Article
Physics, Multidisciplinary
V. P. Shkilev, I. M. Sokolov
Summary: In this work, we revisit the behavior of a subdiffusive continuous time random walk under resetting. We consider both complete resetting, where the random walk starts anew after the resetting event, and incomplete resetting, where the internal memory of the random walk is not erased by the resetting event and it restarts as an aged one. By using a special representation for the waiting time distribution in resetting, we obtain closed-form expressions for the probability density of displacements and the mean first passage time in the case of complete resetting, as well as asymptotic forms for the probability density of displacements (including prefactors) in the case of incomplete resetting.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Physics, Multidisciplinary
Mark Goldsmith, Harto Saarinen, Guillermo Garcia-Perez, Joonas Malmi, Matteo A. C. Rossi, Sabrina Maniscalco
Summary: Protein-protein interaction networks are the basis for network medicine, but they are often incomplete due to the expensive and time-consuming methods used to construct them. We propose a novel link prediction method based on continuous-time classical and quantum walks to infer missing interactions in these networks. The results show that this method can successfully predict missing protein-protein interactions with performance comparable to state-of-the-art methods.
Article
Quantum Science & Technology
Miguel A. Ruiz-Ortiz, Ehyter M. Martin-Gonzalez, Diego Santiago-Alarcon, Salvador E. Venegas-Andraca
Summary: We propose a new probabilistic definition for the hitting time of a continuous-time quantum walk into a marked set of nodes, using measurements with respect to the jump times of a Poisson process. We also derive a formula for the mean hitting time based on our definition, Wald's theorem, and a stochastic process that models our quantum measurement outcomes. This stochastic process results in a Markov chain that incorporates the expected values of the squared norm of random unitary matrix entries, providing a way to embed a Markov chain in a continuous-time quantum walk.
QUANTUM INFORMATION PROCESSING
(2023)
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
Thermodynamics
Emad Awad, Trifce Sandev, Ralf Metzler, Aleksei Chechkin
Summary: Jeffreys equation extends diffusive laws for heat and particle transport, exhibiting various anomalous behaviors in mean squared displacement. Different approaches, such as fractional Taylor series and distributed-order derivatives, transform traditional laws into the time-fractional Jeffreys equation for practical applications.
INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER
(2021)
Article
Mechanics
Kazuhiko Seki
Summary: This study examines a fluctuation relation that represents a non-equilibrium equality indicating that the ratio between the distributions of trajectories obtained by exchanging initial and final positions can be characterized by free energy differences for the duration of the trajectories. By using a continuous-time lattice random walk model with a general waiting-time distribution of transitions, the fluctuation relation for noninteracting charge carriers driven by an external electric field is investigated. The key finding is that the fluctuation relation is obtained regardless of lattice structure factors or the form of the waiting-time distribution. However, it is satisfied only after taking the continuum limit in the presence of a reflecting boundary.
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
(2023)
Article
Statistics & Probability
Itai Benjamini, Hagai Helman Tov, Maksim Zhukovskii
Summary: In this paper, we observe the outcome of the discrete time noisy voter model at a single vertex of a graph. We show that certain pairs of graphs can be distinguished by the frequency of repetitions in the sequence of observations. We prove that this statistic is asymptotically normal and can distinguish between (asymptotically) almost all pairs of finite graphs. We conjecture that the noisy voter model distinguishes between any two graphs other than stars.
ANNALS OF PROBABILITY
(2023)
Article
Multidisciplinary Sciences
Pauline Formaglio, Marina E. Wosniack, Raphael M. Tromer, Jaderson G. Polli, Yuri B. Matos, Hang Zhong, Ernesto P. Raposo, Marcos G. E. da Luz, Rogerio Amino
Summary: Plasmodium sporozoites actively migrate in the dermis and enter blood vessels to induce infection. Through intravital imaging, researchers found that sporozoites adopt a strategy of alternating global superdiffusive skin exploration and local subdiffusive blood vessel exploitation, enabling them to find intravasation hotspots associated with pericytes, enter the bloodstream and initiate malaria infection.
NATURE COMMUNICATIONS
(2023)
Article
Physics, Multidisciplinary
J. D. Cleland, M. A. K. Williams
Summary: This work presents a transiently coupled continuous time random walk framework, where the coupling is between the displacement probability density function (PDF) and the elapsed waiting time, following the form of 1 - exp (-alpha t). Such coupling generates larger displacements for longer waiting times, but decouples on longer timescales. This coupling is proposed to be relevant to systems where diffusion is driven by the development of internal stresses. The article outlines the associated generalised diffusion equation (GDE) and obtains the solution for the position PDF P(x, t) using the properties of the Fox H function.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Quantum Science & Technology
Rebekah Herrman, Thomas G. Wong
Summary: This paper investigates the simplification methods of quantum walks on dynamic graphs, proposes six scenarios for graph simplification, and provides examples of how to simplify dynamic graphs to achieve parallel single-qubit gates.
QUANTUM INFORMATION PROCESSING
(2022)
Article
Physics, Multidisciplinary
M. Dahlenburg, G. Pagnini
Summary: We study the mean first-passage time (MFPT) for asymmetric continuous-time random walks characterized by waiting-times with finite mean and jump-sizes with finite mean and variance. We derive a nonhomogeneous Wiener-Hopf integral equation that allows for the exact calculation of the MFPT, which depends on the distribution of jump-sizes and the mean-value of waiting-times. Through a case study, we show that the MFPT is independent of the jump-sizes distribution in the opposite direction to the boundary and depends on the specific distribution of jump-sizes for starting points near the boundary.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2022)
Article
Chemistry, Medicinal
Ran Liu, Xiang Liu, Jie Wu
Summary: In this study, we propose molecular descriptors based on persistent path-spectral and a machine learning model based on persistent path-spectral for the prediction of protein-ligand binding affinity. Our model combines the molecular descriptors from persistent path-spectral attributes with the gradient boosting tree machine learning model. We test this model on three commonly used datasets and achieve competitive results.
JOURNAL OF CHEMICAL INFORMATION AND MODELING
(2023)
Article
Statistics & Probability
Russell Lyons, Graham White
Summary: We study continuous-time random walks on Cayley graphs, where the rates of each edge depend only on the corresponding generator. We show that the limiting speed is monotone increasing in the rates for infinite Cayley graphs generated by Coxeter systems, but this does not hold for all Cayley graphs. On finite Cayley graphs, we prove that the distance to stationarity is monotone decreasing in the rates for Coxeter systems and abelian groups, but not for all Cayley graphs. We also discover unexpected behavior in the dependence of the distance to stationarity on the rates, including a counterexample to a conjecture on entropy.
ANNALS OF PROBABILITY
(2023)
Article
Quantum Science & Technology
Alessandro Candeloro, Claudia Benedetti, Marco G. Genoni, Matteo G. A. Paris
Summary: This paper addresses the quantum search of a target node on a cycle graph using a quantum walk assisted by continuous measurement and feedback. A dynamical oracle implemented through a feedback Hamiltonian is used. The performance of the protocol is quantified and different constraints on the control strategy are discussed. The results show that the protocol can quickly localize the walker on the target node.
ADVANCED QUANTUM TECHNOLOGIES
(2023)
Article
Quantum Science & Technology
Gabriele Bressanini, Claudia Benedetti, Matteo G. A. Paris
Summary: This paper addresses the decoherence and classicalization of continuous-time quantum walks on graphs. Three different models of decoherence are investigated, and the quantum-classical (QC) dynamical distance is employed to assess the classicalization of the CTQW due to decoherence. The results show that intrinsic decoherence only partially preserves quantum features, while decoherence in the position basis completely destroys the quantumness of the walker. Additionally, the speed of the classicalization process is also examined.
QUANTUM INFORMATION PROCESSING
(2022)
Editorial Material
Physics, Multidisciplinary
Carlo Manzo, Gorka Munoz-Gil, Giovanni Volpe, Miguel Angel Garcia-March, Maciej Lewenstein, Ralf Metzler
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Multidisciplinary
Elisabeth Lemaitre, Igor M. Sokolov, Ralf Metzler, Aleksei Chechkin
Summary: We study the effects of randomly distributed diffusivities and speeds in two models for active particle dynamics. We find that non-Gaussian displacement distributions, including Cauchy-type and exponential shapes, emerge in these models in the long time limit. The resulting shapes of the displacement distributions with distributed diffusivities for the active models are in striking contrast to passive diffusion models. Additionally, we demonstrate that the case with active-noise agrees well with measured data for the displacement distribution of social amoeba.
NEW JOURNAL OF PHYSICS
(2023)
Article
Chemistry, Physical
Shane Scott, Matthias Weiss, Christine Selhuber-Unkel, Younes F. F. Barooji, Adal Sabri, Janine T. T. Erler, Ralf Metzler, Lene B. B. Oddershede
Summary: The emergence of new tools for tracking single particles and molecules has greatly increased experimental data, providing novel insights into the physical properties of living matter. This Perspective presents tools for investigating the dynamics and mechanics of living systems at the molecular and cellular scale using single-particle techniques. It focuses on methods for measuring and interpreting complex data sets associated with forces, materials properties, transport, and organization within biological and soft-matter systems. The article outlines current approaches, challenges, and existing solutions in order to support researchers in the interface of physics and the life sciences.
PHYSICAL CHEMISTRY CHEMICAL PHYSICS
(2023)
Article
Physics, Multidisciplinary
Kiril Zelenkovski, Trifce Sandev, Ralf Metzler, Ljupco Kocarev, Lasko Basnarkov
Summary: We present a refined approach to explore complex networks with stochastic resetting based on node centrality measures. This approach allows a random walker to jump not only to a deliberately chosen resetting node, but also to a node that can reach all other nodes faster. By considering the resetting site as the geometric center, we calculate the Global Mean First Passage Time (GMFPT) using Markov chain theory to determine the search performance of the random walk with resetting. We compare different nodes as resetting sites by comparing their GMFPT values.
Article
Physics, Multidisciplinary
Timo J. Doerries, Ralf Metzler, Aleksei Chechkin
Summary: This article examines the transport of diffusive particles switching between mobile and immobile states with finite rates. The study focuses on the impact of advection on density functions and mean squared displacements (MSDs). Significant anomalous diffusion with cubic scaling in time of the MSD is found at intermediate time scales for high Peclet numbers. This cubic scaling is present for both short and long mean residence times in the immobile state. The study also reveals the newly observed phenomenon of advection-induced subdiffusion for immobilized tracers in the presence of high Peclet numbers. Additionally, the effective advection velocity is reduced in the long-time limit, while the MSD is enhanced by advection. The physical mechanisms behind the emergence of non-Gaussian density functions and the characteristics of the MSD are explored.
NEW JOURNAL OF PHYSICS
(2023)
Article
Physics, Multidisciplinary
Philipp G. Meyer, Ralf Metzler
Summary: In this study, we investigate the overdamped dynamics of various stochastic processes under confinement of an harmonic potential. We analyze the impact of both static and dynamic noise on the dynamics of pure processes and find that noise poses challenges for process inference. We observe that static noise leads to subdiffusive behavior, while dynamic noise results in superdiffusive behavior.
NEW JOURNAL OF PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Alexander Iomin, Ralf Metzler, Trifce Sandev
Summary: The article considers an example of non-Markovian quantum dynamics using a geometrical (topological) subordination approach. The model coincides exactly with the fractional diffusion equation, describing geometric Brownian motion on combs. Both classical diffusion and quantum dynamics are described using the dilatation operator x d/dx. Two examples of geometrical subordinators are considered: the Gaussian function and the Dirac delta function.
FRACTAL AND FRACTIONAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Koushik Goswami, Ralf Metzler
Summary: We propose an extension of the existing model for biomolecular reactions, considering the influence of active noise on the dynamics. Our theoretical study shows that active particles can cross energy barriers at shorter timescales by lowering the effective barrier height. We also find nonmonotonic behavior in the transition-path time under certain conditions.
JOURNAL OF PHYSICS-COMPLEXITY
(2023)
Article
Mathematics, Applied
Joanna Janczura, Marcin Magdziarz, Ralf Metzler
Summary: Modern experiments often generate extensive data on the diffusive dynamics of tracer particles, many of which deviate from the laws of Brownian motion. In this study, we focus on the anomalous dynamics of confined tracer particles and propose new estimators for the parameters. By calculating the empirical quadratic variation of a single trajectory, we are able to recover the subordination process governing the particle motion and use it for parameter estimation.
Article
Mathematics, Interdisciplinary Applications
Petar Jolakoski, Arnab Pal, Trifce Sandev, Ljupco Kocarev, Ralf Metzler, Viktor Stojkoski
Summary: Detailed knowledge of individual income dynamics is crucial for investigating the existence of the American dream and understanding the potential for improving income during one's working life. This study develops a framework that disaggregates the temporal properties of income at the individual level, overcoming the limitations of previous methods that rely on transition matrices. The framework, based on the concept of First Passage Time in a stochastic process, provides improved and more granular estimates of income dynamics. The results contribute to our understanding of income dynamics in real economies and offer tools for policy interventions.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Condensed Matter
Ekrem Aydiner, Andrey G. Cherstvy, Ralf Metzler, Igor M. Sokolov
Summary: In this study, we examine the behavior of a kinetic exchange-trading model under various initial distributions of money using Monte-Carlo simulations. Our findings indicate that the Pareto laws and their exponents show little sensitivity to the initial conditions, regardless of whether the system is closed or open.
EUROPEAN PHYSICAL JOURNAL B
(2023)
Article
Physics, Multidisciplinary
Jakub Slezak, Ralf Metzler
Summary: We introduce a stochastic process called incremental multifractional Brownian motion (IMFBM), which behaves locally like fractional Brownian motion with varying Hurst exponent and diffusivity. We derive formulas for the mean squared displacement and correlations of IMFBM, which are simple and elementary. We also provide simulation comparisons and estimation methods for IMFBM. This mathematically simple process is valuable in understanding anomalous diffusion dynamics in changing environments, such as viscoelastic systems or actively moving particles.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
(2023)
Article
Physics, Fluids & Plasmas
Qing Wei, Wei Wang, Hongwei Zhou, Ralf Metzler, Aleksei Chechkin
Summary: This paper investigates the tools of fractional diffusion and Fokker-Planck equations for describing anomalous diffusion in complex systems, and compares the dynamics of different integrodifferential operators in the Fokker-Planck and Langevin equations. The results demonstrate that the integrodifferential operators with exponential and Mittag-Leffler kernels are not suitable for the physically relevant diffusion scenarios discussed, while the conformable and Caputo operators are more appropriate.
Article
Multidisciplinary Sciences
Ken Sakamoto, Takuma Akimoto, Mayu Muramatsu, Mark S. P. Sansom, Ralf Metzler, Eiji Yamamoto
Summary: Cell membranes undergo phase separation into ordered Lo and disordered Ld domains, which regulate the localization of specific proteins related to cell signaling and trafficking. However, it is still unclear how the heterogeneity of the membranes affects the diffusion and localization of proteins in Lo and Ld domains.
Article
Chemistry, Physical
Koushik Goswami, Ralf Metzler
Summary: This study investigates the dynamics of a tracer that is elastically coupled to active particles and kept at different temperatures in a non-equilibrium bath. Analytical techniques are used to find the exact solution for the probability density function of the tracer's motion, and numerical simulations confirm the analytical results. By analyzing experimentally accessible quantities such as the response function and power spectrum, the non-equilibrium fluctuations are measured in terms of effective temperature. Additionally, the energy dissipation rate is computed to determine the precise effects of activity. This study is relevant for understanding athermal fluctuations in cytoskeletal networks or inside a chromosome.