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The Markov chain Monte Carlo (MCMC) method is widely used in various fields as a powerful numerical integration technique for systems with many degrees of freedom. In MCMC methods, probabilistic state transitions can be considered as a random walk in state space, and random walks allow for sampling from complex distributions. However, paradoxically, it is necessary to carefully suppress the randomness of the random walk to improve computational efficiency. By breaking detailed balance, we can create a probability flow in the state space and perform more efficient sampling along this flow. Motivated by this idea, practical and efficient nonreversible MCMC methods have been developed over the past ten years. In particular, the lifting technique, which introduces probability flows in an extended state space, has been applied to various systems and has proven more efficient than conventional reversible updates. We review and discuss several practical approaches to implementing nonreversible MCMC methods, including the shift method in the cumulative distribution and the directed-worm algorithm. [ABSTRACT FROM AUTHOR]

Motion in bounded domains is a fundamental concept in various fields, including billiard dynamics and random walks on finite lattices, and has important applications in physics, ecology, and biology. An important universal property related to the average return time to the boundary, the Mean Path Length Theorem (MPLT), has been proposed theoretically and experimentally confirmed in various contexts. We investigated a wide range of mechanisms that lead to deviations from this universal behavior, such as boundary effects, reorientation, and memory processes. This study investigates the dynamics of run-and-tumble particles within a confined two-dimensional circular domain. Through a combination of theoretical approaches and numerical simulations, we validate the MPLT under uniform and isotropic particle inflow conditions. This research demonstrates that although the MPLT is generally applicable for different step length distributions, deviations occur for non-uniform angular distributions, non-elastic boundary conditions, or memory processes. These results underline the crucial influence of boundary interactions and angular dynamics on the behavior of particles in confined spaces. Our results provide new insights into the geometry and dynamics of motion in confined spaces and contribute to a better understanding of a broad spectrum of phenomena ranging from the motion of bacteria to neutron transport. This type of analysis is crucial in situations where inhomogeneity occurs, such as multiple real-world scenarios within a limited domain. [ABSTRACT FROM AUTHOR]

Focused ultrasound has experimentally been found to enhance the diffusion of nanoparticles; our aim with this work is to study this effect closer using both experiments and non-equilibrium molecular dynamics. Measurements from single particle tracking of 40 nm polystyrene nanoparticles in an agarose hydrogel with and without focused ultrasound are presented and compared with a previous experimental study using 100 nm polystyrene nanoparticles. In both cases, we observed an increase in the mean square displacement during focused ultrasound treatment. We developed a coarse-grained non-equilibrium molecular dynamics model with an implicit solvent to investigate the increase in the mean square displacement and its frequency and amplitude dependencies. This model consists of polymer fibers and two sizes of nanoparticles, and the effect of the focused ultrasound was modeled as an external oscillating force field. A comparison between the simulation and experimental results shows similar mean square displacement trends, suggesting that the particle velocity is a significant contributor to the observed ultrasound-enhanced mean square displacement. The resulting diffusion coefficients from the model are compared to the diffusion equation for a two-time continuous time random walk. The model is found to have the same frequency dependency. At lower particle velocity amplitude values, the model has a quadratic relation with the particle velocity amplitude as described by the two-time continuous time random walk derived diffusion equation, but at higher amplitudes, the model deviates, and its diffusion coefficient reaches the non-hindered diffusion coefficient. This observation suggests that at higher ultrasound intensities in hydrogels, the non-hindered diffusion coefficient can be used. [ABSTRACT FROM AUTHOR]

Ion channels are proteins that play a significant role in physiological processes, including neuronal excitability and signal transduction. However, the precise mechanisms by which these proteins facilitate ion diffusion through cell membranes are not well understood. This is because experimental techniques to characterize ion channel activity operate on a time scale too large to understand the role of the various protein conformations on diffusion. Meanwhile, computational approaches operate on a time scale too short to rationalize the observed behavior at the microscopic scale. In this paper, we present a continuous-time random walk model that aims to bridge the scales between the atomistic models of ion channels and the experimental measurement of their conductance. We show how diffusion slows down in complex systems by using 3D lattices that map out the pore geometry of two channels: Nav1.7 and gramicidin. We also introduce spatial and dynamic site disorder to account for system heterogeneity beyond the mean field approximation. Computed diffusion coefficients show that an increase in spatial disorder slows down diffusion kinetics, while dynamic disorder has the opposite effect. Our results imply that microscopic or phenomenological models based on the potential of mean force data overlook the functional importance of protein dynamics on ion diffusion through channels. [ABSTRACT FROM AUTHOR]

Numerical methods for analyzing diffusion phenomena involving strong discontinuities and complicated interfaces are of great scientific and technical importance. In this paper, we extend the existing step-balanced random walk, which overcomes the problem of detailed balance of a random walker in three-dimensional (3D), diffusion-tensor discontinuous systems, to particle density (ρ) discontinuous systems, and introduce volumetric heat capacity C and temperature T by considering ρ as heat density, i.e., ρ = C T , to apply it to thermal problems. Two types of thermophysical simulations are demonstrated: one is steady-state heat flow due to a temperature difference at the end surfaces on a two-phase slab model unit cell with periodic boundary conditions; the other is the time variation of temperature distribution due to heat diffusion from a point heat source in a repeated two-phase slab model with no periodic boundary conditions. We see the correct behavior of heat and temperature expected in 3D discontinuous systems composed of two phases with anisotropic thermal conductivity. The applicability to problems other than pure diffusion and the limitations of the method are also discussed. [ABSTRACT FROM AUTHOR]

We report simulation studies of 33 single intrinsically disordered proteins (IDPs) using coarse-grained bead-spring models where interactions among different amino acids are introduced through a hydropathy matrix and additional screened Coulomb interaction for the charged amino acid beads. Our simulation studies of two different hydropathy scales (HPS1, HPS2) [Dignon et al., PLoS Comput. Biol. 14, e1005941 (2018); Tesei et al. Proc. Natl. Acad. Sci. U. S. A. 118, e2111696118 (2021)] and the comparison with the existing experimental data indicate an optimal interaction parameter ϵ = 0.1 and 0.2 kcal/mol for the HPS1 and HPS2 hydropathy scales. We use these best-fit parameters to investigate both the universal aspects as well as the fine structures of the individual IDPs by introducing additional characteristics. (i) First, we investigate the polymer-specific scaling relations of the IDPs in comparison to the universal scaling relations [Bair et al., J. Chem. Phys. 158, 204902 (2023)] for the homopolymers. By studying the scaled end-to-end distances ⟨ R N 2 ⟩ / (2 L ℓ p ) and the scaled transverse fluctuations l ̃ ⊥ 2 = ⟨ l ⊥ 2 ⟩ / L , we demonstrate that IDPs are broadly characterized with a Flory exponent of ν ≃ 0.56 with the conclusion that conformations of the IDPs interpolate between Gaussian and self-avoiding random walk chains. Then, we introduce (ii) Wilson charge index (W) that captures the essential features of charge interactions and distribution in the sequence space and (iii) a skewness index (S) that captures the finer shape variation of the gyration radii distributions as a function of the net charge per residue and charge asymmetry parameter. Finally, our study of the (iv) variation of ⟨Rg⟩ as a function of salt concentration provides another important metric to bring out finer characteristics of the IDPs, which may carry relevant information for the origin of life. [ABSTRACT FROM AUTHOR]

Quantum walks are the quantum counterpart of classical random walks and have various applications in quantum information science. Polar molecules have rich internal energy structure and long coherence time and thus are considered as a promising candidate for quantum information processing. In this paper, we propose a theoretical scheme for implementing discrete-time quantum walks on a circle with dipole–dipole coupled SrO molecules. The states of the walker and the coin are encoded in the pendular states of polar molecules induced by an external electric field. We design the optimal microwave pulses for implementing quantum walks on a four-node circle and a three-node circle by multi-target optimal control theory. To reduce the accumulation of decoherence and improve the fidelity, we successfully realize a step of quantum walk with only one optimal pulse. Moreover, we also encode the walker into a three-level molecular qutrit and a four-level molecular ququart and design the corresponding optimal pulses for quantum walks, which can reduce the number of molecules used. It is found that all the quantum walks on a circle in our scheme can be achieved via optimal control fields with high fidelities. Our results could shed some light on the implementation of discrete-time quantum walks and high-dimensional quantum information processing with polar molecules. [ABSTRACT FROM AUTHOR]

Differential privacy is a mathematical concept that provides an information-theoretic security guarantee. While differential privacy has emerged as a de facto standard for guaranteeing privacy in data sharing, the known mechanisms to achieve it come with some serious limitations. Utility guarantees are usually provided only for a fixed, a priori specified set of queries. Moreover, there are no utility guarantees for more complex-but very common-machine learning tasks such as clustering or classification. In this paper we overcome some of these limitations. Working with metric privacy, a powerful generalization of differential privacy, we develop a polynomial-time algorithm that creates a private measure from a data set. This private measure allows us to efficiently construct private synthetic data that are accurate for a wide range of statistical analysis tools. Moreover, we prove an asymptotically sharp min-max result for private measures and synthetic data in general compact metric spaces, for any fixed privacy budget ε bounded away from zero. A key ingredient in our construction is a new superregular random walk, whose joint distribution of steps is as regular as that of independent random variables, yet which deviates from the origin logarithmically slowly.

In this study, we decompose daily stock return into day and night returns and examine whether stock prices follow random walk over day and night in the Chinese stock market. Both variance ratio test and economic test reject the random walk hypothesis. Specifically, we find a significant return reversal from night to day but a significant return momentum from day to night. We also show that the unique T + 1 trading rule in China attenuates the return reversal from night to day but strengthens the return momentum from day to night. [ABSTRACT FROM AUTHOR]

By measured graphs, we mean graphs endowed with a measure on the set of vertices. In this context, we explore the relations between the appropriate Cheeger constant and Poincaré inequalities. We prove that the so-called Cheeger inequality holds in two cases: when the measure comes from a random walk, or when the measure has a bounded measure ratio. Moreover, we also prove that our measured (asymptotic) expanders are generalised expanders introduced by Tessera. Finally, we present some examples to demonstrate relations and differences between classical expander graphs and the measured ones. This paper is motivated primarily by our previous work on the rigidity problem for Roe algebras. [ABSTRACT FROM AUTHOR]

Let G be a tree on n vertices and let L = D − A denote the Laplacian matrix on G. The second-smallest eigenvalue λ 2 (G) > 0 , also known as the algebraic connectivity, as well as the associated eigenvector have been of substantial interest. We investigate the question of when the maxima and minima of an associated eigenvector are assumed at the endpoints of the longest path in G. Our results also apply to more general graphs that 'behave globally' like a tree but can exhibit more complicated local structure. The crucial new ingredient is a reproducing formula for eigenvectors of graphs. [ABSTRACT FROM AUTHOR]

Let S 0 = 0 , S n = X 1 + ... + X n , n ≥ 1 , be a random walk whose increments belong without centering to the domain of attraction of a stable law with scaling constants an that provide convergence as n → ∞ of the distributions of the sequence {Sn/an, n = 1, 2, ...} to this stable law. Let Lr,n = minr≤m≤nSm be the minimum of the random walk on the interval [r, n]. It is shown that lim r , k , n → ∞ P L r , n ≤ y a k | S n ≤ t a k , L 0 , n ≥ 0 , t ∈ 0 , ∞ , can have five different expressions, the forms of which depend on the relationships between the parameters r, k and n. [ABSTRACT FROM AUTHOR]

Random search theories predict that animals employ movement patterns that optimize encounter rates with target resources. However, animals are not always able to achieve the best search strategy. Energy depletion, for example, limits searchers' movement activities, forcing them to adjust their behaviors before and after encounters. Here, we investigate the cost of mate search in a termite, Reticulitermes speratus , and reveal that the costs associated with mate finding reduce the selectivity of mating partners. After a dispersal flight, termites search for a mating partner with limited reserved energy. We found that their movement activity and diffusiveness progressively declined over extended mate search. Our data-based simulations qualitatively confirmed that the reduced movement diffusiveness decreased the searching efficiency. Also, prolonged search periods reduced survival rate and the number of offspring. Thus, mate search has two different negative effects on termites. Finally, we found that termites with an extended mate search reduced the selectivity of mating partners, where males immediately paired with any encountering females. Thus, termites dramatically changed their mate search behavior depending on their internal states. Our finding highlights that accounting for the searchers' internal states is essential to fill the gap between random search theories and empirical behavioral observations. [ABSTRACT FROM AUTHOR]

The goal of this study was to determine the effects of applying random vs. constant constraint force to the non-paretic leg during walking on enhanced use of the paretic leg in individuals post-stroke, and examine the underlying brain mechanisms. Twelve individuals with chronic stroke were tested under two conditions while walking on a treadmill: random vs. constant magnitude of constraint force applied to the non-paretic leg during swing phase of gait using a custom designed robotic system. Leg kinematics, muscle activity of the paretic leg, and electroencephalography (EEG) were recorded during treadmill walking. Paretic step length and muscle activity of the paretic ankle plantarflexors significantly increased after walking with random and constant constraint forces. Cortico-cortical connectivity between motor cortices and cortico-muscular connectivity from the lesioned motor cortex to the paretic ankle plantarflexors significantly increased for the random force condition but not for the constant force condition. In addition, individuals post-stroke with greater baseline gait variability showed greater improvements in the paretic step length after walking with random force condition but not with the constant force condition. In conclusion, application of random constraint force to the non-paretic leg may enhance the use of the paretic leg during walking by facilitating cortical drive from the lesioned motor cortex to the paretic ankle plantarflexors. Results from this study may be used for the development of constraint induced locomotor intervention approaches aimed at improving locomotor function in individuals after stroke. [ABSTRACT FROM AUTHOR]

In this manuscript, we study a benchmark tracking problem when prices evolve through a Binomial model with a random environment. The agent invests a given fund's capital into different assets in a predetermined market to replicate at each stage of time a financial index or benchmark. To measure the actual deviation between the agent's wealth and the current benchmark, we apply a deviation error expressed as a total sum of quadratic functions. We also assume the agent is obligated to change her/his investment between two markets when it is mandatory. This obligation happens when the fund's wealth falls down a predetermined bankruptcy barrier. The dynamic programming method is then used to get optimal investment strategies that minimize the deviation error as well as to characterize the minimum deviation. We also apply the so-called potential function to analyze the influence of the environment on the prices. Numerical simulations are provided to illustrate our results. [ABSTRACT FROM AUTHOR]

The classification of urban functional zones helps to understand the spatial structure of urban functions. However, achieving high classification accuracy is challenging, because of the complexity and randomness of urban components and their spatial distribution. An important idea in existing urban functional zone classification research is to extract the spatial context of points of interest (POIs) based on their spatial relationships, embed the POI representations, and then calculate the vector representation of the urban functional zones for classification. Important features that could be extracted from the spatial relationships between the POIs are the homogeneity and structural similarity between POIs. Although their important impact on urban functional zone classification has received attention, most studies construct urban functional zone classification methods that are based on the homogeneity of POIs. Limited studies combine them to construct urban functional zone classification methods. In this paper, a novel method for urban functional zone classification was proposed by integrating the homogeneity and structural similarity between POIs. First, the neighborhood structure of the POIs is defined based on the spatial relationships between POIs. Second, biased random walking strategies are designed to generate the spatial contexts of POIs. Third, the spatial contexts of the POIs are input into the Skip-Gram model to generate vectors for the POI types. Then, the vectors of urban functional zones are calculated. Finally, the support vector machine (SVM) is used for urban functional zone classification that is based on their vectors. The model was applied in Chaoyang District, Beijing. The feasibility, accuracy, and stability of the model were verified by comparing it with the Place2vec and the DeepWalk models. [ABSTRACT FROM AUTHOR]

Understanding mass transport in the alteration layers of glass surfaces is a crucial component of the safety assessment of nuclear waste glass. In this work, we model such an alteration layer as a silicate gel with water through a molecular dynamics (MD) simulation with a reactive force field. Gels with various water contents (WCs) ranging from 5.1 to 30.7wt%$30.7 \,{\rm wt}\%$ are produced via high‐temperature annealing with water and silica. It is found that an increase in the water content destroys the polymerized structure of the silicate network and promotes the formation of silanol groups. The pore size and water connectivity formed by the silicate networks are investigated for the modeled gels. Gel with a WC of 5.7wt%$5.7 \,{\rm wt}\%$ is composed of isolated water in the pores; in contrast, pores filled with interconnected water are formed in gel with a WC of 30.7wt%$30.7 \,{\rm wt}\%$. The water diffusivity in the modeled gel is calculated using the mean‐squared displacement at various temperatures. An attempt is made to formulate a linear relationship between the water diffusivity and porosity derived from the MD simulation. The porosity is calculated using a probe atom with a radius, which was optimized from a linear relationship between the water diffusivity and porosity. This approach successfully explains the water diffusivity in terms of the porosity. Random walk (RW) simulations for the structures derived from the MD simulations are performed to determine the geometrical effects of the pores. The diffusivity obtained from RW simulation is compared with the results of the MD simulations, which include chemical interactions such as the formation and breakage of hydrogen bonds. This comparison highlights how geometrical effects and chemical interactions contribute to water diffusivity depending on the WC. [ABSTRACT FROM AUTHOR]

Public transportation systems play a vital role in modern cities, enhancing the quality of life and fostering sustainable economic growth. Modeling and understanding the complexities of these transportation networks are crucial for effective urban planning and management. Traditional models often fall short in capturing the intricate interactions and interdependencies in multimodal public transportation systems. To address this challenge, recent research has embraced multilayer network models, offering a more sophisticated representation of these networks. However, there is a need to explore and develop robustness analysis techniques tailored to these general multilayer networks to fully assess their complexities in real-world scenarios. In this paper, we employ a general multilayer network model to comprehensively analyze a real-world multimodal transportation network in Seoul, South Korea. We leverage a large volume of traffic data to model, visualize, and evaluate the city's mobility patterns. Additionally, we introduce two novel methodologies for robustness analysis, one based on random walk coverage and the other on eigenvalue, specifically designed for general multilayer networks. Extensive experiments using the large volume of real-world data sets demonstrate the effectiveness of the proposed approaches. [ABSTRACT FROM AUTHOR]

Eaton (1992) considered a general parametric statistical model paired with an improper prior distribution for the parameter and proved that if a certain Markov chain, constructed using the model and the prior, is recurrent, then the improper prior is strongly admissible , which (roughly speaking) means that the generalized Bayes estimators derived from the corresponding posterior distribution are admissible. Hobert and Robert (1999) proved that Eaton's Markov chain is recurrent if and only if its so-called conjugate Markov chain is recurrent. The focus of this paper is a family of Markov chains that contains all of the conjugate chains that arise in the context of a Poisson model paired with an arbitrary improper prior for the mean parameter. Sufficient conditions for recurrence and transience are developed and these are used to establish new results concerning the strong admissibility of non-conjugate improper priors for the Poisson mean. [ABSTRACT FROM AUTHOR]

We study random walks on the giant component of Hyperbolic Random Graphs (HRGs), in the regime when the degree distribution obeys a power law with exponent in the range (2,3)$$ \left(2,3\right) $$. In particular, we first focus on the expected time for a random walk to hit a given vertex or visit, that is, cover, all vertices. We show that, a.a.s. (with respect to the HRG), and up to multiplicative constants: the cover time is n(logn)2$$ n{\left(\log n\right)}^2 $$, the maximum hitting time is nlogn$$ n\log n $$, and the average hitting time is n$$ n $$. We then determine the expected time to commute between two given vertices a.a.s., up to a small factor polylogarithmic in n$$ n $$, and under some mild hypothesis on the pair of vertices involved. Our results are proved by controlling effective resistances using the energy dissipated by carefully designed network flows associated to a tiling of the hyperbolic plane, on which we overlay a forest‐like structure. [ABSTRACT FROM AUTHOR]

We analyze the asynchronous version of the DeGroot dynamics: In a connected graph G$$ G $$ with n$$ n $$ nodes, each node has an initial opinions in [0,1]$$ \left[0,1\right] $$ and an independent Poisson clock. When a clock at a node v$$ v $$ rings, the opinion at v$$ v $$ is replaced by the average opinion of its neighbors. It is well known that the opinions converge to a consensus. We show that the expected time 피(τε) to reach ε$$ \varepsilon $$‐consensus is poly(n)$$ (n) $$ in undirected graphs and in Eulerian digraphs, but for some digraphs of bounded degree it is exponential. Our main result is that in undirected graphs and Eulerian digraphs, if the degrees are uniformly bounded and the initial opinions are i.i.d., then 피(τε)=polylog(n) for every fixed ε>0$$ \varepsilon >0 $$. We give sharp estimates for the variance of the limiting consensus opinion, which measures the ability to aggregate information ("wisdom of the crowd"). We also prove generalizations to non‐reversible Markov chains and infinite graphs. New results of independent interest on fragmentation processes and coupled random walks are crucial to our analysis. [ABSTRACT FROM AUTHOR]

In this paper, a new tallying method for a neutron flux distribution using the proper orthogonal decomposition is proposed for dimensionality reduction. The target spatial flux distribution is expanded by orthogonal basis vectors. Expansion coefficients are tallied during the random walk of the Monte Carlo calculation. The orthogonal basis vectors are extracted from the pre-calculated snapshots by the singular value decomposition. The proposed method is verified in the multi-group Monte Carlo calculation with the one-dimensional heterogeneous whole core geometry as a feasibility study. The flux distribution for each of the assemblies and energy groups is expanded by the basis vectors. The fewer basis vectors obtained from snapshots can reconstruct the target distribution well compared with the conventional Legendre polynomials used in the functional expansion tallies. The dimension of the solution in the proposed method is reduced by a factor of twenty compared with the conventional cell tally. In addition, the statistical error is reduced through dimensionality reduction thanks to the methodological feature of the proposed method. The results indicate that the proposed method has the capability of dimensionality reduction to tally the finely discretized flux distribution. [ABSTRACT FROM AUTHOR]

Random generation of fuzzy measures plays a pivotal role in large-scale decision-making and optimization. Random walks ensure uniform generation and adequate coverage. The Möbius representation of set functions is a valuable tool for establishing the sparse structure of fuzzy measures, with its non-negativity closely linked to monotonicity and convexity/supermodularity checking. We propose three efficient methods for monotonicity verification and convexity/supermodularity verification applicable to random walks in Möbius representations, specifically tailored for universal sets larger than ten inputs and k-order fuzzy measures. We first present the baseline methods by directly inspecting monotonicity and convexity constraints. Building on the observation that the majority of initially generated values exhibit non-negativity, we intentionally track negative Möbius values to enhance the computational performance of these baseline approaches. Further, we introduce the more agile methods that employ insertion and merge sorting techniques for both monotonicity and convexity checks in random walks that involve small perturbations of fuzzy measures. To address sparsity in large-scale scenarios, we focus on two major types of measures: k-additive and k-interactive measures, demonstrating their effectiveness through theoretical analysis and experimental results. [ABSTRACT FROM AUTHOR]

This paper introduces a novel method that leverages the capability of the Adam Optimization- Back Propagation model to adaptively select shape parameters in the Multiple-Quadratic Radial Basis Function (MQRBF). This approach has been effectively combined with the Finite Difference (FD) method to generate high-precision solutions for complex Partial Differential Equations (PDEs). The careful selection of shape parameters in MQRBF is crucial to ensure the accuracy of the MQRBF-FD in addressing complex PDE scenarios. We have improved the Random Walk Optimization algorithm and integrated it with Fourier theory and deep learning techniques, establishing a comprehensive framework for adaptive optimization of shape parameters. This significantly enhances the adaptability and accuracy of the MQRBF-FD. A wide range of numerical experiments, including analyses of heat conduction in non-uniform materials and dye transport in fluid channels, highlight the exceptional accuracy, computational efficiency, and versatility of our method. [ABSTRACT FROM AUTHOR]

Partial differential equations can model diverse physical phenomena including heat diffusion, incompressible flows, and electrostatic potentials. Given a description of an object's boundary and interior, traditional methods solve such PDEs by densely meshing the interior and then solving a large and sparse linear system derived from this mesh. Recent grid-free solvers take an alternative approach and avoid this complexity in exchange for randomness: they compute stochastic solution estimates and generally bear a striking resemblance to physically-based rendering algorithms. In this article, we develop algorithms targeting the inverse form of this problem: given an already existing solution of a PDE, we infer parameters characterizing the boundary and interior. In the grid-free setting, there are again significant connections to rendering, and we show how insights from both fields can be combined to compute unbiased derivative estimates that enable gradient-based optimization. In this process, we encounter new challenges that must be addressed to obtain practical solutions. We introduce acceleration and variance reduction strategies and show how to differentiate branching random walks in reverse mode. We finally demonstrate our approach on both simulated data and a real-world electrical impedance tomography experiment, where we reconstruct the position of a conducting object from voltage measurements taken in a saline-filled tank. [ABSTRACT FROM AUTHOR]

This paper extends the fixed-b Phillips–Perron unit root test, namely PP(fb), by using a sieve bootstrap method to deal with serial-correlated errors, especially negative moving average errors. We derive the asymptotic distribution of the proposed PP b (fb) test statistics. Our simulation results show that the PP b (fb) test substantially improves the size performance without losing power when the error innovations have negative autoregressive or moving average components. Applying the PP b (fb) test to both the inflation rates in the U.S. and the Chinese stock market index, we find that the inflation follows a random walk process, just as the Chinese stock market does. [ABSTRACT FROM AUTHOR]

Complex systems are prevalent in nature, and link prediction is crucial for analyzing these systems. This method has gained attention for its ability to uncover various irregular movements with underlying similarities. While individual particle behavior is unpredictable, the collective behavior of large groups can be forecasted more accurately. The variability at lower scales vs universal similarities at higher scales is often overlooked. To address this, we investigate the random walk process on directed networks at a global scale. We propose an improved link prediction method using biased random walks to enhance accuracy and applicability. We first define out-degree neighbors as valid transmission options to prevent conflicts with in-degree paths. We then analyze how out-degrees and in-degrees affect particle transition probabilities, guiding particles toward high out-degrees and low in-degrees for a sustainable process. Finally, we use particle stabilization probabilities at different nodes as a similarity measure for predicting potential connections. Our method improves prediction precision and practicality, as validated by experiments on nine real-world networks, showing significant gains in accuracy and AUC scores. [ABSTRACT FROM AUTHOR]

Temporal graphs are commonly used to represent time-resolved relations between entities in many natural and artificial systems. Many techniques were devised to investigate the evolution of temporal graphs by comparing their state at different time points. However, quantifying the similarity between temporal graphs as a whole is an open problem. Here, we use embeddings based on time-respecting random walks to introduce a new notion of distance between temporal graphs. This distance is well-defined for pairs of temporal graphs with different numbers of nodes and different time spans. We study the case of a matched pair of graphs, when a known relation exists between their nodes, and the case of unmatched graphs, when such a relation is unavailable and the graphs may be of different sizes. We use empirical and synthetic temporal network data to show that the distance we introduce discriminates graphs with different topological and temporal properties. We provide an efficient implementation of the distance computation suitable for large-scale temporal graphs. Temporal graphs can be applied to represent time-evolving complex natural systems, describing the evolution of the interactions between system elements, however quantifying the similarity between temporal graphs remains an open problem. The authors introduce a notion of distance to compare time-resolved interaction patterns, based on their representations as temporal graphs. [ABSTRACT FROM AUTHOR]

Postmenopausal osteoporosis is a major global health concern, particularly affecting aging women, and necessitates innovative treatment options. Herbal medicine, with its multi-compound, multi-target characteristics, offers a promising approach for complex diseases. In this study, we applied multiscale network and random walk-based analyses to identify candidate herbs and their active ingredients for postmenopausal osteoporosis, focusing on their underlying mechanisms. A dataset of medicinal herbs, their active ingredients, and protein targets was compiled, and diffusion profiles were calculated to assess the propagation effects. Through correlation analysis, we prioritized herbs based on their relevance to osteoporosis, identifying the top candidates like Benincasae Semen, Glehniae Radix, Corydalis Tuber, and Houttuyniae Herba. Gene Set Enrichment Analysis (GSEA) revealed that the 49 core protein targets of these herbs were significantly associated with pathways related to inflammation, osteoclast differentiation, and estrogen metabolism. Notably, compounds such as falcarindiol from Glehniae Radix and tetrahydrocoptisine from Corydalis Tuber—previously unstudied for osteoporosis—were predicted to interact with inflammation-related proteins, including IL6, IL1B, and TNF, affecting key biological processes like apoptosis and cell proliferation. This study advances the understanding of herbal therapies for osteoporosis and offers a framework for discovering novel therapeutic agents. [ABSTRACT FROM AUTHOR]

Maintaining consistent model parameters in long-run experiments is challenging. We study the multiple change-points detection problem from this viewpoint for an autocorrelated sample path of a binary response variable. The probabilities of success and correlation structure are linked to explanatory or control variables using a generalized linear model. A Bayesian paradigm is introduced here to estimate the unknown number and locations of change-points and an adaptive RJMCMC algorithm is presented to generate pseudo-random samples from the posterior distributions. This approach allows researchers to incorporate the experts' ideas into the analysis of such data. The features of the proposed method are examined via some simulation studies. We also apply the presented method to COVID-19 data from four countries to detect the change-points in the infection procedures in the presence of some explanatory variables. [ABSTRACT FROM AUTHOR]

Approaching the application of redox‐based resistive switching random access memory (ReRAM), the research focus shifts more and more toward different aspects of reliability. Herein, it is vital to account for the statistics in large memory blocks, as certain failure mechanisms are observed to only affect a few bits per million. In a cooperation between RWTH Aachen and Infineon Technologies, the variability, retention, and endurance of filamentary valence change memory, integrated into 28 nm CMOS on Mbit scale are comprehensively studied. This article reviews the main findings of this project. It is found that the programmed states follow characteristic normal or log‐normal statistics based on dynamic equilibrium in the random walk of oxygen vacancies in the switching layer, experimentally observed as read noise. On long timescales, these statistics are remarkably stable, providing high data retention. However, the existing long‐term degradation can be characterized by shifting and broadening of the programmed high resistive state distributions. A high endurance of more than 500 k cycles is demonstrated on the Mbit scale. Only a tail of a few devices appears to fail to reset. Via kinetic Monte Carlo modeling, the voltage divider of ReRAM cell and periphery has been identified as the origin of this failure. [ABSTRACT FROM AUTHOR]

Numerous Deep Learning (DL) scenarios have been developed for evolving new healthcare systems that leverage large datasets, distributed computing, and the Internet of Things (IoT). However, the data used in these scenarios tend to be noisy, necessitating the incorporation of robust pre-processing techniques, including data cleaning, preparation, normalization, and addressing imbalances. These steps are crucial for generating a robust dataset for training. Designing frameworks capable of handling such data without compromising efficiency is essential to ensuring robustness. This research aims to propose a novel healthcare framework that selects the best features and enhances performance. This robust deep learning framework, called (R-DLH2O), is designed for forecasting cardiovascular crises. Unlike existing methods, R-DLH2O integrates five distinct phases: robust pre-processing, feature selection, feed-forward neural network, prediction, and performance evaluation. This multi-phase approach ensures superior accuracy and efficiency in crisis prediction, offering a significant advancement in healthcare analytics. H2O is utilized in the R-DLH2O framework for processing big data. The main improvement of this paper lies in the unique form of the Whale Optimization Algorithm (WOA), specifically the Modified WOA (MWOA). The Gaussian distribution approach for random walks was employed with the diffusion strategy to choose the optimal MWOA solution during the growth phase. To validate the R-DLH2O framework, six performance tests were conducted. Surprisingly, the MWOA-2 outperformed other heuristic algorithms in speed, despite exhibiting lower accuracy and scalability. The suggested MWOA was further analyzed using benchmark functions from CEC2005, demonstrating its advantages in accuracy and robustness over WOA. These findings highlight that the framework's processing time is 436 s, mean per-class error is 0.150125, accuracy 95.93%, precision 92.57%, and recall 93.6% across all datasets. These findings highlight the framework's potential to produce significant and robust results, outperforming previous frameworks concerning time and accuracy. [ABSTRACT FROM AUTHOR]

This paper introduces the mixed-strategy Harris hawk optimization (MSHHO) algorithm as an enhancement to address the limitations of the conventional Harris hawk optimization (HHO) algorithm in solving complex optimization problems. HHO often faces challenges such as susceptibility to local optima, slow convergence, and inadequate precision in global solution-seeking. MSHHO integrates four innovative strategies to bolster HHO's effectiveness in both local exploitation and global exploration. These include a positive charge repulsion strategy for diverse population initialization, a nonlinear decreasing parameter to heighten competitiveness, the introduction of Gaussian random walk, and mutual benefit-based position updates to enhance mobility and escape local optima. Empirical validation on 12 benchmark functions from CEC2005 and comparison with 10 established algorithms affirm MSHHO's superior performance. Applications to three real-world engineering problems and UAV flight trajectory optimization further demonstrate MSHHO's efficacy in overcoming complex optimization challenges. This study underscores MSHHO as a robust framework with enhanced global exploration capabilities, significantly improving convergence accuracy and speed in engineering applications. [ABSTRACT FROM AUTHOR]

Today, developing economies are of major importance for global macroeconomic development. However, the empirical analysis and especially the forecasting of macroeconomic time series remain difficult due to a lack of sufficient data, data frequency, high volatility, and non-linear developments. These difficulties require more sophisticated approaches to obtain reliable forecasts. Therefore, we propose an improved forecasting method especially for growth data based on a data-driven local linear trend estimation with an extended iterative plug-in algorithm for determining the bandwidth endogenously. This approach allows a smooth trend estimation that takes care of temporary changes in trend processes. Further, the naïve random walk model is extended for forecasting by including a local linear, time-varying drift. We apply this method to GDP development for six developing and two advanced economies and compare different forecast combinations. The combinations that include the local linear approach and the random walk with a local linear trend improve forecasting accuracy and reduce variance. [ABSTRACT FROM AUTHOR]

Random walks find extensive applications across various complex network domains, including embedding generation and link prediction. Despite the widespread utilization of random walks, the precise impact of distinct biases on embedding generation from sequence data and their subsequent effects on link prediction remain elusive. We conduct a comparative analysis of several random walk strategies, including the true self-avoiding random walk and the traditional random walk. We also analyze walks biased towards node degree and those with inverse node degree bias. Diverse adaptations of the node2vec algorithm to induce distinct exploratory behaviors were also investigated. Our empirical findings demonstrate that despite the varied behaviors inherent in these embeddings, only slight performance differences manifest in the context of link prediction. This implies the resilient recovery of network structure, regardless of the specific walk heuristic employed to traverse the network. Consequently, the results suggest that data generated from sequences governed by unknown mechanisms can be successfully reconstructed. [ABSTRACT FROM AUTHOR]

This study examines the nexus between external shocks and micro-transmission aspects of volatility persistence and market efficiency for the Malawian Foreign exchange market. Garch-type models are employed on monthly data stretching back to June 2011 through to October 2021. Results of the study show the presence of two structural breaks for the volatility series and one structural break for the return series that fall within the rolling window for external shock associated with the Russia-Ukrainian war. The negative nature of the shock leads to a significant additive impact on volatility persistence, asymmetry, and threshold at different levels of significance in the three models of Garch, E-Garch and T-Garch respectively. Relaxing the models confirms the presence of domestic influence. However, the external influence remains significant especially for the negative shock. As such, the leverage and volatility feedback effects of external shocks are corroborated. Augmenting the approach with a FRUH analysis reveals that the foreign exchange market does not follow a random walk as it departs from the 1:1 relationship between the spot and forward rate thus being weak-form inefficient. [ABSTRACT FROM AUTHOR]

In structured populations, the ecology of games may vary over neighborhoods. The effect of the ecological variations on population dynamics remains largely unknown. We here incorporate the ecological variations into the set-structured populations to explore the coevolutionary dynamics of the ecology and cooperation. Individuals of a population are distributed over sets. Interactions occur in the form of evolutionary games. When two individuals share more common sets, they play the weak prisoner's dilemma. Otherwise, they play the strong prisoner's dilemma. Both the set memberships and the strategy update in the evolutionary process. Changes in set memberships hold sway over the games to be played, which, in turn, influences the performance of strategies. Combining evolutionary set theory and random walks on graphs, we derived the conditions for cooperation to be selected under the weak selection limit. We find that a denser set-structured population increases the probability of individuals participating in a weak prisoner's dilemma, and thereby promoting the spread of cooperation. Properly modulating the population structure and the payoff feedback can further lower the critical benefit–cost ratio required for cooperation to be selected. Our results may help better understand the effects of ecological variations in enhancing cooperative behavior in set-structured populations. [ABSTRACT FROM AUTHOR]

The Brazilian Amazon region is a highly endemic area for hepatitis Delta and has areas that are difficult to access. Understanding the dynamics of HDV transmission in these remote locations is important for elucidating the routes of infection. To investigate this, a molecular analysis of HDV was conducted to assess the spatio-temporal dynamics of HDV cases. Between 2010 and 2023, 35 patients were recruited from the Viral Hepatitis Outpatient Clinic in Rondônia, Brazil. Conventional PCR was used to amplify the complete HDV genome followed by nucleotide sequencing via the Sanger method. The HDV genotype was determined using maximum likelihood phylogenetic reconstruction. A Skygrid coalescent approach with a Relaxed Random Walk phylogeographic model was used for the spatio-temporal analysis. Most individuals were males (21/35), with a median age of 39 years. HDV-3 was identified in all samples (35/35; 100%). The tMRCA was estimated to be 1824, with a substitution rate of 8.2 × 10−4 substitutions/site/year. The results suggest that HDV likely entered Brazil around 1820, in the state of Amazonas, subsequently spreading to Acre and Rondônia. Notable migration events were observed starting from 2010. This study suggests that HDV-3 has a complex evolutionary history spanning over two centuries, with intricate transmission routes in different locations in Brazil. [ABSTRACT FROM AUTHOR]

Fractal scale-free structures are widely observed across a range of natural and synthetic systems, such as biological networks, internet architectures, and social networks, providing broad applications in the management of complex systems and the facilitation of dynamic processes. The global mean first-passage time (GMFPT) for random walks on the underlying networks has attracted significant attention as it serves as an important quantitative indicator that can be used in many different fields, such as reaction kinetics, network transport, random search, pathway elaboration, etc. In this study, we first introduce two degree-dependent random walk strategies where the transition probability is depended on the degree of neighbors. Then, we evaluate analytically the GMFPT of two degree-dependent random walk strategies on fractal scale-free tree structures by exploring the connection between first-passage times in degree-dependent random walk strategies and biased random walks on the weighted network. The exact results of the GMFPT for the two degree-dependent random walk strategies are presented and are compared with the GMFPT of the classical unbiased random walk strategy. Our work not only presents a way to evaluate the GMFPT for degree-dependent biased random walk strategies on general networks but also offers valuable insights to enrich the controlling of chemical reactions, network transport, random search, and pathway elaboration. [ABSTRACT FROM AUTHOR]

Random walks and Lorentz processes serve as fundamental models for Brownian motion. The study of random walks is a favorite object of probability theory, whereas that of Lorentz processes belongs to the theory of hyperbolic dynamical systems. Here we first present an example where the method based on the probabilistic approach led to new results for the Lorentz process: concretely, the recurrence of the planar periodic Lorentz process with a finite horizon. Afterwards, an unsolved problem—related to a 1981 question of Sinai on locally perturbed periodic Lorentz processes—is formulated as an analogous problem in the language of random walks. [ABSTRACT FROM AUTHOR]

Human pluripotent stem cells (hPSCs) are an important tool in the field of regenerative medicine due to their ability to differentiate towards all tissues of the adult organism. An important task in the study of hPSCs is to understand the factors that influence the maintenance of pluripotent and clonal characteristics of colonies represented by their morphological phenotype. Such factors include the ability of colonies to migrate during growth. In this work, we measured and analyzed the migration trajectories of hPSC colonies obtained from bright-field images of three cell lines, including induced hPSC lines AD3 and HPCASRi002-A (CaSR) and human embryonic stem cell line H9. To represent the pluripotent status, the colonies were visually phenotyped into two classes having a "good" or "bad" morphological phenotype. As for the migration characteristics, we calculated the colony speed and distance traveled (mobility measures), meandering index (motion persistence measures), outreach ratio (trajectory tortuosity characteristic), as well as the velocity autocorrelation function. The analysis revealed that the discrimination of phenotypes by the migration characteristics depended on both the cell line and growth environment. In particular, when the mTESR1/Matrigel culture environment was used, "good" AD3 colonies demonstrated a higher average migration speed than the "bad" ones. The reverse relationship between average speeds of "good" and "bad" colonies was found for the H9 line. The CaSR cell line did not show significant differences in the migration speed between the "good" and "bad" phenotypes. We investigated the type of motion exhibited by the colonies by applying two diffusion models to the mean squared displacement dynamics, one model corresponding to normal and the other to anomalous diffusion. The type of diffusion and diffusion parameter values resulting from the model fitting to data demonstrated a similar cell line, environment, and phenotype dependency. Colonies mainly showed a superdiffusive behavior for the mTESR1/Matrigel culture conditions, characterized by longer migration steps compared to the normal random walk. The specific properties of migration features and the patterns of their variation demonstrated in our work can be useful for the development and/or improvement of automated solutions for quality control of hPSCs. [ABSTRACT FROM AUTHOR]

The classical measures of voting power are based on players' decisiveness or full causal efficacy in vote configurations or divisions. We design an alternative, recursive measure departing from this classical approach. We motivate the measure via an axiomatic characterisation based on reasonable axioms and by offering two complementary interpretations of its meaning: first, we interpret the measure to represent, not the player's probability of being decisive in a voting structure, but its expected probability of being decisive in a uniform random walk from a vote configuration in the subset lattice (through which we represent the voting structure); and, second, we interpret it as representing a player's expected efficacy, thereby incorporating the notion of partial and not just full causal efficacy. We shore up our measure by demonstrating that it satisfies a set of postulates any reasonable voting measure should satisfy, namely, the iso-invariance, dummy, dominance, donation, minimum-power bloc, and quarrel postulates. [ABSTRACT FROM AUTHOR]

In recent years, there has been significant advancement in the field of single-cell data analysis, particularly in the development of clustering methods. Despite these advancements, most algorithms continue to focus primarily on analyzing the provided single-cell matrix data. However, within medical contexts, single-cell data often encompasses a wealth of exogenous information, such as gene networks. Overlooking this aspect could result in information loss and produce clustering outcomes lacking significant clinical relevance. To address this limitation, we introduce an innovative deep clustering method for single-cell data that leverages exogenous gene information to generate discriminative cell representations. Specifically, an attention-enhanced graph autoencoder has been developed to efficiently capture topological signal patterns among cells. Concurrently, a random walk on an exogenous protein–protein interaction network enabled the acquisition of the gene's embeddings. Ultimately, the clustering process entailed integrating and reconstructing gene-cell cooperative embeddings, which yielded a discriminative representation. Extensive experiments have demonstrated the effectiveness of the proposed method. This research provides enhanced insights into the characteristics of cells, thus laying the foundation for the early diagnosis and treatment of diseases. The datasets and code can be publicly accessed in the repository at https://github.com/DayuHuu/scEGG. [ABSTRACT FROM AUTHOR]

The human body is a complex network of systems that is harmonized with multiple biological components. To understand these interactions is very challenging. With rapid development of advanced sequencing technologies, massive amounts of data such as mRNA, miRNA are rapidly accumulated. The integrated analysis of mRNA–miRNA has brought an extensive understanding of complex biological systems and pathological mechanisms. MicroRNAs (miRNAs) are small non-coding RNAs that intricately regulate target gene products, resulting in the inhibition of gene expression. While these miRNAs play crucial roles in essential biological processes—ranging from immunity and metabolism to cell death—their specific impacts on diseases remain unknown. Recent studies have been focused on the integration of miRNA and mRNA expression to reveal the underlying biological pathways and mechanisms responsible for disease manifestation. We proposed a novel approach for integrative analysis of miRNA and mRNA expression data and developed MIMR (Integrative Analysis of miRNA and mRNA), a web-based application that leverages the Random Walk with Restart (RWR) algorithm. MIMR incorporates both direct and indirect interactions by utilizing protein–protein interaction (PPI) networks and experimentally validated mRNA–miRNA target interactions. MIMR provides comprehensive results, including novel pathological pathways associated with a specific disease and interactive network diagrams representing the mRNAs and miRNAs. We applied it to Alzheimer and breast cancer data and successfully identified the novel biological pathways related to these diseases. In summary, MIMR will offer a deeper insight into the hidden mechanisms of diseases and identify potential therapeutic strategies through integrated analysis of miRNAs and mRNAs. [ABSTRACT FROM AUTHOR]

Wireless sensor networks (WSNs) have advanced technologically, allowing for a wide range of Internet of Things (IoT) applications. The Internet of Things (IoT) provides a platform for connecting items to achieve a specific goal with minimal human intervention. Various practical sectors, such as environmental monitoring and defense, demand IoT support with maximum object connectivity, and low human participation, yet face security concerns from strong unauthorized entities. As location privacy is one of these major vulnerabilities, continual monitoring of contextual information may lead the attacker to the asset's position. The location privacy of the source node that detects and reports the presence of an event is critical. In this study, we provide a source location privacy (SLP) preservation technique based on confounding domain angular routing (SLP-CDAR) that attempts to improve security while increasing network lifespan. To avoid traffic analysis attacks, packets first undergo a random walk, followed by a perplexing time domain routing that creates additional diversionary pathways. The packets are then routed via angle routing, followed by a random path, and finally delivered to the base station using the forward random walk technique. The experimental results prove that the proposed scheme enhances the location privacy strength while providing an improved network lifetime, and a swift increase in the entropy. [ABSTRACT FROM AUTHOR]

The formation of spatial patterns is an important issue in reaction–diffusion systems. Previous studies have mainly focused on the spatial patterns in reaction–diffusion models equipped with symmetric diffusion (such as normal or fractional Laplace diffusion), namely, assuming that spatial environments of the systems are homogeneous. However, the complexity and heterogeneity of spatial environments of biochemical reactions in vivo can lead to asymmetric diffusion of reactants. Naturally, there arises an open question of how the asymmetric diffusion affects dynamical behaviors of biochemical reaction systems. To answer this, we build a general asymmetric Lévy diffusion model based on the theory of a continuous time random walk. In addition, we investigate the two-species Brusselator model with asymmetric Lévy diffusion, and obtain a general condition for the formation of Turing and wave patterns. More interestingly, we find that even though the Brusselator model with symmetric diffusion cannot produce steady spatial patterns for some parameters, the asymmetry of Lévy diffusion for this model can produce wave patterns. This is different from the previous result that wave instability requires at least a three-species model. In addition, the asymmetry of Lévy diffusion can significantly affect the amplitude and frequency of the spatial patterns. Our results enrich our knowledge of the mechanisms of pattern formation. [ABSTRACT FROM AUTHOR]

K‐feldspar, which constitutes about 60%$\%$ of the Earth's crust, is crucial for understanding electrical conductivity in porous rocks. Its electrical properties are vital for applications in ceramics, electrical insulation and conductive polymers. In this work, we study the time evolution of electrical conductivity of K‐feldspar‐rich rocks with varying temperatures, at high and low pH, which has been studied through simulation using time domain random walk. Random walkers, mimicking ions in transport, move in accordance with appropriate hydrodynamic equations, dissolution and precipitation kinetics. Electrical conductivity has been calculated considering variations in the parameters of temperature, fluid pH and the abundance of K‐feldspar in rocks. Electrical conductivity is found to increase with temperature up to a critical value, after which it decreases. The sharpness of the rise and fall in electrical conductivity is quantified through a measure defined as the conductivity quality factor Qσ$Q_{\sigma }$. We find that Qσ$Q_{\sigma }$ increases with a decrease in the availability of K‐feldspar mineral. Our simulated results of electrical conductivity show a good match with the experimental trends reported. [ABSTRACT FROM AUTHOR]

Magnetic field lines in magnetohydrodynamic turbulence are stochastic curves and, therefore, understanding their structure is a difficult problem of theoretical physics. One way to study the properties of such field lines is to perform simulations in which field line equations are solved numerically. In most previous articles studies have been performed in the context of the two-component turbulence model where one assumes a superposition of slab and two-dimensional modes. In the current paper we perform simulations for so-called noisy slab turbulence which is an example for three-dimensional turbulence with small Kubo numbers. We discuss in detail the challenges of the numerical magnetic field creation for this type of turbulence, perform the simulations, and compare our findings with analytical theory. It is demonstrated that a large number of wave modes is needed in order to obtain accurate results. Furthermore, we also show that analytical theories are very accurate for this type of turbulence model. The obtained results will also be useful for the analytical description of energetic particle transport in the considered turbulence model. [ABSTRACT FROM AUTHOR]

Attributed networks containing entity-specific information in node attributes are ubiquitous in modeling social networks, e-commerce, bioinformatics, etc. Their inherent network topology ranges from simple graphs to hypergraphs with high-order interactions and multiplex graphs with separate layers. An important graph mining task is node clustering, aiming to partition the nodes of an attributed network into k disjoint clusters such that intra-cluster nodes are closely connected and share similar attributes, while inter-cluster nodes are far apart and dissimilar. It is highly challenging to capture multi-hop connections via nodes or attributes for effective clustering on multiple types of attributed networks. In this paper, we first present AHCKA as an efficient approach to attributed hypergraph clustering (AHC). AHCKA includes a carefully-crafted K-nearest neighbor augmentation strategy for the optimized exploitation of attribute information on hypergraphs, a joint hypergraph random walk model to devise an effective AHC objective, and an efficient solver with speedup techniques for the objective optimization. The proposed techniques are extensible to various types of attributed networks, and thus, we develop ANCKA as a versatile attributed network clustering framework, capable of attributed graph clustering, attributed multiplex graph clustering, and AHC. Moreover, we devise ANCKA-GPU with algorithmic designs tailored for GPU acceleration to boost efficiency. We have conducted extensive experiments to compare our methods with 19 competitors on 8 attributed hypergraphs, 16 competitors on 6 attributed graphs, and 16 competitors on 3 attributed multiplex graphs, all demonstrating the superb clustering quality and efficiency of our methods. [ABSTRACT FROM AUTHOR]