arXiv research

The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.

Extends rigidity and existence results for discrete conformal structures on surfaces with boundary.

This paper completes the classification of discrete conformal structures on surfaces.

NES optimizes discrete structured VAEs effectively without gradient propagation.

Study on deforming discrete conformal structures on surfaces with boundaries.

Study preserves symplectic structure in forced discrete mechanical systems.

Alternative discrete Dirac mechanics using Dirac structures.

Novel symmetry found in nanocarbons' discrete principal curvature structure.

New theorem proves convergence of various discrete conformal structures to conformal maps.

This paper classifies discrete conformal structures on surfaces with boundary.

Study discretizes Dirac and port-Hamiltonian systems using manifolds.

New discrete conformal structures on surfaces with boundary, proving global rigidity and constructing hyperbolic metrics.

The paper studies deformation of discrete conformal structures on surfaces using combinatorial curvature flows.

The paper introduces combinatorial curvature and flow for polyhedral surfaces, proving rigidity and solving the Yamabe problem.

Proposes a differentiable structure learning framework for general binary data.

We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles. For discrete planar quadrilateral nets, circular nets, $Q^*$-nets and conical…

Paper proves rigidity of discrete conformal structures on polyhedral surfaces.

The study identifies all possible vector field structures on specific 2D shapes.

This text explores strategies for learning discrete latent structures in neural networks.

EBMs trained on discrete data using heat equations on graph structures.

Optimal discrete harmonic maps between hyperbolic surfaces are found via minimizing energy.

In the framework of nonassociative geometry (hep-th/0003238) a unified description of continuum and discrete spacetime is proposed. In our approach at the Planck scales the spacetime is described as a so-called "diodular discrete structure" which at large spacetime scales `looks like' a differentiable manifold. After a…

New method for flexible tubes and structures, enabling rigid-foldability.

This paper solves PDEs for embedding discrete lattices into smooth manifolds.

New framework for discrete-state diffusion models reduces sample complexity.

We find a normal form for two-input flat discrete-time systems.

We develop variational integrators from discrete Hamiltonian systems with external forces.

Library learns Bayesian networks from mixed data without discretization.

New spectral clustering method handles discrete covariates for better community detection.

CANDI solves the gap between continuous and discrete diffusion models for text generation.

A piecewise constant curvature manifold is a triangulated manifold that is assigned a geometry by specifying lengths of edges and stipulating that for a chosen background geometry (Euclidean, hyperbolic, or spherical), each simplex has an isometric embedding into the background geometry with the chosen edge lengths. Ad…

In this paper we build the structure equations and the integrable systems for a discrete centroaffine indefinite surface in $\R^3$. At the same time, some centroaffine invariants are obtained according to the structure equations. Using these centroaffine invariants, we study the Laplacian operator and the convexity of …

We describe recent links between two topics: geometric structures on manifolds in the sense of Ehresmann and Thurston, and dynamics "at infinity" for representations of discrete groups into Lie groups.

Unified framework for various geometric constructions.

Discretizes special surfaces using Koenigs nets.

The paper tackles fast rates in structured prediction problems.

Fractional combinatorial flow improves surface conformal structures.

We consider the problem of learning the structure of a pairwise graphical model over continuous and discrete variables. We present a new pairwise model for graphical models with both continuous and discrete variables that is amenable to structure learning. In previous work, authors have considered structure learning of…

The paper proves a discrete positive mass theorem for graphs.

Our aim in this paper is to provide a theory of discrete Riemann surfaces based on quadrilateral cellular decompositions of Riemann surfaces together with their complex structure encoded by complex weights. Previous work, in particular of Mercat, mainly focused on real weights corresponding to quadrilateral cells havin…

The study explores discrete versions of Riemannian geometry structures on manifolds.

This is an unrefereed lecture note based on lectures in 'Introductory Workshop on Discrete Differential Geometry' at Korea University on January 21--24, 2019. In this note, we discuss topological crystallography, which is a mathematical theory of crystal structures. The most symmetric structure among all placements of …

Novel SVAE learns interpretable discrete data representations from deep learning.

New method preserves MHD equations on sphere without costly matrix exponentials.

The paper develops algorithms and topological invariants for distinguishing dynamic systems.

FLOP algorithm speeds up causal structure learning for linear models.

A new method trains discrete EBMs without sampling.

We detail the theory of Discrete Riemann Surfaces. It takes place on a cellular decomposition of a surface, together with its Poincaré dual, equipped with a discrete conformal structure. A lot of theorems of the continuous theory follow through to the discrete case, we define the discrete analogs of period matrices, Ri…