Related papers: From Quantitative Spatial Operator to Qualitative …
Engineering projects for railway infrastructure typically involve many subsystems which need consistent views of the planned and built infrastructure and its underlying topology. Consistency is typically ensured by exchanging and verifying…
Active SLAM is the task of actively planning robot paths while simultaneously building a map and localizing within. Existing work has focused on planning paths with occupancy grid maps, which do not scale well and suffer from long term…
Geometric relational embeddings map relational data as geometric objects that combine vector information suitable for machine learning and structured/relational information for structured/relational reasoning, typically in low dimensions.…
Conditional Gaussian graphical models (cGGM) are a recent reparametrization of the multivariate linear regression model which explicitly exhibits $i)$ the partial covariances between the predictors and the responses, and $ii)$ the partial…
Semantic map models (SMMs) construct a network-like conceptual space from cross-linguistic instances or forms, based on the connectivity hypothesis. This approach has been widely used to represent similarity and entailment relationships in…
Task-oriented grasping (TOG) is more challenging than simple object grasping because it requires precise identification of object parts and careful selection of grasping areas to ensure effective and robust manipulation. While recent…
Cross-view geo-localization (CVGL) aims to estimate the geographic location of a street image by matching it with a corresponding aerial image. This is critical for autonomous navigation and mapping in complex real-world scenarios. However,…
Hypergraphs provide a natural way to represent polyadic relationships in network data. For large hypergraphs, it is often difficult to visually detect structures within the data. Recently, a scalable polygon-based visualization approach was…
Accurate and reliable prediction has profound implications to a wide range of applications. In this study, we focus on an instance of spatio-temporal learning problem--traffic prediction--to demonstrate an advanced deep learning model…
Here we investigate the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks. We do this for a variety of…
We develop a language for describing the relationship among observations, mathematical models, and the underlying principles from which they are derived. Using Information Geometry, we consider geometric properties of statistical models for…
Despite the continuous efforts in improving both the effectiveness and efficiency of code search, two issues remained unsolved. First, programming languages have inherent strong structural linkages, and feature mining of code as text form…
The study of irreducible higher-order interactions has become a core topic of study in complex systems. Two of the most well-developed frameworks, topological data analysis and multivariate information theory, aim to provide formal tools…
Human cognition excels at symbolic reasoning, deducing abstract rules from limited samples. This has been explained using symbolic and connectionist approaches, inspiring the development of a neuro-symbolic architecture that combines both…
Generating an interpretable and compact representation of 3D shapes from point clouds is an important and challenging problem. This paper presents CSG-Stump Net, an unsupervised end-to-end network for learning shapes from point clouds and…
Wheeler emphasized the study of Superspace - the space of 3-geometries on a spatial manifold of fixed topology. This is a configuration space for GR; knowledge of configuration spaces is useful as regards dynamics and QM.In this Article I…
The goal of this document is to survey existing methods for recovering CSG representations from unstructured data such as 3D point-clouds or polygon meshes. We review and discuss related topics such as the segmentation and fitting of the…
Many iterative methods in applied mathematics can be thought of as fixed-point iterations, and such algorithms are usually analyzed analytically, with inequalities. In this paper, we present a geometric approach to analyzing contractive and…
Recognizing precise geometrical configurations of groups of objects is a key capability of human spatial cognition, yet little studied in the deep learning literature so far. In particular, a fundamental problem is how a machine can learn…
A string-theoretic structure of the standard model is defined having a 4-D quantum gravity metric consistent with topological and algebraic first principles. Unique topological diagrams of string states, strong and weak interactions and…