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.
Simple constructions of semi-discrete and discrete surfaces using Jacobi elliptic functions.
Paper studies gradient fields from discrete Morse functions for watershed-cut computation.
Discretizes diffusions and harmonic functions on covering spaces.
Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann equations, the nonlinear one is based on the notion of circle patterns. We clari…
A formula connects discrete harmonic surfaces to holomorphic functions.
New method approximates Gaussian curvature on discrete surfaces.
The paper studies stability of discrete planar curves using variational methods.
Lectures on complex hyperbolic spaces and their groups.
A new method for discrete data normalizing flows using latent transformations.
This is a survey on rigidity and geometrization results obtained with the help of the discrete Hilbert-Einstein functional, written for the proceedings of the "Discrete Curvature" colloquium in Luminy.
We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under Möbius transformations. They can be obtained from discrete harmonic functions in the sense of the cotangent …
We present an explicit formula for the discrete power function introduced by Bobenko, which is expressed in terms of the hypergeometric τfunctions for the sixth Painlevé equation. The original definition of the discrete power function imposes strict conditions on the domain and the value of the exponent. However, we sh…
Discrete Morse functions induce shellings with critical tiles corresponding to function's critical faces.
Authors prove an asymptotic expansion for spectral zeta functions on discrete tori.
Exact Bayesian inference for discrete models using probability generating functions.
New method extends discrete Morse theory to simplicial complexes.
We propose a discretization of classical confocal coordinates. It is based on a novel characterization thereof as factorizable orthogonal coordinate systems. Our geometric discretization leads to factorizable discrete nets with a novel discrete analog of the orthogonality property. A discrete confocal coordinate system…
PDHAMS improves sampling for discrete distributions with quadratic potential functions.
The paper uses MDM theory to analyze multifiltering functions on simplicial complexes.
We derive a discrete analogue of Morse-Bott theory on CW complexes and use this discrete Morse-Bott function to do some Conley theory analysis. It turns out that our discrete Morse-Bott theory is indeed a generalization of Forman's discrete Morse theory.
The study identifies all possible vector field structures on specific 2D shapes.
The paper analyzes Laplacian pyramids for extending and denoising discrete functions.
New method reduces bias in estimating causal effects from discretized variables.
For covering spaces and properly discontinuous actions with compatible diffusion processes, we discuss Lyons-Sullivan discretizations of the processes and the associated function theory.
New proof for discrete Morse theory using combinatorial construction.
We construct explicit solutions to continuous motion of discrete plane curves described by a semi-discrete potential modified KdV equation. Explicit formulas in terms the function are presented. Bäcklund transformations of the discrete curves are also discussed. We finally consider the continuous limit of discrete …
Extends Neural ODEs to model discrete changes in continuous systems.
Confocal quadrics lie at the heart of the system of confocal coordinates (also called elliptic coordinates, after Jacobi). We suggest a discretization which respects two crucial properties of confocal coordinates: separability and all two-dimensional coordinate subnets being isothermic surfaces (that is, allowing a con…
Improved density estimation for mixed discrete-continuous data.
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…
It is proved that every discrete Morse function in the sense of Forman on a finite regular CW complex can be represented by a polyhedral Morse function in the sense of Banchoff on an appropriate embedding in Euclidean space of the barycentric subdivision of the CW complex; such a representation preserves critical point…
We construct explicit solutions to the discrete motion of discrete plane curves that has been introduced by one of the authors recently. Explicit formulas in terms the function are presented. Transformation theory of the motions of both smooth and discrete curves is developed simultaneously.
A new functional for simplicial surfaces is suggested. It is invariant with respect to Moebius transformations and is a discrete analogue of the Willmore functional. Minima of this functional are investigated. as an application a bending energy for discrete thin-shells is derived.
The paper proves a discrete positive mass theorem for graphs.
Paper introduces DMPMs for efficient discrete data generation with sharp convergence bounds.
Paper explores neural network approximations on sphere domains.
Paper tackles functional linear regression using spectral algorithms with discrete observations.
In this paper, we consider the problem of black box continuous submodular maximization where we only have access to the function values and no information about the derivatives is provided. For a monotone and continuous DR-submodular function, and subject to a bounded convex body constraint, we propose Black-box Contin…
Proposes a continuous relaxation for discrete Bayesian optimization.
Lyons and Sullivan have shown how to discretize harmonic functions on a Riemannian manifold whose Brownian motion satisfies a certain recurrence property called -recurrence. We study analogues of this discretization for tensor fields which are harmonic in the sense of the covariant Laplacian. We show that, un…
Proves hardness of semi-discrete optimal transport and proposes regularization methods.
A new method trains discrete EBMs without sampling.
Study shows financial value of weak information converges in discrete vs continuous markets.
Framework for training-free guidance in discrete diffusion models for molecular generation.
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al. (2010a), the method, which support mixed discrete and continuous explanatory variables,…
In the case of smooth manifolds, we use Forman's discrete Morse theory to realize combinatorially any Thom-Smale complex coming from a smooth Morse function by a couple triangulation-discrete Morse function. As an application, we prove that any Euler structure on a smooth oriented closed 3-manifold has a particular rea…
The paper analyzes spectral properties of connection Laplacian on tori, proving convergence to real torus.
Discrete Green's functions are the inverses or pseudo-inverses of combinatorial Laplacians. We present compact formulas for discrete Green's functions, in terms of the eigensystems of corresponding Laplacians, for products of regular graphs with or without boundary. Explicit formulas are derived for the cycle, torus, a…