A simple and efficient method for isomorphism identification of planar kinematic chains

Isomorphism identification plays an important role in structural design and innovative design. Based on the adjacency matrix and loop theory, a new method is proposed in this paper to identify the isomorphic kinematic chains. It enriches the application of loop-based theory for isomorphism identification. In the kinematic chain, links and joints are connected alternatively and every link corresponds to a fixed link degree. Due to the inherent characteristics, the labeled sequence of links can be random, which does not affect the result of isomorphism identification. By the programming software MATLAB, some examples with 6-, 8-, 10-, 11-, 12-link kinematic chains, and 15-vertex topological graphs are presented. Results show that the proposed method applies to topology graphs and kinematic chains with one or multiple joints. Compared with other methods, the proposed method is confirmed correctly. And there is no counterexample. It lays a solid foundation for structural synthesis in the future.

Chronotopic Cartography: Mapping Literary Time-Space

This short methods paper emerges out of the AHRC-funded ‘Chronotopic Cartographies’ project for the digital mapping of place and space as represented in works of literature. The primary aim of that project was to find a way of mapping and visualizing represented literary worlds for which there is no corresponding real ‘ground’. A solution was found in the form of topological graphs which allow for relative rather than absolute mapping (but also permit a relative imaginary map to be lain on top of a pre-existing cartesian form). Using a spatial schema to chunk out the text in terms of chronotopic (time-space) zones enables the generation of a series of visualizations that show different kinds of spatio-temporal constructions in texts. The visualizations are centred upon nodes that consist of chronotopes (e.g. ‘the road’) as well as locations (e.g. ‘road to Geneva’); connections between them of different kinds and toporefs within them (references to other places from this one). The paper will articulate core methods from the project, outlining the stages involved in the process, from marking up the text, using a custom-made schema, through graph generation and into the implications for analysis. This will be illustrated in relation to two Victorian texts: the realist space of Dickens’s Oliver Twist; and the abstract poetic space of Browning’s ‘Childe Roland to the Dark Tower Came’.

DISTANCE DOMINATION ON TOPOLOGICAL GRAPHS AND ITS APPLICATIONS

In this paper we introduce topological graph as bus topological graph, ring topological graph, star topological graph, mesh topological graph and hybrid topological graph. We extend the result that if T is a tree and it has maximum degree m then there exist at least m pendant vertices in to if T is a tree except bus topological graph and it has maximum degree m then there exist exactly m pendant vertices.

Outliers, Connectors, and Textual Periphery: John Dennis’s Social Network in The Dunciad in Four Books

This chapter uses social network analysis to visualize the fields of relations involving John Dennis, the most important critic of the first half of the eighteenth century, with the other protagonists in Alexander Pope’s satire, The Dunciad in Four Books (1743). By using visualizations generated by GraphViz, a program that creates topological graphs from sets of dyadic relations, and ShivaGraph, a tool that helps visualize large networks and navigate through them as through a map, this chapter brings to light data that is structurally embedded in the poem but not immediately legible given the large amount and complexity of information. In Dennis’s case, they reveal the competing stories told by the poem and the apparatus and the critic’s main role as the uncrowned king of The Dunciad’s textual periphery. These visualizations also highlight Dennis’s essential position as a network connector, his camp affiliations, the role played by peripheral characters in the plot network of the poem, and the main dunces targeted by Pope, or the poem’s “hall of infamy.”

Open finite-to-one functions on open topological graphs

The paper describes homotopy classes of open continuous functions on finite open topological graphs

Robust Loop Closure Detection Integrating Visual–Spatial–Semantic Information via Topological Graphs and CNN Features

Loop closure detection is a key module for visual simultaneous localization and mapping (SLAM). Most previous methods for this module have not made full use of the information provided by images, i.e., they have only used the visual appearance or have only considered the spatial relationships of landmarks; the visual, spatial and semantic information have not been fully integrated. In this paper, a robust loop closure detection approach integrating visual–spatial–semantic information is proposed by employing topological graphs and convolutional neural network (CNN) features. Firstly, to reduce mismatches under different viewpoints, semantic topological graphs are introduced to encode the spatial relationships of landmarks, and random walk descriptors are employed to characterize the topological graphs for graph matching. Secondly, dynamic landmarks are eliminated by using semantic information, and distinctive landmarks are selected for loop closure detection, thus alleviating the impact of dynamic scenes. Finally, to ease the effect of appearance changes, the appearance-invariant descriptor of the landmark region is extracted by a pre-trained CNN without the specially designed manual features. The proposed approach weakens the influence of viewpoint changes and dynamic scenes, and extensive experiments conducted on open datasets and a mobile robot demonstrated that the proposed method has more satisfactory performance compared to state-of-the-art methods.

Schematic Diagrams Design of Displacement Suppression Mechanism with One Degree-of-Freedom in a Rope-Guided Hoisting System

Since it is difficult for lateral stiffness of rope-guided rails to meet industry criteria in deep construction shaft, schematic diagrams of displacement suppression mechanisms (DSMs) are designed with a systematic approach demonstrated to reduce the lateral displacement of rope-guided rails in this paper. DSMs are simplified as planar four-bar and six-bar topological graphs based on topological theory. Each corresponding mechanical chain of these four-bar and six-bar mechanisms is divided into a rack, mechanical parts, prismatic, and revolute joints. An extended adjacency matrix is defined to represent the rack position, specific types of kinematic joints, and adjacency relationships between kinematic parts. Then, a symmetric vertex identification method is proposed with regard to planar 1-DOF (one degree of freedom) four-bar and six-bar topological graphs to get the sequences of prismatic joints for kinematic chains of DSMs. Finally, the alternative schematic diagrams of DSMs are obtained. The results show four-bar mechanisms with simple structure; few kinematical parts but less resident force are suitable for a mine shaft with small space and small swing. Six-bar mechanisms with two prismatic joints and three mechanical rack degree are applicable for wide shaft space in deep shaft, due to their stable structure and double resistant force. This development is helpful for DSM dimension synthesis design in future.

RECOVERING THE BOUNDARY PATH SPACE OF A TOPOLOGICAL GRAPH USING POINTLESS TOPOLOGY

First, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $T_{1}$ and sober. We then consider a certain semilattice of basic open sets for this topology on the space of all paths on a graph and impose relations motivated by the definitions of graph C*-algebra in order to recover the boundary path space of a graph. This is done using techniques of pointless topology. Finally, we generalize the results to the case of topological graphs.