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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Unsupervised learning methods such as graph contrastive learning have been used for dynamic graph representation learning to eliminate the dependence of labels. However, existing studies neglect positional information when learning discrete snapshots, resulting in insufficient network topology learning. At the same time, due to the lack of appropriate data augmentation methods, it is difficult to capture the evolving patterns of the network effectively. To address the above problems, a position-aware and subgraph enhanced dynamic graph contrastive learning method is proposed for discrete-time dynamic graphs. Firstly, the global snapshot is built based on the historical snapshots to express the stable pattern of the dynamic graph, and the random walk is used to obtain the position representation by learning the positional information of the nodes. Secondly, a new data augmentation method is carried out from the perspectives of short-term changes and long-term stable structures of dynamic graphs. Specifically, subgraph sampling based on snapshots and global snapshots is used to obtain two structural augmentation views, and node structures and evolving patterns are learned by combining graph neural network, gated recurrent unit, and attention mechanism. Finally, the quality of node representation is improved by combining the contrastive learning between different structural augmentation views and between the two representations of structure and position. Experimental results on four real datasets show that the performance of the proposed method is better than the existing unsupervised methods, and it is more competitive than the supervised learning method under a semi-supervised setting. [ABSTRACT FROM AUTHOR]

Label propagation is frequently encountered in machine learning and data mining applications on graphs, either as a standalone problem or as part of node classification. Many label propagation algorithms utilize random walks (or network propagation), which provide limited ability to take into account negatively-labeled nodes (i.e., nodes that are known to be not associated with the label of interest). Specialized algorithms to incorporate negatively-labeled nodes generally focus on learning or readjusting the edge weights to drive walks away from negatively-labeled nodes and toward positively-labeled nodes. This approach has several disadvantages, as it increases the number of parameters to be learned, and does not necessarily drive the walk away from regions of the network that are rich in negatively-labeled nodes. We reformulate random walk with restarts and network propagation to enable "variable restarts", that is the increased likelihood of restarting at a positively-labeled node when a negatively-labeled node is encountered. Based on this reformulation, we develop CusTaRd, an algorithm that effectively combines variable restart probabilities and edge re-weighting to avoid negatively-labeled nodes. To assess the performance of CusTaRd, we perform comprehensive experiments on network datasets commonly used in benchmarking label propagation and node classification algorithms. Our results show that CusTaRd consistently outperforms competing algorithms that learn edge weights or restart profiles, and that negatives close to positive examples are generally more informative than more distant negatives. [ABSTRACT FROM AUTHOR]

The issue of opinion sharing and formation has received considerable attention in the academic literature, and a few models have been proposed to study this problem. However, existing models are limited to the interactions among nearest neighbors, with those second, third, and higher-order neighbors only considered indirectly, despite the fact that higher-order interactions occur frequently in real social networks. In this paper, we develop a new model for opinion dynamics by incorporating long-range interactions based on higher-order random walks that can explicitly tune the degree of influence of higher-order neighbor interactions. We prove that the model converges to a fixed opinion vector, which may differ greatly from those models without higher-order interactions. Since direct computation of the equilibrium opinion is computationally expensive, which involves the operations of huge-scale matrix multiplication and inversion, we design a theoretically convergence-guaranteed estimation algorithm that approximates the equilibrium opinion vector nearly linearly in both space and time with respect to the number of edges in the graph. We conduct extensive experiments on various social networks, demonstrating that the new algorithm is both highly efficient and effective. [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]

Occupancy models were originally developed to better understand species distribution while accounting for imperfect detection. Because species distribution is not only shaped by habitat quality but also by the ability of individuals to reach suitable habitats, spatial dynamic occupancy models have been proposed to extend the original framework by defining that site colonisation was a function of the Euclidean distance to occupied sites. However, not all sites in the landscape are equally accessible due to the presence of barriers, that of corridors, etc. To account for connectivity between sites, the Euclidean distance has recently been replaced by a least‐cost path distance, which explicitly accounts for landscape resistance, but assumes that individuals will follow the optimal route.To relax this assumption, we first developed a new spatial occupancy model that incorporates commute‐time distance derived from circuit theory to model accessibility across sites. This distance has the advantage of modelling movement as a random walk and accounting for the fact that colonisation could be achieved from multiple paths. Our approach allows for the explicit estimation of landscape connectivity from detection/non‐detection data and a direct measure of connectivity uncertainty.We implemented the model in the Bayesian framework using the nimble R package, which allows useful R connectivity functions to be called from within the model. Second, we carried out a simulation study to assess the performance of our model by considering four scenarios depicting an increasing level of landscape resistance. Third, to illustrate our new approach, we studied the recolonisation of two carnivores in France.We quantified the degree to which rivers facilitate Eurasian otter (Lutra lutra) colonisation and highways impede Eurasian lynx (Lynx lynx) colonisation. Overall, spatial occupancy models provide a flexible framework to accommodate any distance metric designed to align with species dispersal ecology. [ABSTRACT FROM AUTHOR]

We study random walks on the lampshuffler group FSym (H) ⋊ H , where H is a finitely generated group and FSym (H) is the group of finitary permutations of H. We show that for any step distribution μ with a finite first moment that induces a transient random walk on H, the permutation coordinate of the random walk almost surely stabilizes pointwise. Our main result states that for H = Z , the above convergence completely describes the Poisson boundary of the random walk (FSym (Z) ⋊ Z , μ) . [ABSTRACT FROM AUTHOR]

This paper proposes a novel piezo-MEMS pitch/roll gyroscope that co-integrates piezoelectric and electrostatic effects, for the first time achieves electrostatic mode-matching operation for piezoelectric gyroscopes. Movement of operated out-of-plane (OOP) mode (n = 3) and in-plane (IP) mode (n = 2) are orthogonal, ensuring that the OOP amplitude is not significantly limited by parallel plates set at nodes of IP mode. Therefore, a large OOP driving amplitude actuated by piezoelectric and frequency tuning in the IP sense mode trimmed by electrostatic can be achieved together with a low risk of pull-in, hence releases the trade-off between the tuning range and the linear actuation range. At a tuning voltage of 66 V, the frequency split decreased from 171 Hz to 0.1 Hz, resulting in a 167x times improvement in sensitivity. The mode-matched gyroscope exhibits an angle random walk (ARW) of 0.41°/√h and a bias instability (BI) of 8.85°/h on a test board within a customized vacuum chamber, marking enhancements of 68x and 301x, respectively, compared to its performance under mode-mismatch conditions. The BI performance of the presented pitch/roll gyroscope is comparable to that of the highest-performing mechanically trimmed piezo-MEMS yaw gyroscopes known to date, while offering the unique advantage of lower cost, better mode-matching resolution, and the flexibility of real-time frequency control. [ABSTRACT FROM AUTHOR]

Migration is a high‐risk behavior. For the Atlantic salmon, Salmo salar, migrating from its river nursery area to marine feeding grounds, the magnitude of risk varies with habitat type. Passage through lakes, in particular, is associated with low rates of migration success. Downstream migrating salmon smolts are rheotactic when migrating in rivers, but lakes typically provide poorer directional currents for migrating salmon. In this study we tested if, in the absence of clear navigational cues in lakes, Atlantic salmon smolts switch to a random search strategy to find the outflowing river. We constructed random search simulations to test if lake basin shape has an effect on migration success. We also compared simulated migration characteristics with migrations of salmon smolts through five real lakes for which there are telemetry data for migrating salmon. Correlated random walk simulations showed that a random search strategy could be successful for all lake shapes tested but was more successful in curved (round and elliptical) than rectangular basin shapes. Rectangular basins with the migration start and stop points at the ends of the lake had a higher success than those where these points were perpendicular to the axis of the lake. In general, a random walk model predicted the migration success rate of fish tracked through real lakes. However, for two lakes the simulated migration success exceeded that of actual success, suggesting that fish passing through these lakes were not adopting a random search strategy. We speculate that this is the result of either conflicting navigational cues which inhibit smolts from finding the lake outlet or that they temporarily suspend migration (e.g., to feed). Modelling predicted that for small lakes, directional swimming in short steps (ca. 100 m) followed by turns with very low variation from the direction of travel resulted in the highest migration success. For larger lakes, longer step lengths but also with low turn variation (simulated turning angle drawn from distributions of standard deviation 2° and 5° around a mean of 0°) resulted in the highest migration success. We conclude that navigation in downstream migrating salmon smolts switches from rheotaxis in rivers to a random search tactic in lakes except where residual flow cues in some lakes prevent this, at times resulting in suboptimal navigation outcomes. [ABSTRACT FROM AUTHOR]

The scalar product of the state-vectors of the exactly solvable five-vertex model with the fixed boundary conditions is considered. Various relations including those in terms of complete symmetric polynomials are derived. The limiting forms of the obtained answers may be interpreted in terms of random walks on a square grid. [ABSTRACT FROM AUTHOR]

We examine the diffusive dynamics of a lattice random walk subject to resetting in a one-dimensional spatially heterogeneous environment composed of two media separated by an interface. At random times the walker may reset its position to the interface, but only when in the left medium. In addition the spatial heterogeneity results from having unequal diffusivities and biases in the two media. We construct the Master equation for the dynamics of the walker occupation probability in unbounded space, solve it exactly in terms of generating functions, and analyse the dynamics of the first and second moment. Making use of the closed form solution in the unbounded case, we build the analytic solution of the Master equation in finite and semi-infinite domains. By bounding the space on the right with a reflecting boundary we study the first-passage dynamics to a single fully absorbing target placed in the left medium away from the interface. As reset strongly increases the time to reach the target, we find that the first-passage dynamics enter the motion-limited regime even for relative small resetting probability. We also identify a surprising non-monotonic dependence of the first-passage probability mode as a function of the bias. By deriving an analytic expression for the mean first-passage time, we show when its value is independent of the diffusivity and bias in the left medium, uncovering another example of the so-called mean disorder indifference phenomenon. [ABSTRACT FROM AUTHOR]

The global steady state of a system in thermal equilibrium exponentially favors configurations with lesser energy. This principle is a powerful explanation of selforganization because energy is a local property of configurations. For nonequilibrium systems, there is no such property for which an analogous principle holds, hence no common explanation of the diverse forms of self-organization they exhibit. However, a flurry of recent empirical results has shown that a local property of configurations called "rattling" predicts the steady states of some nonequilibrium systems, leading to claims of a far-reaching principle of nonequilibrium self-organization. But for which nonequilibrium systems is rattling accurate, and why? Wedevelop a theory of rattling in terms of Markov processes that gives simple and precise answers to these key questions. Our results show that rattling predicts a broader class of nonequilibrium steady states than has been claimed and for different reasons than have been suggested. Its predictions hold to an extent determined by the relative variance of, and correlation between, the local and global "parts" of a steady state. We show how these quantities characterize the local-global relationships of various random walks on random graphs, spin-glass dynamics, and models of animal collective behavior. Surprisingly, we find that the core idea of rattling is so general as to apply to equilibrium and nonequilibrium systems alike. [ABSTRACT FROM AUTHOR]

In this paper we look at the families of random walks arising from FI-graphs. One may think of these objects as families of nested graphs, each equipped with a natural action by a symmetric group S n , such that these actions are compatible and transitive. Families of graphs of this form were introduced by the authors in [9] , while a systematic study of random walks on these families were considered in [10]. In the present work, we illustrate that these random walks never exhibit the so-called product condition, and therefore also never display total variation cutoff as defined by Aldous and Diaconis [1]. In particular, we provide a large family of algebro-combinatorially motivated examples of collections of Markov chains which satisfy some well-known algebraic heuristics for cutoff, while not actually having the property. [ABSTRACT FROM AUTHOR]

It is a well-established finding that more informative optic flow (e.g., faster, denser, or presented over a larger portion of the visual field) yields decreased variability in heading judgements. Current models of heading perception further predict faster processing under such circumstances, which has, however, not been supported empirically so far. In this study, we validate a novel continuous psychophysics paradigm by replicating the effect of the speed and density of optic flow on variability in performance, and we investigate how these manipulations affect the temporal dynamics. To this end, we tested 30 participants in a continuous psychophysics paradigm administered in Virtual Reality. We immersed them in a simple virtual environment where they experienced four 90-second blocks of optic flow where their linear heading direction (no simulated rotation) at any given moment was determined by a random walk. We asked them to continuously indicate with a joystick the direction in which they perceived themselves to be moving. In each of the four blocks they experienced a different combination of simulated self-motion speeds (SLOW and FAST) and density of optic flow (SPARSE and DENSE). Using a Cross-Correlogram Analysis, we determined that participants reacted faster and displayed lower variability in their performance in the FAST and DENSE conditions than in the SLOW and SPARSE conditions, respectively. Using a Kalman Filter-based analysis approach, we found a similar pattern, where the fitted perceptual noise parameters were higher for SLOW and SPARSE. While replicating previous results on variability, we show that more informative optic flow can speed up heading judgements, while at the same time validating a continuous psychophysics as an efficient method for studying heading perception. [ABSTRACT FROM AUTHOR]

Safeguarding important links is a useful way to promote network vulnerability, especially in sparse networks where random link failures can disconnect the network. Sustaining network connectivity is the main goal of safeguarding and can be handled by selectively safeguarding links belonging to certain cuts of a network. However, due to the inherent high complexity of cut enumeration, existing algorithms can only handle small‐scale networks with limited nodes. It is important to find practical algorithms that are feasible for large‐scale graphs, as a significant portion of real‐world graphs under investigation are not as small as dozens of nodes. To address the problem, we propose to use a high‐precision approximate approach to accelerate the first step of the two‐step safeguard process and thus accelerate the whole process. A Monte Carlo algorithm is proposed to exploit efficient random paths for small cuts enumeration, which can help locate important edges with high probability in large‐scale sparse networks. These edges will then be utilized to find the approximated minimum cost edge set whose safeguarding can sustain the expected network connectivity. The algorithm is validated using various sizes of graphs of random/Barbasi–Albert scale‐free/Clustered scale‐free/unit disk/Watts–Strogatz small‐world and real‐world graphs. The experimental results show that the algorithm can perfectly sustain the network connectivity, and the acceleration ratio of more than 105 can be achieved with a little additional overhead. Specifically, in large graphs of one million nodes, approximated safeguard solutions survive at least 99.9% random link failures, and the solution time can be further reduced to dozens of seconds when the algorithm steps are easily implemented in full parallel. [ABSTRACT FROM AUTHOR]

Zoosporic fungi, also called chytrids, produce single-celled motile spores with flagellar swimming tails (zoospores). 1,2 These fungi are key components of aquatic food webs, acting as pathogens, saprotrophs, and prey. 3,4,5,6,7,8 Little is known about the swimming behavior of fungal zoospores, a crucial factor governing dispersal, biogeographical range, ecological function, and infection dynamics. 6,9 Here, we track the swimming patterns of zoospores from 12 evolutionarily divergent species of zoosporic fungi from across seven orders of the Chytridiomycota and the Blastocladiomycota. We report two major swimming patterns that correlate with the cytoskeletal ultrastructure of these zoospores. Specifically, we show that species without major cytoplasmic tubulin components swim in a circular fashion, while species with prominent cytoplasmic tubulin structures swim in a pattern akin to a random walk (move-stop-redirect-move). We confirm cytoskeletal architecture by performing fluorescence confocal microscopy across all 12 species. We then treat representative species with variant swimming behaviors and cytoplasmic-cytoskeletal arrangements with tubulin-stabilizing (Taxol) and depolymerizing (nocodazole) pharmacological compounds. We observed that when treating the "random walk" species with nocodazole, their swimming behavior changed to a circular-swimming pattern. Confocal imaging of the nocodazole-treated zoospores demonstrates that these cells maintain flagellum tubulin structures but lack their characteristic cytoplasmic tubulin structures. Our data demonstrate that the capability of zoospores to perform "complex" random-walk movement is linked to the presence of prominent cytoplasmic tubulin structures and suggest a link between cytology, sensory systems, and swimming behavior in a diversity of zoosporic fungi. [Display omitted] • Fungal zoospores swim using either a random-walk or a circular pattern • The random walk is linked with the presence of major cytoplasmic tubulin structures • Nocodazole-treated random-walk zoospores transform into circular swimmers • In Blastocladiella, ultrastructure, movement, and light-sensing organelles are linked Galindo et al. find that fungal zoospores swim in either circular or random-walk patterns, the latter being linked with the presence of major cytoplasmic tubulin structures. Random-walk zoospores treated with a tubulin-depolymerizing drug turn into circular swimmers. They note a relationship between cytology, movement, and light-sensing organelles. [ABSTRACT FROM AUTHOR]