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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.

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]

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

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

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]

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

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

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

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

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]

Huang and Merwade (2023), https://doi.org/10.1029/2023wr034947, hereafter conveniently referred to as HM23, wrongly claim improvement of their method for postprocessing multi‐model water stage predictions using Bayesian Model Averaging (BMA). Their results show all signs of a flawed implementation of the Metropolis algorithm. In this comment I will point out the many mistakes and shortcomings of the BMA methodology of HM23. Their method is deficient, inefficient and ineffective and wrongly quantifies BMA model parameter and predictive uncertainty. Furthermore, HM23 misrepresent BMA literature, articulate a poor understanding of Markov chain Monte Carlo methods and misuse the autocorrelation function for monitoring convergence of the sampled Markov chains. A proper implementation of the random walk Metropolis algorithm would have led HM23 to substantially different results and findings about their ensemble of water stage predictions. The MODELAVG toolbox of Vrugt (2018) https://www.researchgate.net/publication/299458373%5fMODELAVG%5fA%5fMATLAB%5fToolbox%5ffor%5fPostprocessing%5fof%5fModel%5fEnsembles satisfies all requirements of HM23 and provides robust estimates of BMA model parameter and prediction uncertainty for symmetric, skewed and truncated conditional forecast distributions of the ensemble members. Plain Language Summary: This comment criticizes the work of Huang and Merwade (2023), https://doi.org/10.1029/2023wr034947 or HM23 on postprocessing forecast ensembles of flood models using Bayesian Model Averaging (BMA). The flawed implementation and use of statistical methods by HM23 has led to nonsensical results, erroneous findings, and invalid statements and conclusions. I will point some of the main flaws and demonstrate how existing methods would have led to fundamentally different findings for their ensemble of water stage predictions. Key Points: This comment criticizes the work of Huang & Merwade (2023) or HM23 on postprocessing water stage model predictions using Bayesian Model Averaging (BMA)The methodology of HM23 is fundamentally flawed and provides erroneous estimates of BMA parameter and predictive uncertaintyThe DREAM(BMA) algorithm in the MODELAVG toolbox of Vrugt (2018) guarantees a robust Bayesian training of mixture models [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]

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]

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]

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]

This study proposed moment-based approximations for the expected value and variance of the ergodic distribution of the semi-Markovian random walk process (X(t)) with gamma distributed interference of chance. Many studies have investigated analogous moment problems by using an asymptotic approach. The key distinguishing aspect of this study from others in the literature is obtaining Kambo's approximations for the moments of X(t) instead of asymptotic expansions. Firstly, the approximation formulas for the moments of boundary functional SN(z) of X(t) were obtained. Then using these results, approximation formulas for the first two moments of the ergodic distributions of X(t) were derived. Finally, the expected value and variance of X(t) were calculated by using the Monte Carlo simulation method for two concrete distributions (Gaussian and Uniform). [ABSTRACT FROM AUTHOR]

The dipping dike model has shown to be a useful approximation for mineral deposits. To make this model more realistic, we include the thickness, which yields the depth to the bottom, as an additional parameter. The magnetic anomaly is obtained by combining the anomalies of two infinite dikes, so that the resulting expression is simpler than the classical prismatic models with polygonal cross section. We employ a Metropolis-Hasting (MH) algorithm coupled with the Levenberg-Marquardt (LM) method to invert magnetic profiles assuming a model of multiple dike-like sources. We use a few iterations of the LM method to improve the candidate solutions at the end of each random walk generated by MH. The following parameters are obtained: depth to the top, thickness, half-width, horizontal location of the top center, geological dip, in addition to two effective parameters that depend on the intensity of magnetization and the directions of the induced and remanent fields. For synthetic anomalies, both noise-free and noisy magnetic data are considered, with examples presented for each scenario. These examples highlight the discrepancy between models with finite and infinite sources. They also illustrate the higher accuracy of the hybrid MH-LM method over the pure MH approach. Moreover, two field examples related to mineral exploration have been considered: the Pima copper mine, United States, where the relative differences between the parameters obtained by our algorithm and those known from drilling are not higher than 10%, and a magnetic profile over iron ore deposits located in Laje, northeast Brazil, where the inverted parameters were useful for detailing previous studies. [ABSTRACT FROM AUTHOR]

This study explores market efficiency and behavior by integrating key theories such as the Efficient Market Hypothesis (EMH), Adaptive Market Hypothesis (AMH), Informational Efficiency and Random Walk theory. Using LSTM enhanced by optimizers like Stochastic Gradient Descent (SGD), Adam, AdaGrad, and RMSprop, we analyze market inefficiencies in the Standard and Poor's (SPX) index over a 22-year period. Our results reveal "pockets in time" that challenge EMH predictions, particularly with the AdaGrad optimizer at a size of the hidden layer (HS) of 64. Beyond forecasting, we apply the Dominguez–Lobato (DL) and General Spectral (GS) tests as part of the Martingale Difference Hypothesis to assess statistical inefficiencies and deviations from the Random Walk model. By emphasizing "informational efficiency", we examine how quickly new information is reflected in stock prices. We argue that market inefficiencies are transient phenomena influenced by structural shifts and information flow, challenging the notion that forecasting alone can refute EMH. Additionally, we compare LSTM with ARIMA with Exponential Smoothing, and LightGBM to highlight the strengths and limitations of these models in financial forecasting. The LSTM model excels at capturing temporal dependencies, while LightGBM demonstrates its effectiveness in detecting non-linear relationships. Our comprehensive approach offers a nuanced understanding of market dynamics and inefficiencies. [ABSTRACT FROM AUTHOR]

Ecosystems and biodiversity across the world are being altered by human activities. Habitat modification and degradation are among the most important drivers of biodiversity loss. These modifications can have an impact on species behavior, which can, in turn, impact their mortality. While several studies have investigated the impacts of habitat degradation and fragmentation on terrestrial species, the extent to which habitat modifications affect the behavior and fitness of marine species is still largely unknown, particularly for pelagic species. Since the early 1990s, industrial purse seine vessels targeting tuna have started deploying artificial floating objects—Drifting Fish Aggregating Devices (DFADs)—in all oceans to increase tuna catchability. Since then, the massive deployment of DFADs has modified tuna surface habitat, by increasing the density of floating objects, with potential impacts on tuna associative behavior and mortality. In this study, we investigate these impacts for yellowfin tuna in the Indian Ocean. Using an individual‐based model based on a correlated random walk and newly available data on DFAD densities, we quantify for the first time how the increase in floating object density, due to DFAD use, affects the percentage of time that yellowfin tuna spend associated, which, in turn, directly impacts their availability to fishers and fishing mortality. This modification of tuna associative behavior could also have indirect impacts on their fitness, by retaining tuna in areas detrimental to them or disrupting schooling behavior. Hence, there is an urgent need to further investigate DFAD impacts on tuna behavior, in particular, taking social behavior into account, and to continue regulation efforts on DFAD use and monitoring. [ABSTRACT FROM AUTHOR]

Inductive link prediction (ILP) in knowledge graphs (KGs) aims to predict missing links between entities that were not seen during the training phase. Recent some subgraph-based methods have shown some advancements, but they all overlook the relational semantics between entities during subgraph extraction. To overcome this limitation, we introduce a novel inductive link prediction model named SASILP (Structure and Semantic Inductive Link Prediction), which comprehensively incorporates relational semantics in both subgraph extraction and node initialization processes. The model employs a random walk strategy to calculate the structural scores of neighboring nodes and utilizes an enhanced graph attention network to determine their semantic scores. By integrating both structural and semantic scores, SASILP strategically selects key nodes to form a subgraph. Furthermore, the subgraph is initialized with a node initialization technique that integrates information about neighboring relations. The experiments conducted on benchmark datasets demonstrate that SASILP outperforms state-of-the-art methods on inductive link prediction tasks, and verify the effectiveness of our approach. [ABSTRACT FROM AUTHOR]

The purpose of entity linking is to connect entity mentions in text to real entities in the knowledge base. Existing methods focus on using the text topic, entity type, linking order, and association between entities to obtain the target entities. Although these methods have achieved good results, they ignore the exploration of candidate entities, leading to insufficient semantic information among entities. In addition, the implicit relationship and discrimination within the candidate entities also affect the accuracy of entity linking. To address these problems, we introduce information about candidate entities from Wikipedia and construct a graph model to capture implicit dependencies between different entity decisions. Specifically, we propose a cascade attention mechanism and develop a novel local entity linkage model termed CAM-LEL. This model leverages the interaction between entity mentions and candidate entities to enhance the semantic representation of entities. Furthermore, a global entity linkage model termed DG-GEL based on a dynamic graph is established to construct an entity association graph, and a random walking algorithm and entity entropy are used to extract the implicit relationships within entities to increase the differentiation between entities. Experimental results and in-depth analyses of multiple datasets show that our model outperforms other state-of-the-art models. [ABSTRACT FROM AUTHOR]

Multi-label text classification refers to assigning multiple relevant category labels to each text, which has been widely applied in the real world. To enhance the performance of multi-label text classification, most existing methods only focus on optimizing document and label representations, assuming accurate label-document similarity is crucial. However, whether the potential relevance between labels and if the problem of the long-tail distribution of labels could be solved are also key factors affecting the performance of multi-label classification. To this end, we propose a multi-label text classification model called DV-MLTC, which is based on a dual-view graph convolutional network to predict multiple labels for text. Specifically, we utilize graph convolutional neural networks to explore the potential correlation between labels in both the global and local views. First, we capture the global consistency of labels on the global label graph based on existing statistical information and generate label paths through a random walk algorithm to reconstruct the label graph. Then, to capture relationships between low-frequency co-occurring labels on the reconstructed graph, we guide the generation of reasonable co-occurring label pairs within the local neighborhood by utilizing the local consistency of labels, which also helps alleviate the long-tail distribution of labels. Finally, we integrate the global and local consistency of labels to address the problem of highly skewed distribution caused by incomplete label co-occurrence patterns in the label co-occurrence graph. The Evaluation shows that our proposed model achieves competitive results compared to existing state-of-the-art methods. Moreover, our model achieves a better balance between efficiency and performance. [ABSTRACT FROM AUTHOR]

The Swarm Guiding and Communication System (SGCS) is a decision-making and information-sharing framework for robot swarms that only needs close-range peer-to-peer communication and no centralized control. Each robot makes decisions based on an incomplete virtual pheromone map that is updated on each interaction with another robot, imitating ant colonial behavior. Similar systems rely on continuous communication with no range limitations, environment modification, or centralized control. A computer simulation is developed to assess the effectiveness and robustness of the framework in covering an area. Consistency and the time needed for 99% coverage are compared with an unbiased random walk. The pheromone approach is shown to outperfom the unbiased one regardless of number of agents. Innate resilience to individual failures is also demonstrated. [ABSTRACT FROM AUTHOR]

During the engineering structure's operation, the mechanical structure's performance and loading will change with time, so the parameter uncertainty and structural reliability will also have dynamic characteristics. The time-varying reliability analysis method can more accurately evaluate structural reliability by fully using this dynamic uncertainty. However, the time-varying reliability analysis was mainly based on the spanning rate method, which was complex and difficult to obtain the final result. Therefore, this study proposed an enhanced dung beetle optimization (EDBO) assisted time-varying reliability analysis method based on the adaptive Kriging model. With the help of the adaptive Kriging model and the EDBO optimization algorithm, the efficiency of the time-varying reliability analysis method was improved. At the same time, to prevent prematurely falling into the local search trap, the method improved the uniformity of the sample by initializing the sample through improved tent chaotic mapping (ITCM). Next, the Gaussian random walk strategy was used to search the updated position, which further improved the accuracy of the reliability analysis results. Finally, the accuracy and effectiveness of the proposed time-varying reliability analysis method were verified by four mechanical structure model examples. From the calculation results, it can be seen that with the help of the new DBO optimization algorithm, the relative error of the proposed reliability analysis results was about 20%~30% lower than that of the traditional reliability analysis method. What's more, the calculation efficiency was higher than that of other reliability analysis methods. [ABSTRACT FROM AUTHOR]

This paper presents a detailed procedure for determining the probability of return for random walks on $ \mathbb{Z} $, whose increment is given by a generalization of a well-known Fibonacci sequence, namely the $ k $-Fibonacci-like sequence $ (G_{k, n})_n $. Also, we study the size of the set of these walks that return to the origin an infinite number of times, in term of fractal dimension. In addition, we investigate the limiting distribution of an adequate Markov chain that encapsulates the entire Tribonacci sequence $ ({\mathsf T}_n) $ to provide the limiting behavior of this sequence.

The Yangtze River Delta (YRD) is an important engine of national economic development and a leading region in international competition. As economic exchanges and resource flows in the YRD region become closer, the inter-regional industrial linkages continue to grow, resulting in the formation of an industrial network structure characterized by a "complex network". The strength of the links between industrial sectors and the value and significance of the existence of industries in the network change over time, thus causing the overall evolution of the industrial network in the YRD region. Based on the input-output tables of the YRD region in 2012 and 2017, this paper uses the prediction index of network structure similarity to construct the prediction model of industrial network link between the YRD regions, and calculates the possibility of future links between industries in the Yangtze River Delta region through comparative analysis and selection of the RWR index of random walk similarity with the best effect, and concludes that: (1) the homogeneity of industries among provinces and cities in the Yangtze River Delta region is relatively high, resulting in homogeneous competition; (2) the overall nature of the industrial layout of the YRD is not prominent, and the depth and intensity of cross-regional industrial cooperation are lacking. On the basis of analysis and research, the countermeasures and suggestions for effectively realizing industrial integration are put forward from the macro level of the government and the meso level of the industry, so as to achieve a more complete industrial network in the YRD region and a more extensive length and width of the cross-regional industrial chain. [ABSTRACT FROM AUTHOR]

People parse continuous experiences at natural breakpoints called event boundaries, which is important for understanding an environment’s causal structure and for responding to uncertainty within it. However, it remains unclear how different forms of uncertainty affect the parsing of continuous experiences and how such uncertainty influences the brain’s processing of ongoing events. We exposed human participants of both sexes (N = 34) to a continuous sequence of semantically meaningless images. We generated sequences from random walks through a graph that grouped images into temporal communities. After learning, we asked participants to segment another sequence at natural breakpoints (event boundaries). Participants segmented the sequence at learned transitions between communities, as well as at novel transitions, suggesting that people can segment temporally extended experiences into events based on learned structure as well as prediction error. Greater segmentation at novel boundaries was associated with enhanced parietal scalp electroencephalography (EEG) activity between 250 and 450 ms after the stimulus onset. Multivariate classification of EEG activity showed that novel and learned boundaries evoked distinct patterns of neural activity, particularly theta band power in posterior electrodes. Learning also led to distinct neural representations for stimuli within the temporal communities, while neural activity at learned boundary nodes showed predictive evidence for the adjacent community. The data show that people segment experiences at both learned and novel boundaries and suggest that learned event boundaries trigger retrieval of information about the upcoming community that could underlie anticipation of the next event in a sequence. [ABSTRACT FROM AUTHOR]

Accurate forecasting of high-resolution particulate matter 2.5 (PM2.5) levels is essential for the development of public health policy. However, datasets used for this purpose often contain missing observations. This study presents a two-stage approach to handle this problem. The first stage is a multivariate spatial time series (MSTS) model, used to generate forecasts for the sampled spatial units and to impute missing observations. The MSTS model utilizes the similarities between the temporal patterns of the time series of the spatial units to impute the missing data across space. The second stage is the high-resolution prediction model, which generates predictions that cover the entire study domain. The second stage faces the big N problem giving rise to complex memory and computational problems. As a solution to the big N problem, we propose a Gaussian Markov random field (GMRF) for innovations with the Matérn covariance matrix obtained from the corresponding Gaussian field (GF) matrix by means of the stochastic partial differential equation (SPDE) method and the finite element method (FEM). For inference, we propose Bayesian statistics and integrated nested Laplace approximation (INLA) in the R-INLA package. The above approach is demonstrated using daily data collected from 13 PM2.5 monitoring stations in Jakarta Province, Indonesia, for 1 January–31 December 2022. The first stage of the model generates PM2.5 forecasts for the 13 monitoring stations for the period 1–31 January 2023, imputing missing data by means of the MSTS model. To capture temporal trends in the PM2.5 concentrations, the model applies a first-order autoregressive process and a seasonal process. The second stage involves creating a high-resolution map for the period 1–31 January 2023, for sampled and non-sampled spatiotemporal units. It uses the MSTS-generated PM2.5 predictions for the sampled spatiotemporal units and observations of the covariate's altitude, population density, and rainfall for sampled and non-samples spatiotemporal units. For the spatially correlated random effects, we apply a first-order random walk process. The validation of out-of-sample forecasts indicates a strong model fit with low mean squared error (0.001), mean absolute error (0.037), and mean absolute percentage error (0.041), and a high R² value (0.855). The analysis reveals that altitude and precipitation negatively impact PM2.5 concentrations, while population density has a positive effect. Specifically, a one-meter increase in altitude is linked to a 7.8% decrease in PM2.5, while a one-person increase in population density leads to a 7.0% rise in PM2.5. Additionally, a one-millimeter increase in rainfall corresponds to a 3.9% decrease in PM2.5. The paper makes a valuable contribution to the field of forecasting high-resolution PM2.5 levels, which is essential for providing detailed, accurate information for public health policy. The approach presents a new and innovative method for addressing the problem of missing data and high-resolution forecasting. [ABSTRACT FROM AUTHOR]

In this study, we describe a deep learning (DL)-based workflow for the three-dimensional (3D) geophysical inversion of magnetotelluric (MT) data. We derived a mathematical connection between a 3D resistivity model and the surface-observed electric/magnetic field response by using a fully connected neural network framework (U-Net). Limited by computer hardware functionality, the resistivity models were generated by using a random walk technique to enlarge the generalization coverage of the neural network model, and 15,000 paired datasets were utilized to train and validate it. Grid search was used to select the optimal configuration parameters. With the optimal model framework from the parameter tuning phase, the metrics showed stable convergence during model training/validation. In the test period, the trained model was applied to predict the resistivity distribution by using both the simulated synthetic and the real MT data from the Mount Meager area, British Columbia. The reliability of the model prediction was verified with noised input data from the synthetic model. The calculated results can be used to reconstruct the position and shape trends of bodies with anomalous resistivity, which verifies the stability and performance of the DL-based 3D inversion algorithm and showcases its potential practical applications. [ABSTRACT FROM AUTHOR]

The modeling of the concrete matrix serves as a foundation for mesoscale analysis of concrete, which provides a crucial avenue for investigating the crack propagation and strength characteristics of concrete. However, the primary prerequisite for conducting such analyses is the generation of aggregate models. By combining the advantages of Voronoi diagrams and the random walk algorithm (RWA), a Voronoi–random walk algorithm is proposed in this paper. The algorithm overcomes the limitations of traditional methods, including constraints on aggregate volume fraction, low computational efficiency, and insufficient randomness in aggregate distribution. The meso-structure of a concrete block was modeled by the proposed method, and then its failure behavior under uniaxial compression was simulated using the finite element method. The numerical results agreed well with the experimental observations, indicating the effectiveness and accuracy of the proposed approach. [ABSTRACT FROM AUTHOR]

Background: Network theory is largely applied in real-world systems to assess landscape connectivity using empirical or theoretical networks. Empirical networks are usually built from discontinuous individual movement trajectories without knowing the effect of relocation frequency on the assessment of landscape connectivity while theoretical networks generally rely on simple movement rules. We investigated the combined effects of relocation sampling frequency and landscape fragmentation on the assessment of landscape connectivity using simulated trajectories and empirical high-resolution (1 Hz) trajectories of Alpine ibex (Capra ibex). We also quantified the capacity of commonly used theoretical networks to accurately predict landscape connectivity from multiple movement processes. Methods: We simulated forager trajectories from continuous correlated biased random walks in simulated landscapes with three levels of landscape fragmentation. High-resolution ibex trajectories were reconstructed using GPS-enabled multi-sensor biologging data and the dead-reckoning technique. For both simulated and empirical trajectories, we generated spatial networks from regularly resampled trajectories and assessed changes in their topology and information loss depending on the resampling frequency and landscape fragmentation. We finally built commonly used theoretical networks in the same landscapes and compared their predictions to actual connectivity. Results: We demonstrated that an accurate assessment of landscape connectivity can be severely hampered (e.g., up to 66% of undetected visited patches and 29% of spurious links) when the relocation frequency is too coarse compared to the temporal dynamics of animal movement. However, the level of landscape fragmentation and underlying movement processes can both mitigate the effect of relocation sampling frequency. We also showed that network topologies emerging from different movement behaviours and a wide range of landscape fragmentation were complex, and that commonly used theoretical networks accurately predicted only 30–50% of landscape connectivity in such environments. Conclusions: Very high-resolution trajectories were generally necessary to accurately identify complex network topologies and avoid the generation of spurious information on landscape connectivity. New technologies providing such high-resolution datasets over long periods should thus grow in the movement ecology sphere. In addition, commonly used theoretical models should be applied with caution to the study of landscape connectivity in real-world systems as they did not perform well as predictive tools. [ABSTRACT FROM AUTHOR]

Genomic surveillance of pathogen evolution is essential for public health response, treatment strategies, and vaccine development. In the context of SARS-COV-2, multiple models have been developed including Multinomial Logistic Regression (MLR) describing variant frequency growth as well as Fixed Growth Advantage (FGA), Growth Advantage Random Walk (GARW) and Piantham parameterizations describing variant Rt. These models provide estimates of variant fitness and can be used to forecast changes in variant frequency. We introduce a framework for evaluating real-time forecasts of variant frequencies, and apply this framework to the evolution of SARS-CoV-2 during 2022 in which multiple new viral variants emerged and rapidly spread through the population. We compare models across representative countries with different intensities of genomic surveillance. Retrospective assessment of model accuracy highlights that most models of variant frequency perform well and are able to produce reasonable forecasts. We find that the simple MLR model provides ∼0.6% median absolute error and ∼6% mean absolute error when forecasting 30 days out for countries with robust genomic surveillance. We investigate impacts of sequence quantity and quality across countries on forecast accuracy and conduct systematic downsampling to identify that 1000 sequences per week is fully sufficient for accurate short-term forecasts. We conclude that fitness models represent a useful prognostic tool for short-term evolutionary forecasting. Author summary: Over the course of the COVID-19 pandemic, SARS-CoV-2 evolved into many different genetic variants such as the well known Alpha, Beta, Gamma and Delta variants in early 2021 and the Omicron variant in late 2021. These genetic variants could more easily spread from person to person and so outcompeted previous versions of the virus. Even if they aren't being given Greek letter names, new variants are still arising with recent waves of COVID-19 caused by variants such as XBB and JN.1. Predicting which variants will increase in frequency and which variants will decrease in frequency is important for public health, particularly in terms of updating the formulation of the annual COVID-19 vaccine. In this paper, we investigate statistical models that use observed frequencies of different variants in the past weeks to estimate the frequency of different variants today and to forecast the frequency of different variants in 30 days time. We find that in countries with sufficient amounts and timeliness of genetic sequence data, that models forecast well and can be a useful tool for public health. [ABSTRACT FROM AUTHOR]

Acoustic telemetry is a common tool used in fisheries management to estimate fish space use (i.e., occupancy) from a local habitat scale to entire systems. Numerous analytical models have been developed to estimate different aspects of fish movement from telemetry datasets, yet evaluations of model performance and comparisons among models are limited. Here, we develop a framework to evaluate model estimates of regional occupancy in large and fragmented systems using an acoustic receiver array in Lake Champlain. We simulated the tracks of 100 acoustically tagged fish using a random walk function and created detection events based on receiver positions and distance-based detection probability. Regional occupancy for the simulated data was estimated by six movement models that ranged in analytical complexity, and results were compared to the true distributions for each simulated track to evaluate model error. The six movement models included: (1) a basic residency index using detections alone; (2) a residency index using last-observation-carried-forward; (3) a centers of activity model; (4) linear and non-linear interpolations (i.e., least-cost paths); and (5 and 6) two dynamic Brownian bridge movement models generated using separate packages in R. We developed a model selection process to compare model performance and select the optimal analysis based on simulation error. This process showed significant differences in model performance among the six movement models based on model error. Overall, the model generating least-cost paths using linear and non-linear interpolations consistently provided the most accurate regional occupancy estimates. Based on these simulation results, we applied this model to a case study that evaluated patterns in the regional distribution of stocked lake trout (Salvelinus namaycush) in Lake Champlain, which demonstrated distinct regional occupancy of two stocked lake trout groups. These results demonstrate potential for large variability in interpretation of acoustic telemetry data for describing regional fish distribution dependent on the analytical method used. [ABSTRACT FROM AUTHOR]

The ERW model was introduced twenty years ago to study memory effects in a one-dimensional discrete-time random walk with a complete memory of its past throughout a parameter p between zero and one. Several variations of the ERW model have recently been introduced. In this work, we investigate the asymptotic normality of the ERW model with a random step size and gradually increasing memory and delays. In particular, we extend some recent results in this subject. [ABSTRACT FROM AUTHOR]

Adaptive spiral flight and multi-strategy fusion are the foundations of a new FOX optimization algorithm that aims to address the drawbacks of the original method, including weak starting individual ergodicity, low diversity, and an easy way to slip into local optimum. In order to enhance the population, inertial weight is added along with Levy flight and variable spiral strategy once the population is initialized using a tent chaotic map. To begin the process of implementing the method, the fox population position is initialized using the created Tent chaotic map in order to provide more ergodic and varied individual beginning locations. To improve the quality of the solution, the inertial weight is added in the second place. The fox random walk mode is then updated using a variable spiral position updating approach. Subsequently, the algorithm's global and local searches are balanced, and the Levy flying method and greedy approach are incorporated to update the fox location. The enhanced FOX optimization technique is then thoroughly contrasted with various swarm intelligence algorithms using engineering application optimization issues and the CEC2017 benchmark test functions. According to the simulation findings, there have been notable advancements in the convergence speed, accuracy, and stability, as well as the jumping out of the local optimum, of the upgraded FOX optimization algorithm. [ABSTRACT FROM AUTHOR]

We present the Gaussian Mixture Periodicity Detection Algorithm (GMPDA), a novel method for detecting periodicity in the binary time series of event onsets. The GMPDA addresses the periodicity detection problem by inferring parameters of a generative model. We introduce two models, the Clock Model and the Random Walk Model, which describe distinct periodic phenomena and provide a comprehensive generative framework. The GMPDA demonstrates robust performance in test cases involving single and multiple periodicities, as well as varying noise levels. Additionally, we evaluate the GMPDA on real-world data from recorded leg movements during sleep, where it successfully identifies expected periodicities despite high noise levels. The primary contributions of this paper include the development of two new models for generating periodic event behavior and the GMPDA, which exhibits high accuracy in detecting multiple periodicities even in noisy environments. [ABSTRACT FROM AUTHOR]

In this current paper, we propose to study a three-dimensional Moran model (X n (1) , X n (2) , X n (3)) , where each random walk (X n (i)) ∈ { 1 , 2 , 3 } increases by one unit or is reset to zero at each unit of time. We analyze the joint law of its final altitude X n = max (X n (1) , X n (2) , X n (3)) via the moment generating tools. Furthermore, we show that the limit distribution of each random walk follows a shifted geometric distribution with parameter 1 − q i , and we analyze the maximum of these three walks, also giving explicit expressions for the mean and variance. [ABSTRACT FROM AUTHOR]

Exploring drought stress-responsive genes in rice is essential for breeding drought-resistant varieties. Rice drought resistance is controlled by multiple genes, and mining drought stress-responsive genes solely based on single omics data lacks stability and accuracy. Multi-omics correlation analysis and biological molecular network analysis provide robust solutions. This study proposed a random walk with a multi-restart probability (RWMRP) algorithm, based on the Restarted Random Walk (RWR) algorithm, to operate on rice MultiPlex biological networks. It explores the interactions between biological molecules across various levels and ranks potential genes. RWMRP uses eigenvector centrality to evaluate node importance in the network and adjusts the restart probabilities accordingly, diverging from the uniform restart probability employed in RWR. In the random walk process, it can be better to consider the global relationships in the network. Firstly, we constructed a MultiPlex biological network by integrating the rice protein–protein interaction, gene pathway, and gene co-expression network. Then, we employed RWMRP to predict the potential genes associated with rice tolerance to drought stress. Enrichment and correlation analyses resulted in the identification of 12 drought-related genes. We further conducted quantitative real-time polymerase chain reaction (qRT-PCR) analysis on these 12 genes, ultimately identifying 10 genes responsive to drought stress. [ABSTRACT FROM AUTHOR]

Influence maximization in online social networks is used to select a set of influential seed nodes to maximize the influence spread under a given diffusion model. However, most existing proposals have huge computational costs and only consider the dyadic influence relationship between two nodes, ignoring the higher-order influence relationships among multiple nodes. It limits the applicability and accuracy of existing influence diffusion models in real complex online social networks. To this end, in this paper, we present a novel information diffusion model by introducing hypergraph theory to determine the most influential nodes by jointly considering adjacent influence and higher-order influence relationships to improve diffusion efficiency. We mathematically formulate the influence maximization problem under higher-order influence relationships in online social networks. We further propose a hypergraph sampling greedy algorithm (HSGA) to effectively select the most influential seed nodes. In the HSGA, a random walk-based influence diffusion method and a Monte Carlo-based influence approximation method are devised to achieve fast approximation and calculation of node influences. We conduct simulation experiments on six real datasets for performance evaluations. Simulation results demonstrate the effectiveness and efficiency of the HSGA, and the HSGA has a lower computational cost and higher seed selection accuracy than comparison mechanisms. [ABSTRACT FROM AUTHOR]

Small molecules (SMs) play a pivotal role in regulating microRNAs (miRNAs). Existing prediction methods for associations between SM–miRNA have overlooked crucial aspects: the incorporation of local topological features between nodes, which represent either SMs or miRNAs, and the effective fusion of node features with topological features. This study introduces a novel approach, termed high-order topological features for SM–miRNA association prediction (HTFSMMA), which specifically addresses these limitations. Initially, an association graph is formed by integrating SM–miRNA association data, SM similarity, and miRNA similarity. Subsequently, we focus on the local information of links and propose target neighborhood graph convolutional network for extracting local topological features. Then, HTFSMMA employs graph attention networks to amalgamate these local features, thereby establishing a platform for the acquisition of high-order features through random walks. Finally, the extracted features are integrated into the multilayer perceptron to derive the association prediction scores. To demonstrate the performance of HTFSMMA, we conducted comprehensive evaluations including five-fold cross-validation, leave-one-out cross-validation (LOOCV), SM-fixed local LOOCV, and miRNA-fixed local LOOCV. The area under receiver operating characteristic curve values were 0.9958 ± 0.0024 (0.8722 ± 0.0021), 0.9986 (0.9504), 0.9974 (0.9111), and 0.9977 (0.9074), respectively. Our findings demonstrate the superior performance of HTFSMMA over existing approaches. In addition, three case studies and the DeLong test have confirmed the effectiveness of the proposed method. These results collectively underscore the significance of HTFSMMA in facilitating the inference of associations between SMs and miRNAs. [ABSTRACT FROM AUTHOR]

Since 2013, the International GNSS Service (IGS) real-time service (RTS) has been providing precise orbit and clock corrections for ten years, which enables real-time positioning at the decimeter level. High precision positioning relies heavily on accurate orbit and clock. However, constrained by the relatively short observation duration, the accuracy of real-time products are often worse than the final products. Previous studies indicate that compensating for errors in orbit and clock can improve positioning accuracy. Based on this theory, we proposed an improved positioning model, which incorporates the signal-in-space range error (SISRE) into the ionosphere-free combination observation equation and treats it as a parameter in the Kalman filter. Through the analysis of SISRE, we find that the time-varying characteristic of the parameter follows a random walk assumption. To find the optimal parameter settings of the SISRE parameters, a two-dimensional sensitivity analysis is employed, and a set of recommended values are provided. In the simulated kinematic positioning experiments, the proposed method achieves positioning accuracies of 17.3 cm, 19.6 cm, and 18.0 cm for GPS, BDS-3, and Galileo, respectively, representing a 10–20 % improvement over traditional methods. In real-time PPP experiment, the accuracy reaches 21.7 cm, indicating a 12.9 % improvement compared to traditional methods. [ABSTRACT FROM AUTHOR]

Experiments to measure a single molecule/particle, i.e., an individual molecule/particle, at room temperature or under physiological conditions without immobilization—for example, on a surface or without significant hydrodynamic flow—have so far failed. This failure has given impetus to the underlying theory of Brownian molecular motion towards its stochastics due to diffusion. Quantifying the thermodynamic jitter of molecules/particles inspires many and forms the theoretical basis of single-molecule/single-particle biophysics and biochemistry. For the first time, our simulation results for a live cell (cytoplasm) show that the tracks of individual single molecules are localized in Brownian motion, while there is fanning out in fractal diffusion (anomalous diffusion). [ABSTRACT FROM AUTHOR]

In response to the challenging conditions that arise after natural disasters, multi-robot systems are utilized as alternatives to humans for searching and rescuing victims. Exploring unknown environments is crucial in mobile robotics, serving as a foundational stage for applications such as search and rescue, cleaning tasks, and foraging. In our study, we introduced a novel search strategy for multi-robot search and rescue operations. This strategy draws inspiration from the hunting behavior of penguins and combines the Penguin Search Optimization Algorithm with the Random Walk Algorithm to regulate the global and local search behaviors of the robots. To assess the strategy's effectiveness, we implemented it in the ARGoS multi-robot simulator and conducted a series of experiments. The results clearly demonstrate the efficiency and effectiveness of our proposed search strategy. [ABSTRACT FROM AUTHOR]