Relative Entropy of Distance Distribution Based Similarity Measure of Nodes in Weighted Graph Data

Many similarity measure algorithms of nodes in weighted graph data have been proposed by employing the degree of nodes in recent years. Despite these algorithms obtaining great results, there may be still some limitations. For instance, the strength of nodes is ignored. Aiming at this issue, the relative entropy of the distance distribution based similarity measure of nodes is proposed in this paper. At first, the structural weights of nodes are given by integrating their degree and strength. Next, the distance between any two nodes is calculated with the help of their structural weights and the Euclidean distance formula to further obtain the distance distribution of each node. After that, the probability distribution of nodes is constructed by normalizing their distance distributions. Thus, the relative entropy can be applied to measure the difference between the probability distributions of the top d important nodes and all nodes in graph data. Finally, the similarity of two nodes can be measured in terms of this above-mentioned difference calculated by relative entropy. Experimental results demonstrate that the algorithm proposed by considering the strength of node in the relative entropy has great advantages in the most similar node mining and link prediction.     

On the Spatial Distribution of Temporal Complexity in Resting State and Task Functional MRI

Measuring the temporal complexity of functional MRI (fMRI) time series is one approach to assess how brain activity changes over time. In fact, hemodynamic response of the brain is known to exhibit critical behaviour at the edge between order and disorder. In this study, we aimed to revisit the spatial distribution of temporal complexity in resting state and task fMRI of 100 unrelated subjects from the Human Connectome Project (HCP). First, we compared two common choices of complexity measures, i.e., Hurst exponent and multiscale entropy, and observed a high spatial similarity between them. Second, we considered four tasks in the HCP dataset (Language, Motor, Social, and Working Memory) and found high task-specific complexity, even when the task design was regressed out. For the significance thresholding of brain complexity maps, we used a statistical framework based on graph signal processing that incorporates the structural connectome to develop the null distributions of fMRI complexity. The results suggest that the frontoparietal, dorsal attention, visual, and default mode networks represent stronger complex behaviour than the rest of the brain, irrespective of the task engagement. In sum, the findings support the hypothesis of fMRI temporal complexity as a marker of cognition.     

Fixed-Time Leader-Following Consensus Tracking Control for Nonliear Multi-Agent Systems under Jointly Connected Graph

This paper researches the fixed-time leader-following consensus problem for nonlinear multi-agent systems (MASs) affected by unknown disturbances under the jointly connected graph. In order to achieve control goal, this paper designs a fixed-time consensus protocol, which can offset the unknown disturbances and the nonlinear item under the jointly connected graph, simultaneously. In this paper, the states of multiple followers can converge to the state of the leader within a fixed time regardless of the initial conditions rather than just converging to a small neighborhood near the leader state. Finally, a simulation example is given to illustrate the theoretical result.     

新型双阈值高g值MEMS惯性开关（英）

在保证引信勤务安全性和正常发射可靠性前提下,为实现引信小型化而设计了一种新型无源双阈值高g值MEMS惯性开关,其主要包括能够识别两种典型加速度环境（载荷1:15 000g-300 ms,载荷2：3000g-3 ms）的环境识别模块M1和为后续电路可靠供电的通电模块M2。环境识别模块M1主要通过控制带有Z型齿的质量块与对应L型挡块之间的碰撞来确定质量块的运动位移,进而控制通电模块M2的工作情况。基于两种典型加速度环境对MEMS惯性开关进行了动力学仿真并优化,仿真结果表明所设计的开关在载荷1环境下保持断开,而在载荷2环境下可靠闭合。     

表面绝缘对平面钨丝阵Z箍缩早期过程的影响

在强光一号装置上研究了表面绝缘对平面钨丝阵早期过程的影响。通过对实验结果的唯象分析,发现相对于标准丝阵,表面绝缘丝阵X射线辐射被强烈延迟,并与丝阵宽度有较强的依赖关系,在X射线辐射之前存在较强的阴极发射;表面绝缘丝阵X射线辐射副脉冲幅值是标准丝阵两倍,且存在较长的平台期,其单丝等离子体膨胀导致的温度降低效应比标准丝阵强;在快速内爆开始之前,两者形成了类似的宏观磁流体不稳定性结构。     

高功率双频宽谱平面倒F天线设计分析

设计了一种双频带的高功率宽谱平面倒F天线。在矩形贴片上开L形槽实现天线双频辐射。采用圆锥过渡实现同轴馈线到平板之间的宽带阻抗匹配;通过折叠振子电容加载和合理增加天线高度和宽度实现天线宽带设计。经过优化设计,实现了274 MHz和680 MHz的双频输出,反射系数S11不超过-6 dB的低频带宽和高频带宽分别达到14.6%和20.1%。天线的低频和高频增益分别达到4.4 dB和4.6 dB,对应辐射效率分别达到98%和99%。主辐射方向上的低频和高频远场辐射场与距离乘积与馈入宽带脉冲幅度比值分别为1.07和1.14。对天线的高功率容量进行了设计,将天线置于充0.2 MPa压力SF6气体的增强尼龙箱体中,天线可承受200 MW宽谱高功率微波。     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

图的{P4}-分解

一个图G的路分解是指一路集合使得G的每条边恰好出现在其中一条路上.记Pl长度为l-1的路,如果G能够分解成若干个Pl,则称G存在{Pl}—分解.关于图的给定长路分解问题主要结果有:(i)连通图G存在{P3}—分解当且仅当G有偶数条边(见[1]);(ii)连通图G存在{P3,P4}—分解当且仅当G不是C3和奇树,这里C3的长度为3的圈而奇树是所有顶点皆度数为奇数的树(见[3]).本文讨论了3正则图的{P4}—分解情况,并构造证明了边数为3k(k热∈Z且k≥2)的完全图Kn和完全二部图Kr,s存在{P4}—分解.     

3D Multiphase Piecewise Constant Level Set Method Based on Graph Cut Minimization

Segmentation of three-dimensional (3D) complicated structures is of great importance for many real applications. In this work we combine graph cut minimization method with a variant of the level set idea for 3D segmentation based on the Mumford-Shah model. Compared with the traditional approach for solving the Euler-Lagrange equation we do not need to solve any partial differential equations. Instead, the minimum cut on a special designed graph need to be computed. The method is tested on data with complicated structures. It is rather stable with respect to initial value and the algorithm is nearly parameter free. Experiments show that it can solve large problems much faster than traditional approaches.     

Calix[4]pyrrolato Aluminates: The Effect of Ligand Modification on the Reactivity of Square-Planar Aluminum Anions

Structural constraint represents an attractive tool to modify p-block element properties without the need for unusual oxidation or valence states. The recently reported methyl-calix[4]pyrrolato aluminate established the effect of forcing a tetrahedral aluminum anion into a square-planar coordination mode. However, the generality of this structural motif and any consequence of ligand modification remained open. Herein, a systematic ligand screening was launched, and the class of square-planar aluminum anions was extended by two derivatives that differ in the meso-substitution at the calix[4]pyrrolato ligand. Strikingly, this modification provoked opposing trends in the preference for a Lewis acidic binding mode with σ-donors versus the aluminum-ligand cooperative binding mode with carbonyls. Insights into the origin of these counterintuitive experimental observations were provided by computation and bond analysis. Importantly, this rationale might allow to exploit mode-selective binding for catalytic rate control.