A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Expanding on previous work, this note generalizes geometric structures results.
We propose a method to learn object representations from 3D point clouds using bundles of geometrically interpretable hidden units, which we call geometric capsules. Each geometric capsule represents a visual entity, such as an object or a part, and consists of two components: a pose and a feature. The pose encodes whe…
In this paper we study a collection of jet geometrical concepts, we refer to d-tensors, relativistic time dependent semisprays, harmonic curves and nonlinear connections on the 1-jet space J1(R;M), necessary to the construction of a Miron's-like geometrization for Lagrangians depending on a relativistic time. The geome…
Soft geometric bias improves physical dynamics predictions.
We classify the torsion pairs in a tube category and show that they are in bijection with maximal rigid objects in the extension of the tube category containing the Pruefer and adic modules. We show that the annulus geometric model for the tube category can be extended to the larger category and interpret torsion pairs…
The paper introduces a new method to measure the shape relations between biological objects using r-parallel sets.
In this paper we study some geometrical objects (d-tensors, multi-time semisprays of polymomenta and nonlinear connections) on the dual 1-jet vector bundle . Some geometrical formulas, which connect the last two geometrical objects, are also derived. Finally, a canonical nonlinear…
The aim of the present paper is to provide an \emph{intrinsic} investigation of the properties of the most important geometric objects associated with the fundamental linear connections in Finsler geometry. We investigate intrinsically the most general relations concerning the torsion tensor fields and the curvature te…
Introduces VB-structures for geometric objects on manifolds.
The study reveals chaos in geometric objects embedded in higher dimensions.
New proof confirms rolling objects can follow any path.
The aim of this paper is to obtain on the dual 1-jet space J^{1*}(R;M) the main geometrical objects used in the dual jet geometry of time-dependent Hamiltonians. We talk about distinguished (d-) tensors, time-dependent semisprays, nonlinear connections and their mathematical connections.
Classifies objects in graded skew-gentle algebras using geometric models.
Deep models generate geometric objects with global properties.
The approach we present is a modification of the Morse theory for unital C*-algebras. We provide tools for the geometric interpretation of noncommutative CW complexes. These objects were introduced and studied in [2],[7] and [14]. Some examples to illustrate these geometric information in practice are given. A classifi…
Introduces three types of partial bihamiltonian structures.
In this paper we construct some natural geometrical objects on the 1-jet space J^1(R,R^3), like a nonlinear connection, a Cartan linear connection (together with its d-torsions and d-curvatures), a jet "electromagnetic" d-field and its geometric "electromagnetic" Yang-Mills energy, starting from a given dynamical syste…
Method learns symmetries in curves without augmentation.
Variational approach to basic manifold structures.
Improved private geometric median estimation with nearly-linear time complexity.
Cactus doodles are geometric objects derived from cactus groups.
New geometric object for polynomials simplifies complex data.
This document contains a description of physics entirely based on a geometric presentation: all of the theory is described giving only a pseudo-riemannian manifold (M, g) of dimension n > 5 for which the g tensor is, in studied domains, almost everywhere of signature (-, -, +, ..., +). No object is added to this space-…
This paper presents KeypointNet, an end-to-end geometric reasoning framework to learn an optimal set of category-specific 3D keypoints, along with their detectors. Given a single image, KeypointNet extracts 3D keypoints that are optimized for a downstream task. We demonstrate this framework on 3D pose estimation by pro…
Machine learning methods struggle with geometric data, but shape space analysis provides a framework for studying and analyzing geometric variability.
We propose to jointly learn multi-view geometry and warping between views of the same object instances for robust cross-view object detection. What makes multi-view object instance detection difficult are strong changes in viewpoint, lighting conditions, high similarity of neighbouring objects, and strong variability i…
We provide a draft of a theory of geometric integration of rough differential forms which are generalizations of classical (smooth) differential forms to similar objects with very low regularity, for instance, involving Hölder continuous functions that may be nowhere differentiable. Borrowing ideas from the theory of r…
In this paper we provide a \emph{global} investigation of the geometry of parallelizable manifolds (or absolute parallelism geometry) frequently used for application. We discuss the different linear connections and curvature tensors from a global point of view. We give an existence and uniqueness theorem for a remarkab…
In this paper are constructed a series of geometrical objects on the 1-jet fibre bundle , which is a basic object in the study of classical and quantum field.
Geometric framework links clustering accuracy to structural recovery.
The paper geometrically characterizes graded manifolds and proves the Frobenius theorem.
Objects are composed of a set of geometrically organized parts. We introduce an unsupervised capsule autoencoder (SCAE), which explicitly uses geometric relationships between parts to reason about objects. Since these relationships do not depend on the viewpoint, our model is robust to viewpoint changes. SCAE consists …
We propose approaches based on deep learning to localize objects in images when only a small training dataset is available and the images have low quality. That applies to many problems in medical image processing, and in particular to the analysis of fluoroscopic (low-dose) X-ray images, where the images have low cont…
PackIt creates a virtual space for testing geometric planning skills.
Study para-Ricci-like solitons on special Riemannian manifolds, proving geometric properties and providing an example.
The study explores how different Grothendieck topologies and functors between categories preserve locality.
SpatialSim benchmarks machine learning in recognizing object spatial configurations.
Robot learns to manipulate objects using multiple geometric representations.
The aim of this paper is to construct natural geometrical objects on the 1-jet space J^1(T,R^5), where , like a non-linear connection, a generalized Cartan connection, together with its d-torsions and d-curvatures, a jet electromagnetic d-field and a jet Yang-Mills energy, starting from the given Lorenz atm…
Geometric analysis improves convergence of variational inference.
New methods improve accuracy in detecting concentric objects.
The main results on the theory of conformal and almost Grassmann structures are presented. The common properties of these structures and also the differences between them are outlined. In particular, the structure groups of these structures and their differential prolongations are found. A complete system of geometric …
Geometric approach to majorizing measures for polyhedra and general compact objects.
We elaborate an unified geometric approach to classical mechanics, Riemann-Finsler spaces and gravity theories on Lie algebroids provided with nonlinear connection (N-connection) structure. There are investigated the conditions when the fundamental geometric objects like the anchor, metric and linear connection, almost…
3D convolutional neural networks (3D-CNN) have been used for object recognition based on the voxelized shape of an object. In this paper, we present a 3D-CNN based method to learn distinct local geometric features of interest within an object. In this context, the voxelized representation may not be sufficient to captu…
A fundamental problem in computer vision is boundary estimation, where the goal is to delineate the boundary of objects in an image. In this paper, we propose a method which jointly incorporates geometric and topological information within an image to simultaneously estimate boundaries for objects within images with mo…
We prove that "generalized Lie algebroid", a geometric object which appeared recently in the literature, is a misconception.
With the renewed and growing interest in geometric continuity in mind, this article gives a general definition of geometrically continuous polygonal surfaces and geometrically continuous spline functions on them. Polynomial splines defined by G1 gluing data in terms of rational functions are analyzed further. A general…