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
Mathematics, Interdisciplinary Applications
Andrei A. Klishin, Dani S. Bassett
Summary: Random walks are commonly used as a model for exploring and discovering complex networks. Exposure theory, a statistical mechanics framework, is introduced to predict the learning of nodes and edges in various types of networks and demonstrates a universal trajectory for edge learning.
JOURNAL OF COMPLEX NETWORKS
(2022)
Article
Mathematics, Applied
Gianni Pagnini, Silvia Vitali
Summary: The study focuses on Markovian continuous-time random walk models for Levy flights, and highlights that convergence to stable densities is not guaranteed in certain cases when jumps follow a bi-modal power-law distribution. This result is significant for both the probabilistic derivation of the fractional diffusion equation and the concept of site fidelity in Levy-like motion for wild animals.
FRACTIONAL CALCULUS AND APPLIED ANALYSIS
(2021)
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.
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, 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.
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
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
Satya N. Majumdar, Philippe Mounaix, Sanjib Sabhapandit, Gregory Schehr
Summary: This study computes the mean number of records in a time-series, which represents the positions of a random walker with resetting. The results show that the mean number of records is independent of the jump distribution, and it grows very slowly as N increases for large N.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Satya N. Majumdar, Philippe Mounaix, Gregory Schehr
Summary: We investigate the universal properties of record statistics in a discrete-time random walk model on a line, where the statistics are independent of the probability parameter p and the distribution f(0)(eta). The two-time correlation function for record-breaking events is also universal, with nonzero p inducing additional anti-correlations. The presence of these anti-correlations leads to a reduction in record number fluctuations as p increases.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2021)
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
Computer Science, Information Systems
Lucas Guerreiro, Filipi N. Silva, Diego R. Amancio
Summary: Discovery processes in network science focus on knowledge acquisition through exploring nodes. Different learning strategies can lead to the same learning performance, indicating the need to combine learning curves with other sequence features for inferring network topology.
INFORMATION SCIENCES
(2021)
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
Computer Science, Artificial Intelligence
Arzu Gorgulu Kakisim
Summary: Attributed network embedding method ANEA generates low-dimensional representations of network objects by incorporating attribute data into the embedding process. It captures high-order semantic relations between attributes by performing random walks on two different graph structures. ANEA learns embeddings through a joint space of the network structure and attributes, effectively modeling the proximity among nodes.
APPLIED INTELLIGENCE
(2022)
Article
Physics, Multidisciplinary
M. Serva, D. Vergni, D. Volchenkov, A. Vulpiani
Article
Mathematics, Applied
D. Volchenkov, R. Lima
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2008)
Review
Mathematics, Applied
Dimitri Volchenkov
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2010)
Article
Computer Science, Artificial Intelligence
Ph. Blanchard, F. Petroni, M. Serva, D. Volchenkov
COMPUTER SPEECH AND LANGUAGE
(2011)
Review
Physics, Multidisciplinary
D. Volchenkov
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2009)
Review
Physics, Multidisciplinary
Ph Blanchard, J. R. Dawin, D. Volchenkov
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2010)
Article
Physics, Mathematical
D. Volchenkov, P. Blanchard
JOURNAL OF STATISTICAL PHYSICS
(2008)
Article
Multidisciplinary Sciences
Maurizio Serva, Filippo Petroni, Dima Volchenkov, Soren Wichmann
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2012)
Article
Multidisciplinary Sciences
Dimitri Volchenkov, Jonathan Helbach, Marko Tscherepanow, Sina Kuehnel
JOURNAL OF THE ROYAL SOCIETY INTERFACE
(2013)
Article
Mathematical & Computational Biology
William M. Land, Dima Volchenkov, Bettina E. Blaesing, Thomas Schack
FRONTIERS IN COMPUTATIONAL NEUROSCIENCE
(2013)
Article
Computer Science, Interdisciplinary Applications
Dimitri Volchenkov, Bettina Blaesing
JOURNAL OF COMPUTATIONAL SCIENCE
(2013)
Article
Physics, Multidisciplinary
Dmitry Kovalevsky, Dimitri Volchenkov, Juergen Scheffran
Summary: Climate change causes sea level rise and high coastal hazards, impacting many urban areas worldwide, especially those with high urbanization growth rates. Understanding and modeling multifaceted urban dynamics is crucial for developing tailored coastal climate services. A coastal urban model family has been developed to simulate population growth, urbanization rates, and population density distributions, using the maximum entropy principle to predict coastal urban dynamics affected by climate change.
Article
Computer Science, Information Systems
Dimitri Volchenkov
Summary: Canonical ensembles provide properly normalized probability distributions to nodes, subgraphs, and nodal subsets in finite connected graphs at different time and connectivity scales during diffusion processes. The use of information theory methods in graph problems, known as information graph theory, allows for evaluating navigability, walkability, and perspicacity of different modes of the diffusion process. Information graph theory is highly demanded in various applications, such as network-on-chip architecture design and engineering urban morphology in the concept of smart city, as it assesses communication efficiency between individual system units at different scales.
Article
Computer Science, Theory & Methods
Dimitri Volchenkov, Jonathan Helbach, Marko Tscherepanow, Sina Kueheel
ELECTRONIC NOTES IN THEORETICAL COMPUTER SCIENCE
(2013)
Article
Mathematics, Applied
Hao Liu, Yuzhe Li
Summary: This paper investigates the finite-time stealthy covert attack on reference tracking systems with unknown-but-bounded noises. It proposes a novel finite-time covert attack method that can steer the system state into a target set within a finite time interval while being undetectable.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Nikolay A. Kudryashov, Aleksandr A. Kutukov, Sofia F. Lavrova
Summary: The Chavy-Waddy-Kolokolnikov model with dispersion is analyzed, and new properties of the model are studied. It is shown that dispersion can be used as a control mechanism for bacterial colonies.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Qiang Ma, Jianxin Lv, Lin Bi
Summary: This paper introduces a linear stability equation based on the Boltzmann equation and establishes the relationship between small perturbations and macroscopic variables. The numerical solutions of the linear stability equations based on the Boltzmann equation and the Navier-Stokes equations are the same under the continuum assumption, providing a theoretical foundation for stability research.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Samuel W. Akingbade, Marian Gidea, Matteo Manzi, Vahid Nateghi
Summary: This paper presents a heuristic argument for the capacity of Topological Data Analysis (TDA) to detect critical transitions in financial time series. The argument is based on the Log-Periodic Power Law Singularity (LPPLS) model, which characterizes financial bubbles as super-exponential growth (or decay) with increasing oscillations approaching a tipping point. The study shows that whenever the LPPLS model fits the data, TDA generates early warning signals. As an application, the approach is illustrated using positive and negative bubbles in the Bitcoin historical price.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Xavier Antoine, Jeremie Gaidamour, Emmanuel Lorin
Summary: This paper is interested in computing the ground state of nonlinear Schrodinger/Gross-Pitaevskii equations using gradient flow type methods. The authors derived and analyzed Fractional Normalized Gradient Flow methods, which involve fractional derivatives and generalize the well-known Normalized Gradient Flow method proposed by Bao and Du in 2004. Several experiments are proposed to illustrate the convergence properties of the developed algorithms.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Lianwen Wang, Xingyu Wang, Zhijun Liu, Yating Wang
Summary: This contribution presents a delayed diffusive SEIVS epidemic model that can predict and quantify the transmission dynamics of slowly progressive diseases. The model is applied to fit pulmonary tuberculosis case data in China and provides predictions of its spread trend and effectiveness of interventions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shuangxi Huang, Feng-Fei Jin
Summary: This paper investigates the error feedback regulator problem for a 1-D wave equation with velocity recirculation. By introducing an invertible transformation and an adaptive error-based observer, an observer-based error feedback controller is constructed to regulate the tracking error to zero asymptotically and ensure bounded internal signals.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Weimin Liu, Shiqi Gao, Feng Xu, Yandong Zhao, Yuanqing Xia, Jinkun Liu
Summary: This paper studies the modeling and consensus control of flexible wings with bending and torsion deformation, considering the vibration suppression as well. Unlike most existing multi-agent control theories, the agent system in this study is a distributed parameter system. By considering the mutual coupling between the wing's deformation and rotation angle, the dynamics model of each agent is expressed using sets of partial differential equations (PDEs) and ordinary differential equations (ODEs). Boundary control algorithms are designed to achieve control objectives, and it is proven that the closed-loop system is asymptotically stable. Numerical simulation is conducted to demonstrate the effectiveness of the proposed control scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Gourav Mandal, Lakshmi Narayan Guin, Santabrata Chakravarty
Summary: The ecological framework investigates the dynamical complexity of a system influenced by prey refuge and alternative food sources for predators. This study provides a thorough investigation of the stability-instability phenomena, system parameters sensitivity, and the occurrence of bifurcations. The bubbling phenomenon, which indicates a change in the amplitudes of successive cycles, is observed in the current two-dimensional continuous system. The controlling system parameter for the bubbling phenomena is found to be the most sensitive. The prediction and identification of bifurcations in the dynamical system are crucial for theoretical and field researchers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Damian Trofimowicz, Tomasz P. Stefanski, Jacek Gulgowski, Tomasz Talaska
Summary: This paper presents the application of control engineering methods in modeling and simulating signal propagation in time-fractional electrodynamics. By simulating signal propagation in electromagnetic media using Maxwell's equations with fractional-order constitutive relations in the time domain, the equations in time-fractional electrodynamics can be considered as a continuous-time system of state-space equations in control engineering. Analytical solutions are derived for electromagnetic-wave propagation in the time-fractional media based on state-transition matrices, and discrete time zero-order-hold equivalent models are developed and their analytical solutions are derived. The proposed models yield the same results as other reference methods, but are more flexible in terms of the number of simulation scenarios that can be tackled due to the application of the finite-difference scheme.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yuhao Zhao, Fanhao Guo, Deshui Xu
Summary: This study develops a vibration analysis model of a nonlinear coupling-layered soft-core beam system and finds that nonlinear coupling layers are responsible for the nonlinear phenomena in the system. By using reasonable parameters for the nonlinear coupling layers, vibrations in the resonance regions can be reduced and effective control of the vibration energy of the soft-core beam system can be achieved.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
S. Kumar, H. Roy, A. Mitra, K. Ganguly
Summary: This study investigates the nonlinear dynamic behavior of bidirectional functionally graded plates (BFG) and unidirectional functionally graded plates (UFG). Two different methods, namely the whole domain method and the finite element method, are used to formulate the dynamic problem. The results show that all three plates exhibit hardening type nonlinearity, with the effect of material gradation parameters being more pronounced in simply supported plates.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Isaac A. Garcia, Susanna Maza
Summary: This paper analyzes the role of non-autonomous inverse Jacobi multipliers in the problem of nonexistence, existence, localization, and hyperbolic nature of periodic orbits of planar vector fields. It extends and generalizes previous results that focused only on the autonomous or periodic case, providing novel applications of inverse Jacobi multipliers.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Yongjian Liu, Yasi Lu, Calogero Vetro
Summary: This paper introduces a new double phase elliptic inclusion problem (DPEI) involving a nonlinear and nonhomogeneous partial differential operator. It establishes the existence and extremality results to the elliptic inclusion problem and provides definitions for weak solutions, subsolutions, and supersolutions.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
Article
Mathematics, Applied
Shangshuai Li, Da-jun Zhang
Summary: In this paper, the Cauchy matrix structure of the spin-1 Gross-Pitaevskii equations is investigated. A 2 x 2 matrix nonlinear Schrodinger equation is derived using the Cauchy matrix approach, serving as an unreduced model for the spin-1 BEC system with explicit solutions. Suitable constraints are provided to obtain reductions for the classical and nonlocal spin-1 GP equations and their solutions, including one-soliton solution, two-soliton solution, and double-pole solution.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2024)
