BLOW-UP PROBLEMS FOR NONLINEAR PARABOLIC EQUATIONS ON LOCALLY FINITE GRAPHS

Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.

Rigid graph-based three-dimension localization algorithm for wireless sensor networks

This paper investigates the node localization problem for wireless sensor networks in three-dimension space. A distributed localization algorithm is presented based on the rigid graph. Before location, the communication radius is adaptively increasing to add the localizability. The localization process includes three steps: firstly, divide the whole globally rigid graph into several small rigid blocks; secondly, set up the local coordinate systems and transform them to global coordinate system; finally, use the quadrilateration iteration technology to locate the nodes in the wireless sensor network. This algorithm has the advantages of low energy consumption, low computational complexity as well as high expandability and high localizability. Moreover, it can achieve the unique and accurate localization. Finally, some simulations are provided to demonstrate the effectiveness of the proposed algorithm.

Index-adaptive Triangle-Based Graph Local Clustering

Motif-based graph local clustering(MGLC)algorithms are gen-erally designed with the two-phase framework,which gets the motif weight for each edge beforehand and then conducts the local clustering algorithm on the weighted graph to output the result.Despite correctness,this frame-work brings limitations on both practical and theoretical aspects and is less applicable in real interactive situations.This research develops a purely local and index-adaptive method,Index-adaptive Triangle-based Graph Local Clustering(TGLC+),to solve the MGLC problem w.r.t.triangle.TGLC+combines the approximated Monte-Carlo method Triangle-based Random Walk(TRW)and deterministic Brute-Force method Triangle-based Forward Push(TFP)adaptively to estimate the Personalized PageRank(PPR)vector without calculating the exact triangle-weighted transition probability and then outputs the clustering result by conducting the standard sweep procedure.This paper presents the efficiency of TGLC+through theoretical analysis and demonstrates its effectiveness through extensive experiments.To our knowl-edge,TGLC+is the first to solve the MGLC problem without computing the motif weight beforehand,thus achieving better efficiency with comparable effectiveness.TGLC+is suitable for large-scale and interactive graph analysis tasks,including visualization,system optimization,and decision-making.

Locally Transitive Graphs Admitting a Group with Cyclic Sylow Subgroups

All graphs are finite simple undirected and of no isolated vertices in this paper. Using the theory of coset graphs and permutation groups, it is completed that a classification of locally transitive graphs admitting a non-Abelian group with cyclic Sylow subgroups. They are either the union of the family of arc-transitive graphs, or the union of the family of bipartite edge-transitive graphs.

A Semi-Supervised WLAN Indoor Localization Method Based on l1-Graph Algorithm

For indoor location estimation based on received signal strength( RSS) in wireless local area networks( WLAN),in order to reduce the influence of noise on the positioning accuracy,a large number of RSS should be collected in offline phase. Therefore,collecting training data with positioning information is time consuming which becomes the bottleneck of WLAN indoor localization. In this paper,the traditional semisupervised learning method based on k-NN and ε-NN graph for reducing collection workload of offline phase are analyzed,and the result shows that the k-NN or ε-NN graph are sensitive to data noise,which limit the performance of semi-supervised learning WLAN indoor localization system. Aiming at the above problem,it proposes a l1-graph-algorithm-based semi-supervised learning( LG-SSL) indoor localization method in which the graph is built by l1-norm algorithm. In our system,it firstly labels the unlabeled data using LG-SSL and labeled data to build the Radio Map in offline training phase,and then uses LG-SSL to estimate user's location in online phase. Extensive experimental results show that,benefit from the robustness to noise and sparsity ofl1-graph,LG-SSL exhibits superior performance by effectively reducing the collection workload in offline phase and improving localization accuracy in online phase.

A NEW CLASS OF LOCALLY CONVEX SPACES AND THE GENERALIZATION OF KALTON'S CLOSED GRAPH THEOREM

By introducing the notions of L-spaces and L_r-spaces, a complete generalization of Kalton's closed graph theorem is obtained. It points out the class of L_r-spaces is the maximal class of range spaces for the closed graph theorem when the class of domain spaces is the class of Mackey spaces with weakly * sequentially complete dual.Some examples are constructed showing that the class of L_r-spaces is strictly larger than the class of separable B_r-complete spaces.Some properties of L-spaces and L_r-spaces are discussed and the relations between B-complete (resp. B_r-complete) spaces and L-spaces (resp. L_r-spaces) are given.

面向无人机协同定位的机载深度计算编译优化

随着无人机技术快速发展,在定位信号缺失的情况下进行无人机定位成为一个研究难题。而近几年图神经网络的出现与发展,为解决这一难题提供了一种新的解决思路。然而在资源受限的无人机端侧部署图神经网络面临着无人机算储资源受限及实时性难以满足等挑战。提出面向无人机协同定位的机载深度计算编译优化方法。采用了一种轻量化的时间图卷积神经网络模型,该时间图卷积网络由图卷积网络和门控递归单元组成,将无人机群的空间依赖性和无人机位置变化的时间依赖性同时加以考虑,对无人机群位置进行精确的预测;针对该模型在时间图卷积网络上的冗余特性,提出了基于逆向Cuthill-McKee图重排和基于双深度确定性策略梯度的全局自适应剪枝算法。在保证无人机群坐标精确预测的同时,不仅能提高数据在主存的空间局部性,加速模型的运算速度,而且能够对模型进行自适应的非结构化剪枝,降低模型的存储复杂度。实验结果表明,相对于已有的时间图卷积神经网络模型,编译优化后的轻量化时间图卷积神经网络模型在保留78.8%准确率的同时,模型计算时间降低37.9%,模型的平均剪枝率达到90.3%。

一种鲁棒闭环的增量式Graph SLAM算法

针对常规增量式Graph SLAM算法的后端优化无法高效排除错误闭环影响的问题,基于i SAM算法和SC算法,提出一种鲁棒闭环的增量式Graph SLAM算法R-i SAM。R-i SAM在增量式过程中对当前时刻引入的闭环约束的转换变量进行初步近似计算,得到合理的机器人节点位姿。在离线式过程中对当前时期的所有闭环约束转换变量进行精确计算,判断当前时期闭环的正确性,并作为以后优化节点的基础。对公开的数据集进行的算法实验表明,在添加不同类型、不同数量的错误闭环条件下,所提算法对不同数据集具有良好适应性,且收敛速度满足增量式SLAM实时性要求,证明了算法的有效性。

基于本地边差分隐私的有向图聚类算法

基于本地差分隐私的图聚类工作成为近年来的一个研究热点.已有工作主要针对的是无向图,且大多利用位向量技术通过模块化聚合实现.由于噪声量与向量维度成线性关系,使得聚类质量和隐私性难以很好地兼顾.此外,针对无向图中边的有/无设计的2元扰动机制在面对有向图时,因无法对边的方向性进行处理而无法适用.针对上述问题,提出一种基于本地边差分隐私(edge local differential privacy,Edge-LDP)的有向图聚类算法DGC-LDP(directed graph clustering under LDP).具体来说,为了降低噪音量同时适用于有向图,基于直接编码方式设计了一种适用于有向星型图的动态扰动机制,通过自适应添加噪声来平衡隐私性和统计效用.在此基础上,在终端和收集者之间构建迭代机制.收集者依据终端上传的噪声数据提取节点间的相似性信息,并设计基于轮廓系数测量模型的节点聚合算法,通过迭代机制不断地优化节点聚合形式形成高质量簇.理论分析和实验结果表明,所提算法在满足Edge-LDP的同时能够有效兼顾聚类精度.

基于回环边残差聚焦权重模型的位姿图优化算法

基于图优化的同时定位与建图(SLAM)系统中含有大噪声的回环边,可能严重阻碍优化器迅速收敛到最优解,显著降低定位精确性和地图一致性。因此,针对大噪声回环边的优化算法的鲁棒性至关重要。引入K-means聚类思想,对回环边残差值进行分类,进而建立了一种新的残差阈值模型,自适应调整回环边在优化时的权重,减少回环边对优化的影响;然后,基于迭代重加权最小二乘的思想形成了RW-RLSPGO算法(residual weighted enhancement for recursive least squares pose graph optimization algorithm,RWRLSPGO);最后,在模拟和真实的PGO数据集上进行蒙特卡罗实验。实验结果表明,RW-RLSPGO算法在准确性和鲁棒性方面都取得了显著的提高,验证了其在大噪声环境下的有效性。

ASSESSMENT OF LOCAL INFLUENCE IN MULTIVARIATE REGRESSION MODEL

In this article, authors introduce a method to assess local influence of obser- vations on the parameter estimates and prediction in multivariate regression model. The diagnostics under the perturbations of error variance, response variables and explanatory variables are derived, and the results are compared with those of case- deletion. Two examples are analyzed for illustration.

A GENERAL VERSION OF KALTON'S CLOSED GRAPH THEOREM

By investigating the properties of Hellinger-Toeplitz topologies, we establish a general version of Kalton's cioed graph theorem. From this general version, we deduce a number of new closed graph theorems, which are convenient for application. Particularly we improve some results of Kalton.

基于时空图卷积神经网络的强迫振荡定位与传播预测

振荡源定位与传播预测是抑制强迫振荡和保证电力系统稳定的关键。现有方法未能充分利用电网的空间拓扑信息和振荡的时序特征,限制了定位和预测的精度。因此,该文提出一种基于时空图卷积神经网络的强迫振荡定位与传播预测方法。首先,根据节点特征和拓扑信息构建图数据,考虑到强迫振荡传播的快速性,通过切比雪夫多项式扩大节点空间感受野,提取振荡空间特征。同时,利用门控循环单元网络提取多个节点振荡数据的时序关联,通过时空图卷积单元融合空间和时序特征。然后,将定位与传播预测分别建模为分类和回归问题,训练时空图卷积神经网络模型。算例分析表明,所提方法具有更高的准确率,且在噪声和部分节点数据缺失的情况下依然具有较好的性能。

Zero-divisor Graphs for Direct Products of Rings

In [1], Joe Warfel investigated the diameter of a zero-divisor graph for a direct product R 1 × R 2 with respect to the diameter of the zero-divisor graph of R 1 and R 2 . But the author only considered those graphs whose diameters ≥ 1 and discussed six cases. This paper further discusses the other nine cases and also gives a complete characterization for the possible diameters for left Artin rings.

Simulated annealing algorithm for detecting graph isomorphism

Evolutionary computation techniques have mostly been used to solve various optimization problems, and it is well known that graph isomorphism problem （GIP） is a nondeterministic polynomial problem. A simulated annealing （SA） algorithm for detecting graph isomorphism is proposed, and the proposed SA algorithm is well suited to deal with random graphs with large size. To verify the validity of the proposed SA algorithm, simulations are performed on three pairs of small graphs and four pairs of large random graphs with edge densities 0.5, 0.1, and 0.01, respectively. The simulation results show that the proposed SA algorithm can detect graph isomorphism with a high probability.

基于多尺度骨架图和局部视觉上下文融合的驾驶员行为识别方法

识别非驾驶行为是提高驾驶安全性的重要手段之一。目前基于骨架序列和图像的融合识别方法具有计算量大和特征融合困难的问题。针对上述问题,本文提出一种基于多尺度骨架图和局部视觉上下文融合的驾驶员行为识别模型(skeleton-image based behavior recognition network,SIBBR-Net)。SIBBR-Net通过基于多尺度图的图卷积网络和基于局部视觉及注意力机制的卷积神经网络,充分提取运动和外观特征,较好地平衡了模型表征能力和计算量间的关系。基于手部运动的特征双向引导学习策略、自适应特征融合模块和静态特征空间上的辅助损失,使运动和外观特征间互相引导更新并实现自适应融合。最终在Drive&Act数据集进行算法测试,SIBBR-Net在动态标签和静态标签条件下的平均正确率分别为61.78%和80.42%,每秒浮点运算次数为25.92G,较最优方法降低了76.96%。

基于特征图网络和多种生物信息预测关键蛋白质的深度学习框架

针对生物实验识别关键蛋白质费时费力,使用计算方法预测关键蛋白质无法有效整合生物信息的问题,提出一个深度学习框架.首先利用网络拓扑结构、基因表达数据和GO(gene ontology)注释数据构建加权蛋白质相互作用网络;然后分别使用特征图网络和双向长短期记忆细胞从亚细胞定位数据、蛋白质复合物数据和基因表达数据中提取特征向量;最后将这些特征向量输入到任务学习层预测关键蛋白质.实验结果表明,相比于现有的计算方法,该方法预测性能更好.

图采样泛化行人重识别算法

最近的研究表明,度量学习中的深度特征匹配方法,结合大规模、多样化的训练数据,可以显著增强人员再识别的泛化能力。然而,许多现有的方法会产生大量的内存和计算成本,如分类参数或类记忆学习等。为解决上述问题,提出了一种新的基于相关性图采样(correlation graph sampler,CGS)的泛化行人重识别算法,CGS的基本思想是在训练开始时使用局部敏感哈希函数(locality-sensitive Hashing,LSH)和特征度量为所有类构造最近邻关系图。这确保了每一小批训练样本由随机选择的基类和与基类具有相似性的近邻类组成,以提供信息量大且具有挑战性的学习示例,提高行人重识别模型的判别性学习能力。CGS的采样原理会受主干网提取的特征质量影响,因此CGS采样能力会随着主干网的训练而增强,具有可学习性。通过在大规模数据集(包括CUHK03、Market-1501和MSMT17)上交叉评估该方法,广泛的实验结果证实了该方法的有效性,并展示了其在行人重识别应用中的潜力。

压缩感知和图卷积神经网络相结合的宽频振荡扰动源定位方法

新能源并网引发的宽频振荡严重威胁电网安全,实现宽频振荡源的在线定位并及时采取抑制措施以保证系统安全稳定尤为必要。为此,提出一种压缩采样和图卷积神经网络相结合的宽频振荡源定位方法,该方法首先在子站对时序的振荡信号进行稀疏采样,获得其低维观测序列,作为节点的时序信息,然后在主站融合系统的拓扑结构捕捉各节点的邻接关系,综合考虑系统振荡的时空特性,运用图卷积神经网络实现振荡源定位。最后利用宽频振荡样本集进行仿真验证,结果表明所提方法在量测数据含有噪声、传输数据缺失以及传输数据偏差的情况下都有较高的定位准确度。

基于GT模型的多编码下一个兴趣点推荐模型

下一个兴趣点推荐是推荐算法领域的热点,旨在为用户推荐适合的下一地点。较新的研究通过图和序列方法模拟用户与POI的交互以及POI之间转换关系,性能得到显著提升。然而,现有模型仍然存在需要解决的问题。针对现有的下一个兴趣点推荐模型的局限性,特别是如何充分捕捉User-POI交互图上全局和局部信息,以及缓解图神经网络的过平滑特性导致图上信息丢失的问题,提出了基于graph Transformer的多编码模型(multi-coding network based on GT model)对下一个兴趣点进行推荐。首先,从位置和结构的视角上联合对user-POI交互图上进行全局、局部以及相对信息进行编码;然后,将编码后生成的图嵌入通过graph Transformer网络层更新图上节点与边信息;最后通过MLP网络层生成预测;最终,MCGT在Gowalla和TKY两个公开数据集进行对比实验。结果表明,在Gowalla数据集上recall和NDCG指标至少有3.79%的提升,在TKY数据集上recall和NDCG指标至少有2.5%的提升,证明了MCGT设计的合理性与有效性。