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In this paper we consider a generalization of the coupon collector problem where we assume that the set of available coupons consists of standard coupons and an additional penalty coupon, which does not belong to the collection and interferes with collecting standard coupons. Applying Markov chain approach the following problem is solved: how many coupons (on average) one has to purchase in order to complete a collection without interference or to collect n more penalty coupons than standard coupons. Also, we obtain additional results related to the distribution of the waiting time until the collection is sampled without interference or until n more penalty coupons than standard coupons is sampled. [ABSTRACT FROM AUTHOR]

Network embedding can effectively dig out potentially useful information and discover the relationships and rules which exist in the data, that has attracted increasing attention in many real-world applications. The goal of network embedding is to map high-dimensional and sparse networks into low-dimensional and dense vector representations. In this paper, we propose a network embedding method based on high-degree penalty and adaptive negative sampling (NEPS). First, we analyze the problem of imbalanced node training in random walk and propose an indicator base on high-degree penalty, which can control the random walk and avoid over-sampling high-degree neighbor node. Then, we propose a two-stage adaptive negative sampling strategy, which can dynamically obtain negative samples suitable for the current training according to the training stage to improve training effect. By comparing with seven well-known network embedding algorithms on eight real-world data sets, experiments show that the NEPS has good performance in node classification, network reconstruction and link prediction. The code is available at: https://github.com/Andrewsama/NEPS-master. [ABSTRACT FROM AUTHOR]

In this paper, we study (1,2) and (2,1) random walks in spatially inhomogeneous environments on the lattice of positive half line. We assume that the transition probabilities at site n are asymptotically constant as n → ∞. We get some elaborate limit behaviors of various escape probabilities and hitting probabilities of the walk. Such observations and some delicate analysis of continued fractions and the product of nonnegative matrices enable us to give criteria for finiteness of the number of cutpoints of both (1,2) and (2,1) random walks, which generalize Csáki et al. (J Theor Probab 23:624–638, 2010) and Wang (Markov Process Relat Fields 25:125–148, 2019). For near-recurrent random walks, we also study the asymptotics of the number of cutpoints in [0, n]. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Computer-Aided Design & Computer Graphics / Jisuanji Fuzhu Sheji Yu Tuxingxue Xuebao is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mining key nodes in complex networks has been a hotly debated topic as it played an important role in solving real-world problems.However, the existing key node mining algorithms focused on finding key nodes from a global perspective.This approach became problematic for large-scale social networks due to the unacceptable storage and computing resource overhead and the inability to utilize known query node information.A key node mining algorithm based on multiple query nodes was proposed to address the issue of key suspect mining.In this method, the known suspects were treated as query nodes, and the local topology was extracted.By calculating the critical degree of non-query nodes in the local topology, nodes with higher critical degrees were selected for recommendation.Aiming to overcome the high computational complexity of key node mining and the difficulty of effectively utilizing known query node information in existing methods, a two-stage key node mining algorithm based on multi-query was proposed to integrate the local topology information and the global node aggregation feature information of multiple query nodes.It reduced the calculation range from global to local and quantified the criticality of related nodes.Specifically, the local topology of multiple query nodes was obtained using the random walk algorithm with restart strategy.An unsupervised graph neural network model was constructed based on the graphsage model to obtain the embedding vector of nodes.The model combined the unique characteristics of nodes with the aggregation characteristics of neighbors to generate the embedding vector, providing input for similarity calculations in the algorithm framework.Finally, the criticality of nodes in the local topology was measured based on their similarity to the features of the query nodes.Experimental results demonstrated that the proposed algorithm outperformed traditional key node mining algorithms in terms of time efficiency and result effectiveness.

Vehicular transportation design and control are critical topics of research. In two-dimensional topological systems, edge states exist at the boundary and support transport along the system edges. In this study, we demonstrate the directional flow of vehicular traffic in a hexagonal street network with a two-dimensional topological structure. We model the network structure by the topology of vertices and edges, and vehicular transport as a symmetric random walk between the vertices. We show that the proposed structure provides a macroscopically unidirectional traffic flow to a group of vehicles. Furthermore, we note that such unidirectional properties deteriorate because of the decay of the topological edge mode. To overcome the disappearance of traffic unidirectionarity, we propose a strategy for controlling the entry–exit timing of vehicles in a street network and confirm its effectiveness through simulations. The proposed vehicle management strategy sustainably allows unidirectional traffic in street networks. Our work thus provides a critical building block for designing and controlling transportation networks.

In power systems, failures of vulnerable lines can trigger large-scale cascading failures, and vulnerability assessment is dedicated to locating these lines and reducing the risks of such failures. Based on a structure and attribute network embedding (SANE) algorithm, a novel quantitative vulnerability analysis method is proposed to identify vulnerable lines in this research. First, a two-layered random walk network with topological and electrical properties of transmission lines is established. Subsequently, based on the weighted degree of nodes in the two-layered network, the inter-layer and intra-layer walking transition probabilities are developed to obtain walk sequences. Then, a Word2Vec algorithm is applied to obtain low-dimension vectors representing transmission lines, according to obtained walk sequences for calculating the vulnerability index of transmissions lines. Finally, the proposed method is compared with three widely used methods in two test systems. Results show the network embedding based method is superior to those comparison methods and can provide guidance for identifying vulnerable lines.

Community discovery refers to the process of searching for clusters in a network that are sparsely connected to other nodes and formed dense connections internally. In many real networks, some communities often overlap with each other, meaning that a node may belong to multiple communities simultaneously. Revealing these (overlapping) community structures is an important issue in complex network analysis, as it helps to better analyze the characteristics and organizational structure of the network. Community expansion methods are very important in the study of community detection problems. However, one of the key issues in developing effective community expansion methods is that the position of seed nodes greatly affects the performance of these algorithms, resulting in low robustness of these algorithms. Meanwhile, it is also difficult for them to provide high-quality results for community detection task. To solve the above problem, this paper proposes a seed selection method based on the weak equiconcepts in a network formal context, which integrates the attribute information of nodes during random walk to detect overlapping communities. Specifically, the weak equiconcepts are constructed by establishing a network formal context to obtain seed sets, and an improved PageRank clustering algorithm is used to expand these seed sets to better reveal the overlapping community structure in the network. Experiments show that seed selection is helpful to improving the performance of overlapping community detection algorithms.

Plasma generation by cathodic arc spots plays a crucial role for coating processes that make use of the Arc-PVD technology. Usually, the arc spot motion over the cathode is steered by a magnetic field of a particular distribution and magnitude to ensure a continuous plasma generation, the avoidance of liquid droplets, and a proper utilization of cathode material by homogeneous erosion. This study presents a semi-empirical model that allows for an examination and characterization of the arc spot motion with regard to direction and speed as a function of an imposed magnetic field. This model considers the different components of random walk, retrograde, and Robson drift motion. Introduced empirical coefficients were determined by corresponding experimental investigations. The calibrated model describes the arc spot motion in good agreement to the recorded spot tracks and can therefore be applied for an evaluation of different magnetic field configurations.

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.

The genomic positions of nucleosomes are a defining feature of the cell's epigenomic state, but signal-dependent transcription factors (SDTFs), upon activation, bind to specific genomic locations and modify nucleosome positioning. Here we leverage SDTFs as perturbation probes to learn about nucleosome dynamics in living cells. We develop Markov models of nucleosome dynamics and fit them to time course sequencing data of DNA accessibility. We find that (1) the dynamics of DNA unwrapping are significantly slower in cells than reported from cell-free experiments, (2) only models with cooperativity in wrapping and unwrapping fit the available data, (3) SDTF activity produces the highest eviction probability when its binding site is adjacent to but not on the nucleosome dyad, and (4) oscillatory SDTF activity results in high location variability. Our work uncovers the regulatory rules governing SDTF-induced nucleosome dynamics in live cells, which can predict chromatin accessibility alterations during inflammation at single-nucleosome resolution.

In complex networks, important nodes have a significant impact, both functional and structural. From the perspective of data flow pattern detection, the evaluation of the importance of a node in a network, taking into account the role it plays as a transition element in random paths between two other nodes, has important applications in many areas. Advances in complex networks and improved data generation are very important for the growth of computational materials science. The search for patterns of behavior of the elements that make up steels through complex networks can be very useful in understanding their mechanical properties. This work aims to study the influence of the connections between the elements of steel and the impact of these connections on their mechanical properties, more specifically on the yield strength. The patterns found in the results show the significance of the proposed approach for the development of new steel compositions. [ABSTRACT FROM AUTHOR]

This paper conducts a numerical analysis of the behavior of the average value of the Maximum Local Time, L n ∗ , in the Simple Random Walk on the square lattice. It has been established in the literature that the sequence ζ n : = (log n) 2 L n ∗ converges to π. The author found numerical evidence that the average value of ζ n ( ζ n ¯) increases until a certain value of n , denoted as n c , after which it decreases and approaches π. Furthermore, estimates are presented for n c and ζ n c ¯. [ABSTRACT FROM AUTHOR]

Graph products have been extensively applied to model complex networks with striking properties observed in real-world complex systems. In this paper, we study the hitting times for random walks on a class of graphs generated iteratively by edge corona product. We first derive recursive solutions to the eigenvalues and eigenvectors of the normalized adjacency matrix associated with the graphs. Based on these results, we further obtain interesting quantities about hitting times of random walks, providing iterative formulas for two-node hitting time, as well as closed-form expressions for the Kemeny's constant defined as a weighted average of hitting times over all node pairs, as well as the arithmetic mean of hitting times of all pairs of nodes. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Network & Information Security is the property of Beijing Xintong Media Co., Ltd. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

A time-continuous random walk on a multidimensional lattice which underlies the branching random walk with an infinite number of phase states is considered. The random walk with a countable number of states can be reduced to a system with a finite number of states by aggregating them. The asymptotic behavior of the residence time of the transformed system in each of the states depending on the lattice dimension under the assumption of a finite variance and under the condition leading to an infinite variance of jumps of the original system is studied. It is shown that the aggregation of states in terms of the described process leads to the loss of the Markov property. [ABSTRACT FROM AUTHOR]

Online reviews have a significant influence on consumers' purchasing decisions. Unfortunately, many sellers exploit these reviews by employing a large number of spammers who strategically craft fake reviews to enhance their own reputation or tarnish their competitors'. Although several models have been proposed to address this issue in recent years, they often overlook the importance of considering a combination of structural and behavioural features, focusing solely on either structural or textual aspects. To overcome these limitations, we propose a novel model for detecting organized spammer groups called the Fake Reviewers Groups Detection Model. This model comprehensively considers the network structure and reviewer behavioural features to identify such groups. By extracting user, product, review time, and rating information, we construct a heterogeneous information network using a Meta-graph, which explores user relationships. Then apply the Node Ranking Walk2Vec algorithm to generate random walks within this heterogeneous information network, enabling us to obtain low-dimensional vector representations of the user nodes. Subsequently, utilize the Gaussian fuzzy Cluster Means algorithm for clustering, thereby identifying candidate groups of reviewers. The dynamic weight of each detection indicator is determined using the entropy approach, allowing us to assign an appropriate rank to reviewer groups based on their level of suspiciousness and identify them as fake reviewer groups. [ABSTRACT FROM AUTHOR]

We consider the simple random walk (or Pólya walk) on the one-dimensional lattice subject to stochastic resetting to the origin with probability r at each time step. The focus is on the joint statistics of the numbers N t × of spontaneous returns of the walker to the origin and N t ∙ of resetting events up to some observation time t. These numbers are extensive in time in a strong sense: all their joint cumulants grow linearly in t, with explicitly computable amplitudes, and their fluctuations are described by a smooth bivariate large deviation function. A non-trivial crossover phenomenon takes place in the regime of weak resetting and late times. Remarkably, the time intervals between spontaneous returns to the origin of the reset random walk form a renewal process described in terms of a single 'dressed' probability distribution. These time intervals are probabilistic copies of the first one, the 'dressed' first-passage time. The present work follows a broader study, covered in a companion paper, on general nested renewal processes. [ABSTRACT FROM AUTHOR]

We tracked locations of three fish species in two bays with differing hydrology in SW Florida in 2018–2020 to test the hypotheses about fish residency, movements, and environmental variables. Due to extensive watershed modification, one bay receives less freshwater and the other receives more relative to natural conditions. Home range duration differed for gray snapper (54 ± 6 days), red drum (132 ± 39), and goliath grouper (226 ± 63). Distances between relocation movements were similar for gray snapper and red drum (~ 1.2 km), but farther for goliath grouper (2.3 ± 0.3 km). Relocations were primarily seaward for gray snapper (83%) but varied for the other species. Home range duration related to age for goliath grouper (< 100 days for 1–1.5-year-olds, 300–425 days for 4–4.5-year-olds). Generalized additive models marginally related probability of gray snapper relocating to salinity and temperature whereas relocations of the other species occurred during all environmental conditions. Movement simulations lacking environmental cues produced similar emigration patterns as observed in tagged fish. Overall, results suggest that movements here are not strongly linked to environmental conditions, will be resilient to watershed restoration that should moderate salinity, and have implications for understanding the impacts of localized depletion due to recreational fishing. [ABSTRACT FROM AUTHOR]

In this article we study a one dimensional model for a polymer in a poor solvent: the random walk on Z penalized by its range. More precisely, we consider a Gibbs transformation of the law of the simple symmetric random walk by a weight exp(-hn|Rn|), with |Rn| the number of visited sites and hn a size-dependent positive parameter. We use gambler's ruin estimates to obtain exact asymptotics for the partition function, that enables us to obtain a precise description of trajectories, in particular scaling limits for the center and the amplitude of the range. A phase transition for the fluctuations around an optimal amplitude is identified at hn n1/4, inherent to the underlying lattice structure. [ABSTRACT FROM AUTHOR]

The large deviations rate function Λ(d) of d-dimensional symmetric simple random walk S(d)(n) describes the log-asymptotic behavior of the fundamental probability P(S(d)(n) = x) in the large deviations regime, that is, when n = O || |x|), but also in the so-called moderate deviations regime, that is, when n1/2 = o(|x|) and |x| = o(n). In Beneš (2019), we provided precise asymptotics for P(S(d)(n) = x) in dimensions 1 and 2 and, as an immediate consequence, we obtained (d) for d = 1 and d = 2. The techniques developed in that paper do not translate readily to higher dimensions. In the present paper, we show that for d Z+, (d)(a) = log d + 1 2 Xd i=1 (ai + ai) log(ai + ai) + (ai - ai) log(ai - ai), where a = (a1, . . ., ad) satisfies Pd i=1 |ai| = 1. The quantities ai = ai(a) are not explicit but are given in terms of the solution of a system of quadratic equations. This result represents partial progress towards the generalization of the results in Beneš (2019) to any dimension d Z+. [ABSTRACT FROM AUTHOR]

Copyright of Financial Research Journal (FRJ) is the property of University of Tehran, Faculty of Management and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The large deviations rate function Λ(d) of d-dimensional symmetric simple random walk S(d)(n) describes the log-asymptotic behavior of the fundamental probability P(S(d)(n) = x) in the large deviations regime, that is, when n = O || |x|), but also in the so-called moderate deviations regime, that is, when n1/2 = o(|x|) and |x| = o(n). In Beneš (2019), we provided precise asymptotics for P(S(d)(n) = x) in dimensions 1 and 2 and, as an immediate consequence, we obtained (d) for d = 1 and d = 2. The techniques developed in that paper do not translate readily to higher dimensions. In the present paper, we show that for d Z+, (d)(a) = log d + 1 2 Xd i=1 (ai + ai) log(ai + ai) + (ai - ai) log(ai - ai), where a = (a1, . . ., ad) satisfies Pd i=1 |ai| = 1. The quantities ai = ai(a) are not explicit but are given in terms of the solution of a system of quadratic equations. This result represents partial progress towards the generalization of the results in Beneš (2019) to any dimension d Z+. [ABSTRACT FROM AUTHOR]

A graph neural network-based recommendation system treats the relationship between user items as a graph, and achieves deep feature mining by modelling the graph nodes. However, the complexity of the features of graph neural network-based recommendation systems brings poor interpretability and suffers from data sparsity problems. To address the above problems, a graph convolutional neural network recommendation model (RWESA-GNNR) based on random walk embedding combined with sentiment analysis is proposed. Firstly, a random walk-based matrix factorization is designed as the initial embedding. Secondly, the user and item nodes are modelled using a convolutional neural network with an injected attention mechanism. Then, sentiment analysis is performed on the review text, and attention mechanism is introduced to fuse text sentiment features and semantic features. Finally, node features and text features are aggregated to generate recommendation results. The experimental results show that our proposed algorithm outperforms traditional recommendation algorithms and other graph neural network-based recommendation algorithms in terms of recommendation results, with an improvement of about 2.43%-5.75%. [ABSTRACT FROM AUTHOR]

Social Internet of Things (SIoT) has the ability to create object-to-object interconnections (sensors, transceivers, actuators, etc.), which is a relatively difficult process in traditional Internet of Things(IoT). It widens the practical usability of IoT by exploiting the interconnections between heterogeneous objects. With the expansion in multiple domains, the threat to privacy goes hand in hand. Source location privacy is a critical concern in recent times. Data transmission through wireless channels leads attackers to continuously eavesdrop and backtrack to discover the source node. Source location discovery by attackers can cost the asset's life and is highly undesirable. To address the need for source location privacy preservation (SLP), this paper presents two novel grid-based schemes i.e. Vertical Random Greedy (VRG) and Randomized Interference Horizontal Routing (RIHR). VRG makes use of vertical walk followed by randomized routing, and greedy approach to route the event packets to the base station successfully. RIHR makes use of interference ring routing followed by a horizontal walk, and then the equidistant phase finally followed by greedy routing. The simulated results prove that in comparison to Phantom Routing based L-Path Random Walk (PRLPRW), the safety period improves by 4.7% and 17%, and the network lifetime is enhanced by 86% and 81.78% for VRG and RIHR, respectively. [ABSTRACT FROM AUTHOR]

With the use of daily panel data for industrial countries, we study the essentialness of liquidity premiums and interest rate differentials in predicting nominal exchange rates at short horizons. We find that information about higher‐order moments of exchange rates helps predict nominal exchange rates. Before the global financial crisis, interest rate differentials were crucial for forecasting exchange rates. Interest rate differentials and liquidity premia provide additional information for predicting nominal exchange rates in the post‐crisis period even if we have controlled for latent fundamental exchange rates. Moreover, the economic significance analysis results echo those of the statistical significance analysis. [ABSTRACT FROM AUTHOR]

The simple random walk on Z p shows two drastically different behaviors depending on the value of p : it is recurrent when p ∈ { 1 , 2 } while it escapes (with a rate increasing with p) as soon as p ≥ 3. This classical example illustrates that the asymptotic properties of a random walk provides some information on the structure of its state space. This paper aims to explore analogous questions on space made up of combinatorial objects with no algebraic structure. We take as a model for this problem the space of unordered unlabeled rooted trees endowed with Zhang edit distance. To this end, it defines the canonical unbiased random walk on the space of trees and provides an efficient algorithm to evaluate its escape rate. Compared to Zhang algorithm, it is incremental and computes the edit distance along the random walk approximately 100 times faster on trees of size 500 on average. The escape rate of the random walk on trees is precisely estimated using intensive numerical simulations, out of reasonable reach without the incremental algorithm. [ABSTRACT FROM AUTHOR]

Consider a sequence (X n) n ≥ 1 of i.i.d. 2 × 2 stochastic matrices with each X n distributed as μ. This μ is described as follows. Let (C n , D n) T denote the first column of X n and for a given real r with 0 < r < 1 , let r − 1 C n and r − 1 D n each be Bernoulli distributions with parameters p 1 and p 2 , respectively, and 0 < p 1 , p 2 < 1 . Clearly, the weak limit of the sequence μ n , namely λ , is known to exist, whose support is contained in the set of all 2 × 2 rank one stochastic matrices. In a previous paper, we considered 0 < r ≤ 1 2 and obtained λ explicitly. We showed that λ is supported countably on many points, each with positive λ -mass. Of course, the case 0 < r ≤ 1 2 is tractable, but the case r > 1 2 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r = 5 − 1 2 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation. [ABSTRACT FROM AUTHOR]

For change point models and autoregressive conditional heteroscedasticity (ARCH) models, which have long been important especially in econometrics, we develop information criteria that work well even when considering a combination of these models. Since the change point model does not satisfy the conventional statistical asymptotics, a formal Akaike information criterion (AIC) with twice the number of parameters as the penalty term would clearly result in overfitting. Therefore, we derive an AIC‐type information criterion from its original definition using asymptotics peculiar to the change point model. Specifically, we suppose time series data treated in econometrics and derive Takeuchi information criterion (TIC) as the main information criterion allowing for model misspecification. It is confirmed that the penalty for the change point parameter is almost three times larger than the penalty for the regular parameter. We also derive the AIC in this setting from the TIC by removing the consideration of the model misspecification. In numerical experiments, the derived TIC and AIC are compared with the formal AIC and Bayesian information criterion (BIC). It is shown that the derived information criteria clearly outperform the others in light of the original purpose of AIC, which is to give an estimate close to the true structure. We also ensure that the TIC seems to be superior to the AIC in the presence of model misspecification. [ABSTRACT FROM AUTHOR]

We count cycles of an unbounded length in generalized Johnson graphs. Asymptotics of the number of such cycles is obtained for certain growth rates of the cycle length. [ABSTRACT FROM AUTHOR]

A stochastic difference game is considered in which a player wants to minimize the time spent by a controlled one-dimensional symmetric random walk { X n , n = 0 , 1 , ... } in the continuation region C : = { 1 , 2 , ... } , and the second player seeks to maximize the survival time in C. The process starts at X 0 = x > 0 and the game ends the first time X n ≤ 0 . An exact expression is derived for the value function, from which the optimal solution is obtained, and particular problems are solved explicitly. [ABSTRACT FROM AUTHOR]

Critical genes of diseases can be used to diagnose diseases, predict and evaluate the effectiveness of new drugs or new therapies, so it is very important to identify critical genes closely related to diseases. However, the samples of some diseases are limited. It is difficult to apply the traditional methods based on large sample data to mine critical genes for these diseases. In this paper, for diseases with small amount of samples, we first construct sample-specific network for each sample with the single-sample network constructing methods, and construct a multilayer gene network by estabishing inter-layer connections between genes. A tensor-based multi-layer network centrality approach is then used to assess the interactions between genes in each layer of the network and the interlayer effects to score the genes for importance and identify disease key genes. Finally, the method is used to two asthma datasets and compared with the classical algorithm. The results show that compared with other methods, the approved drug target genes rank higher in the gene rankings obtained by this method. And function and pathway enrichment analysis of the new potential critical genes TP53, PUS10, MAP3K1, etc. indicat that they were closely related to asthma. [ABSTRACT FROM AUTHOR]

The inferred rate of default (IRD) was first introduced as an indicator of default risk computable from information publicly reported by the Bulgarian National Bank. We have provided a more detailed justification for the suggested methodology for forecasting the IRD on the bank-group- and bank-system-level based on macroeconomic factors. Furthermore, we supply additional empirical evidence in the time-series analysis. Additionally, we demonstrate that IRD provides a new perspective for comparing credit risk across bank groups. The estimation methods and model assumptions agree with current Bulgarian regulations and the IFRS 9 accounting standard. The suggested models could be used by practitioners in monthly forecasting the point-in-time probability of default in the context of accounting reporting and in monitoring and managing credit risk. [ABSTRACT FROM AUTHOR]

We tackle the problem of efficiently approximating the volume of convex polytopes, when these are given in three different representations: H-polytopes, which have been studied extensively, V-polytopes, and zonotopes (Z-polytopes). We design a novel practical Multiphase Monte Carlo algorithm that leverages random walks based on billiard trajectories, as well as a new empirical convergence test and a simulated annealing schedule of adaptive convex bodies. After tuning several parameters of our proposed method, we present a detailed experimental evaluation of our tuned algorithm using a rich dataset containing Birkhoff polytopes and polytopes from structural biology. Our open-source implementation tackles problems that have been intractable so far, offering the first software to scale up in thousands of dimensions for H-polytopes and in the hundreds for V- and Z-polytopes on moderate hardware. Last, we illustrate our software in evaluating Z-polytope approximations. [ABSTRACT FROM AUTHOR]

The paper is concerned with a new approach for the recurrence properties of the oscillating random walk on Z in the sense of Kemperman. In the case when the random walk is ascending on Z - and descending on Z + , the invariant measure of the embedded process of successive crossing times is explicitly determined, which yields a sufficient condition for recurrence. Finally, we make use of this result to show that the general oscillating random walk is recurrent under some moment assumptions. [ABSTRACT FROM AUTHOR]

We completely characterize when the free effective resistance of an infinite graph whose vertices have finite degrees can be expressed in terms of simple hitting probabilities of the random walk on the graph. [ABSTRACT FROM AUTHOR]

Many network presentation learning algorithms (NPLA) have originated from the process of the random walk between nodes in recent years. Despite these algorithms can obtain great embedding results, there may be also some limitations. For instance, only the structural information of nodes is considered when these kinds of algorithms are constructed. Aiming at this issue, a label and community information-based network presentation learning algorithm (LC-NPLA) is proposed in this paper. First of all, by using the community information and the label information of nodes, the first-order neighbors of nodes are reconstructed. In the next, the random walk strategy is improved by integrating the degree information and label information of nodes. Then, the node sequence obtained from random walk sampling is transformed into the node representation vector by the Skip-Gram model. At last, the experimental results on ten real-world networks demonstrate that the proposed algorithm has great advantages in the label classification, network reconstruction and link prediction tasks, compared with three benchmark algorithms. [ABSTRACT FROM AUTHOR]

Link prediction is a crucial area of study within complex networks research. Mapping nodes to low-dimensional vectors through network embeddings is a vital technique for link prediction. Most of the existing methods employ "node–edge"-structured networks to model the data and learn node embeddings. In this paper, we initially introduce the Clique structure to enhance the existing model and investigate the impact of introducing two Clique structures (LECON: Learning Embedding based on Clique Of the Network) and nine motifs (LEMON: Learning Embedding based on Motif Of the Network), respectively, on experimental performance. Subsequently, we introduce a hypergraph to model the network and reconfigure the network by mapping hypermotifs to two structures: open hypermotif and closed hypermotif, respectively. Then, we introduce hypermotifs as supernodes to capture the structural similarity between nodes in the network (HMRLH: HyperMotif Representation Learning on Hypergraph). After that, taking into account the connectivity and structural similarity of the involved nodes, we propose the Depth and Breadth Motif Random Walk method to acquire node sequences. We then apply this method to the LEMON (LEMON-DB: LEMON-Depth and Breadth Motif Random Walk) and HMRLH (HMRLH-DB: HMRLH-Depth and Breadth Motif Random Walk) algorithms. The experimental results on four different datasets indicate that, compared with the LEMON method, the LECON method improves experimental performance while reducing time complexity. The HMRLH method, utilizing hypernetwork modeling, proves more effective in extracting node features. The LEMON-DB and HMRLH-DB methods, incorporating new random walk approaches, outperform the original methods in the field of link prediction. Compared with state-of-the-art baselines, the proposed approach in this paper effectively enhances link prediction accuracy, demonstrating a certain level of superiority. [ABSTRACT FROM AUTHOR]

This paper discusses random walks on edge‐changing dynamic graphs. We prove general and improved bounds for mixing, hitting, and cover times for a random walk according to a sequence of irreducible and reversible transition matrices with the time‐invariant stationary distribution. An interesting consequence is the tight bounds of the lazy Metropolis walk on any dynamic connected graph. We also prove bounds for multiple random walks on dynamic graphs. Our results extend previous upper bounds for simple random walks on dynamic graphs and give improved and tight upper bounds in several cases. Our results reinforce the observation that time‐inhomogeneous Markov chains with an invariant stationary distribution behave almost identically to a time‐homogeneous chain. [ABSTRACT FROM AUTHOR]

We study the family of integral equations, called the Robin mean value equations (RMV), that are local averaged approximations to the Robin-Laplace boundary value problem (RL). When posed on C 1 , 1 -regular domains, we prove existence, uniqueness, equiboundedness and the comparison principle for solutions to (RMV). For the continuous right hand side of (RL), we show that solutions to (RMV) converge uniformly, in the limit of the vanishing radius of averaging, to the unique W2,p solution, which coincides with the unique viscosity solution of (RL). We further prove the lower bound on solutions to (RMV), which is consistent with the optimal lower bound for solutions to (RL). Our proofs employ martingale techniques, where (RMV) is interpreted as the dynamic programming principle along a suitable discrete stochastic process, interpolating between the reflecting and the stopped-at-exit Brownian walks. [ABSTRACT FROM AUTHOR]

The given text discusses various methods for calculating survival probabilities in different mathematical models. It provides equations, formulas, and numerical examples to illustrate the calculations and outcomes. The text emphasizes the importance of assumptions and conditions in the calculations and references previous research on the topic. The aim of the text is to provide a theoretical framework for analyzing risk models in queuing theory and insurance mathematics. [Extracted from the article]

Mathematical models describing the spatial spreading and invasion of populations of biological cells are often developed in a continuum modelling framework using reaction–diffusion equations. While continuum models based on linear diffusion are routinely employed and known to capture key experimental observations, linear diffusion fails to predict well-defined sharp fronts that are often observed experimentally. This observation has motivated the use of nonlinear degenerate diffusion; however, these nonlinear models and the associated parameters lack a clear biological motivation and interpretation. Here, we take a different approach by developing a stochastic discrete lattice-based model incorporating biologically inspired mechanisms and then deriving the reaction–diffusion continuum limit. Inspired by experimental observations, agents in the simulation deposit extracellular material, which we call a substrate, locally onto the lattice, and the motility of agents is taken to be proportional to the substrate density. Discrete simulations that mimic a two-dimensional circular barrier assay illustrate how the discrete model supports both smooth and sharp-fronted density profiles depending on the rate of substrate deposition. Coarse-graining the discrete model leads to a novel partial differential equation (PDE) model whose solution accurately approximates averaged data from the discrete model. The new discrete model and PDE approximation provide a simple, biologically motivated framework for modelling the spreading, growth and invasion of cell populations with well-defined sharp fronts. Open-source Julia code to replicate all results in this work is available on GitHub.

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 Background The rapid devolvement of single cell RNA sequencing (scRNA-seq) technology leads to huge amounts of scRNA-seq data, which greatly advance the research of many biomedical fields involving tissue heterogeneity, pathogenesis of disease and drug resistance etc. One major task in scRNA-seq data analysis is to cluster cells in terms of their expression characteristics. Up to now, a number of methods have been proposed to infer cell clusters, yet there is still much space to improve their performance. Results In this paper, we develop a new two-step clustering approach to effectively cluster scRNA-seq data, which is called TSC — the abbreviation of Two-Step Clustering. Particularly, by dividing all cells into two types: core cells (those possibly lying around the centers of clusters) and non-core cells (those locating in the boundary areas of clusters), we first clusters the core cells by hierarchical clustering (the first step) and then assigns the non-core cells to the corresponding nearest clusters (the second step). Extensive experiments on 12 real scRNA-seq datasets show that TSC outperforms the state of the art methods. Conclusion TSC is an effective clustering method due to its two-steps clustering strategy, and it is a useful tool for scRNA-seq data analysis.

Abstract Pitfall traps are frequently used to capture ground‐dwelling arthropods, particularly beetles, ants and spiders. The capture efficiency of a pitfall trapping system strongly depends on the number and opening size of traps, how traps are distributed over the sampling area (spatial arrangement) and the movement characteristics of arthropods. We use numerical simulations for a single species to analyse the trap count patterns that emerge from these variables. Arthropod movement of individuals is modelled as correlated random walks, with multiple traps placed over an area, and catches are simulated as individual interaction with traps. We consider four different types of spatial arrangements of traps across a homogeneous landscape: grid (i.e. rectangular array), transect, nested‐cross and randomised. We contextualise our results by considering the locomotion of Pterostichus melanarius, a highly active carabid beetle often serving as a biocontrol agent for the suppression of pest insects and weeds. By simulating the trapping of randomly moving ground‐dwelling arthropods, we show that there is an optimal inter‐trap separation distance (trap spacing) that maximises captures, that can be expressed using exact formulae in terms of trap opening sizes, sampling area and trap number. Moreover, for the grid and nested‐cross arrangements, larger trap spacing to maximise spatial coverage over the whole sampling area is suboptimal. Also, we find that over a large sampling area, there is a hierarchical order for spatial arrangements in relation to capture efficiency: grid, randomised, transect, followed by the nested‐cross. However, over smaller sampling areas, this order is changed as the rate at which trap counts accumulate with trap number varies across arrangements—eventually saturating at different levels. In terms of movement effects, capture efficiency is maximised over a narrow diffusive range and does not depend strongly on the type of spatial arrangement—indicating an approximate optimal mode of arthropod activity, i.e. rate of spread. Our approach simultaneously considers several important experimental design aspects of pitfall trapping providing a basis to optimise and adapt sampling protocols to other types of traps to better reflect their various purposes, such as monitoring, conservation or pest management.