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.
We create a smooth manifold of triangular meshes with a geodesically complete metric.
This work develops discrete Gaussian models for vector-valued data on triangular meshes.
We study the problem of approximating a surface in by a high quality mesh, a piecewise-flat triangulated surface whose triangles are as close as possible to equilateral. The MidNormal algorithm generates a triangular mesh that is guaranteed to have angles in the interval . As the mesh size $…
For mobile robots to operate autonomously in general environments, perception is required in the form of a dense metric map. For this purpose, we present the stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of the surface of the environment using a continuous mesh of triangular surface element…
In this note, we derive an approximation for the mean curvature normal vector on vertices of triangulated surface meshes from the Young-Laplace equation and the force balance principle. We then demonstrate that the approximation expression from our physics-based derivation is equivalent to the discrete Laplace-Beltrami…
New method for mesh denoising using TGV of normal vector field.
Discretizes Helfrich-type energies on surfaces using triangular complexes.
Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networ…
A conservative discretization of incompressible Navier-Stokes equations is developed based on discrete exterior calculus (DEC). A distinguishing feature of our method is the use of an algebraic discretization of the interior product operator and a combinatorial discretization of the wedge product. The governing equatio…
We will develop simple relations between the arc-lengths of a pair of geodesics that share common end-points. The two geodesics differ only by the requirement that one is constrained to lie in a subspace of the parent manifold. We will present two applications of our results. In the first example we explore the converg…
We propose a novel Bayesian nonparametric method to learn translation-invariant relationships on non-Euclidean domains. The resulting graph convolutional Gaussian processes can be applied to problems in machine learning for which the input observations are functions with domains on general graphs. The structure of thes…
This paper details the techniques and algorithms implemented in Kahler, a Python library that implements discrete exterior calculus on arbitrary Hermitian manifolds. Borrowing techniques and ideas first implemented in PyDEC, Kahler provides a uniquely general framework for computation using discrete exterior calculus. …
Given a triangulated region in the complex plane, a discrete vector field assigns a vector to every vertex. We call such a vector field holomorphic if it defines an infinitesimal deformation of the triangulation that preserves length cross ratios. We show that each holomorphic vector field can b…
The paper uses MDM theory to analyze multifiltering functions on simplicial complexes.
Differentiable voxelization for 3D meshes with GPU acceleration.
Deep network improves electrical tomography across multiple frequencies.
Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenien…
In this paper we study geometric, algebraic, and computational aspects of flexibility and infinitesimal flexibility of Kokotsakis meshes. A Kokotsakis mesh is a mesh that consists of a face in the middle and a certain band of faces attached to the middle face by its perimeter. In particular any 3x3-mesh made of quadran…
Generalized meshes for non-regular geometries, including fractures.
Paper presents a new triangular form for flat systems.
PolyGen models 3D meshes directly, predicting vertices and faces sequentially.
New method improves human mesh recovery for obese people.
Extends geometric decompositions to arbitrary meshes and forms.
The paper explores the topology of polygonal meshes and their properties.
Proposes a new CNN for meshes that can handle orientation.
Approximates smooth surfaces using Laguerre geometry meshes.
AQFC method estimates mesh curvatures using quadratic surfaces.
We consider the problem of approximate joint triangularization of a set of noisy jointly diagonalizable real matrices. Approximate joint triangularizers are commonly used in the estimation of the joint eigenstructure of a set of matrices, with applications in signal processing, linear algebra, and tensor decomposition.…
RFM simplifies generative modeling on complex geometries without simulation.
New findings on mesh group-planes validate Signature-inverse Theorem under specific conditions.
We construct a three-point compact finite difference scheme on a non-uniform mesh for the time-fractional Black-Scholes equation. We show that for special graded meshes used in finance, the Tavella-Randall and the quadratic meshes the numerical solution has a fourth-order accuracy in space. Numerical experiments are di…
The spectral geometry of mesh matrices of graphs is explored, leading to new formulas and eigenvalue estimates.
Introduces triangular transport for uncertain data.
Batch-splitting (data-parallelism) is the dominant distributed Deep Neural Network (DNN) training strategy, due to its universal applicability and its amenability to Single-Program-Multiple-Data (SPMD) programming. However, batch-splitting suffers from problems including the inability to train very large models (due to…
Solves problem of describing transformations for upper triangular Toeplitz operators.
Some methods based on simple regularizing geometric element transformations have heuristically been shown to give runtime efficient and quality effective smoothing algorithms for meshes. We describe the mathematical framework and a systematic approach to global optimization-based versions of such methods for mixed volu…
Triangular flows ensure statistical consistency and fast rates in generative modeling.
A novel algorithm for unbiased graph kernel estimation with subquadratic time complexity.
In this paper, we describe in detail a model of geometric-functional variability between fshapes. These objects were introduced for the first time by the authors in [Charlier et al. 2015] and are basically the combination of classical deformable manifolds with additional scalar signal map. Building on the aforementione…
Eliciting semantic similarity between concepts in the biomedical domain remains a challenging task. Recent approaches founded on embedding vectors have gained in popularity as they risen to efficiently capture semantic relationships The underlying idea is that two words that have close meaning gather similar contexts. …
A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of inform…
In this paper, we present a structurally flat triangular form which is based on the extended chained form. We provide necessary and sufficient conditions for an affine input system with two inputs to be static feedback equivalent to the proposed triangular form, and thus a sufficient condition for an affine input syste…
Paper uses GNNs to efficiently detect profitable triangular arbitrage opportunities.
Approximates surfaces using Laguerre geometry with spherical faces.
In this paper, the author considers the numerical computation of CVA for large systems by Mote Carlo methods. He introduces two types of stochastic mesh methods for the computations of CVA. In the first method, stochastic mesh method is used to obtain the future value of the derivative contracts. In the second method, …
New mesh network preserves symmetries in deep learning.
Paper proves discrete uniformizations converge to continuous for surfaces of genus ≥1.
We study the problem to provide a triangular form based on implicit differential equations for non-linear multi-input systems with respect to the flatness property. Furthermore, we suggest a constructive method for the transformation of a given system into that special triangular shape, if possible. The well known Brun…