Graph SLAM-Based 2.5D LIDAR Mapping Module for Autonomous Vehicles

This paper proposes a unique Graph SLAM framework to generate precise 2.5D LIDAR maps in an XYZ plane. A node strategy was invented to divide the road into a set of nodes. The LIDAR point clouds are smoothly accumulated in intensity and elevation images in each node. The optimization process is decomposed into applying Graph SLAM on nodes’ intensity images for eliminating the ghosting effects of the road surface in the XY plane. This step ensures true loop-closure events between nodes and precise common area estimations in the real world. Accordingly, another Graph SLAM framework was designed to bring the nodes’ elevation images into the same Z-level by making the altitudinal errors in the common areas as small as possible. A robust cost function is detailed to properly constitute the relationships between nodes and generate the map in the Absolute Coordinate System. The framework is tested against an accurate GNSS/INS-RTK system in a very challenging environment of high buildings, dense trees and longitudinal railway bridges. The experimental results verified the robustness, reliability and efficiency of the proposed framework to generate accurate 2.5D maps with eliminating the relative and global position errors in XY and Z planes. Therefore, the generated maps significantly contribute to increasing the safety of autonomous driving regardless of the road structures and environmental factors.

GraphPrompt: Biomedical Entity Normalization Using Graph-based Prompt Templates

Biomedical entity normalization unifies the language across biomedical experiments and studies, and further enables us to obtain a holistic view of life sciences. Current approaches mainly study the normalization of more standardized entities such as diseases and drugs, while disregarding the more ambiguous but crucial entities such as pathways, functions and cell types, hindering their real-world applications. To achieve biomedical entity normalization on these under-explored entities, we first introduce an expert-curated dataset OBO-syn encompassing 70 different types of entities and 2 million curated entity-synonym pairs. To utilize the unique graph structure in this dataset, we propose GraphPrompt, a prompt-based learning approach that creates prompt templates according to the graphs. GraphPrompt obtained 41.0% and 29.9% improvement on zero-shot and few-shot settings respectively, indicating the effectiveness of these graph-based prompt templates. We envision that our method GraphPrompt and OBO-syn dataset can be broadly applied to graph-based NLP tasks, and serve as the basis for analyzing diverse and accumulating biomedical data.

The Optimal Graph Whose Least Eigenvalue is Minimal among All Graphs via 1-2 Adjacency Matrix

All graphs under consideration are finite, simple, connected, and undirected. Adjacency matrix of a graph G is 0,1 matrix A = a i j = 0 , i f v i = v j o r d v i , v j ≥ 2 1 , i f d v i , v j = 1. . Here in this paper, we discussed new type of adjacency matrix known by 1-2 adjacency matrix defined as A 1,2 G = a i j = 0 , i f v i = v j o r d v i , v j ≥ 3 1 , i f d v i , v j = 2 , from eigenvalues of the graph, we mean eigenvalues of the 1-2 adjacency matrix. Let T n c be the set of the complement of trees of order n . In this paper, we characterized a unique graph whose least eigenvalue is minimal among all the graphs in T n c .

On the Reformulated Multiplicative First Zagreb Index of Trees and Unicyclic Graphs

The multiplicative first Zagreb index of a graph H is defined as the product of the squares of the degrees of vertices of H . The line graph of a graph H is denoted by L H and is defined as the graph whose vertex set is the edge set of H where two vertices of L H are adjacent if and only if they are adjacent in H . The multiplicative first Zagreb index of the line graph of a graph H is referred to as the reformulated multiplicative first Zagreb index of H . This paper gives characterization of the unique graph attaining the minimum or maximum value of the reformulated multiplicative first Zagreb index in the class of all (i) trees of a fixed order (ii) connected unicyclic graphs of a fixed order.

On graft transformations decreasing distance spectral radius of graphs

The distance spectral radius of a connected graph is the largest eigenvalue of its distance matrix. In this paper, we give several less restricted graft transformations that decrease the distance spectral radius, and determine the unique graph with minimum distance spectral radius among homeomorphically irreducible unicylic graphs on $n\geq 6$ vertices, and the unique tree with minimum distance spectral radius among trees on $n$ vertices with given number of vertices of degree two, respectively.

A Graph Neural Network for Predicting Energy and Stability of Known and Hypothetical Crystal Structures

The discovery of new inorganic materials in unexplored chemical spaces necessitates calculating total energy quickly and with sufficient accuracy. Machine learning models that provide such a capability for both ground-state (GS) and higher-energy structures would be instrumental in accelerating the screening for new materials over vast chemical spaces. Here, we develop a unique graph neural network model to accurately predict the total energy of both GS and higher-energy hypothetical structures. We use ~16,500 density functional theory calculated total energy from the NREL Materials Database and ~11,000 in-house generated hypothetical structures to train our model, thus making sure that the model is not biased towards either GS or higher-energy structures. We also demonstrate that our model satisfactorily ranks the structures in the correct order of their energies for a given composition. Furthermore, we present a thorough error analysis to explain several failure modes of the model, which highlights both prediction outliers and occasional inconsistencies in the training data. By peeling back layers of the neural network model, we are able to derive chemical trends by analyzing how the model represents learned structures and properties.

A Graph Neural Network for Predicting Energy and Stability of Known and Hypothetical Crystal Structures

The discovery of new inorganic materials in unexplored chemical spaces necessitates calculating total energy quickly and with sufficient accuracy. Machine learning models that provide such a capability for both ground-state (GS) and higher-energy structures would be instrumental in accelerating the screening for new materials over vast chemical spaces. Here, we develop a unique graph neural network model to accurately predict the total energy of both GS and higher-energy hypothetical structures. We use ~16,500 density functional theory calculated total energy from the NREL Materials Database and ~11,000 in-house generated hypothetical structures to train our model, thus making sure that the model is not biased towards either GS or higher-energy structures. We also demonstrate that our model satisfactorily ranks the structures in the correct order of their energies for a given composition. Furthermore, we present a thorough error analysis to explain several failure modes of the model, which highlights both prediction outliers and occasional inconsistencies in the training data. By peeling back layers of the neural network model, we are able to derive chemical trends by analyzing how the model represents learned structures and properties.

GoGNN: Graph of Graphs Neural Network for Predicting Structured Entity Interactions

Entity interaction prediction is essential in many important applications such as chemistry, biology, material science, and medical science. The problem becomes quite challenging when each entity is represented by a complex structure, namely structured entity, because two types of graphs are involved: local graphs for structured entities and a global graph to capture the interactions between structured entities. We observe that existing works on structured entity interaction prediction cannot properly exploit the unique graph of graphs model. In this paper, we propose a Graph of Graphs Neural Network, namely GoGNN, which extracts the features in both structured entity graphs and the entity interaction graph in a hierarchical way. We also propose the dual-attention mechanism that enables the model to preserve the neighbor importance in both levels of graphs. Extensive experiments on real-world datasets show that GoGNN outperforms the state-of-the-art methods on two representative structured entity interaction prediction tasks: chemical-chemical interaction prediction and drug-drug interaction prediction. Our code is available at Github.

The second-minimum Wiener index of cacti with given cycles

The Wiener index [Formula: see text] of a connected graph [Formula: see text] is the sum of distances between all pairs of vertices of [Formula: see text]. A connected graph [Formula: see text] is said to be a cactus if each of its blocks is either a cycle or an edge. Let [Formula: see text] be the set of all [Formula: see text]-vertex cacti containing exactly [Formula: see text] cycles. Liu and Lu (2007) determined the unique graph in [Formula: see text] with the minimum Wiener index. Gutman, Li and Wei (2017) determined the unique graph in [Formula: see text] with maximum Wiener index. In this paper, we present the second-minimum Wiener index of graphs in [Formula: see text] and identify the corresponding extremal graphs, which solve partially the problem proposed by Gutman et al. [Cacti with [Formula: see text]-vertices and [Formula: see text] cycles having extremal Wiener index, Discrete Appl. Math. 232 (2017) 189–200] in 2017.

On minimum algebraic connectivity of graphs whose complements are bicyclic

The second smallest eigenvalue of the Laplacian matrix of a graph (network) is called its algebraic connectivity which is used to diagnose Alzheimer’s disease, distinguish the group differences, measure the robustness, construct multiplex model, synchronize the stability, analyze the diffusion processes and find the connectivity of the graphs (networks). A connected graph containing two or three cycles is called a bicyclic graph if its number of edges is equal to its number of vertices plus one. In this paper, firstly the unique graph with a minimum algebraic connectivity is characterized in the class of connected graphs whose complements are bicyclic with exactly three cycles. Then, we find the unique graph of minimum algebraic connectivity in the class of connected graphs $\begin{array}{} {\it\Omega}^c_{n}={\it\Omega}^c_{1,n}\cup{\it\Omega}^c_{2,n}, \end{array}$ where $\begin{array}{} {\it\Omega}^c_{1,n} \end{array}$ and $\begin{array}{} {\it\Omega}^c_{2,n} \end{array}$ are classes of the connected graphs in which the complement of each graph of order n is a bicyclic graph with exactly two and three cycles, respectively.