Article
Physics, Multidisciplinary
Alejandro P. Riascos, Denis Boyer, Jose L. Mateos
Summary: This paper investigates the spectral theory of random walks subject to resetting on networks of arbitrary topology and presents a general criterion for determining the resetting probability that minimizes the mean first passage time at a target node. The results can be applied to the study of optimal transport.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Fluids & Plasmas
Yating Wang, Hanshuang Chen
Summary: In this paper, the authors investigate the effects of stochastic resetting on the entropy rate of discrete-time Markovian processes. The study reveals nontrivial and interesting features of stochastic dynamics, showing a nonmonotonic dependence of the entropy rate on the resetting probability. The research also explores the mixing properties of stochastic processes on different network topologies.
Article
Physics, Fluids & Plasmas
Hanshuang Chen, Yanfei Ye
Summary: This study investigates discrete-time random walks on networks subject to time-dependent stochastic resetting. The results demonstrate that time-modulated resetting protocols can be more advantageous in accelerating the completion of a target search process compared to constant-probability resetting.
Article
Physics, Fluids & Plasmas
Feng Huang, Hanshuang Chen
Summary: This study investigates discrete-time random walks with first-passage resetting processes on arbitrary networks, deriving exact expressions for stationary occupation probability, average number of resets, and mean first-passage time. Results show that these quantities can be expressed in terms of the fundamental matrix, demonstrating the advantage of first-passage resetting in global search on various networks.
Review
Mathematics, Interdisciplinary Applications
A. P. Riascos, Jose L. Mateos
Summary: This article presents a survey of various types of random walk models on undirected weighted networks, including local and non-local transitions, and explores their applications in different contexts. By defining dynamics as a discrete-time Markovian process with transition probabilities expressed in terms of a symmetric matrix of weights, explicit relations for characterizing random walks are obtained. The results allow for the study and comparison of global dynamics of different types of random walk models.
JOURNAL OF COMPLEX NETWORKS
(2021)
Article
Physics, Multidisciplinary
L. Regnier, O. Benichou, P. L. Krapivsky
Summary: We introduce range-controlled random walks with hopping rates depending on the range N, that is, the total number of previously distinct visited sites. We analyze a one-parameter class of models with a hopping rate Na and determine the large time behavior of the average range, as well as its complete distribution in two limit cases. We find that the behavior drastically changes depending on whether the exponent a is smaller, equal, or larger than the critical value, ad, depending only on the spatial dimension d.
PHYSICAL REVIEW LETTERS
(2023)
Article
Physics, Multidisciplinary
Yan Wang, Xinxin Ca, Tongfeng Weng, Huijie Yang, Changgui Gu
Summary: In this study, we introduced lowest-degree preference random walks on complex networks, which significantly reduced search time compared to random walks on the majority of real networks. The optimal tuning parameter showed a strong positive correlation with entropy of degree sequence, indicating how much the search time could be reduced. This work opens up a new path for designing efficient search strategies with only local information available.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2021)
Article
Mathematics
Massimiliano Turchetto, Michele Bellingeri, Roberto Alfieri, Ngoc-Kim-Khanh Nguyen, Quang Nguyen, Davide Cassi
Summary: Investigating the network response to node removal and the efficacy of the node removal strategies is fundamental to network science. In this study, we propose four new measures of node centrality based on random walk and compare them with existing strategies for synthesizing and real-world networks. The results indicate that the degree nodes attack is the best strategy overall, and the new node removal strategies based on random walk show the highest efficacy in relation to specific network topology.
Article
Engineering, Mechanical
Jiao Wu, Xiyun Zhang, Changgui Gu, Hongjie Bi, Kesheng Xu, Muhua Zheng
Summary: Using a decentralized navigation protocol in spatially embedded networks, this study investigated the effects of long-range connections on navigation in SCN networks. The results showed that SCN networks can be embedded into hidden hyperbolic metric spaces, and the hyperbolic distances can determine the long-range connections. Efficient navigation in hyperbolic space was found to better support the circadian rhythm.
NONLINEAR DYNAMICS
(2023)
Article
Statistics & Probability
Andrea Collevecchio, Kais Hamza, Tuan-Minh Nguyen
Summary: We studied one-dimensional excited random walks with non-nearest neighbour jumps. The process moves to the right with positive drift at new vertices, and switches to simple symmetric random walk at visited vertices. We provided a condition for the process to have positive speed.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2021)
Article
Physics, Fluids & Plasmas
Fei Ma, Ping Wang
Summary: The study proposes a simple algorithmic framework for generating power-law graphs with small diameters and examines their structural properties. The results show that these graphs have unique features such as density characteristics and higher trapping efficiency compared to existing scale-free models, confirmed through extensive simulations.
Article
Physics, Multidisciplinary
Ward L. Vleeshouwers, Vladimir Gritsev
Summary: Unitary matrix integrals over symmetric polynomials have important applications in random matrix theory, gauge theory, number theory, and enumerative combinatorics. Our study provides novel results on these integrals and applies them to correlation functions of long-range random walks involving hard-core bosons. We propose a generalized identity for computing these integrals, allowing us to derive expressions for unitary matrix integrals over Schur polynomials. We also present a particle-hole duality between different LRRW models and suggest using fermionic systems instead of bosonic systems for computing correlation functions.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Multidisciplinary Sciences
Alexandre Bovet, Jean-Charles Delvenne, Renaud Lambiotte
Summary: This article introduces a method based on a dynamical process evolving on a temporal network, which uncovers different dynamic scales in a system by considering the ordering of edges in forward and backward time. The method provides a new approach to extracting a simplified view of time-dependent network interactions in a system.
Article
Multidisciplinary Sciences
Alexander Ponomarenko, Leonidas Pitsoulis, Marat Shamshetdinov
Summary: The LPAM method introduces a new approach for detecting overlapping communities in networks, considering different distance functions and evaluating its performance on real life instances and synthetic network benchmarks. It utilizes link partitioning and partitioning around medoids to detect overlapping communities in graphs.
Article
Physics, Multidisciplinary
Alejandro P. Riascos, Francisco Hernandez Padilla
Summary: In this paper, a framework for comparing differences in occupation probabilities of two random walk processes on networks is presented. The framework considers modifications of the network or the transition probabilities between nodes. A dissimilarity measure is defined using the eigenvalues and eigenvectors of the normalized Laplacian. The framework is used to examine differences in diffusive dynamics, the effect of new edges and rewiring in networks, and divergences in transport in degree-biased random walks and random walks with stochastic reset.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Review
Pharmacology & Pharmacy
Juliana Rincon-Lopez, Yara C. Almanza-Arjona, Alejandro P. Riascos, Yareli Rojas-Aguirre
Summary: This research reveals the evolution of cyclodextrin-based pharmaceutical technologies with a focus on solubility, stability, and taste-masking enhancement. The majority of these technologies are directed toward parenteral aqueous solutions, while oral and ocular formulations are rapidly growing. Although formulations for nasal and pulmonary routes are emerging, other routes such as topical, transdermal, vaginal, and rectal have not been widely explored but may hold great potential. The progress in materials sciences, supramolecular chemistry, and nanotechnology is expected to further influence the development of these pharmaceutical technologies.
JOURNAL OF DRUG DELIVERY SCIENCE AND TECHNOLOGY
(2021)
Article
Thermodynamics
Michael Bestehorn, Alejandro P. Riascos, Thomas M. Michelitsch, Bernard A. Collet
Summary: The study analyzed the dynamics of independent random walkers on a graph and developed a model of epidemic spreading. By implementing this model in computer simulations, researchers studied the space-time evolution of emerging infection patterns.
CONTINUUM MECHANICS AND THERMODYNAMICS
(2021)
Article
Mechanics
Long Gao, Junhao Peng, Chunming Tang, A. P. Riascos
Summary: This paper investigates biased random walks on weighted scale-free trees, analyzing the trapping efficiency through average trapping time (ATT) and global mean first-passage times (GMFPT) metrics, and explores the impact of parameter w on trapping efficiency. The results suggest that in non-fractal scenarios, lower values of w lead to higher ATT, while proper settings of w can enhance trapping efficiency on fractal trees. Additionally, the highest trapping efficiency is observed in unweighted networks for the non-fractal case, with a reduction in trapping frequency for other values of w.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Mechanics
L. K. Eraso-Hernandez, A. P. Riascos, T. M. Michelitsch, J. Wang-Michelitsch
Summary: This paper explores the reduction of functionality in a complex system as a result of cumulative random damage and imperfect repair, which is modeled as a dynamical process in networks. The global characteristics of the diffusive movement of random walkers on networks are analyzed, with the impact of damage and bias on transport asymmetry quantified at both local and global scales. The findings suggest that systems with greater complexity tend to live longer.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2021)
Article
Multidisciplinary Sciences
Jaspe U. Martinez-Gonzalez, Alejandro P. Riascos
Summary: This paper analyzes the movement of vehicles in the Metrobus bus rapid transit system in Mexico City using a massive dataset from February 2020 to April 2021. Statistical analysis of speeds in different geographical zones is used to characterize the vehicles' activity, and the Kullback-Leibler distance and community detection algorithms are employed to compare and classify the movement of vehicles in different segments.
SCIENTIFIC REPORTS
(2022)
Article
Mathematics, Applied
Thomas M. Michelitsch, Federico Polito, Alejandro P. Riascos
Summary: The article introduces a new class of asymmetric random walks, ADTRW and ACTRW, and explores their characteristics and connections with the generator process and waiting time density.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Physics, Multidisciplinary
Alejandro P. Riascos, Denis Boyer, Jose L. Mateos
Summary: This paper investigates the spectral theory of random walks subject to resetting on networks of arbitrary topology and presents a general criterion for determining the resetting probability that minimizes the mean first passage time at a target node. The results can be applied to the study of optimal transport.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Computer Science, Interdisciplinary Applications
J. A. Ruiz-Gayosso, A. P. Riascos
Summary: In this research, the air transportation network of the United States was analyzed using databases with detailed domestic flight records. Different properties of the air transport network from 2011 to 2020 were studied and compared with a gravity law-based model for human mobility. The predictions of this model were confirmed through Monte Carlo simulations, reproducing the dynamics of passengers in the airport transportation network.
INTERNATIONAL JOURNAL OF MODERN PHYSICS C
(2023)
Article
Mathematics
Thomas M. Michelitsch, Federico Polito, Alejandro P. Riascos
Summary: In this paper, we introduce the squirrel random walk (SRW), a semi-Markovian discrete-time random walk model. By studying the different step direction switch times in the SRW, we find that it exhibits several regimes of anomalous diffusion.
Article
Physics, Multidisciplinary
Alejandro P. Riascos, Francisco Hernandez Padilla
Summary: In this paper, a framework for comparing differences in occupation probabilities of two random walk processes on networks is presented. The framework considers modifications of the network or the transition probabilities between nodes. A dissimilarity measure is defined using the eigenvalues and eigenvectors of the normalized Laplacian. The framework is used to examine differences in diffusive dynamics, the effect of new edges and rewiring in networks, and divergences in transport in degree-biased random walks and random walks with stochastic reset.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Fluids & Plasmas
Teo Granger, Thomas M. Michelitsch, Michael Bestehorn, Alejandro P. Riascos, Bernard A. Collet
Summary: This paper studies an epidemic model for a constant population, considering four compartments representing the health states of individuals. The authors derive memory evolution equations for the macroscopic S-C-I-R-S model and analyze different cases. They also implement a random-walker approach in computer simulations and compare the results with the macroscopic model for validation. The S-C-I-R-S models have a wide range of applications in understanding epidemic dynamics.
Article
Physics, Fluids & Plasmas
Christopher Sebastian Hidalgo Calva, Alejandro P. Riascos
Summary: This research proposes a method of local-biased random walks on networks, where different biases are defined in each node to establish transitions to neighbors. The study finds that local bias can optimize the exploration of the network.
Article
Physics, Fluids & Plasmas
Michael Bestehorn, Thomas M. Michelitsch, Bernard A. Collet, Alejandro P. Riascos, Andrzej F. Nowakowski
Summary: This study introduces a compartment model with memory to analyze the dynamics of epidemic spreading in a constant population. The model incorporates a random duration of immunity, which introduces a memory effect that significantly impacts the epidemic dynamics. Computer simulations are used to investigate the influence of this memory effect on the space-time dynamics of the spreading, identifying relevant parameters for the spread or extinction of an epidemic.
Article
Physics, Fluids & Plasmas
Fernanda H. Gonzalez, Alejandro P. Riascos, Denis Boyer
Summary: The study focuses on diffusive transport of Markovian random walks on networks with stochastic resetting to multiple nodes. Analytical expressions for stationary occupation probability, mean, and global first passage times are derived to characterize the effect of resetting on random walk strategies. The methods are applied to various dynamics, including Levy flights and Google random walk strategy.
Article
Physics, Fluids & Plasmas
Alejandro P. Riascos, David P. Sanders
Summary: This study introduces a general approach for studying the collective dynamics of noninteracting random walkers on connected networks. By analyzing the movement of independent walkers and using their transition matrices, analytical expressions for collective stationary distribution and average steps have been deduced. These results have been applied to studying mean first-encounter times for random walk strategies on various networks.
