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
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
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
The no-cloning theorem has sparked considerable interest in achieving high-fidelity approximate quantum cloning.Most of the previous studies mainly focused on the cloning of single particle states,and cloning schemes ...The no-cloning theorem has sparked considerable interest in achieving high-fidelity approximate quantum cloning.Most of the previous studies mainly focused on the cloning of single particle states,and cloning schemes used there are incapable of cloning quantum entangled states in multipartite systems.Few schemes were proposed for cloning multiparticle states,which consume more entanglement resources with loss of qubits,and the fidelity of the cloned state is relatively low.In this paper,cloning schemes for bipartite and tripartite entangled states based on photonic quantum walk and entanglement swapping are proposed.The results show that according to the proposed schemes,two high-fidelity(up to 0.75)cloned states can be obtained with less quantum resource consumption.Because of the simple cloning steps,few quantum resources and high fidelity,these schemes are both efficient and feasible.Moreover,this cloning machine eliminates the need for tracing out cloning machine,thereby minimizing resource waste.展开更多
Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
The physical layer key generation technique provides an efficient method,which utilizes the natural dynamics of wireless channel.However,there are some extremely challenging security scenarios such as static or quasi-...The physical layer key generation technique provides an efficient method,which utilizes the natural dynamics of wireless channel.However,there are some extremely challenging security scenarios such as static or quasi-static environment,which lead to the low randomness of generated keys.Meanwhile,the coefficients of the static channel may be dropped into the guard space and discarded by the quantization approach,which causes low key generation rate.To tackle these issues,we propose a random coefficient-moving product based wireless key generation scheme(RCMP-WKG),where new random resources with remarkable fluctuations can be obtained by applying random coefficient and by moving product on the legitimate nodes.Furthermore,appropriate quantization approaches are used to increase the key generation rate.Moreover,the security of our proposed scheme is evaluated by analyzing different attacks and the eavesdropper’s mean square error(MSE).The simulation results reveal that the proposed scheme can achieve better performances in key capacity,key inconsistency rate(KIR)and key generation rate(KGR)compared with the prior works in static environment.Besides,the proposed scheme can deteriorate the MSE performance of the eavesdropper and improve the key generation performance of legitimate nodes by controlling the length of the moving product.展开更多
BACKGROUND:This study aims to explore the causal relationship of body weight,body mass index(BMI),and waist circumference (WC) with the risk of cardiac arrest (CA) using two-sample Mendelian randomization (MR).METHODS...BACKGROUND:This study aims to explore the causal relationship of body weight,body mass index(BMI),and waist circumference (WC) with the risk of cardiac arrest (CA) using two-sample Mendelian randomization (MR).METHODS:Data were summarized using genome-wide association studies (GWAS).Twosample MR analyses were performed using the inverse variance weighting (IVW) method,the weighted median method,and the MR-Egger analysis.Heterogeneity test and sensitivity analysis were performed using Cochran’s Q test and the leave-one-out method,respectively.The Steiger test was used to detect reverse causality.Bayesian model-averaged MR was used to identify the most influential risk factors.RESULTS:A total of 13 GWAS data were collected for BMI,body weight and WC.IVW analyses showed a positive correlation of body weight,BMI,and WC with CA (all OR>1 and P<0.05),with MR-Egger and weighted median methods confirming the IVW findings.No horizontal pleiotropy or heterogeneity was observed.Sensitivity analysis indicated that no single nucleotide polymorphism(SNP) caused significant changes in overall causality.Bayesian model-averaged MR was also used to rank causality based on marginal inclusion probability (MIP),and the corresponding modelaveraged causal estimate (MACE) were confirmed,which indicated that WC (GWAS ID:ukb-b-9405)was the highest-ranked risk factor (MIP=0.119,MACE=0.011);its posterior probability was 0.057.A total of 14 sex-specific GWAS data on weight,BMI,and WC were analyzed in relationship with CA,and the MR results showed no significant effects of sex-specific factors.CONCLUSION:Body weight,BMI,and WC are causally associated with an increased risk of CA,with WC identified as the most important risk factor.展开更多
Background:Evidence regarding the effectiveness of prenatal nutritional supplements has mainly considered anthropometric pregnancy outcomes.The effect on markers of health and disease,such as offspring telomere length...Background:Evidence regarding the effectiveness of prenatal nutritional supplements has mainly considered anthropometric pregnancy outcomes.The effect on markers of health and disease,such as offspring telomere length(TL)and mitochondrial DNA content(mtDNAc)is unknown.Objectives:We assessed the efficacy of maternal multiple micronutrient(MMN)-fortified balanced-energy protein(BEP)and iron-folic acid(IFA)supplementation on newborn TL as a secondary outcome and mtDNAc as a non-declared outcome.Design:We conducted a randomized controlled trial in rural Burkina Faso,among pregnant females(15-40 years old)enrolled at<21 weeks of gestation.Mothers received either MMN-fortified BEP and IFA(intervention)or IFA only(control)throughout pregnancy.Whole arterial blood samples were collected from the umbilical cord of 104 control and 90 intervention group infants,respectively.Average relative TL and mtDNAc were measured using quantitative polymerase chain reaction.Linear regression models were fitted to assess TL and mtDNAc differences across trial arms.Results:We found that a combined daily MMN-fortified BEP supplement and IFA tablet did not affect newborn TL[β=-0.010(95%CI:-0.057,0.036);P=0.662]or mtDNAc[β=0.065(95%CI:-0.203,0.073);P=0.354],as compared to an IFA tablet alone.These findings were confirmed(P>0.05)by adjusting the regression models for potential prognostic factors of study outcomes at enrollment.Exploratory analyses indicated higher,but non-significantly different mtDNAc among children born either small-for-gestational age,low birthweight,or preterm.Conclusion:Newborns from mothers who received daily nutritional supplements across gestation did not have different relative TL or mtDNAc.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
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, 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
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
This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the se...This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.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
This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the opt...This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.展开更多
Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z...Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.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].
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 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.
文摘The no-cloning theorem has sparked considerable interest in achieving high-fidelity approximate quantum cloning.Most of the previous studies mainly focused on the cloning of single particle states,and cloning schemes used there are incapable of cloning quantum entangled states in multipartite systems.Few schemes were proposed for cloning multiparticle states,which consume more entanglement resources with loss of qubits,and the fidelity of the cloned state is relatively low.In this paper,cloning schemes for bipartite and tripartite entangled states based on photonic quantum walk and entanglement swapping are proposed.The results show that according to the proposed schemes,two high-fidelity(up to 0.75)cloned states can be obtained with less quantum resource consumption.Because of the simple cloning steps,few quantum resources and high fidelity,these schemes are both efficient and feasible.Moreover,this cloning machine eliminates the need for tracing out cloning machine,thereby minimizing resource waste.
文摘Isoperimetric type inequalities for integral geometric invariants of random lines in the Euclidean space are shown.Entropy inequalities of probability densities on the affine Grassmann manifold of lines are given.
基金supported in part by the National Natural Science Foundation of China(Numbers 62171445,62471477 and 62201592).
文摘The physical layer key generation technique provides an efficient method,which utilizes the natural dynamics of wireless channel.However,there are some extremely challenging security scenarios such as static or quasi-static environment,which lead to the low randomness of generated keys.Meanwhile,the coefficients of the static channel may be dropped into the guard space and discarded by the quantization approach,which causes low key generation rate.To tackle these issues,we propose a random coefficient-moving product based wireless key generation scheme(RCMP-WKG),where new random resources with remarkable fluctuations can be obtained by applying random coefficient and by moving product on the legitimate nodes.Furthermore,appropriate quantization approaches are used to increase the key generation rate.Moreover,the security of our proposed scheme is evaluated by analyzing different attacks and the eavesdropper’s mean square error(MSE).The simulation results reveal that the proposed scheme can achieve better performances in key capacity,key inconsistency rate(KIR)and key generation rate(KGR)compared with the prior works in static environment.Besides,the proposed scheme can deteriorate the MSE performance of the eavesdropper and improve the key generation performance of legitimate nodes by controlling the length of the moving product.
基金This study is supported by the National Natural Science Foundation of China (No. 82072127)。
文摘BACKGROUND:This study aims to explore the causal relationship of body weight,body mass index(BMI),and waist circumference (WC) with the risk of cardiac arrest (CA) using two-sample Mendelian randomization (MR).METHODS:Data were summarized using genome-wide association studies (GWAS).Twosample MR analyses were performed using the inverse variance weighting (IVW) method,the weighted median method,and the MR-Egger analysis.Heterogeneity test and sensitivity analysis were performed using Cochran’s Q test and the leave-one-out method,respectively.The Steiger test was used to detect reverse causality.Bayesian model-averaged MR was used to identify the most influential risk factors.RESULTS:A total of 13 GWAS data were collected for BMI,body weight and WC.IVW analyses showed a positive correlation of body weight,BMI,and WC with CA (all OR>1 and P<0.05),with MR-Egger and weighted median methods confirming the IVW findings.No horizontal pleiotropy or heterogeneity was observed.Sensitivity analysis indicated that no single nucleotide polymorphism(SNP) caused significant changes in overall causality.Bayesian model-averaged MR was also used to rank causality based on marginal inclusion probability (MIP),and the corresponding modelaveraged causal estimate (MACE) were confirmed,which indicated that WC (GWAS ID:ukb-b-9405)was the highest-ranked risk factor (MIP=0.119,MACE=0.011);its posterior probability was 0.057.A total of 14 sex-specific GWAS data on weight,BMI,and WC were analyzed in relationship with CA,and the MR results showed no significant effects of sex-specific factors.CONCLUSION:Body weight,BMI,and WC are causally associated with an increased risk of CA,with WC identified as the most important risk factor.
基金supported by the Bill&Melinda Gates Foundation(OPP1175213)supported by the Research Foundation Flanders(12X9620N and 12X9623N)the European Research Council(ERC)under the European Union’s Horizon 2020 research and innovation program(946192,HUMYCO)。
文摘Background:Evidence regarding the effectiveness of prenatal nutritional supplements has mainly considered anthropometric pregnancy outcomes.The effect on markers of health and disease,such as offspring telomere length(TL)and mitochondrial DNA content(mtDNAc)is unknown.Objectives:We assessed the efficacy of maternal multiple micronutrient(MMN)-fortified balanced-energy protein(BEP)and iron-folic acid(IFA)supplementation on newborn TL as a secondary outcome and mtDNAc as a non-declared outcome.Design:We conducted a randomized controlled trial in rural Burkina Faso,among pregnant females(15-40 years old)enrolled at<21 weeks of gestation.Mothers received either MMN-fortified BEP and IFA(intervention)or IFA only(control)throughout pregnancy.Whole arterial blood samples were collected from the umbilical cord of 104 control and 90 intervention group infants,respectively.Average relative TL and mtDNAc were measured using quantitative polymerase chain reaction.Linear regression models were fitted to assess TL and mtDNAc differences across trial arms.Results:We found that a combined daily MMN-fortified BEP supplement and IFA tablet did not affect newborn TL[β=-0.010(95%CI:-0.057,0.036);P=0.662]or mtDNAc[β=0.065(95%CI:-0.203,0.073);P=0.354],as compared to an IFA tablet alone.These findings were confirmed(P>0.05)by adjusting the regression models for potential prognostic factors of study outcomes at enrollment.Exploratory analyses indicated higher,but non-significantly different mtDNAc among children born either small-for-gestational age,low birthweight,or preterm.Conclusion:Newborns from mothers who received daily nutritional supplements across gestation did not have different relative TL or mtDNAc.
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.
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）.
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.
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.
基金supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.
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supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.
文摘Consider a branching random walk, where the underlying branching mechanism is governed by a Galton-Watson process and the moving law of particles by a discrete random variable on the integer lattice Z. Denote by Zn（z） the number of particles in the n-th generation in the model for each z ∈ Z. We derive the exact convergence rate in the local limit theorem for Zn（z） assuming a condition like ＂EN（logN）1＋λ 〈 ∞＂ for the offspring distribution and a finite moment condition on the motion law. This complements the known results for the strongly non-lattice branching random walk on the real line and for the simple symmetric branching random walk on the integer lattice.
