Qualitative representation of spatial knowledge in two-dimensional space

Various relation-based systems, concerned with the qualitative representation and processing of spatial knowledge, have been developed in numerous application domains. In this article, we identify the common concepts underlying qualitative spatial knowledge representation, we compare the representational properties of the different systems, and we outline the computational tasks involved in relation-based spatial information processing. We also describesymbolic spatial indexes, relation-based structures that combine several ideas in spatial knowledge representation. A symbolic spatial index is an array that preserves only a set of spatial relations among distinct objects in an image, called the modeling space; the index array discards information, such as shape and size of objects, and irrelevant spatial relations. The construction of a symbolic spatial index from an input image can be thought of as a transformation that keeps only a set of representative points needed to define the relations of the modeling space. By keeping the relative arrangements of the representative points in symbolic spatial indexes and discarding all other points, we maintain enough information to answer queries regarding the spatial relations of the modeling space without the need to access the initial image or an object database. Symbolic spatial indexes can be used to solve problems involving route planning, composition of spatial relations, and update operations.     

开流形的曲率与拓扑

应用比较几何的方法研究了完备非紧且具有特定曲率条件的黎曼流形，证明了在一定Pinching条件限制下，流形具有有限拓扑型或者微分同胚于R^n。     

控制系统设计与分析中的潜通路分析技术

介绍了潜通路分析的有关概念和技术，着重讨论了计算机辅助潜通路分析的关键技术，包括网络树拓扑模式识别及线索表制作、定性仿真及基于人工智能的自动缺陷分析技术，最后简要介绍了潜通路分析技术在航空航天控制系统设计与分析中的应用。     

Automating the identification and analysis of protein {beta}-barrels

ßBarrels are widespread and well-studied featuresof a great many protein structures. In this paper an unsuper-visedmethod for the detection of P-barrels is developed based ontechniques from graph theory. The hydrogen bonded connectivityof ß-sheets is derived using standard pattern recognitiontechniques and expressed as a graph. Barrels correspond to topologicalrings in these connectivity graphs and can thus be identifiedusing ring perception algorithms. Following from this, the characteristictopological structure of a barrel can be expressed using a novelform of reduced nomenclature that counts sequence separationsbetween successive members of the ring set These techniquesare tested by applying them to the detection of barrels in anon-redundant subset of the Brookhaven database. Results indicatethat topological rings do seem to correspond uniquely to ß-barrelsand that the technique, as implemented, finds the majority ofbarrels present in the dataset.     

A Novel Topological Index F and Its Correlation With Standard Formaton Enthalpies of AB_n(g) Molecules

The topological index F* is defined and obtained by the method of a non-dimensional unit calculation in which three matrices multiply with each other. These matrices represent the connective cases of atoms in a molecule, the structural features of atoms on top and the bonded cases of the adjacent atoms respectively. The standard formation enthalpies of ABn(g) molecules were correlated with F'* (A = C, Al, Si, Ti, Zr, B = F, Cl, Br, I, H, n=1 -4) and these correlation coefficients are all more than 0.96. Some molecules (e.g CH4, SiH4,etc. )can be preferably handled by F* but can not be dealt with by other topological indices. By contrast to traditional hydrogen suppressed graph, the contribution of hydrogen atoms to structures and properties of molecules is considered.     

模拟电路的模块级故障诊断

本文以多端口元件或子网络为基本单元，提出了一种模块级故障诊断方案，这种方案的故障模型更符合电路的实际情况，因而具有更广泛的实际意义，文中首先推导了模块故障诊断议程，并对模块故障可测性问题进行了一般性讨论。然后，给出了模块故障可测的几个拓扑条件，并通过定义广义独立通路使这些拓扑条件适用于一般的非互易网络。     

光学全交叉网络与SW榕树（F＝S＝2）网络拓扑等价的多样性

本文对有关互连网络拓扑等价的分析方法作了简单评述。并采用互连网络拓扑等价的图分析法分析了自由空间光学互连全交叉网络与ＳＷ榕树网络的拓扑等价及其多样性，拓展了全交叉网络在数字光计算、光子交换及多处理机系统的潜在应用。     

TopoAct: Visually Exploring the Shape of Activations in Deep Learning

Deep neural networks such as GoogLeNet, ResNet, and BERT have achieved impressive performance in tasks such as image and text classification. To understand how such performance is achieved, we probe a trained deep neural network by studying neuron activations, i.e.combinations of neuron firings, at various layers of the network in response to a particular input. With a large number of inputs, we aim to obtain a global view of what neurons detect by studying their activations. In particular, we develop visualizations that show the shape of the activation space, the organizational principle behind neuron activations, and the relationships of these activations within a layer. Applying tools from topological data analysis, we present TopoAct , a visual exploration system to study topological summaries of activation vectors. We present exploration scenarios using TopoAct that provide valuable insights into learned representations of neural networks. We expect TopoAct to give a topological perspective that enriches the current toolbox of neural network analysis, and to provide a basis for network architecture diagnosis and data anomaly detection.     

基于目标导向行为和空间拓扑记忆的视觉导航方法

针对在具有动态因素且视觉丰富环境中的导航问题,受路标机制空间记忆方式启发,提出一种可同步学习目标导向行为和记忆空间结构的视觉导航方法.首先,为直接从原始输入中学习控制策略,以深度强化学习为基本导航框架,同时添加碰撞预测作为模型辅助任务;然后,在智能体学习导航过程中,利用时间相关性网络祛除冗余观测及寻找导航节点,实现通过情景记忆递增描述环境结构;最后,将空间拓扑地图作为路径规划模块集成到模型中,并结合动作网络用于获取更加通用的导航方法.实验在3D仿真环境DMlab中进行,实验结果表明,本文方法可从视觉输入中学习目标导向行为,在所有测试环境中均展现出更高效的学习方法和导航策略,同时减少构建地图所需数据量;而在包含动态堵塞的环境中,该模型可使用拓扑地图动态规划路径,从而引导绕路行为完成导航任务,展现出良好的环境适应性.