An application of neighbourhoods in digraphs to the classification of binary dynamics

A binary state on a graph means an assignment of binary values to its vertices. A time dependent sequence of binary states is referred to as binary dynamics. We describe a method for the classification of binary dynamics of digraphs, using particular choices of closed neighbourhoods. Our motivation and application comes from neuroscience, where a directed graph is an abstraction of neurons and their connections, and where the simplification of large amounts of data is key to any computation. We present a topological/graph theoretic method for extracting information out of binary dynamics on a graph, based on a selection of a relatively small number of vertices and their neighbourhoods. We consider existing and introduce new real-valued functions on closed neighbourhoods, comparing them by their ability to accurately classify different binary dynamics. We describe a classification algorithm that uses two parameters and sets up a machine learning pipeline. We demonstrate the effectiveness of the method on simulated activity on a digital reconstruction of cortical tissue of a rat, and on a non-biological random graph with similar density.

Conceptual configuration design of line-foldable deployable space truss structures employing graph theory

From the perspective of the truss as a whole, this research investigates the conceptual configuration design for deployable space truss structures that are line-foldable with the help of graph theory. First, the bijection between a truss and its graph model is established. Therefore, operations can be performed based on graph models. Second, by introducing Maxwell’s rule, maximum clique, and chordless cycle, the principle of conceptual configuration synthesis is analyzed. A corresponding procedure is formed and it is verified by a truss with seven nodes. Third, assisted by some theorems of graph theory, the simplified double-color topological graph of deployable space truss structures is acquired and it also displays the procedure with a case. Finally, based on the above analysis, it obtains the optimal conceptual configurations. This novel research lays the foundation for kinematic synthesis and geometric dimension designs.

Semisupervised Classification with High-Order Graph Learning Attention Neural Network

At present, the graph neural network has achieved good results in the semisupervised classification of graph structure data. However, the classification effect is greatly limited in those data without graph structure, incomplete graph structure, or noise. It has no high prediction accuracy and cannot solve the problem of the missing graph structure. Therefore, in this paper, we propose a high-order graph learning attention neural network (HGLAT) for semisupervised classification. First, a graph learning module based on the improved variational graph autoencoder is proposed, which can learn and optimize graph structures for data sets without topological graph structure and data sets with missing topological structure and perform regular constraints on the generated graph structure to make the optimized graph structure more reasonable. Then, in view of the shortcomings of graph attention neural network (GAT) that cannot make full use of the graph high-order topology structure for node classification and graph structure learning, we propose a graph classification module that extends the attention mechanism to high-order neighbors, in which attention decays according to the increase of neighbor order. HGLAT performs joint optimization on the two modules of graph learning and graph classification and performs semisupervised node classification while optimizing the graph structure, which improves the classification performance. On 5 real data sets, by comparing 8 classification methods, the experiment shows that HGLAT has achieved good classification results on both a data set with graph structure and a data set without graph structure.

Distributed Event-Triggered Consensus Control of Multi-Agent Systems under Denial-of-Service Jamming Attacks

This work focuses on the consensus problem of multi-agent systems (MASs) under event-triggered control (ETC) subject to denial-of-service (DoS) jamming attacks. To reduce the cost of communication networks, a novel event-triggering mechanism (ETM) is applied to the sleeping interval to determine whether the sampled signal should be transmitted or not. Unlike periodic DoS attacks model, the DoS attacks occurrence are irregular, where attack attributes such as attack frequency and attack duration are taken into account. Moreover, compared with the fixed topological graph, the communication topologies may change due to DoS jamming attacks in this work. In view of this, based on the piecewise Lyapunov functional, sufficient conditions are derived to guarantee that consensus problem of the MASs can be solved. Finally, the effectiveness and correctness of the theoretical results are verified by a numerical example.

Multi-camera object tracking system

The article proposes a multi-camera tracking system for an object, implemented using computer vision technologies and allowing the video surveillance operator in real time to select an object that will be monitored by the system in future. It will be ready to give out the location of the object at any time. The solution to this problem is divided into three main stages: the detection stage, the tracking stage and the stage of interaction of several cameras. Methods of detection, tracking of objects and the interaction of several cameras have been investigated. To solve the problem of detection, the method of optical flow and the method of removing the background were investigated, to solve the problem of tracking — the method of matching key points and the correlation method, to solve the problem of interaction between several surveillance cameras — the method of the topological graph of a network of cameras. An approach is proposed for constructing a system that uses a combination of the background removal method, the correlation method and the method of the topological graph of a network of cameras. The stages of detection and tracking have been experimentally implemented, that is, the task of tracking an object within the coverage area of one video camera has been solved. The implemented system showed good results: a sufficiently high speed and accuracy with rare losses of the tracked object and with a slight decrease in the frame rate.

ChemRL-GEM: Geometry Enhanced Molecular Representation Learning for Property Prediction

Effective molecular representation learning is of great importance to facilitate molecular property prediction, which is a fundamental task for the drug and material industry. Recent advances in graph neural networks (GNNs) have shown great promise in applying GNNs for molecular representation learning. Moreover, a few recent studies have also demonstrated successful applications of self-supervised learning methods to pre-train the GNNs to overcome the problem of insufficient labeled molecules. However, existing GNNs and pre-training strategies usually treat molecules as topological graph data without fully utilizing the molecular geometry information. Whereas, the three-dimensional (3D) spatial structure of a molecule, a.k.a molecular geometry, is one of the most critical factors for determining molecular physical, chemical, and biological properties. To this end, we propose a novel Geometry Enhanced Molecular representation learning method (GEM) for Chemical Representation Learning (ChemRL). At first, we design a geometry-based GNN architecture that simultaneously models atoms, bonds, and bond angles in a molecule. To be specific, we devised double graphs for a molecule: The first one encodes the atom-bond relations; The second one encodes bond-angle relations. Moreover, on top of the devised GNN architecture, we propose several novel geometry-level self-supervised learning strategies to learn spatial knowledge by utilizing the local and global molecular 3D structures. We compare ChemRL-GEM with various state-of-the-art (SOTA) baselines on different molecular benchmarks and exhibit that ChemRL-GEM can significantly outperform all baselines in both regression and classification tasks. For example, the experimental results show an overall improvement of 8.8% on average compared to SOTA baselines on the regression tasks, demonstrating the superiority of the proposed method.