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We provide a comparison between marginal likelihood and data augmented Markov chain Monte Carlo (MCMC) algorithms for Bayesian estimation of hidden Markov models. In particular, we focus on a specification of these models based on a multivariate Gaussian distribution for the response variables. We evaluate the performance of both methods on the basis of simulated samples and an empirical application, where we compare these approaches in terms of standard measures of estimation and time efficiency. The results show that the augmented algorithm is preferable, obtaining optimal convergence properties and producing larger values of the effective sample size. Instead of using variable dimensional techniques for model selection, we suggest a method based on the so-called parallel sampling for this aim. [ABSTRACT FROM AUTHOR]

This paper focused on the point-of-interest (POI) recommendation task. Recently, graph representation learning-based POI recommendation models have gained significant attention due to the powerful modeling capacity of graph structural data. Despite their effectiveness, we have found that recent methods struggle to effectively utilize information from POIs that have not been checked in, which could limit their performance. Hence, in this paper, we proposed a new model, named the multi-contextual graph contrastive learning (MCGCL) model, which introduces the contrastive learning into graph representation learning-based methods. First, MCGCL extracts interactions between POIs under different contextual factors from user check-in records using predefined graph structure information. Next, it samples important POI sets from different contextual factors using a random walk-based method. Then, it introduces a new contrastive learning loss that incorporates contextual information into traditional contrastive learning to enhance its ability to capture contextual information. Finally, MCGCL employs a graph neural network (GNN) model to learn representations of users and POIs. Extensive experiments on real-world datasets have demonstrated the effectiveness of MCGCL on the POI recommendation task compared to representative POI recommendation approaches. [ABSTRACT FROM AUTHOR]

One direction to investigate the relation between quantum walks and their underlying graphs is to define geometric quantity concerning quantum walks. In order to contribute to this direction, we define a transport distance between Grover walks, which can be seen as a quantum analogue of symmetric random walks. We employ signed optimal transport theory to formulate this distance. Also, we define coarse Ricci curvature induced by Grover walks and investigate its property. It has been found that this coarse Ricci curvature has similar properties to those of coarse Ricci curvature induced by random walks. [ABSTRACT FROM AUTHOR]

We discuss the limit distribution of open quantum walks on the periodic graphs, particularly on the cycles. We show that under certain hypothesis, we can benefit from the theory of the classical Markov chains. Thereby we can show that under certain condition the stationary distribution is unique. For certain models, we show directly the stationary distribution. We also notice that the open quantum walks cannot be always modeled as classical Markov chains by showing that it can break some classical probability rule. By providing with some examples, we show that there can be multiple stationary states for the open quantum walks on the cycles. [ABSTRACT FROM AUTHOR]

Quantum random walks represent a powerful tool for the implementation of various quantum algorithms. We consider a convolution problem for the graphs which provide quantum and classical random walks. We suggest a new method for lattices and hypercycle convolution that preserves quantum walk dynamics. Our method is based on the fact that some graphs represent a result of Kronecker's product of line graphs. We support our methods by means of various numerical experiments that check quantum and classical random walks on hypercycles and their convolutions. Our findings may be useful for saving a significant number of qubits required for algorithms that use quantum walk simulation on quantum devices. [ABSTRACT FROM AUTHOR]

Permutation entropy and its associated frameworks are remarkable examples of physics-inspired techniques adept at processing complex and extensive datasets. Despite substantial progress in developing and applying these tools, their use has been predominantly limited to structured datasets such as time series or images. Here, we introduce the k -nearest neighbor permutation entropy, an innovative extension of the permutation entropy tailored for unstructured data, irrespective of their spatial or temporal configuration and dimensionality. Our approach builds upon nearest neighbor graphs to establish neighborhood relations and uses random walks to extract ordinal patterns and their distribution, thereby defining the k -nearest neighbor permutation entropy. This tool not only adeptly identifies variations in patterns of unstructured data but also does so with a precision that significantly surpasses conventional measures such as spatial autocorrelation. Additionally, it provides a natural approach for incorporating amplitude information and time gaps when analyzing time series or images, thus significantly enhancing its noise resilience and predictive capabilities compared to the usual permutation entropy. Our research substantially expands the applicability of ordinal methods to more general data types, opening promising research avenues for extending the permutation entropy toolkit for unstructured data. [ABSTRACT FROM AUTHOR]

The use of the global mean first-passage time (GMFPT) in random walks on networks has been widely explored in the field of statistical physics, both in theory and practical applications. The GMFPT is the estimated interval of time needed to reach a state j in a system from a starting state i. In contrast, there exists an intrinsic measure for a stochastic process, known as Kemeny's constant, which is independent of the initial state. In the literature, it has been used as a measure of network efficiency. This article deals with a graph-spectrum-based method for finding both the GMFPT and Kemeny's constant of random walks on spiro-ring networks (that are organic compounds with a particular graph structure). Furthermore, we calculate the Laplacian matrix for some specific spiro-ring networks using the decomposition theorem of Laplacian polynomials. Moreover, using the coefficients and roots of the resulting matrices, we establish some formulae for both GMFPT and Kemeny's constant in these spiro-ring networks. [ABSTRACT FROM AUTHOR]

To profit from price oscillations, investors frequently use threshold-type strategies where changes in the portfolio position are triggered by some indicators reaching prescribed levels. In this paper we investigate threshold-type strategies in the context of ergodic control. We make the first steps towards their optimization by proving ergodic properties of related functionals. Assuming Markovian price increments satisfying a minorization condition and (one-sided) boundedness we show, in particular, that for given thresholds, the distribution of the gains converges in the long run. We also extend recent results on the stability of overshoots of random walks from the i.i.d. increment case to Markovian increments, under suitable conditions. [ABSTRACT FROM AUTHOR]

To compare the diagnostic performance of different mathematical models for DWI and explore whether parameters reflecting spatial and temporal heterogeneity can demonstrate better diagnostic accuracy than the diffusion coefficient parameter in distinguishing benign and malignant breast lesions, using whole-tumor histogram analysis. This retrospective study was approved by the institutional ethics committee and included 104 malignant and 42 benign cases. All patients underwent breast magnetic resonance imaging (MRI) with a 3.0 T MR scanner using the simultaneous multi-slice (SMS) readout-segment ed echo-planar imaging (rs-EPI). Histogram metrics of Mono- apparent diffusion coefficient (ADC), CTRW, and FROC-derived parameters were compared between benign and malignant breast lesions, and the diagnostic performance of each diffusion parameter was evaluated. Statistical analysis was performed using Mann-Whitney U test and receiver operating characteristic (ROC) curve. The D FROC -median exhibited the highest AUC for distinguishing benign and malignant breast lesions (AUC = 0.965). The temporal heterogeneity parameter α CTRW -median generated a statistically higher AUC compared to the spatial heterogeneity parameter β CTRW -median (AUC = 0.850 and 0.741, respectively; p = 0.047). Finally, the combination of median values of CTRW parameters displayed a slightly higher AUC than that of FROC parameters, with no significant difference however (AUC = 0.971 and 0.965, respectively; p = 0.172). The diffusion coefficient parameter exhibited superior diagnostic performance in distinguishing breast lesions when compared to the temporal and spatial heterogeneity parameters. [ABSTRACT FROM AUTHOR]

The problem of asymptotic behavior of the expectation of a pairwise interaction type functional on branching random walk is considered. [ABSTRACT FROM AUTHOR]

Explicit formulas for the expected volume and expected number of facets of the convex hull of several multidimensional Gaussian random walks are derived in terms of the Gaussian persistence probabilities. Special cases include the already known results about the convex hull of a single Gaussian random walk and the d-dimensional Gaussian polytope with or without origin. [ABSTRACT FROM AUTHOR]

In this paper, we propose a method of route optimization of vacant taxicab based on the abstract grid network. Firstly, an abstract grid network is built by the quadtree technology with the vacant trajectory data embedded. Secondly, the Markov decision process framework considering the sequential dependence is used to model the problem. Finally, we solve this problem by the policy iteration and compare the method by taking the GPS trajectory data in different hours of 797 taxicabs in a typical working day in Shenzhen, comparing that with the optimal strategy without considering sequential dependence, MNP, local hotspot and random walk algorithm by simulation, respectively. The results show that: The use of quadtree can reduce the sparseness of matching probability from 80.46% to 30.18%. The average revenue per unit distance has increased by 6.10%, 8.75%, 33.24% and 60.06%. The vacant driving rate has decreased by 5.33%, 6.15%, 18.86%, and 23.18%. [ABSTRACT FROM AUTHOR]

Interspecific trait divergence may reflect adaptation and reproductive isolation, particularly after the rapid differentiation that may follow the colonization of new environments. Although new lineages are generally expected to be morphologically and ecologically similar to their ancestors, environmental forces can also drive adaptive differentiation along specific phenotypic axes. We used climate niche models and comparative analyses based on a previously inferred phylogeny to examine the history of ecological and morphological divergence of Neotropical firs (Abies Mill., Pinaceae), a group of conifers that have recently colonized and diversified in the mountains of Mexico and northern Central America. We inferred past secondary contact zones by comparing current and past climate niche projections and looked for evidence of recent interspecific gene flow using genomic data. Neotropical firs have similar niches to each other and show a strong phylogenetic signal for most evaluated morphological traits. Analyses based on individual variables suggested a random walk model of differentiation. However, early adaptation to tropical conditions is inferred in the ancestor of the southernmost firs, as all modern southern taxa are differentiated climatically from Abies concolor, the northernmost species. In addition, observed autapomorphic traits for soil properties and the number of resin ducts in needles are consistent with possible species‐specific adaptations. Thus, a combination of nonadaptive and adaptive processes along different phenotypic axes, some related to the environment, likely operated after the southward migration of this plant lineage from North America and its subsequent radiation in the Neotropics. [ABSTRACT FROM AUTHOR]

To ensure the security of node location privacy in the perception layer of the Internet of Things, this study proposes a location privacy protection method based on RFID location awareness algorithm. This method first introduces an adaptive multi tree anti‐collision algorithm based on collision trees when perceiving and locating the location information of nodes in the perception layer of the Internet of Things, to prevent signal collisions between multiple readers and writers. Then, based on the obtained node location results, a IoT perception layer node location privacy protection scheme based on virtual ring strategy is used to randomly initiate directed co hop routing using the virtual nodes generated after random walking, avoiding the visible area of the source node location, and transmitting data to the aggregation node in the form of the shortest routing path to protect the privacy and security of the node location. Finally, experiments are carried out to prove the progressiveness of the proposed method. The experimental results show that this method can prolong the security period of the source and aggregation nodes in the perception layer of the Internet of Things, protect the privacy and security of node positions, and has great application value. [ABSTRACT FROM AUTHOR]

The UV/optical light curves of Active Galactic Nuclei (AGNs) are commonly described by the Damped Random Walk (DRW) model. However, the physical interpretation of the damping timescale, a key parameter in the DRW model, remains unclear. Particularly, recent observations indicate a weak dependence of the damping timescale upon both wavelength and accretion rate, clearly being inconsistent with the accretion-disk theory. In this study, we investigate the damping timescale in the framework of the Corona Heated Accretion disk Reprocessing (CHAR) model, a physical model that describes AGN variability. We find that while the CHAR model can reproduce the observed power spectral densities of the 20 yr light curves for 190 sources from Stone et al., the observed damping timescale, as well as its weak dependence on wavelength, can also be well recovered through fitting the mock light curves with DRW. We further demonstrate that such weak dependence is artificial due to the effect of inadequate durations of light curves, which leads to best-fitting damping timescales lower than the intrinsic ones. After eliminating this effect, the CHAR model indeed yields a strong dependence of the intrinsic damping timescale on the bolometric luminosity and rest-frame wavelength. Our results highlight the demand for sufficiently long light curves in AGN variability studies and important applications of the CHAR model in such studies. [ABSTRACT FROM AUTHOR]

We study epidemic spreading in complex networks by a multiple random walker approach. Each walker performs an independent simple Markovian random walk on a complex undirected (ergodic) random graph where we focus on the Barabási–Albert (BA), Erdös–Rényi (ER), and Watts–Strogatz (WS) types. Both walkers and nodes can be either susceptible (S) or infected and infectious (I), representing their state of health. Susceptible nodes may be infected by visits of infected walkers, and susceptible walkers may be infected by visiting infected nodes. No direct transmission of the disease among walkers (or among nodes) is possible. This model mimics a large class of diseases such as Dengue and Malaria with the transmission of the disease via vectors (mosquitoes). Infected walkers may die during the time span of their infection, introducing an additional compartment D of dead walkers. Contrary to the walkers, there is no mortality of infected nodes. Infected nodes always recover from their infection after a random finite time span. This assumption is based on the observation that infectious vectors (mosquitoes) are not ill and do not die from the infection. The infectious time spans of nodes and walkers, and the survival times of infected walkers, are represented by independent random variables. We derive stochastic evolution equations for the mean-field compartmental populations with the mortality of walkers and delayed transitions among the compartments. From linear stability analysis, we derive the basic reproduction numbers R M , R 0 with and without mortality, respectively, and prove that R M < R 0 . For R M , R 0 > 1 , the healthy state is unstable, whereas for zero mortality, a stable endemic equilibrium exists (independent of the initial conditions), which we obtained explicitly. We observed that the solutions of the random walk simulations in the considered networks agree well with the mean-field solutions for strongly connected graph topologies, whereas less well for weakly connected structures and for diseases with high mortality. Our model has applications beyond epidemic dynamics, for instance in the kinetics of chemical reactions, the propagation of contaminants, wood fires, and others. [ABSTRACT FROM AUTHOR]

We study the problem of learning good heuristic functions for classical planning tasks with neural networks based on samples represented by states with their cost-to-goal estimates. The heuristic function is learned for a state space and goal condition with the number of samples limited to a fraction of the size of the state space, and must generalize well for all states of the state space with the same goal condition. Our main goal is to better understand the influence of sample generation strategies on the performance of a greedy best-first heuristic search (GBFS) guided by a learned heuristic function. In a set of controlled experiments, we find that two main factors determine the quality of the learned heuristic: the algorithm used to generate the sample set and how close the sample estimates to the perfect cost-to-goal are. These two factors are dependent: having perfect cost-to-goal estimates is insufficient if the samples are not well distributed across the state space. We also study other effects, such as adding samples with high-value estimates. Based on our findings, we propose practical strategies to improve the quality of learned heuristics: three strategies that aim to generate more representative states and two strategies that improve the cost-to-goal estimates. Our practical strategies result in a learned heuristic that, when guiding a GBFS algorithm, increases by more than 30% the mean coverage compared to a baseline learned heuristic. [ABSTRACT FROM AUTHOR]

With the development of civil engineering, lightweight and high-strength materials, as well as large-span, low-frequency structural systems, are increasingly used. However, its self-oscillation frequency is often close to the stride frequency of pedestrians, which is easily affected by human activities. To study the effect of human activities on the dynamic response of structures, it is crucial to choose an appropriate anthropogenic load model. Considering the inter-subject and intra-subject variability of pedestrian walking parameters and induced forces in a crowd, we introduce the interaction rules between pedestrians based on the floor field cellular automata (FFCA). A stochastic crowd-loading model coupling walking parameters, induced forces between pedestrians, and induced forces between pedestrians and structures is proposed for simulating crowd-walking loads. The feasibility of the model is verified by comparing the measured response of a space large-span structure with the predicted response of the proposed stochastic crowd-loading model. The comfort level of the structure under different crowd densities was also evaluated based on the model. It was found that both random combinations of walking parameters and dynamic behaviors of pedestrians can cause significant differences in the structural response. Therefore, the crowd-loading model should consider the influence of pedestrian behavioral factors on the structural response. [ABSTRACT FROM AUTHOR]

We show that for every integer m≥2$$ m\ge 2 $$ and large n$$ n $$, every properly edge‐colored graph on n$$ n $$ vertices with at least n(logn)53$$ n{\left(\log n\right)}^{53} $$ edges contains a rainbow subdivision of Km$$ {K}_m $$. This is sharp up to a polylogarithmic factor. Our proof method exploits the connection between the mixing time of random walks and expansion in graphs. [ABSTRACT FROM AUTHOR]

Recommender systems provide important functions in areas such as dealing with data overload, providing personalized consulting services, and assisting clients in investment decisions. However, the cold start problem in recommender systems has always been in urgent need of solution and optimization. Based on this, this paper classifies the traditional methods and cutting- edge methods to solve the cold start problem, and expounds the research progress and excellent methods in recent years. Firstly, three traditional solutions to the cold start problem are summarized: recommendation based on content filtering, recommendation based on collaborative filtering, and hybrid recommendation. Secondly, the current cutting-edge recommendation algorithms to solve the cold start problem are summarized, and they are classified into the data-driven strategy and the method-driven strategy. The method-driven strategy is divided into algorithms based on meta-learning, algorithms based on context information and session strategy, algorithms based on random walk, algorithms based on heterogeneous graph information and attribute graph, and algorithms based on adversarial mechanism. According to the type of cold start problem, the algorithms are divided into two categories: new users and new items. Then, according to the particularity of the recommendation field, the cold start problem of the recommendation in the multimedia information field and the online e-commerce platform field is expounded. Finally, the possible research directions to solve the cold start problem in the future are summarized. [ABSTRACT FROM AUTHOR]

Existing group recommendation models often have a monotonous approach when solving user representation, and only simple social relationships between users are utilized. This makes user representation inaccurate and most models do not consider the impact of user common intention and social interaction on group preferences. As a result, recommended items are not aligned with user needs. To address these issues, a new group recommendation model based on user common intention and social interaction (GR-UCISI) is proposed. Firstly, a user intention separation model that combines user- item interaction history with social interaction is constructed. Graph neural networks are utilized to collect user-item interaction and social interaction information, and to solve user intention and item representation. Secondly, by utilizing the social network random walk algorithm and the K - means clustering algorithm, users can be grouped. User group, user intention and group intention aggregation process are combined to obtain group common intention representation. Finally, group common intention representation and item representation are calculated to obtain the list of recommended items for the group. This method fully considers the impact of user individuality and commonality among group members on group preferences. It also utilizes social relationships to alleviate the problem of data sparsity and improve model performance. The experimental results show that compared with the model with the best recommendation effect of nine models, on the Gowalla dataset, the Precision and NDCG of the GR-UCISI model are increased by 3.01% and 5.26% respectively, on the Yelp-2018 dataset, the Precision and NDCG of the GR-UCISI model are increased by 2.96% and 1.12% respectively. [ABSTRACT FROM AUTHOR]

Graph Neural Networks (GNNs) play a significant role in tasks related to homophilic graphs. Traditional GNNs, based on the assumption of homophily, employ low-pass filters for neighboring nodes to achieve information aggregation and embedding. However, in heterophilic graphs, nodes from different categories often establish connections, while nodes of the same category are located further apart in the graph topology. This characteristic poses challenges to traditional GNNs, leading to issues of "distant node modeling deficiency" and "failure of the homophily assumption". In response, this paper introduces the Spatial-Frequency domain Adaptive Heterophilic Graph Neural Networks (SFA-HGNN), which integrates adaptive embedding mechanisms for both spatial and frequency domains to address the aforementioned issues. Specifically, for the first problem, we propose the "Distant Spatial Embedding Module", aiming to select and aggregate distant nodes through high-order random walk transition probabilities to enhance modeling capabilities. For the second issue, we design the "Proximal Frequency Domain Embedding Module", constructing adaptive filters to separate high and low-frequency signals of nodes, and introduce frequency-domain guided attention mechanisms to fuse the relevant information, thereby reducing the noise introduced by the failure of the homophily assumption. We deploy the SFA-HGNN on six publicly available heterophilic networks, achieving state-of-the-art results in four of them. Furthermore, we elaborate on the hyperparameter selection mechanism and validate the performance of each module through experimentation, demonstrating a positive correlation between "node structural similarity", "node attribute vector similarity", and "node homophily" in heterophilic networks. [ABSTRACT FROM AUTHOR]

Herein, we investigate the temperature compensation for a dual-mass MEMS gyroscope. After introducing and simulating the dual-mass MEMS gyroscope's working modes, we propose a hybrid algorithm for temperature compensation relying on improved complete ensemble empirical mode decomposition with adaptive noise (ICEEMDAN), sample entropy, time–frequency peak filtering, non-dominated sorting genetic algorithm-II (NSGA II) and extreme learning machine. Firstly, we use ICEEMDAN to decompose the gyroscope's output signal, and then we use sample entropy to classify the decomposed signals. For noise segments and mixed segments with different levels of noise, we use time–frequency peak filtering with different window lengths to achieve a trade-off between noise removal and signal retention. For the feature segment with temperature drift, we build a compensation model using extreme learning machine. To improve the compensation accuracy, NSGA II is used to optimize extreme learning machine, with the prediction error and the 2-norm of the output-layer connection weight as the optimization objectives. Enormous simulation experiments prove the excellent performance of our proposed scheme, which can achieve trade-offs in signal decomposition, classification, denoising and compensation. The improvement in the compensated gyroscope's output signal is analyzed based on Allen variance; its angle random walk is decreased from 0.531076°/h/√Hz to 6.65894 × 10−3°/h/√Hz and its bias stability is decreased from 32.7364°/h to 0.259247°/h. [ABSTRACT FROM AUTHOR]

In order to overcome the difficulty of parameter tuning caused by the large lag and time-varying nonlinearity of the tank for lysozyme fermentation, a temperature control method based on LRWOA-LSTM-PID is proposed in this paper. Firstly, according to the intrinsic mechanism of the fermenter, a temperature mechanism model based on a dynamic equation is designed, which can better reflect the temperature changes in the fermenter. Secondly, a Proportional Integral Derivative (PID) parameter tuning method based on a Long-Short Term Memory Network (LSTM) is proposed, which takes advantage of the ability of LSTM to learn time sequence information and obtains the variation trend between error sequences under continuous time sampling, thereby adjusting network weights more reasonably and accelerating PID parameter tuning. Finally, a Whale Optimization Algorithm (WOA) based on the Lévy flight and random walk strategy (LRWOA) is proposed for the initialization of LSTM parameters; this algorithm has excellent optimization capabilities and overcomes the problem of LSTM falling into local optimal solutions prematurely during parameter randomization. The results show that the method proposed in this paper can achieve rapid tuning of PID parameters, thereby improving the convergence speed of the system and reducing system overshoot. [ABSTRACT FROM AUTHOR]

This study presents a meticulously edited article that assesses the uncertainty associated with contamination dispersion in a porous aquifer environment. The article employs a conceptual model incorporating finite difference flow modeling and particle tracking methods grounded in particle movement theory within groundwater flow. The groundwater flow model utilizes an automatic calibration technique, PES, and independent verification, to minimize statistical discrepancies in the optimized parameters. The statistical summary of the model output reveals the average pollution concentration in the study area, specifically the landfill aquifer in northern Iran. The results indicate that the initial contamination value at the boundaries is zero, whereas 91,802 units are discharged into the sea. Moreover, approximately 3,317,290,003 pollution units have been extracted from pumping wells along the contamination plume over 10 years. Furthermore, the drainage network releases 1,778,680,001 pollution units, resulting in a net outflow of 5,082,740,007 units from the same drainage network. Additionally, 9,912,180,003 units were discharged from the leaky boundaries. It should be noted that these statistics can be reversed depending on the specified period. The difference between the input and output pollution values in the study area indicates a net accumulation of 8192 units. To analyze the sensitivity of contamination dispersion in the porous aquifer environment and the variations in coastal drainage patterns obtained from the finite difference simulation, the explicit and implicit methods, as well as the random walk particle tracking method, were investigated in a portion of the basin area using the South Side Implicit method. One of the main objectives of this sensitivity analysis is to evaluate the results of the uncalibrated qualitative model and examine the particle dispersion in the adjacent area of the contaminated landfill region to assess the error of the proposed model by developing a limited test. The calculated error or computational difference between the explicit and implicit methods and the applet model is considered negligible. For example, the calculated error between the explicit and backward methods and the applet model ranges from 0.086 to 0.372 units for a concentration interval of 0.512 units and 0.680 units for a time interval 0.537. Therefore, the computational differences are not significant. Furthermore, based on theoretical sensitivity analysis of contamination dispersion, the laboratory model demonstrates that the flow direction in this modeling is from west to east, as expected. [ABSTRACT FROM AUTHOR]

Random walk with restart (RWR) is a widely-used measure of node similarity in graphs, and it has proved useful for ranking, community detection, link prediction, anomaly detection, etc. Since RWR is typically required to be computed separately for a larger number of query nodes or even for all nodes, fast computation of it is indispensable. However, for hypergraphs, the fast computation of RWR has been unexplored, despite its great potential. In this paper, we propose ARCHER, a fast computation framework for RWR on hypergraphs. Specifically, we first formally define RWR on hypergraphs, and then we propose two computation methods that compose ARCHER. Since the two methods are complementary (i.e., offering relative advantages on different hypergraphs), we also develop a method for automatic selection between them, which takes a very short time compared to the total running time. Through our extensive experiments on 18 real-world hypergraphs, we demonstrate (a) the speed and space efficiency of ARCHER, (b) the complementary nature of the two computation methods composing ARCHER, (c) the accuracy of its automatic selection method, and (d) its successful application to anomaly detection on hypergraphs. [ABSTRACT FROM AUTHOR]

Knowledge graph embeddings represent a group of machine learning techniques which project entities and relations of a knowledge graph to continuous vector spaces. RDF2vec is a scalable embedding approach rooted in the combination of random walks with a language model. It has been successfully used in various applications. Recently, multiple variants to the RDF2vec approach have been proposed, introducing variations both on the walk generation and on the language modeling side. The combination of those different approaches has lead to an increasing family of RDF2vec variants. In this paper, we evaluate a total of twelve RDF2vec variants on a comprehensive set of benchmark models, and compare them to seven existing knowledge graph embedding methods from the family of link prediction approaches. Besides the established GEval benchmark introducing various downstream machine learning tasks on the DBpedia knowledge graph, we also use the new DLCC (Description Logic Class Constructors) benchmark consisting of two gold standards, one based on DBpedia, and one based on synthetically generated graphs. The latter allows for analyzing which ontological patterns in a knowledge graph can actually be learned by different embedding. With this evaluation, we observe that certain tailored RDF2vec variants can lead to improved performance on different downstream tasks, given the nature of the underlying problem, and that they, in particular, have a different behavior in modeling similarity and relatedness. The findings can be used to provide guidance in selecting a particular RDF2vec method for a given task. [ABSTRACT FROM AUTHOR]

Cancer development is driven by an accumulation of a small number of driver genetic mutations that confer the selective growth advantage to the cell, while most passenger mutations do not contribute to tumor progression. The identification of these driver genes responsible for tumorigenesis is a crucial step in designing effective cancer treatments. Although many computational methods have been developed with this purpose, the majority of existing methods solely provided a single driver gene list for the entire cohort of patients, ignoring the high heterogeneity of driver events across patients. It remains challenging to identify the personalized driver genes. Here, we propose a novel method (PDRWH), which aims to prioritize the mutated genes of a single patient based on their impact on the abnormal expression of downstream genes across a group of patients who share the co-mutation genes and similar gene expression profiles. The wide experimental results on 16 cancer datasets from TCGA showed that PDRWH excels in identifying known general driver genes and tumor-specific drivers. In the comparative testing across five cancer types, PDRWH outperformed existing individual-level methods as well as cohort-level methods. Our results also demonstrated that PDRWH could identify both common and rare drivers. The personalized driver profiles could improve tumor stratification, providing new insights into understanding tumor heterogeneity and taking a further step toward personalized treatment. We also validated one of our predicted novel personalized driver genes on tumor cell proliferation by vitro cell-based assays, the promoting effect of the high expression of Low-density lipoprotein receptor-related protein 1 (LRP1) on tumor cell proliferation. Author summary: In this study, using the TCGA dataset studies as benchmark datasets, we explored the application of the commonality among patients of the same cancer type in personalized driver gene prediction. We proposed a hypergraph model and a generalized random walk method to rank the mutated genes of a patient based on their impact on the abnormal expression of downstream genes in a group of samples rather than an individual sample. Following the extensive experimental results on 16 cancer datasets and the comparative analysis across five cancer types, we have observed that the PDRWH method exhibits remarkable effectiveness in identifying known general driver genes and tumor-specific driver genes. In a few words, our method can provide a more accurate personalized catalog of driver mutations for each patient, and the predicted personalized driver genes can be applied to improve tumor stratification. It can also provide oncologists with a reliable candidate gene list to assist treatment decisions, thus potentially promoting the development of personalized medicine. [ABSTRACT FROM AUTHOR]

Forecasting changes in stock prices is extremely challenging given that numerous factors cause these prices to fluctuate. The random walk hypothesis and efficient market hypothesis essentially state that it is not possible to systematically, reliably predict future stock prices or forecast changes in the stock market overall. Nonetheless, machine learning (ML) techniques that use historical data have been applied to make such predictions. Previous studies focused on a small number of stocks and claimed success with limited statistical confidence. In this study, we construct feature vectors composed of multiple previous relative returns and apply the random forest (RF), support vector machine (SVM), and long short-term memory (LSTM) ML methods as classifiers to predict whether a stock can return 2% more than its index in the following 10 days. We apply this approach to all S&P 500 companies for the period 2017–2022. We assess performance using accuracy, precision, and recall and compare our results with a random choice strategy. We observe that the LSTM classifier outperforms RF and SVM, and the data-driven ML methods outperform the random choice classifier (p = 8.46e−17 for accuracy of LSTM). Thus, we demonstrate that the probability that the random walk and efficient market hypotheses hold in the considered context is negligibly small. [ABSTRACT FROM AUTHOR]

We study the invariant measure of the transport correlator for a chiral Hamiltonian and analyze its properties. The Jacobian of the invariant measure is a function of random phases. Then we distinguish the invariant measure before and after the phase integration. In the former case we found quantum diffusion of fermions and a uniform zero mode that is associated with particle conservation. After the phase integration the transport correlator reveals two types of evolution processes, namely classical diffusion and back-folded random walks. Which one dominates the other depends on the details of the underlying chiral Hamiltonian and may lead either to classical diffusion or to the suppression of diffusion. [ABSTRACT FROM AUTHOR]

This paper presents an enhanced whale optimization algorithm based on virtual force to optimize coverage and address the problem of uneven coverage during the deployment of underwater sensor networks. This method is guided by the Lévy flight and virtual force algorithms and adopts a differential mutation strategy based on random walks. This improves the fitness of the initial population and population richness of the algorithm. The effectiveness of this method was verified through simulation. [ABSTRACT FROM AUTHOR]

The Dickey-Fuller test (DF test) and its various modified versions have been widely used for unit root or random walk testing, though advices are necessary regarding their proper use in hands-on statistical algorithm software. In this paper, we review the development of such tests over several decades. We examine why such modified versions of DF tests were developed and proper instructions regarding their use are essential. In addition, we discuss a simple way to overcome this hurdle. [ABSTRACT FROM AUTHOR]

Let G be a graph on n vertices. For a given integer k such that 1 ≤ k ≤ n , the k -token graph F k (G) of G is defined as the graph whose vertices are the k -subsets of the vertex set of G , and two of them are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. In this article, we study the structural and spectral properties of token graphs. We describe the adjacency matrix and the Laplacian matrix of F k (G) and obtain bounds on the adjacency and Laplacian spectral radii of F k (G). Interestingly, it is found that S n , the star graph on n vertices, has the same Laplacian spectral radius as that of F k (S n). It was conjectured that for any graph G , the algebraic connectivity of F k (G) is equal to the algebraic connectivity of G. This result turned out to be a theorem, as it was proved by using the theory of the continuous Markov chain of random walks and the interchange process. However, proving this theorem using algebraic and combinatorial methods is still an open and interesting problem. Using combinatorial techniques, we prove that the theorem holds for a class of graphs that have a cut-vertex of degree n − 1. We also prove it by restricting the smallest degree of the k -token graph of G. [ABSTRACT FROM AUTHOR]

We analyse how financial market analysts' expectations in the Czech National Bank's Financial Market Inflation Expectations survey perform relative to the random-walk forecast when it comes to predicting five financial variables. Using data from 2001 to 2022, our results indicate that the analysts are able to significantly outperform the random-walk forecast in terms of forecast precision for the repo rate and Prague Interbank Offered Rate at the one-month forecasting horizon. For the five- and ten-year interest rate swap rates, the random walk significantly outperforms the analysts at both the one-month and one-year forecasting horizons. For the CZK/EUR exchange rate, the random-walk forecast has a lower root mean squared forecast error than that of the analysts' forecast at the one-month horizon whereas at the one-year horizon the opposite is found; however, none of these differences are statistically significant. [ABSTRACT FROM AUTHOR]

We present a novel method for analysing socio-spatial segregation in cities by considering constraints imposed by transportation networks. Using a multilayered network approach, we model the interaction probabilities of socio-economic groups with random walks and Lévy flights. This method allows for evaluation of new transport infrastructure's impact on segregation while quantifying each network's contribution to interaction opportunities. The proposed random walk segregation index measures the probability of individuals encountering diverse social groups based on their available means of transit via random walks. The index incorporates temporal constraints in urban mobility with a parameter, α ∈ [ 0 , 1) , of the probability of the random walk continuing at each time step. By applying this to a toy model and conducting a sensitivity analysis, we explore how the index changes dependent on this temporal constraint. When the parameter equals zero, the measure simplifies to an isolation index. When the parameter approaches one it represents the city's overall socio-economic distribution by mirroring the steady-state of the random walk process. Using Cuenca, Ecuador as a case study, we illustrate the method's applicability in transportation planning as a valuable tool for policymakers, addressing spatial distribution of socio-economic groups and the connectivity of existing transport networks, thus promoting equitable interactions throughout the city. [ABSTRACT FROM AUTHOR]

The motor neuroscience literature suggests that the central nervous system may encode some motor commands in terms of velocity. In this work, we tackle the question: what consequences would velocity commands produce at the behavioral level? Considering the ubiquitous presence of noise in the neuromusculoskeletal system, we predict that velocity commands affected by stationary noise would produce "random walks", also known as Brownian processes, in position. Brownian motions are distinctively characterized by a linearly growing variance and a power spectral density that declines in inverse proportion to frequency. This work first shows that these Brownian processes are indeed observed in unbounded motion tasks e.g., rotating a crank. We further predict that such growing variance would still be present, but bounded, in tasks requiring a constant posture e.g., maintaining a static hand position or quietly standing. This hypothesis was also confirmed by experimental observations. A series of descriptive models are investigated to justify the observed behavior. Interestingly, one of the models capable of accounting for all the experimental results must feature forward-path velocity commands corrupted by stationary noise. The results of this work provide behavioral support for the hypothesis that humans plan the motion components of their actions in terms of velocity. [ABSTRACT FROM AUTHOR]

The survival of an animal depends on its success as a forager, and understanding the adaptations that result in successful foraging strategies is an enduring endeavour of behavioral ecology. Random walks are one of the primary mathematical descriptions of foraging behavior. Power law distributions are often used to model random walks, as they can characterize a wide range of behaviors, including Lévy walks. Empirical evidence indicates the prevalence and efficiency of Lévy walks as a foraging strategy, and theoretical work suggests an evolutionary origin. However, previous evolutionary models have assumed a priori that move lengths are drawn from a power law or other families of distributions. Here, we remove this restriction with a model that allows for the evolution of any distribution. Instead of Lévy walks, our model unfailingly results in the evolution of intermittent search, a random walk composed of two disjoint modes—frequent localized walks and infrequent extensive moves—that consistently outcompeted Lévy walks. We also demonstrate that foraging using intermittent search may resemble a Lévy walk because of interactions with the resources within an environment. These extrinsically generated Lévy-like walks belie an underlying behavior and may explain the prevalence of Lévy walks reported in the literature. [ABSTRACT FROM AUTHOR]

We derive conditions for recurrence and transience for time-inhomogeneous birth-and-death processes considered as random walks with positively biased drifts. We establish a general result, from which the earlier known particular results by Menshikov and Volkov ['Urn-related random walk with drift $\rho x^\alpha /t^\beta $ ', Electron. J. Probab. 13 (2008), 944–960] follow. [ABSTRACT FROM AUTHOR]

Analysis of small‐angle scattering (SAS) data requires intensive modeling to infer and characterize the structures present in a sample. This iterative improvement of models is a time‐consuming process. Presented here is Scattering Equation Builder (SEB), a C++ library that derives exact analytic expressions for the form factors of complex composite structures. The user writes a small program that specifies how the sub‐units should be linked to form a composite structure and calls SEB to obtain an expression for the form factor. SEB supports e.g. Gaussian polymer chains and loops, thin rods and circles, solid spheres, spherical shells and cylinders, and many different options for how these can be linked together. The formalism behind SEB is presented and simple case studies are given, such as block copolymers with different types of linkage, as well as more complex examples, such as a random walk model of 100 linked sub‐units, dendrimers, polymers and rods attached to the surfaces of geometric objects, and finally the scattering from a linear chain of five stars, where each star is built up of four diblock copolymers. These examples illustrate how SEB can be used to develop complex models and hence reduce the cost of analyzing SAS data. [ABSTRACT FROM AUTHOR]

In this paper, we consider the friendship paradox in the context of random walks and paths. Among our results, we give an equality connecting long-range degree correlation, degree variability, and the degree-wise effect of additional steps for a random walk on a graph. Random paths are also considered, as well as applications to acquaintance sampling in the context of core-periphery structure. [ABSTRACT FROM AUTHOR]

In the Fastest Mixing Markov Chain problem, we are given a graph G = (V , E) and desire the discrete-time Markov chain with smallest mixing time τ subject to having equilibrium distribution uniform on V and non-zero transition probabilities only across edges of the graph. It is well-known that the mixing time τ RW of the lazy random walk on G is characterised by the edge conductance Φ of G via Cheeger's inequality: Φ - 1 ≲ τ RW ≲ Φ - 2 log | V | . Analogously, we characterise the fastest mixing time τ ⋆ via a Cheeger-type inequality but for a different geometric quantity, namely the vertex conductance Ψ of G: Ψ - 1 ≲ τ ⋆ ≲ Ψ - 2 (log | V |) 2 . This characterisation forbids fast mixing for graphs with small vertex conductance. To bypass this fundamental barrier, we consider Markov chains on G with equilibrium distribution which need not be uniform, but rather only ε -close to uniform in total variation. We show that it is always possible to construct such a chain with mixing time τ ≲ ε - 1 (diam G) 2 log | V | . Finally, we discuss analogous questions for continuous-time and time-inhomogeneous chains. [ABSTRACT FROM AUTHOR]

We consider random walks on countable groups. A celebrated result of Kesten says that the spectral radius of a symmetric walk (whose support generates the group as a semigroup) is equal to one if and only if the group is amenable. We give an analogue of this result for walks that are not symmetric. We also conclude a ratio limit theorem for amenable groups. [ABSTRACT FROM AUTHOR]

The voter model is a classical interacting particle system, modeling how global consensus is formed by local imitation. We analyze the time to consensus for a particular family of voter models when the underlying structure is a scale-free inhomogeneous random graph in the high edge-density regime, where this graph features a giant component. In this regime, we verify that the polynomial orders of consensus agree with those of their mean-field approximation in [A. Moinet, A. Barrat, and R. Pastor-Satorras, Phys. Rev. E, 98 (2018), 022303]. This "discursive" family of models has a symmetrized interaction to better model discussions and is indexed by a temperature parameter that, for certain parameters of the power law tail of the network's degree distribution, is seen to produce two distinct phases of consensus speed. Our proofs rely on the well-known duality to coalescing random walks and a novel bound on the mixing time of these walks using the known fast mixing of the Erdös-Rényi giant subgraph. Unlike in the subcritical case [J. Fernley and M. Ortgiese, Random Structures Algorithms, 62 (2023), pp. 376-429], which requires tail exponent of the limiting degree distribution τ = 1 +1/γ > 3 as well as low edge density, in the giant component case, we also address the "ultrasmall world" power law exponents τ ∈ (2,3]. [ABSTRACT FROM AUTHOR]

It is known that any open necklace with beads of t types, in which the number of beads of each type is divisible by k, can be partitioned by at most (k -- 1)t cuts into intervals that can be distributed into k collections, each containing the same number of beads of each type. This is tight for all values of k and t. Here, we consider the case of random necklaces, where the number of beads of each type is km. Then the minimum number of cuts required for a "fair" partition with the above property is a random variable X(k,t,m). We prove that for fixed k,t and large m, this random variable is at least (k -- 1)(t + 1)/2 with high probability. For k = 2, fixed t, and large m, we determine the asymptotic behavior of the probability that X(2,t,m) = s for all values of s ≤ t. We show that this probability is polynomially small when s < (t + 1)/2, is bounded away from zero when s > (t + 1)/2, and decays like ɵ(1/logm) when s = (t + 1)/2. We also show that for large t, X(2,t,1) is at most (0.4 + o(1))t with high probability and that for large t and large ratio k/logt, X(k,t,1) is o(kt) with high probability. [ABSTRACT FROM AUTHOR]

We describe a robust methodology, based on the martingale argument of Nachmias and Peres and random walk estimates, to obtain simple upper and lower bounds on the size of a maximal component in several random graphs at criticality. Even though the main result is not new, we believe the material presented here is interesting because it unifies several proofs found in the literature into a common framework. More specifically, we give easy-to-check conditions that, when satisfied, allow an immediate derivation of the above-mentioned bounds. [ABSTRACT FROM AUTHOR]

Suppose that a sequence of random variables is a homogeneous irreducible Markov chain with finite set of states. Let , , be random variables defined on the chain transitions. The renewal function where and , , is introduced. It is shown that this function converges to its limit at an exponential rate, and an explicit description of the exponent is given. [ABSTRACT FROM AUTHOR]

We consider a random walk with zero mean and finite variance whose steps are arithmetic. The arcsine law for the time the walk reaches its maximum is well known. In this paper, we consider the distribution of the moment of reaching the maximum under the assumption that the maximum value itself is fixed. We show that, in the case of a moderate deviation of the maximum, the distribution of the moment of the maximum with appropriate normalization converges to the chi-square distribution with one degree of freedom. Similar results are obtained in the nonlattice case. [ABSTRACT FROM AUTHOR]

One of the most important tasks in handling real-world global optimization problems is to achieve a balance between exploration and exploitation in any nature-inspired optimization method. As a result, the search agents of an algorithm constantly strive to investigate the unexplored regions of a search space. Aquila Optimizer (AO) is a recent addition to the field of metaheuristics that finds the solution to an optimization problem using the hunting behavior of Aquila. However, in some cases, AO skips the true solutions and is trapped at sub-optimal solutions. These problems lead to premature convergence (stagnation), which is harmful in determining the global optima. Therefore, to solve the above-mentioned problem, the present study aims to establish comparatively better synergy between exploration and exploitation and to escape from local stagnation in AO. In this direction, firstly, the exploration ability of AO is improved by integrating Dynamic Random Walk (DRW), and, secondly, the balance between exploration and exploitation is maintained through Dynamic Oppositional Learning (DOL). Due to its dynamic search space and low complexity, the DOL-inspired DRW technique is more computationally efficient and has higher exploration potential for convergence to the best optimum. This allows the algorithm to be improved even further and prevents premature convergence. The proposed algorithm is named DAO. A well-known set of CEC2017 and CEC2019 benchmark functions as well as three engineering problems are used for the performance evaluation. The superior ability of the proposed DAO is demonstrated by the examination of the numerical data produced and its comparison with existing metaheuristic algorithms. [ABSTRACT FROM AUTHOR]

We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a quasi-maximum likelihood estimator, based on a second order Taylor approximation of the log-likelihood function. We show the almost sure convergence of our estimate in the diffusive, critical and superdiffusive regimes. The local asymptotic normality of our statistical procedure is established in the diffusive regime, while the local asymptotic mixed normality is proven in the superdiffusive regime. Asymptotic and exact confidence intervals as well as statistical tests are also provided. All our analysis relies on asymptotic results for martingales and the quadratic variations associated. [ABSTRACT FROM AUTHOR]