals) in a lifetime of the walker and related distributions. We explore both analytically and numerically various scenarios affecting the life expectancy of the walker.

cond-mat.stat-mech↗

arXiv2025

Stochastic Compartment Model of Epidemic Spreading in Complex Networks with Mortality and Resetting

We propose an epidemic compartment model, which includes mortality caused by the disease, but excludes demographic birth and death processes. Individuals are represented by random walkers, which are in one of the following states (compartments) S (susceptible to infection), E (exposed: infected but not infectious corresponding to the latency period), I (infected and infectious), R (recovered, immune), D (dead). The disease is transmitted with a certain probability at contacts of I to S walkers. The compartmental sojourn times are independent random variables drawn from specific (here Gamma-) distributions. We implement this model into random walk simulations. Each walker performs an independent simple Markovian random walk on a graph, where we consider a Watts-Strogatz (WS) network. Only I walkers may die. For zero mortality, we prove the existence of an endemic equilibrium for basic reproduction number ${\cal R}_0 > 1$ and for which the disease free (globally healthy) state is unstable. We explore the effects of long-range-journeys (stochastic resetting) and mortality. Our model allows for various interpretations, such as certain chemical reactions, the propagation of wildfires, and in population dynamics.

cond-mat.stat-mech↗

arXiv2025

Mean first-encounter times of simultaneous random walkers with resetting on networks

We investigate the dynamics of simultaneous random walkers with resetting on networks and derive exact analytical expressions for the mean first-encounter times of Markovian random walkers. Specifically, we consider two cases for the simultaneous dynamics of two random walkers on networks: when only one walker resets to the initial node, and when both walkers return to their initial positions. In both cases, the encounter times are expressed in terms of the eigenvalues and eigenvectors of the transition matrix of the normal random walk, providing a spectral interpretation of the impact of resetting. We validate our approach through examples on rings, Cayley trees, and random networks generated using the Erdős-Rényi, Watts-Strogatz, and Barabási-Albert algorithms, where resetting significantly reduces encounter times. The proposed framework can be extended to other types of random walk dynamics, transport processes, or multiple-walker scenarios, with potential applications in human mobility, epidemic spreading, and search strategies in complex systems.

cond-mat.stat-mech↗

arXiv2025

From random walks to epidemic spreading: Compartment model with mortality for vector transmitted diseases

We propose a compartmental model for vector-transmitted diseases, such as Malaria and Dengue, spreading over complex networks. Individuals are represented by independent random walkers and vectors by infected nodes. Both walkers and nodes can be susceptible (S) or infected (I). Infected walkers may die (entering the dead compartment D), while infected nodes remain alive. Susceptible walkers can be infected by visiting infected nodes, and susceptible nodes by visits from infected walkers. We derive explicit expressions for the basic reproduction numbers $R_0$ (without mortality) and $R_M$ (with mortality), proving that $R_M < R_0$. When $R_M , R_0 > 1$, the healthy state is unstable, and for zero mortality, an endemic equilibrium emerges. We also study the effects of confinement measures. Simulations align well with mean-field predictions on strongly connected graphs but deviate for weakly connected networks. Our model has various interdisciplinary applications which include the modeling of chemical reaction kinetics, contaminant spread, and wildfire propagation.

q-bio.PE↗

arXiv2024

Random walks with long-range memory on networks

We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way, such that the most visited nodes have proportionally a higher probability to be chosen for revisit. The occupation probability can be expressed as a sum over the eigenmodes of the standard random walk matrix of the network, where the amplitudes slowly decay as power-laws at large time, instead of exponentially. The stationary state is the same as in the absence of memory and detailed balance is fulfilled. However, the relaxation of the transient part becomes critically self-organized at late times, as it is dominated by a single power-law whose exponent depends on the second largest eigenvalue and on the resetting probability. We apply our findings to finite networks such as rings, complete graphs, Watts-Strogatz and Barabási-Albert networks, and to Barbell and comb-like graphs. Our study could be of interest for modeling complex transport phenomena, such as human mobility, epidemic spreading, or animal foraging.

cond-mat.stat-mech↗

arXiv2024

Random walks with stochastic resetting in complex networks: a discrete time approach

We consider a discrete-time Markovian random walk with resets on a connected undirected network. The resets, in which the walker is relocated to randomly chosen nodes, are governed by an independent discrete-time renewal process. Some nodes of the network are target nodes, and we focus on the statistics of first hitting of these nodes. In the non-Markov case of the renewal process, we consider both light- and fat-tailed inter-reset distributions. We derive the propagator matrix in terms of discrete backward recurrence time PDFs and in the light-tailed case we show the existence of a non-equilibrium steady state. In order to tackle the non-Markov scenario, we derive a defective propagator matrix which describes an auxiliary walk characterized by killing the walker as soon as it hits target nodes. This propagator provides the information on the mean first passage statistics to the target nodes. We establish sufficient conditions for ergodicity of the walk under resetting. Furthermore, we discuss a generic resetting mechanism for which the walk is non-ergodic. Finally, we analyze inter-reset time distributions with infinite mean where we focus on the Sibuya case. We apply these results to study the mean first passage times for Markovian and non-Markovian (Sibuya) renewal resetting protocols in realizations of Watts-Strogatz and Barabási-Albert random graphs. We show non trivial behavior of the dependence of the mean first passage time on the proportions of the relocation nodes, target nodes and of the resetting rates. It turns out that, in the large-world case of the Watts-Strogatz graph, the efficiency of a random searcher particularly benefits from the presence of resets.

math.PR↗

arXiv2024

Dissimilarity between synchronization processes on networks

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a metric on a hypertorus, allowing us to compare the phases of coupled oscillators. In the first part, this formalism is implemented to examine systems of networked identical phase oscillators that evolve with the Kuramoto model. In particular, we analyze the effect of the weight of an edge in the synchronization of two oscillators, the introduction of new sets of edges in interacting cycles, the effect of bias in the couplings, and the addition of a link in a ring. We also compare the synchronization of nonisomorphic graphs with four nodes. Finally, we explore the dissimilarities generated when we contrast the Kuramoto model with its linear approximation for different random initial phases in deterministic and random networks. The approach introduced provides a general tool for comparing synchronization processes on networks, allowing us to understand the dynamics of a complex system as a consequence of the coupling structure and the processes that can occur in it.

cond-mat.stat-mech↗

arXiv2024

Stochastic compartment model with mortality and its application to epidemic spreading in complex networks

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on Barabási-Albert (BA), Erdös-Rényi (ER) and Watts-Strogatz (WS) types. Both, walkers and nodes can be either susceptible (S) or infected and infectious (I) representing their states of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with transmission of the disease via vectors (mosquitos). Infected walkers may die during the time span of their infection introducing an additional compartment D of dead walkers. Infected nodes never die and always recover from their infection after a random finite time. We derive stochastic evolution equations for the mean-field compartmental populations with mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers R M , R 0 with and without mortality, respectively, and prove that R M < R 0 . For R M , R 0 > 1 the healthy state is unstable whereas for zero mortality a stable endemic equilibrium exists (independent of the initial conditions) which we obtained explicitly. We observe that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality.

q-bio.PE↗

arXiv2023

Influence of cumulative damage on synchronization of Kuramoto oscillators on networks

In this paper, we study the synchronization of identical Kuramoto phase oscillators under cumulative stochastic damage to the edges of networks. We analyze the capacity of coupled oscillators to reach a coherent state from initial random phases. The process of synchronization is a global function performed by a system that gradually changes when the damage weakens individual connections of the network. We explore diverse structures characterized by different topologies. Among these are deterministic networks as a wheel or the lattice formed by the movements of the knight on a chess board, and random networks generated with the Erdős-Rényi and Barabási-Albert algorithms. In addition, we study the synchronization times of 109 non-isomorphic graphs with six nodes. The synchronization times and other introduced quantities are sensitive to the impact of damage, allowing us to measure the reduction of the capacity of synchronization and classify the effect of damage in the systems under study. This approach is general and paves the way for the exploration of the effect of damage accumulation in diverse dynamical processes in complex systems.

cond-mat.stat-mech↗

arXiv2023

Temporal visitation patterns of points of interest in cities on a planetary scale: a network science and machine learning approach

We aim to study the temporal patterns of activity in points of interest of cities around the world. In order to do so, we use the data provided by the online location-based social network Foursquare, where users make check-ins that indicate points of interest in the city. The data set comprises more than 90 million check-ins in 632 cities of 87 countries in 5 continents. We analyzed more than 11 million points of interest including all sorts of places: airports, restaurants, parks, hospitals, and many others. With this information, we obtained spatial and temporal patterns of activities for each city. We quantify similarities and differences of these patterns for all the cities involved and construct a network connecting pairs of cities. The links of this network indicate the similarity of temporal visitation patterns of points of interest between cities and is quantified with the Kullback-Leibler divergence between two distributions. Then, we obtained the community structure of this network and the geographic distribution of these communities worldwide. For comparison, we also use a Machine Learning algorithm - unsupervised agglomerative clustering - to obtain clusters or communities of cities with similar patterns. The main result is that both approaches give the same classification of five communities belonging to five different continents worldwide. This suggests that temporal patterns of activity can be universal, with some geographical, historical, and cultural variations, on a planetary scale.

physics.soc-ph↗

arXiv2023

A measure of dissimilarity between diffusive processes on networks

In this paper, we present a framework to compare the differences in the occupation probabilities of two random walk processes, which can be generated by modifications of the network or the transition probabilities between the nodes of the same network. We explore a dissimilarity measure defined in terms of the eigenvalues and eigenvectors of the normalized Laplacian of each process. This formalism is implemented to examine differences in the diffusive dynamics described by circulant matrices, the effect of new edges, and the rewiring in networks as well as to evaluate divergences in the transport in degree-biased random walks and random walks with stochastic reset. Our results provide a general tool to compare dynamical processes on networks considering the evolution of states and capturing the complexity of these structures.

cond-mat.stat-mech↗

arXiv2023

A four compartment epidemic model with retarded transition rates

We study an epidemic model for a constant population by taking into account four compartments of the individuals characterizing their states of health. Each individual is in one of the compartments susceptible (S); incubated - infected yet not infectious (C), infected and infectious (I), and recovered - immune (R). An infection is 'visible' only when an individual is in state I. Upon infection, an individual performs the transition pathway S to C to I to R to S remaining in each compartments C, I, and R for certain random waiting times, respectively. The waiting times for each compartment are independent and drawn from specific probability density functions (PDFs) introducing memory into the model. We derive memory evolution equations involving convolutions (time derivatives of general fractional type). We obtain formulae for the endemic equilibrium and a condition of its existence for cases when the waiting time PDFs have existing means. We analyze the stability of healthy and endemic equilibria and derive conditions for which the endemic state becomes oscillatory (Hopf) unstable. We implement a simple multiple random walker's approach (microscopic model of Brownian motion of Z independent walkers) with random SCIRS waiting times into computer simulations. Infections occur with a certain probability by collisions of walkers in compartments I and S. We compare the endemic states predicted in the macroscopic model with the numerical results of the simulations and find accordance of high accuracy. We conclude that a simple random walker's approach offers an appropriate microscopic description for the macroscopic model.

q-bio.PE↗

arXiv2023

Semi-Markovian discrete-time telegraph process with generalized Sibuya waiting times

In a recent work we introduced a semi-Markovian discrete-time generalization of the telegraph process. We referred this random walk to as squirrel random walk (SRW). The SRW is a discrete-time random walk on the one-dimensional infinite lattice where the step direction is reversed at arrival times of a discrete-time renewal process and remains unchanged at uneventful time instants. We first recall general notions of the SRW. The main subject of the paper is the study of the SRW where the step direction switches at the arrival times of a generalization of the Sibuya discrete-time renewal process (GSP) which only recently appeared in the literature. The waiting time density of the GSP, the `generalized Sibuya distribution' (GSD) is such that the moments are finite up to a certain order $r\leq m-1$ ($m \geq 1$) and diverging for orders $r \geq m$ capturing all behaviors from broad to narrow and containing the standard Sibuya distribution as a special case ($m=1$). We also derive some new representations for the generating functions related to the GSD. We show that the generalized Sibuya SRW exhibits several regimes of anomalous diffusion depending on the lowest order $m$ of diverging GSD moment. The generalized Sibuya SRW opens various new directions in anomalous physics.

math.PR↗

arXiv2022

Squirrels can remember little: A random walk with jump reversals induced by a discrete-time renewal process

We consider a class of discrete-time random walks with directed unit steps on the integer line. The direction of the steps is reversed at the time instants of events in a discrete-time renewal process and is maintained at uneventful time instants. This model represents a discrete-time semi-Markovian generalization of the telegraph process. We derive exact formulae for the propagator using generating functions. We prove that for geometrically distributed waiting times in the diffusive limit, this walk converges to the classical telegraph process. We consider the large-time asymptotics of the expected position: For waiting time densities with finite mean the walker remains in the average localized close to the departure site whereas escapes for fat-tailed waiting-time densities (i.e. densities with infinite mean) by a sublinear power-law. We explore anomalous diffusion features by accounting for the `aging effect' as a hallmark of non-Markovianity where the discrete-time version of the `aging renewal process' comes into play. By deriving pertinent distributions of this process we obtain explicit formulae for the variance when the waiting-times are Sibuya-distributed. In this case and generally for fat-tailed waiting time PDFs a $t^2$-ballistic superdiffusive scaling emerges in the large time limit. In contrast if the waiting time PDF between the step reversals is light-tailed (`narrow' with finite mean and variance) the walk exhibits normal diffusion and for `broad' waiting time PDFs (with finite mean and infinite variance) superdiffusive large time scaling. We also consider time-changed versions where the walk is subordinated to a continuous-time point process such as the time-fractional Poisson process. This defines a new class of biased continuous-time random walks exhibiting several regimes of anomalous diffusion.

math.PR↗