Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in t...Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O(√N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.展开更多
在这篇论文，我们定义图的直接产品并且为获得在顶点上观察粒子在的概率给一个配方连续时间古典并且量随机散步。在配方，在图的直接产品上观察粒子的概率被概率的增加获得在上相应于亚图，在这个方法对在复杂的图上决定散步的概率有用...在这篇论文，我们定义图的直接产品并且为获得在顶点上观察粒子在的概率给一个配方连续时间古典并且量随机散步。在配方，在图的直接产品上观察粒子的概率被概率的增加获得在上相应于亚图，在这个方法对在复杂的图上决定散步的概率有用的地方。用这个方法，我们计算概率连续时间古典并且有限直接产品 Cayley 图的许多上的量随机散步(完全的周期，完全的 K <SUB > n </SUB>, 宪章和 n 立方体) 。另外，我们询问古典状态静止一致分发作为 t →
被到达∞
要不是量，状态总是没满足。展开更多
We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a ...We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et al. in [1] that in most cases, a non-backtracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.展开更多
Gait recognition is the key question of functional electrical stimulation (FES) system control for paraplegic walking. A new risk-tendency-graph (RTG) method was proposed to recognize the stability information in FES-...Gait recognition is the key question of functional electrical stimulation (FES) system control for paraplegic walking. A new risk-tendency-graph (RTG) method was proposed to recognize the stability information in FES-assisted walking gait. The main instrument was a specialized walker dynamometer system based on a multi-channel strain-gauge bridge network fixed on the walker frame. During walking process, this system collected the reaction forces between patient's upper extremities and walker and converted them into RTG morphologic curves of dynamic gait stability in temporal and spatial domains. To demonstrate the potential usefulness of RTG, preliminary clinical trials were done with paraplegic patients. The gait stability levels of two walking cases with 4- and 12-week FES training from one subject were quantified (0.43 and 0.19) from the results of temporal and spatial RTG. Relevant instable phases in gait cycle and dangerous inclinations of patient's body during walking process were also brought forward. In conclusion, the new RTG method is practical for distinguishing more useful gait stability information for FES system control.展开更多
In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the ad...In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.展开更多
Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between ve...Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.展开更多
识别潜在颠覆性技术有助于国家和企业加强颠覆性技术供给,使其在国际科技竞争中赢得竞争优势或实现变轨超车。传统基于文献计量的颠覆性技术识别方法通常利用论文和专利数据先构建关键词网络或关键词集,然后人工构造高阶数据特征进行分...识别潜在颠覆性技术有助于国家和企业加强颠覆性技术供给,使其在国际科技竞争中赢得竞争优势或实现变轨超车。传统基于文献计量的颠覆性技术识别方法通常利用论文和专利数据先构建关键词网络或关键词集,然后人工构造高阶数据特征进行分析。这种人工构造高阶特征的方法容易使关键词网络等的结构信息表达不充分,导致识别的准确性降低。本文提出一种基于图表示学习的半监督潜在颠覆性技术识别方法。首先,基于科技文献数据库数据,利用关键词共现频率和期刊影响力构建技术关键词加权网络;然后,通过反向传播算法基于匿名游走序列学习获得关键词网络的向量表示;接着,通过比较待识别技术关键词网络的向量序列与公认颠覆性技术关键词网络的向量序列之间的相似程度,反映技术演化特征的相似性,从而识别出潜在的颠覆性技术;最后,从近年来国内外与颠覆性技术有关的战略规划、预测报告中选取10项技术作为实验对象,采集WoS(Web of Science)数据对本文提出的方法进行实验验证,发现在预给定5项颠覆性技术的条件下,本文方法能较好地将其中潜在的3项颠覆性技术识别出来,并能够将2项伪颠覆性技术判断为非颠覆性技术。展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61502101 and 61170321)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20140651)the Research Fund for the Doctoral Program of Higher Education of China(Grant No.20110092110024)
文摘Janmark, Meyer, and Wong showed that continuous-time quantum walk search on known families of strongly regular graphs(SRGs) with parameters(N, k, λ, μ) achieves full quantum speedup. The problem is reconsidered in terms of scattering quantum walk, a type of discrete-time quantum walks. Here, the search space is confined to a low-dimensional subspace corresponding to the collapsed graph of SRGs. To quantify the algorithm's performance, we leverage the fundamental pairing theorem, a general theory developed by Cottrell for quantum search of structural anomalies in star graphs.The search algorithm on the SRGs with k scales as N satisfies the theorem, and results can be immediately obtained, while search on the SRGs with k scales as√N does not satisfy the theorem, and matrix perturbation theory is used to provide an analysis. Both these cases can be solved in O(√N) time steps with a success probability close to 1. The analytical conclusions are verified by simulation results on two SRGs. These examples show that the formalism on star graphs can be applied more generally.
文摘在这篇论文，我们定义图的直接产品并且为获得在顶点上观察粒子在的概率给一个配方连续时间古典并且量随机散步。在配方，在图的直接产品上观察粒子的概率被概率的增加获得在上相应于亚图，在这个方法对在复杂的图上决定散步的概率有用的地方。用这个方法，我们计算概率连续时间古典并且有限直接产品 Cayley 图的许多上的量随机散步(完全的周期，完全的 K <SUB > n </SUB>, 宪章和 n 立方体) 。另外，我们询问古典状态静止一致分发作为 t →
被到达∞
要不是量，状态总是没满足。
文摘We study the mixing rate of non-backtracking random walks on graphs by looking at non-backtracking walks as walks on the directed edges of a graph. A result known as Ihara’s Theorem relates the adjacency matrix of a graph to a matrix related to non-backtracking walks on the directed edges. We prove a weighted version of Ihara’s Theorem which relates the transition probability matrix of a non-backtracking walk to the transition matrix for the usual random walk. This allows us to determine the spectrum of the transition probability matrix of a non-backtracking random walk in the case of regular graphs and biregular graphs. As a corollary, we obtain a result of Alon et al. in [1] that in most cases, a non-backtracking random walk on a regular graph has a faster mixing rate than the usual random walk. In addition, we obtain an analogous result for biregular graphs.
基金Supported by National Natural Science Foundation of China (No.60501005)Key Programof Tianjin Science Technology Support Plan(No.2007-68)
文摘Gait recognition is the key question of functional electrical stimulation (FES) system control for paraplegic walking. A new risk-tendency-graph (RTG) method was proposed to recognize the stability information in FES-assisted walking gait. The main instrument was a specialized walker dynamometer system based on a multi-channel strain-gauge bridge network fixed on the walker frame. During walking process, this system collected the reaction forces between patient's upper extremities and walker and converted them into RTG morphologic curves of dynamic gait stability in temporal and spatial domains. To demonstrate the potential usefulness of RTG, preliminary clinical trials were done with paraplegic patients. The gait stability levels of two walking cases with 4- and 12-week FES training from one subject were quantified (0.43 and 0.19) from the results of temporal and spatial RTG. Relevant instable phases in gait cycle and dangerous inclinations of patient's body during walking process were also brought forward. In conclusion, the new RTG method is practical for distinguishing more useful gait stability information for FES system control.
文摘In this paper, we obtain explicit formulae for the number of 7-cycles and the total number of cycles of lengths 6 and 7 which contain a specific vertex v<sub>i</sub> in a simple graph G, in terms of the adjacency matrix and with the help of combinatorics.
文摘Let?G=(V,E)? be a graph. If φ is a function from the vertex set V(G) to the set of positive integers. Then two vertices?u, v ∈ V(G)? are?φ -equitable if|φ(u)-φ(v)|≤1.By the degree, equitable adjacency between vertices can be redefine almost all of the variants of the graphs. In this paper we study the degree equitability of the graph by defining equitable connectivity, equitable regularity, equitable connected graph and equitable complete graph. Some new families of graphs and some interesting results are obtained.
文摘识别潜在颠覆性技术有助于国家和企业加强颠覆性技术供给,使其在国际科技竞争中赢得竞争优势或实现变轨超车。传统基于文献计量的颠覆性技术识别方法通常利用论文和专利数据先构建关键词网络或关键词集,然后人工构造高阶数据特征进行分析。这种人工构造高阶特征的方法容易使关键词网络等的结构信息表达不充分,导致识别的准确性降低。本文提出一种基于图表示学习的半监督潜在颠覆性技术识别方法。首先,基于科技文献数据库数据,利用关键词共现频率和期刊影响力构建技术关键词加权网络;然后,通过反向传播算法基于匿名游走序列学习获得关键词网络的向量表示;接着,通过比较待识别技术关键词网络的向量序列与公认颠覆性技术关键词网络的向量序列之间的相似程度,反映技术演化特征的相似性,从而识别出潜在的颠覆性技术;最后,从近年来国内外与颠覆性技术有关的战略规划、预测报告中选取10项技术作为实验对象,采集WoS(Web of Science)数据对本文提出的方法进行实验验证,发现在预给定5项颠覆性技术的条件下,本文方法能较好地将其中潜在的3项颠覆性技术识别出来,并能够将2项伪颠覆性技术判断为非颠覆性技术。
