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

Pinning phenomena for long linear polymers have been studied for a long time. In 2009 Caravenna and Pétrélis (Electron J Probab 14(70):2038–2067, 2009) investigated the effect of a periodic and repulsive multi-interface medium on a (1 + 1) -directed polymer model, when the distance between consecutive interfaces scales with the length of the polymer and with a constant temperature. In this paper, we extend that model and consider weak repulsion, by letting both the temperature and the distance between interfaces scale with the length of the polymer. We obtain a full diagram for this model, showing the behaviour of the polymer depending on the scaling exponents associated to the repulsion and the spacing parameters. When the repulsion is not too weak compared to the interface spacing, we obtain different regimes that extend those obtained by Caravenna and Pétrélis, and either finitely or infinitely many interfaces are visited. When the two exponents match we obtain a diffusive regime with a non-trivial and temperature-dependent diffusion constant. Our key tools include the renewal approach used in the original paper as well as new sharp results on the simple random walk evolving between interfaces. [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]

The 6-vertex model holds significance in various mathematical and physical domains. The configurations of the 6-vertex model correspond to the paths in multigraphs. This article focuses on calculating the transition probability for the simple random walk on these multigraphs. An intriguing aspect of the findings is the utilization of continued fractions in the computation of the transition probability. [ABSTRACT FROM AUTHOR]

Link prediction is a network analysis model used to discover missing links or future relationships that may appear, which has been widely used in many real network systems to predict the potential relationship between two individuals. However, link prediction can also be used by attackers to identify sensitive links that users are unwilling to expose, which makes only removing sensitive links from the original network ineffective and leads to the disclosure of privacy. In this paper, we propose a target link protection mechanism via artificial bee colony algorithm based on random walk (RABC), which can defend the link prediction attacks based on resource allocation (RA) metric effectively. To enhance the local search ability of RABC, the random walk algorithm is combined with the original artificial bee colony algorithm. Then, we compare our method with other existing methods, which shows that RABC has higher efficiency while ensuring the effectiveness. Finally, extensive experiments on real social networks are conducted to demonstrate the good performance of RABC on protecting sensitive links from being detected successfully by link prediction model. Furthermore, the perturbed networks generated by RABC is transferable to defend against other link prediction attacks. [ABSTRACT FROM AUTHOR]

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

Accurate positioning using the Global Positioning System relies on accurate modeling of tropospheric delay. Estimated tropospheric delay must vary sufficiently to capture true variations; otherwise, systematic errors propagate into estimated positions, particularly the vertical. However, if the allowed delay variation is too large, the propagation of data noise into all parameters is amplified, reducing precision. Here we investigate the optimal choice of tropospheric constraints applied in the GipsyX software, which are specified by values of random walk process noise. We use the variability of 5-min estimated positions as a proxy for tropospheric error. Given that weighted mean 5-min positions closely replicate 24-h solutions, our ultimate goal is to improve 24-h positions and other daily products, such as precise orbit parameters. The commonly adopted default constraint for the zenith wet delay (ZWD) is 3 mm/√(hr) for 5-min data intervals. Using this constraint, we observe spurious wave-like patterns of 5-min vertical displacement estimates with amplitudes ~ 100 mm coincident with Winter Storm Ezekiel of November 27, 2019, across the central/eastern USA. Loosening the constraint suppresses the spurious waves and reduces 5-min vertical displacement variability while improving water vapor estimates. Further improvement can be achieved when optimizing constraints regionally, or for each station. Globally, results are typically optimized in the range of 6–12 mm/√(hr). Generally, we at least recommend loosening the constraint from the current default of 3 mm/√(hr) to 6 mm/√(hr) for ZWD every 300 s. Constraint values must be scaled by √(x/300) for alternative data intervals of x seconds. [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]

Over the last few years, network science has proved to be useful in modelling a variety of complex systems, composed of a large number of interconnected units. The intricate pattern of interactions often allows the system to achieve complex tasks, such as synchronization or collective motions. In this regard, the interplay between network structure and dynamics has long been recognized as a cornerstone of network science. Among dynamical processes, random walks are undoubtedly among the most studied stochastic processes. While traditionally, the random walkers are assumed to be independent, this assumption breaks down if nodes are endowed with a finite carrying capacity, a feature shared by many real-life systems. Recently, a class of nonlinear diffusion processes accounting for the finite carrying capacities of the nodes was introduced. The stationary nodes densities were shown to be nonlinearly correlated with the nodes degrees, allowing to uncover the network structure by performing a few measurements of the stationary density at the level of a single arbitrary node and by solving an inverse problem. In this work, we extend this class of nonlinear diffusion processes to the case of multigraphs, in which links between nodes carry distinct attributes. Assuming the knowledge of the pattern of interactions associated with one type of links, we show how the degree distribution of the whole multigraph can be reconstructed. The effectiveness of the reconstruction algorithm is demonstrated through simulations on various multigraph topologies. [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]

Typically, honeybees (Apis mellifera L.), rely on waggle dances performed by scout bees to communicate information about fruitful nectar and pollen sources across the landscape. However, when this communication is absent, inaccurate, or when resources become depleted, bees resort to alternative search strategies. Field experiments utilizing harmonic radar have revealed that honeybees follow flight patterns that demonstrate a scale-free (Lévy-flight) behavior, representing an optimal search strategy for relocating the original feeder location. If honeybees adhere to a Lévy flight pattern to discover resources, where would honeybees demonstrate the highest flower visitation rates in agricultural landscapes? We generated simulated landscapes with varying proportions of forest cover scenarios, ranging from 5 to 50% of the total landscape area, along with different levels of fragmentation per se. Subsequently, we constrained the richness of flower farm cells in each landscape. To predict honeybee visitation rates, three different methodologies based on random movement were utilized: (1) moving window, (2) random walk, and (3) Lévy flight. We found that honeybee visitation rates were influenced by the degree of forest fragmentation in each scenario. Across all visitation scenarios, the highest average number of visited flowers per cell was observed in landscapes with maximum fragmentation per se. In landscapes with lower forest cover and higher fragmentation, honeybees were more likely to visit a greater number of flowers due to the increased probability of traversing the landscape and encountering more flower cells. honeybee visitation rates in agricultural landscapes are significantly influenced by the degree of forest fragmentation. The study highlights the importance of considering landscape structure, specifically forest fragmentation, when predicting honeybee visitation rates and underscores the need for further research to better understand the intricate relationship between landscape characteristics and pollinator behavior. [ABSTRACT FROM AUTHOR]

Summary: The wireless sensor network (WSN) has been assimilated into modern society and is utilized in many crucial application domains, including animal monitoring, border surveillance, asset monitoring, and so forth. These technologies aid in protecting the place of the event's occurrence from the adversary. Maintaining privacy concerning the source location is challenging due to the sensor nodes' limitations and efficient routing strategies. Hence, this research introduces a novel source location privacy preservation using the awareness‐based Gannet with random‐Dijkstra's algorithm (AGO‐RD). The network is initialized by splitting the hotspot and non‐hotspot region optimally using the proposed awareness‐based Gannet (AGO) algorithm. Here, the multi‐objective fitness function is utilized to initialize the network based on factors like throughput, energy consumption, latency, and entropy. Then, the information is forwarded to the phantom node in the non‐hotspot region to preserve the source location's privacy, which is far from the sink node. The proposed random‐Dijkstra algorithm is utilized to route the information from the phantom node to the sink with more security. Analysis of the proposed AGO‐RD‐based source location privacy preservation technique in terms of delay, throughput, network lifetime, and energy consumption accomplished the values of 6.52 ms, 95.68%, 7109.9 rounds, and 0.000125 μJ. [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]

Growth in agricultural total factor productivity (TFP), which explains most of the long‐term growth in U.S. agricultural output, may be slowing. The Economic Research Service (ERS) of the USDA is confident that current levels of below‐average growth will eventually regain the long‐term trend line. Others disagree, arguing instead that due to declining public expenditures on agricultural research, TFP growth experienced a downward and seemingly permanent structural shift about 30 years ago. In this paper, I argue that neither perspective is accurate since agricultural TFP is best modeled as a random walk with drift and thus not governed by a deterministic trend line. When I use a first difference model to accommodate the unit root, I do not find a structural break in the rate of drift. However, I acknowledge that this finding may not be general because I show that my test for a structural break has low power. To add theoretical relevance, I develop a simple model of stochastic innovation and farm technology adoption, and then use simulation results from my model to explain why a random walk for agricultural TFP is a theoretically sound proposition. [ABSTRACT FROM AUTHOR]

We establish laws of the iterated logarithm for intrinsic volumes of the convex hull of many-step, multidimensional random walks whose increments have two moments and a non-zero drift. Analogous results in the case of zero drift, where the scaling is different, were obtained by Khoshnevisan [Probab. Theory Related Fields 93 (1992), pp. 377–392]. Our starting point is a version of Strassen's functional law of the iterated logarithm for random walks with drift. For the special case of the area of a planar random walk with drift, we compute explicitly the constant in the iterated-logarithm law by solving an isoperimetric problem reminiscent of the classical Dido problem. For general intrinsic volumes and dimensions, our proof exploits a novel zero–one law for functionals of convex hulls of walks with drift, of some independent interest. As another application of our approach, we obtain iterated-logarithm laws for intrinsic volumes of the convex hull of the centre of mass (running average) process associated to the random walk. [ABSTRACT FROM AUTHOR]

We prove that the local time of random walks conditioned to stay positive converges to the corresponding local time of three-dimensional Bessel processes by proper scaling. Our proof is based on Tanaka's pathwise construction for conditioned random walks and the derivation of asymptotics for mixed moments of the local time. [ABSTRACT FROM AUTHOR]

In this paper, we show that traditional comparisons of mean squared prediction error (MSPE) between two competing forecasts may be highly controversial. This is so because when some specific conditions of efficiency are not met, the forecast displaying the lowest MSPE will also display the lowest correlation with the target variable. Given that violations of efficiency are usual in the forecasting literature, this opposite behavior in terms of accuracy and correlation with the target variable may be a fairly common empirical finding that we label here as "the MSPE paradox." We characterize "paradox zones" in terms of differences in correlation with the target variable and conduct some simple simulations to show that these zones may be non‐empty sets. Finally, we illustrate the relevance of the paradox with a few empirical applications. [ABSTRACT FROM AUTHOR]

The discovery of novel therapeutic targets, defined as proteins which drugs can interact with to induce therapeutic benefits, typically represent the first and most important step of drug discovery. One solution for target discovery is target repositioning, a strategy which relies on the repurposing of known targets for new diseases, leading to new treatments, less side effects and potential drug synergies. Biological networks have emerged as powerful tools for integrating heterogeneous data and facilitating the prediction of biological or therapeutic properties. Consequently, they are widely employed to predict new therapeutic targets by characterizing potential candidates, often based on their interactions within a Protein-Protein Interaction (PPI) network, and their proximity to genes associated with the disease. However, over-reliance on PPI networks and the assumption that potential targets are necessarily near known genes can introduce biases that may limit the effectiveness of these methods. This study addresses these limitations in two ways. First, by exploiting a multi-layer network which incorporates additional information such as gene regulation, metabolite interactions, metabolic pathways, and several disease signatures such as Differentially Expressed Genes, mutated genes, Copy Number Alteration, and structural variants. Second, by extracting relevant features from the network using several approaches including proximity to disease-associated genes, but also unbiased approaches such as propagation-based methods, topological metrics, and module detection algorithms. Using prostate cancer as a case study, the best features were identified and utilized to train machine learning algorithms to predict 5 novel promising therapeutic targets for prostate cancer: IGF2R, C5AR, RAB7, SETD2 and NPBWR1.

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

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

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

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

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

Abstract The study of drug–target interaction plays an important role in the process of drug development. The subject of DTI forecasting has advanced significantly in the last several years, yielding numerous significant research findings and methodologies. Heterogeneous data sources provide richer information and comprehensive perspectives for drug–target interaction prediction, so many existing methods rely on heterogeneous networks, and graph embedding technology becomes an important technology to extract information from heterogeneous networks. These approaches, however, are less concerned with potential noisy information in heterogeneous networks and more focused on the extent of information extraction in those networks. Based on this, a potential DTI predictive network model called FBRWPC is proposed in this paper. It uses a fine-grained similarity selection program to first integrate similarity on similar networks and then a bidirectional random walk graph embedding learning method with restart to obtain an updated drug target interaction matrix. Through the use of similarity selection and fine-grained selection similarity integration, the framework can effectively filter out the noise present in heterogeneous networks and enhance the model's prediction performance. The experimental findings demonstrate that, even after being split up into four distinct types of data sets, FBRWPC can still retain great prediction performance, a sign of the model's resilience and good generalization.

In recent years, with the strong development of information technology, detecting communities in large real networks is a very important issue which is of interest to many scientists. Community detection in large real networks with millions of nodes is often difficult. To solve this problem, many online community search algorithms have been proposed with many different approaches. One of the approaches is to coordinate the vertices of the graph and build a reasonable distance between those vertices. It has been observed that vertices in the same community have approximately the same probability of reaching other vertices through a random walk. Based on this principle, the authors propose a way to coordinate vertices and build distances between vertices in the graph that reduces computational complexity compared to existing techniques. This approach involves representing peaks as vectors and using the Kmeans++ algorithm for community detection, whose effectiveness is evaluated through experimental results presented.

In a previous work, we defined and studied random walk labelings of graphs. These are graph labelings that are obtainable by performing a random walk on the graph, such that each vertex is labeled upon its first visit. In this work, we calculate the number of random walk labelings of several natural graph families: The wheel, fan, barbell, lollipop, tadpole, friendship, and snake graphs. Additionally, we prove several combinatorial identities that emerged during the calculations. [ABSTRACT FROM AUTHOR]

The study of drug–target interaction plays an important role in the process of drug development. The subject of DTI forecasting has advanced significantly in the last several years, yielding numerous significant research findings and methodologies. Heterogeneous data sources provide richer information and comprehensive perspectives for drug–target interaction prediction, so many existing methods rely on heterogeneous networks, and graph embedding technology becomes an important technology to extract information from heterogeneous networks. These approaches, however, are less concerned with potential noisy information in heterogeneous networks and more focused on the extent of information extraction in those networks. Based on this, a potential DTI predictive network model called FBRWPC is proposed in this paper. It uses a fine-grained similarity selection program to first integrate similarity on similar networks and then a bidirectional random walk graph embedding learning method with restart to obtain an updated drug target interaction matrix. Through the use of similarity selection and fine-grained selection similarity integration, the framework can effectively filter out the noise present in heterogeneous networks and enhance the model's prediction performance. The experimental findings demonstrate that, even after being split up into four distinct types of data sets, FBRWPC can still retain great prediction performance, a sign of the model's resilience and good generalization. [ABSTRACT FROM AUTHOR]

We study the mixing time of a random walker who moves inside a dynamical random cluster model on the d-dimensional torus of side-length n. In this model, edges switch at rate μ between open and closed, following a Glauber dynamics for the random cluster model with parameters p, q. At the same time, the walker jumps at rate 1 as a simple random walk on the torus, but is only allowed to traverse open edges. We show that for small enough p the mixing time of the random walker is of order n 2 / μ . In our proof we construct a non-Markovian coupling through a multi-scale analysis of the environment, which we believe could be more widely applicable. [ABSTRACT FROM AUTHOR]

A complex network is an abstract modeling of complex systems in the real world, which plays an important role in analyzing the function of complex systems. Community detection is an important tool for analyzing network structure. In this paper, we propose a new community detection algorithm (RWBS) based on different seed nodes which aims to understand the community structure of the network, which provides a new idea for the allocation of resources in the network. RWBS provides a new centrality metric ( M C ) to calculate node importance, which calculates the ranking of nodes as seed nodes. Furthermore, two algorithms are proposed for determining seed nodes on networks with and without ground truth, respectively. We set the number of steps for the random walk to six according to the six degrees of separation theory to reduce the running time of the algorithm. Since some traditional community detection algorithms may detect smaller communities, e.g., two nodes become one community, this may make the resource allocation unreasonable. Therefore, modularity (Q) is chosen as the optimization function to combine communities, which can improve the quality of detected communities. Final experimental results on real-world and synthetic networks show that the RWBS algorithm can effectively detect communities. [ABSTRACT FROM AUTHOR]

A celebrated result in probability theory is that a simple symmetric random walk on the d-dimensional lattice \mathbb {Z}^d is recurrent for d=1,2 and transient for d\geq 3. In this note, we derive a closed-form expression, in terms of the Lauricella function F_C, for the return probability for all d\geq 3. Previously, a closed-form formula had only been available for d=3. [ABSTRACT FROM AUTHOR]

The effectiveness of agricultural spraying processes depends considerably on the ability of the atomized droplets to reach the target site in the desired amount. In this work, two mathematical models to study the trajectories and deposition of atomized droplets are implemented and compared. On the one hand, a computational fluid dynamics (CFD) coupled with discrete phase model (DPM) is implemented to calculate the trajectories of atomized droplets and determine distances at which the droplets are deposited. The continuous phase (atmospheric air) is modelled by continuity, momentum, and energy equations. On the other hand, a Lagrangian random‐walk (LRW) model based on force and energy balances to predict the pulverization process of a nozzle is formulated and implemented in Python. Both models take into account the effects of drag, gravity, buoyancy, and evaporation on individual droplets, as well as the impact of atmospheric stability and dispersion. By tracking a large number of trajectories, meaningful estimates of dispersal statistics can be obtained. The LRW model accurately replicated the trajectories, deposition distances, and final diameters of atomized droplets for three atmospheric stability cases, compared with CFD simulation results. The results of both models agreed that 100 μm droplets were most susceptible to wind‐induced spray drift, depositing at the furthest distances from the nozzle. In addition, 50 μm droplets exhibited a significant tendency to evaporate entirely before reaching the ground. The LRW model is found to be a cost‐effective alternative for estimating spray drift compared to the computationally intensive CFD approach. [ABSTRACT FROM AUTHOR]

In this paper, we provide the mathematical foundation for an explicit and universal feature of cover time for a large class of random work processes, which was previously observed by Chupeau et al (2015 Nat. Phys. 11 844–7). Specifically, we rigorously establish that the fluctuations of the cover time, normalized by the mean first passage time, follow a Gumbel distribution, for finite-range, symmetric, irreducible random walks on a torus of dimension three or higher. The result contributes to a better understanding of cover-time behavior in random search processes, especially on the efficiency of exhaustive searches. Our approach builds upon the work of Belius (2013 Probab. Theory Relat. Fields 157 635–89) on cover times for simple random walks, leveraging a strong coupling between the random walk and random interlacements. [ABSTRACT FROM AUTHOR]

The study of matter fields on an ensemble of random geometries is a difficult problem still in need of new methods and ideas. We will follow a point of view inspired by probability theory techniques that relies on an expansion of the two point function as a sum over random walks. An analogous expansion for Fermions on non-Euclidean geometries is still lacking. Casiday et al (2022 Linear Multilinear Algebr. 72 325–65) proposed a classical 'Dirac walk' diffusing on vertices and edges of an oriented graph with a square root of the graph Laplacian. In contrast to the simple random walk, each step of the walk is given a sign depending on the orientation of the edge it goes through. In a toy model, we propose here to study the Green functions, spectrum and the spectral dimension of such 'Dirac walks' on the Bethe lattice, a d -regular tree. The recursive structure of the graph makes the problem exactly solvable. Notably, we find that the spectrum develops a gap and that the spectral dimension of the Dirac walk matches that of the simple random walk ( d s = 1 for d = 2 and d s = 3 for d ⩾ 3 ). [ABSTRACT FROM AUTHOR]

By the dimension reduction idea, overshoot for random walks, coupling and martingale arguments, we obtain a simpler and easily computable expression for the first-order correction constant between discrete harmonic measures for random walks with rotationally invariant step distribution in R d (d ≥ 2) and the corresponding continuous counterparts. This confirms and extends a conjecture in Jiang and Kennedy (J Theor Probab 30(4):1424–1444, 2017), and simplifies the related expression of Wang et al. (Bernoulli 25(3):2279–2300, 2019). Furthermore, we propose a universality conjecture on high-order corrections for error estimation between generalized discrete harmonic measures and their continuous counterparts, which generalizes the universality conjecture of the first-order correction in Kennedy (J Stat Phys 164(1):174–189, 2016); and we prove this conjecture heuristically for the rotationally invariant case, and also provide several examples of second-order error corrections to check the conjecture by a numerical simulation argument. [ABSTRACT FROM AUTHOR]

A random walk with counterbalanced steps is a process of partial sums Š(n) = X1 + • • • + Xn whose steps Xn are given recursively as follows. For each n ≥ 2, with a fixed probability p, Xn is a new independent sample from some fixed law μ, and with complementary probability 1 - p, Xn = -Xυ(n) counterbalances a previous step, with υ(n) uniform random pick from {1,...,n -1} We determine the asymptotic behavior of Š(n) in terms of p and the first two moments of μ. Our approach relies on a coupling with a reinforcement algorithm due to H. A. Simon, and on properties of random recursive trees and Eulerian numbers, which may be of independent interest. The method can be adapted to the situation where the step distribution μ belongs to the domain of attraction of a stable law. [ABSTRACT FROM AUTHOR]

The Grey Wolf Optimization Algorithm (GWO) is a member of the swarm intelligence algorithm family, which possesses the highlights of easy realization, simple parameter settings and wide applicability. However, in some large-scale application problems, the grey wolf optimization algorithm easily gets trapped in local optima, exhibits poor global exploration ability and suffers from premature convergence. Since grey wolf's update is guided only by the best three wolves, it leads to low population multiplicity and poor global exploration capacity. In response to the above issues, we design a multi-strategy collaborative grey wolf optimization algorithm (NOGWO). Firstly, we use a random walk strategy to extend the exploration scope and enhance the algorithm's global exploration capacity. Secondly, we add an opposition-based learning model influenced by refraction principle to generate an opposite solution for each population, thereby improving population multiplicity and preventing the algorithm from being attracted to local optima. Finally, to balance local exploration and global exploration and elevate the convergence effect, we introduce a novel convergent factor. We conduct experimental testing on NOGWO by using 30 CEC2017 test functions. The experimental outcomes indicate that compared with GWO and some swarm intelligence algorithms, NOGWO has better global exploration capacity and convergence accuracy. In addition, we also apply NOGWO to three engineering problems and an unmanned aerial vehicle path planning problem. The outcomes of the experiment suggest that NOGWO performs well in solving these practical problems. [ABSTRACT FROM AUTHOR]

The article offers a method for estimating the volatility covariance matrix of vectors of financial time series data using a change point approach. The proposed method supersedes general varying-coefficient parametric models, such as GARCH, whose coefficients may vary with time, by a change point model. In this study, an adaptive pointwise selection of homogeneous segments with a given right-end point by a local change point analysis is introduced. Sufficient conditions are obtained under which the maximum likelihood process is adaptive against the covariance estimate to yield an optimal rate of convergence with respect to the change size. This rate is preserved while allowing the jump size to diminish. Under these circumstances, argmax results of a two-sided negative Brownian motion or a two-sided negative drift random walk under vanishing and non-vanishing jump size regimes, respectively, provide inference for the change point parameter. Theoretical results are supported by the Monte–Carlo simulation study. A bivariate data on daily log returns of two US stock market indices as well as tri-variate data on daily log returns of three banks are analyzed by constructing confidence interval estimates for multiple change points that have been identified previously for each of the two data sets. [ABSTRACT FROM AUTHOR]

Purpose — The current study seeks to understand whether individual stock returns exhibit random movement and are not dependent (efficient at weak form) on fourteen out of sixteen actively traded Arab stock markets in the Middle East and North Africa (MENA) region, based on the size of the market value. Method — Various non-parametric methods, including autocorrelation test, variance ratio test, Phillips-Perron unit root test, and runs test, are used to assess the random walk hypothesis for daily data following the Covid-19 vaccination program. This analysis covers the period from January 3, 2021, to March 28, 2023. Result — The study results present evidence that all individual stock returns deviate from random walk behavior. However, only Kuwait, Jordan, and Palestine stock returns follow the random walk based on the run test results at a significance level of 10%. Therefore, it can be concluded that all stock returns are inefficient at the weak-form, suggesting that investors have opportunities for unexpected gains.. Practical implications — The findings of this study suggest that investors in the MENA region may have opportunities for unexpected gains, as individual stock returns deviate from random walk behavior, highlighting the importance of considering market dynamics and employing informed investment strategies. Additionally, policymakers could benefit from understanding the inefficiencies in stock returns to implement measures that promote market stability and efficiency. [ABSTRACT FROM AUTHOR]

We consider fractional integral operators (I − T) d , d ∈ (− 1 , 1) acting on functions g : Z ν → R , ν ≥ 1 , where T is the transition operator of a random walk on Z ν . We obtain the sufficient and necessary conditions for the existence, invertibility, and square summability of kernels τ (s ; d) , s ∈ Z ν of (I − T) d . The asymptotic behavior of τ (s ; d) as | s | → ∞ is identified following the local limit theorem for random walks. A class of fractionally integrated random fields X on Z ν solving the difference equation (I − T) d X = ε with white noise on the right-hand side is discussed and their scaling limits. Several examples, including fractional lattice Laplace and heat operators, are studied in detail. [ABSTRACT FROM AUTHOR]

We investigate three aspects of weak* convergence of the n-step distributions of random walks on finite volume homogeneous spaces $ G/\Gamma $ G / Γ of semisimple real Lie groups. First, we look into the obvious obstruction to the upgrade from Cesàro to non-averaged convergence: periodicity. We give examples where it occurs and conditions under which it does not. In a second part, we prove convergence towards Haar measure with exponential speed from almost every starting point. Finally, we establish a strong uniformity property for the Cesàro convergence towards Haar measure for uniquely ergodic random walks. [ABSTRACT FROM AUTHOR]

We discuss the qualitatively new properties of random walks on groups that arise in the situation when the entropy of the step distribution is infinite. [ABSTRACT FROM AUTHOR]

This paper deals with a reliability system hit by three types of shocks ranked as harmless, critical, or extreme, depending on their magnitudes, being below H 1 , between H 1 and H 2 , and above H 2 , respectively. The system's failure is caused by a single extreme shock or by a total of N critical shocks. In addition, the system fails under occurrences of M pairs of shocks with lags less than some δ (δ -shocks) in any order. Thus, the system fails when one of the three named cumulative damages occurs first. Thus, it fails due to the competition of the three associated shock processes. We obtain a closed-form joint distribution of the time-to-failure, shock count upon failure, δ -shock count, and cumulative damage to the system on failure, to name a few. In particular, the reliability function directly follows from the marginal distribution of the failure time. In a modified system, we restrict δ -shocks to those with small lags between consecutive harmful shocks. We treat the system as a generalized random walk process and use an embellished variant of discrete operational calculus developed in our earlier work. We demonstrate analytical tractability of our formulas which are also validated, through Monte Carlo simulation. [ABSTRACT FROM AUTHOR]

For any fixed real a > 0 and x ∈ R d , d ≥ 1 , we consider the real-valued random process (S n) n ≥ 0 defined by S 0 = a , S n = a + ln | g n ⋯ g 1 x | , n ≥ 1 , where the g k , k ≥ 1 , are i.i.d. nonnegative random matrices. By using the strategy initiated by Denisov and Wachtel to control fluctuations in cones of d-dimensional random walks, we obtain an asymptotic estimate and bounds on the probability that the process (S n) n ≥ 0 remains nonnegative up to time n and simultaneously belongs to some compact set [ b , b + ℓ ] ⊂ R ∗ + at time n. [ABSTRACT FROM AUTHOR]

In this paper, we consider (upward skip-free) discrete-time and discrete-space Markov additive chains (MACs) and develop the theory for the so-called W ~ and Z ~ scale matrices, which are shown to play a vital role in the determination of a number of exit problems and related fluctuation identities. The theory developed in this fully discrete set-up follows similar lines of reasoning as the analogous theory for Markov additive processes in continuous time and is exploited to obtain the probabilistic construction of the scale matrices, identify the form of the generating function and produce a simple recursion relation for W ~ , as well as its connection with the so-called occupation mass formula. In addition to the standard one- and two-sided exit problems (upwards and downwards), we also derive distributional characteristics for a number of quantities related to the one- and two-sided 'reflected' processes. [ABSTRACT FROM AUTHOR]

We consider an asymptotically stable multidimensional random walk S (n) = (S 1 (n) , ... , S d (n)) . For every vector x = (x 1 ... , x d) with x 1 ≥ 0 , let τ x : = min { n > 0 : x 1 + S 1 (n) ≤ 0 } be the first time the random walk x + S (n) leaves the upper half space. We obtain the asymptotics of p n (x , y) : = P (x + S (n) ∈ y + Δ , τ x > n) as n tends to infinity, where Δ is a fixed cube. From that, we obtain the local asymptotics for the Green function G (x , y) : = ∑ n p n (x , y) , as | y | and/or | x | tend to infinity. [ABSTRACT FROM AUTHOR]

We study the simple random walk on trees and give estimates on the mixing and relaxation times. Relying on a seminal result by Basu, Hermon and Peres characterizing cutoff on trees, we give geometric criteria that are easy to verify and allow to determine whether the cutoff phenomenon occurs. We provide a general characterization of families of trees with cutoff, and show how our criteria can be used to prove the absence of cutoff for several classes of trees, including spherically symmetric trees, Galton–Watson trees of a fixed height, and sequences of random trees converging to the Brownian continuum random tree. [ABSTRACT FROM AUTHOR]

We study a counterbalanced random walk S ˇ n = X ˇ 1 + ⋯ + X ˇ n , which is a discrete time non-Markovian process and X ˇ n are given recursively as follows. For n ≥ 2, X ˇ n is a new independent sample from some fixed law μ ≠ 0 with a fixed probability p, and X ˇ n = − X ˇ v (n) with probability 1 − p, where v(n) is a uniform random variable on {1, ⋯, n − 1}. We apply martingale method to obtain a strong invariance principle for Šn. [ABSTRACT FROM AUTHOR]