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
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
This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this ...This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover＇s algorithm.展开更多
Many network presentation learning algorithms(NPLA)have originated from the process of the random walk between nodes in recent years.Despite these algorithms can obtain great embedding results,there may be also some l...Many network presentation learning algorithms(NPLA)have originated from the process of the random walk between nodes in recent years.Despite these algorithms can obtain great embedding results,there may be also some limitations.For instance,only the structural information of nodes is considered when these kinds of algorithms are constructed.Aiming at this issue,a label and community information-based network presentation learning algorithm(LC-NPLA)is proposed in this paper.First of all,by using the community information and the label information of nodes,the first-order neighbors of nodes are reconstructed.In the next,the random walk strategy is improved by integrating the degree information and label information of nodes.Then,the node sequence obtained from random walk sampling is transformed into the node representation vector by the Skip-Gram model.At last,the experimental results on ten real-world networks demonstrate that the proposed algorithm has great advantages in the label classification,network reconstruction and link prediction tasks,compared with three benchmark algorithms.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
One of the key challenges in ad-hoc networks is the resource discovery problem.How efciently&quickly the queried resource/object can be resolved in such a highly dynamic self-evolving network is the underlying que...One of the key challenges in ad-hoc networks is the resource discovery problem.How efciently&quickly the queried resource/object can be resolved in such a highly dynamic self-evolving network is the underlying question?Broadcasting is a basic technique in the Mobile Ad-hoc Networks(MANETs),and it refers to sending a packet from one node to every other node within the transmission range.Flooding is a type of broadcast where the received packet is retransmitted once by every node.The naive ooding technique oods the network with query messages,while the random walk scheme operates by contacting subsets of each node’s neighbors at every step,thereby restricting the search space.Many earlier works have mainly focused on the simulation-based analysis of ooding technique,and its variants,in a wired network scenario.Although,there have been some empirical studies in peer-to-peer(P2P)networks,the analytical results are still lacking,especially in the context of mobile P2P networks.In this article,we mathematically model different widely used existing search techniques,and compare with the proposed improved random walk method,a simple lightweight approach suitable for the non-DHT architecture.We provide analytical expressions to measure the performance of the different ooding-based search techniques,and our proposed technique.We analytically derive 3 relevant key performance measures,i.e.,the avg.number of steps needed to nd a resource,the probability of locating a resource,and the avg.number of messages generated during the entire search process.展开更多
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 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.
基金Project supported by the National Basic Research Program of China(Grant No.2013CB338002)
文摘This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover＇s algorithm.
基金What is more,we thank the National Natural Science Foundation of China(Nos.61966039,62241604)the Scientific Research Fund Project of the Education Department of Yunnan Province(No.2023Y0565)Also,this work was supported in part by the Xingdian Talent Support Program for Young Talents(No.XDYC-QNRC-2022-0518).
文摘Many network presentation learning algorithms(NPLA)have originated from the process of the random walk between nodes in recent years.Despite these algorithms can obtain great embedding results,there may be also some limitations.For instance,only the structural information of nodes is considered when these kinds of algorithms are constructed.Aiming at this issue,a label and community information-based network presentation learning algorithm(LC-NPLA)is proposed in this paper.First of all,by using the community information and the label information of nodes,the first-order neighbors of nodes are reconstructed.In the next,the random walk strategy is improved by integrating the degree information and label information of nodes.Then,the node sequence obtained from random walk sampling is transformed into the node representation vector by the Skip-Gram model.At last,the experimental results on ten real-world networks demonstrate that the proposed algorithm has great advantages in the label classification,network reconstruction and link prediction tasks,compared with three benchmark algorithms.
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One of the key challenges in ad-hoc networks is the resource discovery problem.How efciently&quickly the queried resource/object can be resolved in such a highly dynamic self-evolving network is the underlying question?Broadcasting is a basic technique in the Mobile Ad-hoc Networks(MANETs),and it refers to sending a packet from one node to every other node within the transmission range.Flooding is a type of broadcast where the received packet is retransmitted once by every node.The naive ooding technique oods the network with query messages,while the random walk scheme operates by contacting subsets of each node’s neighbors at every step,thereby restricting the search space.Many earlier works have mainly focused on the simulation-based analysis of ooding technique,and its variants,in a wired network scenario.Although,there have been some empirical studies in peer-to-peer(P2P)networks,the analytical results are still lacking,especially in the context of mobile P2P networks.In this article,we mathematically model different widely used existing search techniques,and compare with the proposed improved random walk method,a simple lightweight approach suitable for the non-DHT architecture.We provide analytical expressions to measure the performance of the different ooding-based search techniques,and our proposed technique.We analytically derive 3 relevant key performance measures,i.e.,the avg.number of steps needed to nd a resource,the probability of locating a resource,and the avg.number of messages generated during the entire search process.
