Biased random walk with restart for essential proteins prediction

Predicting essential proteins is crucial for discovering the process of cellular organization and viability.We propose biased random walk with restart algorithm for essential proteins prediction,called BRWR.Firstly,the common process of practice walk often sets the probability of particles transferring to adjacent nodes to be equal,neglecting the influence of the similarity structure on the transition probability.To address this problem,we redefine a novel transition probability matrix by integrating the gene express similarity and subcellular location similarity.The particles can obtain biased transferring probabilities to perform random walk so as to further exploit biological properties embedded in the network structure.Secondly,we use gene ontology(GO)terms score and subcellular score to calculate the initial probability vector of the random walk with restart.Finally,when the biased random walk with restart process reaches steady state,the protein importance score is obtained.In order to demonstrate superiority of BRWR,we conduct experiments on the YHQ,BioGRID,Krogan and Gavin PPI networks.The results show that the method BRWR is superior to other state-of-the-art methods in essential proteins recognition performance.Especially,compared with the contrast methods,the improvements of BRWR in terms of the ACC results range in 1.4%–5.7%,1.3%–11.9%,2.4%–8.8%,and 0.8%–14.2%,respectively.Therefore,BRWR is effective and reasonable.

CENTRAL LIMIT THEOREMS FOR A BRANCHING RANDOM WALK WITH A RANDOM ENVIRONMENT IN TIME

We consider a branching random walk with a random environment m time, in which the offspring distribution of a particle of generation n and the distribution of the displacements of its children depend on an environment indexed by the time n. The envi- ronment is supposed to be independent and identically distributed. For A C R, let Zn（A） be the number of particles of generation n located in A. We show central limit theorems for the counting measure Zn （-） with appropriate normalization.

A NOTE ON ASYMPTOTIC BEHAVIOR FOR NEGATIVE DRIFT RANDOM WALK WITH DEPENDENT HEAVY-TAILED STEPS AND ITS APPLICATION TO RISK THEORY

In this article, the dependent steps of a negative drift random walk are modelled as a two-sided linear process. Xn=-u＋∑j=-∞^∞ φn-jεj, where { ε, εn; -∞〈n〈＋∞} is a sequence of independent, identically distributed random variables with zero mean, u 〉 0 is a constant and the coefficients {φi; -∞〈i〈∞} satisfy 0〈 ∑j=-∞^∞ ｜jφj｜〈 ∞ . Under the conditions that the distribution function of ｜ε｜ has dominated variation and ε satisfies certain tail balance conditions, the asymptotic behavior of P{sup n≥0 （-qu＋∑j=-∞^∞ εj βnj）〉x} is discussed. Then the result is applied to ultimate ruin probability.

EQUIVALENT CONDITIONS OF LOCAL ASYMPTOTICS FOR THE OVERSHOOT OF A RANDOM WALK WITH HEAVY-TAILED INCREMENTS

This article gives the equivalent conditions of the local asymptotics for the overshoot of a random walk with heavy-tailed increments, from which we find that the above asymptotics are different from the local asymptotics for the supremum of the random walk. To do this, the article first extends and improves some existing results about the solutions of renewal equations.

Strong invariance principle for a counterbalanced random walk

We study a counterbalanced random walkS_(n)=X_(1)+…+X_(n),which is a discrete time non-Markovian process andX_(n) are given recursively as follows.For n≥2,X_(n) is a new independent sample from some fixed law̸=0 with a fixed probability p,andX_(n)=−X_(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 forS_(n).

ON THE EMPTY BALLS OF A CRITICAL OR SUBCRITICAL BRANCHING RANDOM WALK

Let{Z_(n)}_(n)≥0 be a critical or subcritical d-dimensional branching random walk started from a Poisson random measure whose intensity measure is the Lebesugue measure onℝ^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈ℝ^(d):∣x∣<u})=0}the radius of the largest empty ball centered at the origin of Zn.In this work,we prove that after suitable renormalization,Rn converges in law to some non-degenerate distribution as n→∈.Furthermore,our work shows that the renormalization scales depend on the offspring law and the dimension of the branching random walk.This completes the results of Révész[13]for the critical binary branching Wiener process.

A random walk with a branching system in random environments

We consider a branching random walk in random environments, where the particles are reproduced as a branching process with a random environment (in time), and move independently as a random walk on ? with a random environment (in locations). We obtain the asymptotic properties on the position of the rightmost particle at time n, revealing a phase transition phenomenon of the system.

Exact scaling for the mean first-passage time of random walks on a generalized Koch network with a trap

In this paper, we study the scaling for the mean first-passage time （MFPT） of the random walks on a generalized Koch network with a trap. Through the network construction, where the initial state is transformed from a triangle to a polygon, we obtain the exact scaling for the MFPT. We show that the MFPT grows linearly with the number of nodes and the dimensions of the polygon in the large limit of the network order. In addition, we determine the exponents of scaling efficiency characterizing the random walks. Our results are the generalizations of those derived for the Koch network, which shed light on the analysis of random walks over various fractal networks.

Enhancing personalized exercise recommendation with student and exercise portraits

The exercise recommendation system is emerging as a promising application in online learning scenarios,providing personalized recommendations to assist students with explicit learning directions.Existing solutions generally follow a collaborative filtering paradigm,while the implicit connections between students(exercises)have been largely ignored.In this study,we aim to propose an exercise recommendation paradigm that can reveal the latent connections between student-student(exercise-exercise).Specifically,a new framework was proposed,namely personalized exercise recommendation with student and exercise portraits(PERP).It consists of three sequential and interdependent modules:Collaborative student exercise graph(CSEG)construction,joint random walk,and recommendation list optimization.Technically,CSEG is created as a unified heterogeneous graph with students’response behaviors and student(exercise)relationships.Then,a joint random walk to take full advantage of the spectral properties of nearly uncoupled Markov chains is performed on CSEG,which allows for full exploration of both similar exercises that students have finished and connections between students(exercises)with similar portraits.Finally,we propose to optimize the recommendation list to obtain different exercise suggestions.After analyses of two public datasets,the results demonstrated that PERP can satisfy novelty,accuracy,and diversity.

Return Probability of the Open Quantum Random Walk with Time-Dependence

We study the open quantum random walk (OQRW) with time-dependence on the one-dimensional lattice space and obtain the associated limit distribution. As an application we study the return probability of the OQRW. We also ask, "What is the average time for the return probability of the OQRW?"

Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates

In this paper,we analyze the explicit Runge-Kutta discontinuous Galerkin(RKDG)methods for the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology.The RKDG methods use a third order explicit total-variation-diminishing Runge-Kutta(TVDRK3)time discretization and upwinding numerical fluxes.By using the energy method,under a standard CourantFriedrichs-Lewy(CFL)condition,we obtain L2stability for general solutions and a priori error estimates when the solutions are smooth enough.The theoretical results are proved for piecewise polynomials with any degree k 1.Finally,since the solutions to this system are non-negative,we discuss a positivity-preserving limiter to preserve positivity without compromising accuracy.Numerical results are provided to demonstrate these RKDG methods.

LYAPOUNOLYAPOUNOV EXPONENTS AND LAW OF LARGE NUMBERS FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

In this article, the authors mainly discuss the law of large number under Kalikow＇s condition for multi-dimensional random walks in random environment with holding times. The authors give an expression to the escape speed of random walks in terms of the Lyapounov exponents, which have been precisely used in the context of large deviation.

Estimates for the Tail Probability of the Supremum of a Random Walk with Independent Increments

The authors investigate the tail probability of the supremum of a random walk with independent increments and obtain some equivalent assertions in the case that the increments are independent and identically distributed random variables with Osubexponential integrated distributions.A uniform upper bound is derived for the distribution of the supremum of a random walk with independent but non-identically distributed increments,whose tail distributions are dominated by a common tail distribution with an O-subexponential integrated distribution.

ASYMPTOTIC BEHAVIOR FOR RANDOM WALK IN RANDOM ENVIRONMENT WITH HOLDING TIMES

In this article, we mainly discuss the asymptotic behavior for multi-dimensional continuous-time random walk in random environment with holding times. By constructing a renewal structure and using the point ＂environment viewed from the particle＂, under General Kalikow＇s Condition, we show the law of large numbers （LLN） and central limit theorem （CLT） for the escape speed of random walk.

The Random Walk and Trend Stationary Models with an Analysis of the US Real GDP: Can We Distinguish between the Two Models?

The unit root can lead to major problems in economic time series analyses. I obtain the asymptotic distributions of the ordinary least squares (OLS) estimator when the true model is trend stationary for the following three cases: 1) the null model is a random walk without drift, and the auxiliary regression model does not contain a constant;2) the null model is a random walk with drift, and the auxiliary regression model contains a constant;and 3) the null model is a random walk with drift, and the auxiliary regression model contains both a constant and a time trend. In the third case, the asymptotic distribution of the OLS estimator is determined by the first order of the autocorrelation, and we can distinguish between the random walk and trend stationary models, unlike in previous studies. Based on these results, the real US gross domestic product is analyzed. A time trend model with autoregressive error terms is chosen. The results suggest that the impacts of a shock can become larger than the original shock in some periods and then gradually decline. However, the impacts continue for a long period, and policy makers should account for this to design better economic policies.

Efficiency-Controllable Random Walks on a Class of Recursive Scale-Free Trees with a Deep Trap

Controls, especially effficiency controls on dynamical processes, have become major challenges in many complex systems. We study an important dynamical process, random walk, due to its wide range of applications for modeling the transporting or searching process. For lack of control methods for random walks in various structures, a control technique is presented for a class of weighted treelike scale-free networks with a deep trap at a hub node. The weighted networks are obtained from original models by introducing a weight parameter. We compute analytically the mean first passage time （MFPT） as an indicator for quantitatively measurinM the et^ciency of the random walk process. The results show that the MFPT increases exponentially with the network size, and the exponent varies with the weight parameter. The MFPT, therefore, can be controlled by the weight parameter to behave superlinearly, linearly, or sublinearly with the system size. This work provides further useful insights into controllinM eftlciency in scale-free complex networks.

基于Random-Walk算法的DR图像分割方法

本文算法对原图像进行快速Mallat小波分解得到骨干图后,利用其高频子带梯度信息优化边的权重,并在概率阈值的准则下对争议区域做进一步划分,最后把最大到达概率所在类的标签赋予未标定顶点,并扩展到原图像,得到分割边界。用微软GrabCut分割数据库图像和实际DR图像对该算法进行了验证,该算法能快速而有效地分割出特定的图像,适用于DR图像的分割,为进行组织增强和进一步提高DR图像质量打下基础。

Immunization for scale-free networks by random walker

Based on the random walk and the intentional random walk, we propose two types of immunization strategies which require only local connectivity information. On several typical scale-free networks, we demonstrate that these strategies can lead to the eradication of the epidemic by immunizing a small fraction of the nodes in the networks. Particularly, the immunization strategy based on the intentional random walk is extremely efficient for the assortatively mixed networks.

Random walk search in unstructured P2P

Unstructured P2P has power-law link distribution, and the random walk in power-law networks is analyzed. The analysis results show that the probability that a random walker walks through the high degree nodes is high in the power-law network, and the information on the high degree nodes can be easily found through random walk. Random walk spread and random walk search method （RWSS） is proposed based on the analysis result. Simulation results show that RWSS achieves high success rates at low cost and is robust to high degree node failure.

A random walk evolution model of wireless sensor networks and virus spreading

In this paper, considering both cluster heads and sensor nodes, we propose a novel evolving a network model based on a random walk to study the fault tolerance decrease of wireless sensor networks （WSNs） due to node failure, and discuss the spreading dynamic behavior of viruses in the evolution model. A theoretical analysis shows that the WSN generated by such an evolution model not only has a strong fault tolerance, but also can dynamically balance the energy loss of the entire network. It is also found that although the increase of the density of cluster heads in the network reduces the network efficiency, it can effectively inhibit the spread of viruses. In addition, the heterogeneity of the network improves the network efficiency and enhances the virus prevalence. We confirm all the theoretical results with sufficient numerical simulations.