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).

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.

Non-Backtracking Random Walks and a Weighted Ihara’s Theorem

We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et al. in [1] that in most cases, a non-backtracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.

基于Random Walk算法的CT图像肺实质自动分割

针对复杂情况下肺实质的分割问题,提出了一种基于Random Walk算法对肺实质自动分割的方法。首先,根据胸部组织解剖学及其计算机断层扫描(CT)图像的影像学特征,在肺实质及其周围组织分别确定目标区域种子点和背景种子点位置;然后,使用Random Walk算法对CT图像进行分割,提取近似肺区域的掩模;接下来,对掩模实施数学形态学运算,来进一步调整目标区域种子点和背景种子点的标定位置,使其适合具体的复杂情况;最后,再次使用Random Walk算法分割图像,得到最终的肺实质分割结果。实验结果显示,该方法与金标准的平均绝对距离为0.44±0.13 mm,重合率(DC)为99.21%±0.38%。与其他分割方法相比,该方法在分割精度上得到了显著提高。结果表明,提出的方法能够解决复杂情况下肺实质分割的问题,确保了分割的完整性、准确性、实时性和鲁棒性,分割结果和时间均可满足临床需求。

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 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.

Some Probability Properties of Random Walk in Time-Random Environment

A general formulation of the stochastic model for random walk in time-random environment and an equivalent definition is established in this paper. Moreover, some basic probability relations similar to the classical case which are very useful in the corresponding research of fractal properties are given. At the end, a typical example is provided to show the recurrence and transience. Key words random environment - random walk in timerandom environment - skew product Markov chain CLC number O 211.6 Foudation item: Supported by the National Natural Science Foundation of China (10371092) and Foundation of Wuhan University.Biography: Zhang Xiao-min (1977-), male, Ph. D candidate, research direction: stochastic processes and random fractal.

Random walk modeling of wake dispersion for the exhaust tower of an underground tunnel in urban area

In this paper, some experimental studies on the impact of effluent from an exhaust tower of an underground tunnel with special construction are reported. By measuring the flow field downstream of the tower in NJU meteorological wind tunnel, some flow characteristics in the make area were established. Based on these, an advanced random\|walk dispersion model was set up and applied successfully to the simulation of dispersion in the wake area. The modelling results were in accordance with wind tunnel measurements. The computed maximum of ground surface concentration in the building case was a factor of 3-4 higher than that in the flat case and appeared much closer to the source. The simulation indicated that random walk modelling is an effective and practical tool for the wake stream impact assessment.

RENEWAL THEOREM FOR(L,1)-RANDOM WALK IN RANDOM ENVIRONMENT

We consider a random walk on Z in random environment with possible jumps {-L,…, -1, 1}, in the case that the environment {ωi ： i ∈ Z} are i.i.d.. We establish the renewal theorem for the Markov chain of ＂the environment viewed from the particle＂ in both annealed probability and quenched probability, which generalize partially the results of Kesten （1977） and Lalley （1986） for the nearest random walk in random environment on Z, respectively. Our method is based on （L, 1）-RWRE formulated in Hong and Wang the intrinsic branching structure within the （2013）.

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.

Modelling of the behavior of marine oil spills: applications based on random walk techniques

A numerical model has been developed to simulate the transport and fate of oil spilled at sea. The model combines the transport and fate processes of spilled oil with the random walk technique. Oil movement under the influence of tidal currents, wind driven currents, and turbulent eddies is simulated by the PLUME RW dispersion model developed by HR Wallingford. The weathering processes in the model represent physical and chemical changes of soil slicks with time, and comprise mechanical spreading, dispersion, evaporation and emulsification. Shoreline stranding is determined approximately using a capacity method for different shoreline types. This paper presents details of the model, and describe the results of various sensitivity tests. The model is suitable for oil spill contingency planning.

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.

Study on application of random walk method to calculate water exchange in large-scale bay

The water exchange matrix is an efficient tool to study the water exchange among the sub-areas in large-scale bays. The application of the random walk method to calculate the water exchange matrix is studied. Compared with the advection-diffusion model, the random walk model is more flexible to calculate the water exchange matrix. The forecast matrix suggested by Thompson et al. is used to evaluate the water exchange characteristics among the sub-areas fast. According to the theoretic analysis, it is found that the precision of the predicted results is mainly affected by three factors, namely, the particle number, the generated time of the forecast matrix, and the number of the sub-areas. The impact of the above factors is analyzed based on the results of a series of numerical tests. The results show that the precision of the forecast matrix increases with the increase of the generated time of the forecast matrix and the number of the particles. If there are enough particles in each sub-area, the precision of the forecast matrix will increase with the number of the sub-areas. Moreover, if the particles in each sub-area are not enough, the excessive number of the sub-areas can result in the decrease of the precision of the forecast matrix.

Ergodicity recovery of random walk in heterogeneous disordered media

Significant and persistent trajectory-to-trajectory variance are commonly observed in particle tracking experiments,which have become a major challenge for the experimental data analysis.In this theoretical paper we investigate the ergodicity recovery behavior,which helps clarify the origin and the convergence of trajectory-to-trajectory fluctuation in various heterogeneous disordered media.The concepts of self-averaging and ergodicity are revisited in the context of trajectory analysis.The slow ergodicity recovery and the non-Gaussian diffusion in the annealed disordered media are shown as the consequences of the central limit theorem in different situations.The strange ergodicity recovery behavior is reported in the quenched disordered case,which arises from a localization mechanism.The first-passage approach is introduced to the ergodicity analysis for this case,of which the central limit theorem can be employed and the ergodicity is recovered in the length scale of diffusivity correlation.

基于LBP的改进Random Walks算法在颅脑磁共振影像分割中的应用

目的由于颅脑结构复杂且颅脑磁共振影像易受噪声、磁场不均匀性、部分容积效应等因素的影响,精确的脑组织分割方法仍需深入研究。方法本文提出一种基于Random Walks的改进算法以提高脑白质、脑灰质及脑脊液分割的准确性。通过引入局部二值模式(local binary patterns,LBP)改进了传统Random Walks权重函数的构造,在反映相邻像素灰度变化信息的同时包含了局部图像的纹理信息,有利于合并同质区域并增强边缘轮廓的识别。本文还使用了灰度先验概率模型减少Random Walks种子点交互的次数。结果实验结果表明基于LBP的改进算法在多种不同水平的噪声及不均匀场作用下,能够有效识别磁共振影像中脑组织区域的边缘轮廓,并对噪声有良好的鲁棒性。结论基于LBP的改进Random Walks算法可精确分割颅脑磁共振影像。

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.

Powder Mixing Simulation Using Random Walk Model in Eco-material Preparation

The eco-material composition is not well-distributed in preparation. The eco-material samples were taken for computer image analysis, and its particle numbers and appearance parameters were measured. Based on the mechanism of connective mixing and diffusion, the particles distribution was simulated by a computer using the random walk with Levy flight. The results show that the eco-material microstructure simulated by a computer has an idealized porous structure. The particles distribution has a cluster characteristic that changes with the different size and number of particles in Levy flight trajectory. Each cluster consists of a collection of clusters and shows a structure of self-similar cluster,hence presents a well-defined fractal property. The results obtained from SEM observation are in good agreement with the numerical simulations, and show that the convective mixing presents in the Levy flight walk.

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.

THE DIMENSIONS OF THE RANGE OF RANDOM WALKS IN TIME-RANDOM ENVIRONMENTS

Suppose {Xn} is a random walk in time-random environment with state space Z^d, ｜Xn｜ approaches infinity, then under some reasonable conditions of stability, the upper bound of the discrete Packing dimension of the range of {Xn} is any stability index α. Moreover, if the environment is stationary, a similar result for the lower bound of the discrete Hausdorff dimension is derived. Thus, the range is a fractal set for almost every environment.