Alejandro Perez Riascos

In this paper, the evolution of surface damage of asphalt pavements under studded tire traffic is examined using a combined experimental and stochastic modeling approach. Laboratory tests on six asphalt mixtures were integrated into a Monte Carlo framework that represents rutting wear as the cumulative effect of random stud impacts. The introduced model accurately captures the transition from the initial phase to the steady linear rutting regime and exhibits consistency with the experimental results. A strong linear relationship was identified between the stochastic detachment parameter Λ and the laboratory rutting rate κ lab , as well as with the abrasion resistance AbrA, confirming the model’s ability to reproduce measurable material responses. By linking key mixture parameters to probabilistic descriptions of surface deterioration, the proposed framework provides a predictive tool for assessing and guiding the design of more durable pavements in cold climate regions.

Antifragility refers to the counterintuitive phenomenon whereby a system improves its global performance in response to damage. Although antifragile behavior has been reported in a variety of complex systems, the structural and dynamical mechanisms underlying this response remain poorly understood. In this work, we investigate antifragility in the synchronization dynamics of identical oscillators on networks, focusing on the effect of damage defined as the reduction in the weight of an edge connecting pairs of nodes in the network. Using a linearized description of the Kuramoto model with normalized couplings, we introduce a spectral measure of antifragility based on the response of the second eigenvalue of the normalized Laplacian. This framework enables an analytical and numerical characterization of how local reductions in coupling strength can accelerate global synchronization. Through first-order perturbation theory, we show that the sign and magnitude of the response are controlled by the structure of the slowest relaxation mode. In networks with modular organization, this mechanism leads to a systematic distinction between intra- and inter-community links: damage to intra-community edges is typically antifragile, whereas damage to inter-community edges is fragile. These predictions are validated by numerical simulations on deterministic, random, and real-world networks with community structure. Overall, our results establish a direct connection between spectral properties, modular topology, and antifragility in synchronization processes.

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.

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 2828 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.

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 T1∈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 target-hitting counting process (THCP) for an arbitrary set of target nodes. In the special case where a single target node coincides with the starting node, the THCP reduces to a renewal counting process. We establish connections with classical results from the literature. 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 a set of characteristic scenarios, including a forager scenario, in which frequent encounters with target nodes extend the walker’s lifetime, and a detrimental scenario, where such encounters instead reduce it. Finally, we identify a neutral scenario in which frequent visits to target nodes have no effect on the walker’s lifetime. Our analytical results are validated through random walk simulations.

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.

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.

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 Erdös–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.