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1. Enumeration and Identification of Unique 3D Spatial Topologies of Interconnected Engineering Systems Using Spatial Graphs

   https://doi.org/10.1115/1.4062978  

   Peddada, Satya_R T; Dunfield, Nathan M; Zeidner, Lawrence E; Givans, Zane R; James, Kai A; Allison, James T (October 2023, Journal of Mechanical Design)

   Systematic enumeration and identification of unique 3D spatial topologies (STs) of complex engineering systems (such as automotive cooling systems, electric power trains, satellites, and aero-engines) are essential to navigation of these expansive design spaces with the goal of identifying new spatial configurations that can satisfy challenging system requirements. However, efficient navigation through discrete 3D ST options is a very challenging problem due to its combinatorial nature and can quickly exceed human cognitive abilities at even moderate complexity levels. This article presents a new, efficient, and scalable design framework that leverages mathematical spatial graph theory to represent, enumerate, and identify distinctive 3D topological classes for a generic 3D engineering system, given its system architecture (SA)—its components and their interconnections. First, spatial graph diagrams (SGDs) are generated for a given SA from zero to a specified maximum number of interconnect crossings. Then, corresponding Yamada polynomials for all the planar SGDs are generated. SGDs are categorized into topological classes, each of which shares a unique Yamada polynomial. Finally, within each topological class, 3D geometric models are generated using the SGDs having different numbers of interconnect crossings. Selected case studies are presented to illustrate the different features of our proposed framework, including an industrial engineering design application: ST enumeration of a 3D automotive fuel cell cooling system (AFCS). Design guidelines are also provided for practicing engineers to aid the application of this framework to different types of real-world problems such as configuration design and spatial packaging optimization. 

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2. Learning and Visualizing Localized Geometric Features Using 3D-CNN: An Application to Manufacturability Analysis of Drilled Holes

   Ghadai, Sambit; Balu, Aditya; Krishnamurthy, Adarsh; Sarkar, Soumik (January 2017, NIPS Symposium on Interpretable Machine Learning)

   3D Convolutional Neural Networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. However, interpreting the decision making process of these 3D-CNNs is still an infeasible task. In this paper, we present a unique 3D-CNN based Gradient-weighted Class Activation Mapping method (3D-GradCAM) for visual explanations of the distinct local geometric features of interest within an object. To enable efficient learning of 3D geometries, we augment the voxel data with surface normals of the object boundary. We then train a 3D-CNN with this augmented data and identify the local features critical for decision-making using 3D GradCAM. An application of this feature identification framework is to recognize difficult-to-manufacture drilled hole features in a complex CAD geometry. The framework can be extended to identify difficult-to-manufacture features at multiple spatial scales leading to a real-time design for manufacturability decision support system. 

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3. Earth Imagery Segmentation on Terrain Surface with Limited Training Labels: A Semi-supervised Approach based on Physics-Guided Graph Co-Training

   https://doi.org/10.1145/3481043  

   He, Wenchong; Sainju, Arpan Man; Jiang, Zhe; Yan, Da; Zhou, Yang (April 2022, ACM Transactions on Intelligent Systems and Technology)

   Given earth imagery with spectral features on a terrain surface, this paper studies surface segmentation based on both explanatory features and surface topology. The problem is important in many spatial and spatiotemporal applications such as flood extent mapping in hydrology. The problem is uniquely challenging for several reasons: first, the size of earth imagery on a terrain surface is often much larger than the input of popular deep convolutional neural networks; second, there exists topological structure dependency between pixel classes on the surface, and such dependency can follow an unknown and non-linear distribution; third, there are often limited training labels. Existing methods for earth imagery segmentation often divide the imagery into patches and consider the elevation as an additional feature channel. These methods do not fully incorporate the spatial topological structural constraint within and across surface patches and thus often show poor results, especially when training labels are limited. Existing methods on semi-supervised and unsupervised learning for earth imagery often focus on learning representation without explicitly incorporating surface topology. In contrast, we propose a novel framework that explicitly models the topological skeleton of a terrain surface with a contour tree from computational topology, which is guided by the physical constraint (e.g., water flow direction on terrains). Our framework consists of two neural networks: a convolutional neural network (CNN) to learn spatial contextual features on a 2D image grid, and a graph neural network (GNN) to learn the statistical distribution of physics-guided spatial topological dependency on the contour tree. The two models are co-trained via variational EM. Evaluations on the real-world flood mapping datasets show that the proposed models outperform baseline methods in classification accuracy, especially when training labels are limited. 

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4. Graph-based autoencoder integrates spatial transcriptomics with chromatin images and identifies joint biomarkers for Alzheimer’s disease

   https://doi.org/10.1038/s41467-022-35233-1  

   Zhang, Xinyi; Wang, Xiao; Shivashankar, G_V; Uhler, Caroline (December 2022, Nature Communications)

   Abstract Tissue development and disease lead to changes in cellular organization, nuclear morphology, and gene expression, which can be jointly measured by spatial transcriptomic technologies. However, methods for jointly analyzing the different spatial data modalities in 3D are still lacking. We present a computational framework to integrate Spatial Transcriptomic data using over-parameterized graph-based Autoencoders with Chromatin Imaging data (STACI) to identify molecular and functional alterations in tissues. STACI incorporates multiple modalities in a single representation for downstream tasks, enables the prediction of spatial transcriptomic data from nuclear images in unseen tissue sections, and provides built-in batch correction of gene expression and tissue morphology through over-parameterization. We apply STACI to analyze the spatio-temporal progression of Alzheimer’s disease and identify the associated nuclear morphometric and coupled gene expression features. Collectively, we demonstrate the importance of characterizing disease progression by integrating multiple data modalities and its potential for the discovery of disease biomarkers. 

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5. A Majority Theorem for the Uncapacitated p = 2 Median Problem and Local Spatial Autocorrelation

   https://doi.org/10.3390/math13020249  

   Griffith, Daniel A; Chun, Yongwan; Kim, Hyun (January 2025, Mathematics)

   The existing quantitative geography literature contains a dearth of articles that span spatial autocorrelation (SA), a fundamental property of georeferenced data, and spatial optimization, a popular form of geographic analysis. The well-known location–allocation problem illustrates this state of affairs, although its empirical geographic distribution of demand virtually always exhibits positive SA. This latent redundant attribute information alludes to other tools that may well help to solve such spatial optimization problems in an improved, if not better than, heuristic way. Within a proof-of-concept perspective, this paper articulates connections between extensions of the renowned Majority Theorem of the minisum problem and especially the local indices of SA (LISA). The relationship articulation outlined here extends to the p = 2 setting linkages already established for the p = 1 spatial median problem. In addition, this paper presents the foundation for a novel extremely efficient p = 2 algorithm whose formulation demonstratively exploits spatial autocorrelation. 

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