In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are dif...In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].展开更多
Missiles provide long-range precision strike capabilities and have become a cornerstone of modern warfare.The contrail clouds formed by missile during their active flight phase present significant chal-lenges to high-...Missiles provide long-range precision strike capabilities and have become a cornerstone of modern warfare.The contrail clouds formed by missile during their active flight phase present significant chal-lenges to high-altitude environmental observation and target detection and tracking.Existing studies primarily focus on specific airspace regions,leaving critical gaps in understanding the effects of long dispersion times,wide altitude ranges,and variable atmospheric conditions on missile contrail clouds.To address these gaps,this article develops a numerical method based on the Lagrangian random walk model,which incorporates various velocity variation terms,including particle velocity caused by the difference of wind field,by the thermal motion of local gas molecules and by random collisions between contrail cloud particles to capture the influence of environmental wind fields,atmospheric conditions,and particle concentrations on the motion of contrail cloud particles.A general coordinate system aligned with the missile's flight trajectory is employed to represent particle distribution characteristics.The proposed method is in good agreement with the conducted experiments as well as with the available numerical simulations.The results demonstrate that the proposed model effectively simulates the dispersion state of contrail clouds,accurately reflecting the impact of large-scale wind field variations and altitude changes with high computational efficiency.Additionally,simulation results indicate that the increased distance between gas molecules in rarefied environments facilitates enhanced particle dispersion,while larger particles exhibit a faster dispersion rate due to their greater mass.展开更多
The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region.Despite intensive studies on the partitioning of urban road networ...The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region.Despite intensive studies on the partitioning of urban road networks,the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open question.This paper proposes to partition the network into homogeneous sub-regions based on random walk algorithm.Starting from selected random walkers,the road network is partitioned from the early morning when congestion emerges.A modified Akaike information criterion is defined to find the optimal number of partitions.Region boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of partitions.The traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.展开更多
Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we de...Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.展开更多
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 on R^(d).Denote by R_(n):=sup{u>0:Z_(n)({x∈...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 on R^(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 Z_(n).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.展开更多
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
We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that t...We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.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
We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoti...We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.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
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, 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
基金supported by the National Natural Science Foundation of China(Grant No.11671145)the Science and Technology Commission of Shanghai Municipality(Grant No.18dz2271000).
文摘In this paper,large deviations principle(LDP)and moderate deviations principle(MDP)of record numbers in random walks are studied under certain conditions.The results show that the rate functions of LDP and MDP are different from those of weak record numbers,which are interesting complements of the conclusions by Li and Yao[1].
文摘Missiles provide long-range precision strike capabilities and have become a cornerstone of modern warfare.The contrail clouds formed by missile during their active flight phase present significant chal-lenges to high-altitude environmental observation and target detection and tracking.Existing studies primarily focus on specific airspace regions,leaving critical gaps in understanding the effects of long dispersion times,wide altitude ranges,and variable atmospheric conditions on missile contrail clouds.To address these gaps,this article develops a numerical method based on the Lagrangian random walk model,which incorporates various velocity variation terms,including particle velocity caused by the difference of wind field,by the thermal motion of local gas molecules and by random collisions between contrail cloud particles to capture the influence of environmental wind fields,atmospheric conditions,and particle concentrations on the motion of contrail cloud particles.A general coordinate system aligned with the missile's flight trajectory is employed to represent particle distribution characteristics.The proposed method is in good agreement with the conducted experiments as well as with the available numerical simulations.The results demonstrate that the proposed model effectively simulates the dispersion state of contrail clouds,accurately reflecting the impact of large-scale wind field variations and altitude changes with high computational efficiency.Additionally,simulation results indicate that the increased distance between gas molecules in rarefied environments facilitates enhanced particle dispersion,while larger particles exhibit a faster dispersion rate due to their greater mass.
基金Project supported by the National Natural Science Foundation of China(Grant No.12072340)the Chinese Scholarship Council and the Australia Research Council through a linkage project fund。
文摘The successful application of perimeter control of urban traffic system strongly depends on the macroscopic fundamental diagram of the targeted region.Despite intensive studies on the partitioning of urban road networks,the dynamic partitioning of urban regions reflecting the propagation of congestion remains an open question.This paper proposes to partition the network into homogeneous sub-regions based on random walk algorithm.Starting from selected random walkers,the road network is partitioned from the early morning when congestion emerges.A modified Akaike information criterion is defined to find the optimal number of partitions.Region boundary adjustment algorithms are adopted to optimize the partitioning results to further ensure the correlation of partitions.The traffic data of Melbourne city are used to verify the effectiveness of the proposed partitioning method.
基金supported by the Fundamental Research Funds for the Central Universities,the National Natural Science Foundation of China(Grant Nos.12371132,12075159,12171044,12071179,and 12405006)the specific research fund of the Innovation Platform for Academicians of Hainan Province.
文摘Quantum algorithms have demonstrated provable speedups over classical counterparts,yet establishing a comprehensive theoretical framework to understand the quantum advantage remains a core challenge.In this work,we decode the quantum search advantage by investigating the critical role of quantum state properties in random-walk-based algorithms.We propose three distinct variants of quantum random-walk search algorithms and derive exact analytical expressions for their success probabilities.These probabilities are fundamentally determined by specific initial state properties:the coherence fraction governs the first algorithm’s performance,while entanglement and coherence dominate the outcomes of the second and third algorithms,respectively.We show that increased coherence fraction enhances success probability,but greater entanglement and coherence reduce it in the latter two cases.These findings reveal fundamental insights into harnessing quantum properties for advantage and guide algorithm design.Our searches achieve Grover-like speedups and show significant potential for quantum-enhanced machine learning.
基金supported by the National Key R&D Program of China(2022YFA1006102).
文摘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 on R^(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 Z_(n).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.
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).
文摘We primarily provide several estimates for the heat kernel defined on the 2-dimensional simple random walk. Additionally, we offer an estimate for the heat kernel on high-dimensional random walks, demonstrating that the heat kernel in higher dimensions converges rapidly. We also compute the constants involved in the estimate for the 1-dimensional heat kernel. Furthermore, we discuss the general case of on-diagonal estimates for the heat kernel.
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benefited from the support of the French government Investissements d’Avenir program ANR-11-LABX-0020-01partially supported by the National Natural Science Foundation of China(11571052,11401590,11731012 and 11671404)by Hunan Natural Science Foundation(2017JJ2271)
文摘We consider a branching random walk in an independent and identically distributed random environment ξ=(ξn) indexed by the time. Let W be the limit of the martingale Wn=∫e^-txZn(dx)/Eξ∫e^-txZn(dx), with Zn denoting the counting measure of particles of generation n, and Eξ the conditional expectation given the environment ξ. We find necessary and sufficient conditions for the existence of quenched moments and weighted moments of W, when W is non-degenerate.
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）.
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.
