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 wit...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).展开更多
A model is proposed to describe the competition between two kinds of information among N random-walking individuals in an L x L square, starting from a half-and-half mixture of two kinds of information. Individuals re...A model is proposed to describe the competition between two kinds of information among N random-walking individuals in an L x L square, starting from a half-and-half mixture of two kinds of information. Individuals remain or change their information according to their neighbors' information. When the moving speed of individuals v is zero, the two kinds of information typically coexist, and the ratio between them increases with L and decreases with N. In the dynamic case (v 〉 0), only one information eventually remains, and the time required for one information being left scales as Td -v^αL^β^γ.展开更多
Efficient cell migration is crucial for the functioning of biological processes, e.g., morphogenesis, wound healing, and cancer metastasis. In this study, we monitor the migratory behavior of the 3D fibroblast cluster...Efficient cell migration is crucial for the functioning of biological processes, e.g., morphogenesis, wound healing, and cancer metastasis. In this study, we monitor the migratory behavior of the 3D fibroblast clusters using live cell microscopy,and find that crowded environment affects cell migration, i.e., crowding leads to directional migration at the cluster’s periphery. The number of cell layers being stacked during seeding determines the directional-to-random transition. Intriguingly,the migratory behavior of cell clusters resembles the dispersion dynamics of clouds of passive particles, indicating that the biological process is driven by physical effects(e.g., entropy) rather than cell communication. Our findings highlight the role of intrinsic physical characteristics, such as crowding, in regulating biological behavior, and suggest new therapeutic approaches targeting at cancer metastasis.展开更多
Cell migration plays a significant role in physiological and pathological processes.Understanding the characteristics of cell movement is crucial for comprehending biological processes such as cell functionality,cell ...Cell migration plays a significant role in physiological and pathological processes.Understanding the characteristics of cell movement is crucial for comprehending biological processes such as cell functionality,cell migration,and cell–cell interactions.One of the fundamental characteristics of cell movement is the specific distribution of cell speed,containing valuable information that still requires comprehensive understanding.This article investigates the distribution of mean velocities along cell trajectories,with a focus on optimizing the efficiency of cell food search in the context of the entire colony.We confirm that the specific velocity distribution in the experiments corresponds to an optimal search efficiency when spatial weighting is considered.The simulation results indicate that the distribution of average velocity does not align with the optimal search efficiency when employing average spatial weighting.However,when considering the distribution of central spatial weighting,the specific velocity distribution in the experiment is shown to correspond to the optimal search efficiency.Our simulations reveal that for any given distribution of average velocity,a specific central spatial weighting can be identified among the possible central spatial weighting that aligns with the optimal search strategy.Additionally,our work presents a method for determining the spatial weights embedded in the velocity distribution of cell movement.Our results have provided new avenues for further investigation of significant topics,such as relationship between cell behavior and environmental conditions throughout their evolutionary history,and how cells achieve collective cooperation through cell-cell communication.展开更多
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 gen...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.展开更多
Quantitative examination of cellular motion and intercellullar interactions possesses substantial relevance for both biology and medicine.However,the effects of intercellular interactions during cellular locomotion re...Quantitative examination of cellular motion and intercellullar interactions possesses substantial relevance for both biology and medicine.However,the effects of intercellular interactions during cellular locomotion remain under-explored in experimental research.As such,this study seeks to bridge this research gap,adopting Dictyostelium discoideum(Dicty)cells as a paradigm to investigate variations in cellular motion during reciprocal collisions.We aim to attain a comprehensive understanding of how cell interactions influence cell motion.By observing and processing the motion trajectories of colliding cells under diverse chemical environments,we calculated the diffusion coefficient(D)and the persistence time(τ),using mean square displacement.Our analysis of the relationship dynamics between D andτprior to the collisions reveals intricate and non-monotonic alterations in cell movements during collisions.By quantitatively scrutinizing theτtrend,we were able to categorize the cellular responses to interactions under different conditions.Importantly,we ascertained that the effect of cell interactions during collisions in Dicty cells emulates a classical sigmoid function.This discovery suggests that cellular responses might comply with a pattern akin to the Weber–Fechner law.展开更多
The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the unc...The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.展开更多
Two new solutions of the homogeneous diffusion equation in 1D are derived in the presence of losses and a trigonometric profile for a profile of density. A simulation for the ankle in the energy distribution of cosmic...Two new solutions of the homogeneous diffusion equation in 1D are derived in the presence of losses and a trigonometric profile for a profile of density. A simulation for the ankle in the energy distribution of cosmic rays (CRs) is provided in the framework of the fine tuning of the involved parameters. A theoretical image for the overall diffusion of CRs in galactic coordinates is provided.展开更多
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 ...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.展开更多
In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTR...In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...展开更多
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 environmen...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.展开更多
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 ...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.展开更多
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...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.展开更多
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 c...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.展开更多
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 mete...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.展开更多
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 envi...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).展开更多
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...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.展开更多
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 th...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.展开更多
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 di...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.展开更多
基金Supported by the National Natural Science Foundation of China(11671373).
文摘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).
基金supported by the National Natural Science Foundation of China (Grant Nos. 61173183, 60973152, and 60573172)the Superior University Doctor Subject Special Scientific Research Foundation of China (Grant No. 20070141014)the Natural Science Foundation of Liaoning Province of China (Grant No. 20082165)
文摘A model is proposed to describe the competition between two kinds of information among N random-walking individuals in an L x L square, starting from a half-and-half mixture of two kinds of information. Individuals remain or change their information according to their neighbors' information. When the moving speed of individuals v is zero, the two kinds of information typically coexist, and the ratio between them increases with L and decreases with N. In the dynamic case (v 〉 0), only one information eventually remains, and the time required for one information being left scales as Td -v^αL^β^γ.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 51927804 and 12174306)the Natural Science Basic Research Program of Shaanxi Province of China (Grant No. 2023-JC-JQ-02)。
文摘Efficient cell migration is crucial for the functioning of biological processes, e.g., morphogenesis, wound healing, and cancer metastasis. In this study, we monitor the migratory behavior of the 3D fibroblast clusters using live cell microscopy,and find that crowded environment affects cell migration, i.e., crowding leads to directional migration at the cluster’s periphery. The number of cell layers being stacked during seeding determines the directional-to-random transition. Intriguingly,the migratory behavior of cell clusters resembles the dispersion dynamics of clouds of passive particles, indicating that the biological process is driven by physical effects(e.g., entropy) rather than cell communication. Our findings highlight the role of intrinsic physical characteristics, such as crowding, in regulating biological behavior, and suggest new therapeutic approaches targeting at cancer metastasis.
基金Project supported by the National Natural Science Foundation of China(Grant No.31971183).
文摘Cell migration plays a significant role in physiological and pathological processes.Understanding the characteristics of cell movement is crucial for comprehending biological processes such as cell functionality,cell migration,and cell–cell interactions.One of the fundamental characteristics of cell movement is the specific distribution of cell speed,containing valuable information that still requires comprehensive understanding.This article investigates the distribution of mean velocities along cell trajectories,with a focus on optimizing the efficiency of cell food search in the context of the entire colony.We confirm that the specific velocity distribution in the experiments corresponds to an optimal search efficiency when spatial weighting is considered.The simulation results indicate that the distribution of average velocity does not align with the optimal search efficiency when employing average spatial weighting.However,when considering the distribution of central spatial weighting,the specific velocity distribution in the experiment is shown to correspond to the optimal search efficiency.Our simulations reveal that for any given distribution of average velocity,a specific central spatial weighting can be identified among the possible central spatial weighting that aligns with the optimal search strategy.Additionally,our work presents a method for determining the spatial weights embedded in the velocity distribution of cell movement.Our results have provided new avenues for further investigation of significant topics,such as relationship between cell behavior and environmental conditions throughout their evolutionary history,and how cells achieve collective cooperation through cell-cell communication.
基金supported by the Industrial Support Project of Gansu Colleges under Grant No.2022CYZC-11Gansu Natural Science Foundation Project under Grant No.21JR7RA114+1 种基金National Natural Science Foundation of China under Grants No.622760736,No.1762078,and No.61363058Northwest Normal University Teachers Research Capacity Promotion Plan under Grant No.NWNU-LKQN2019-2.
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant No.31971183)。
文摘Quantitative examination of cellular motion and intercellullar interactions possesses substantial relevance for both biology and medicine.However,the effects of intercellular interactions during cellular locomotion remain under-explored in experimental research.As such,this study seeks to bridge this research gap,adopting Dictyostelium discoideum(Dicty)cells as a paradigm to investigate variations in cellular motion during reciprocal collisions.We aim to attain a comprehensive understanding of how cell interactions influence cell motion.By observing and processing the motion trajectories of colliding cells under diverse chemical environments,we calculated the diffusion coefficient(D)and the persistence time(τ),using mean square displacement.Our analysis of the relationship dynamics between D andτprior to the collisions reveals intricate and non-monotonic alterations in cell movements during collisions.By quantitatively scrutinizing theτtrend,we were able to categorize the cellular responses to interactions under different conditions.Importantly,we ascertained that the effect of cell interactions during collisions in Dicty cells emulates a classical sigmoid function.This discovery suggests that cellular responses might comply with a pattern akin to the Weber–Fechner law.
文摘The topic of this article is one-sided hypothesis testing for disparity, i.e., the mean of one group is larger than that of another when there is uncertainty as to which group a datum is drawn. For each datum, the uncertainty is captured with a given discrete probability distribution over the groups. Such situations arise, for example, in the use of Bayesian imputation methods to assess race and ethnicity disparities with certain insurance, health, and financial data. A widely used method to implement this assessment is the Bayesian Improved Surname Geocoding (BISG) method which assigns a discrete probability over six race/ethnicity groups to an individual given the individual’s surname and address location. Using a Bayesian framework and Markov Chain Monte Carlo sampling from the joint posterior distribution of the group means, the probability of a disparity hypothesis is estimated. Four methods are developed and compared with an illustrative data set. Three of these methods are implemented in an R-code and one method in WinBUGS. These methods are programed for any number of groups between two and six inclusive. All the codes are provided in the appendices.
文摘Two new solutions of the homogeneous diffusion equation in 1D are derived in the presence of losses and a trigonometric profile for a profile of density. A simulation for the ankle in the energy distribution of cosmic rays (CRs) is provided in the framework of the fine tuning of the involved parameters. A theoretical image for the overall diffusion of CRs in galactic coordinates is provided.
文摘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.
基金Supported by the National Natural Science Foundation of China (10771185 and 10871200)
文摘In Section 1, the authors establish the models of two kinds of Markov chains in space-time random environments (MCSTRE and MCSTRE(+)) with abstract state space. In Section 2, the authors construct a MCSTRE and a MCSTRE(+) by an initial distribution Φ and a random Markov kernel (RMK) p(γ). In Section 3, the authors es-tablish several equivalence theorems on MCSTRE and MCSTRE(+). Finally, the authors give two very important examples of MCMSTRE, the random walk in spce-time random environment and the Markov br...
基金partially supported by the National Natural Science Foundation of China(NSFC,11101039,11171044,11271045)a cooperation program between NSFC and CNRS of France(11311130103)+1 种基金the Fundamental Research Funds for the Central UniversitiesHunan Provincial Natural Science Foundation of China(11JJ2001)
文摘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.
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 61103231 and 61103230)the Innovation Program of Graduate Scientific Research in Institution of Higher Education of Jiangsu Province, China (Grant No. CXZZ11 0401)
文摘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.
文摘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.
文摘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.
文摘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).
基金Project supported by the Research Foundation of Hangzhou Dianzi University,China (Grant Nos. KYF075610032 andzx100204004-7)the Hong Kong Research Grants Council,China (Grant No. CityU 1114/11E)
文摘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.
文摘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.
基金Research supported by National Science Foundation of China (70671018 and 10371117)
文摘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.