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.
Paper solves capillary Orlicz-Minkowski problem with new inequalities.
Study of a flow related to the Orlicz-Minkowski problem for convex hypersurfaces.
Study anisotropic flows solving Orlicz-Minkowski problems, proving existence and new results.
Study an anisotropic capillary flow to solve capillary Orlicz-Minkowski problem.
New method solves generalized Minkowski problem for torsional rigidity.
Study anisotropic inverse Gauss curvature flows and solve dual Orlicz Minkowski problems.
Smooth even solutions found for a generalized convex geometry problem.
In this paper the dual Orlicz-Minkowski problem, a generalization of the dual Minkowski problem, is studied. By studying a flow involving the Gauss curvature and support function, we obtain a new existence result of solutions to this problem for smooth measures.
In this paper, the dual Orlicz curvature measure is proposed and its basic properties are provided. A variational formula for the dual Orlicz-quermassintegral is established in order to give a geometric interpretation of the dual Orlicz curvature measure. Based on the established variational formula, a solution to the …
Paper solves Minkowski problem for q-torsional rigidity using curvature flow.
Study proves only origin-centered spheres solve certain curvature problems.
This paper introduces the dual Orlicz-Brunn-Minkowski theory for star sets. A radial Orlicz addition of two or more star sets is proposed and a corresponding dual Orlicz-Brunn-Minkowski inequality is established. Based on a radial Orlicz linear combination of two star sets, a formula for the dual Orlicz mixed volume is…
This paper develops basic setting for the dual Orlicz-Brunn-Minkowski theory for star bodies. An Orlicz -radial addition of two or more star bodies is proposed and related dual Orlicz-Brunn-Minkowski inequality is established. Based on a linear Orlicz -radial addition of two star bodies, we derive a f…
Study anisotropic flows without global terms and solve dual Orlicz Christoffel-Minkowski problems.
The general volume of a star body, a notion that includes the usual volume, the th dual volumes, and many previous types of dual mixed volumes, is introduced. A corresponding new general dual Orlicz curvature measure is defined that specializes to the -dual curvature measures introduced recently by Lutwak, Ya…
This paper solves the dual Minkowski problem for q-torsional rigidity.
We survey the status of some decision problems for 3-manifolds and their fundamental groups. This includes the classical decision problems for finitely presented groups (Word Problem, Conjugacy Problem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold gr…
Optimal transport reformulates multiple quantile hedging problem.
Solves four problems related to circle families in the plane.
Solves four problems related to sphere families in 3D space.
The paper solves optimal control problems for various convex sets using convex trigonometry.
This paper is a tutorial for eigenvalue and generalized eigenvalue problems. We first introduce eigenvalue problem, eigen-decomposition (spectral decomposition), and generalized eigenvalue problem. Then, we mention the optimization problems which yield to the eigenvalue and generalized eigenvalue problems. We also prov…
This paper solves the Christoffel problem in hyperbolic space and its equivalent on spheres.
In the present paper, the primal-dual problem consisting of the investment risk minimization problem and the expected return maximization problem in the mean-variance model is discussed using replica analysis. As a natural extension of the investment risk minimization problem under only a budget constraint that we anal…
MathChat uses LLM agents to solve challenging math problems through conversational problem-solving.
The paper solves a generalized Christoffel-Minkowski problem using a curvature flow.
Paper solves Gromov-Wasserstein for point clouds efficiently.
The paper explains how microlocal analysis solves geometric inverse problems.
Proves NP and co-NP status for knot core recognition in solid torus.
The min-max problem, also known as the saddle point problem, is a class of optimization problems which minimizes and maximizes two subsets of variables simultaneously. This class of problems can be used to formulate a wide range of signal processing and communication (SPCOM) problems. Despite its popularity, most exist…
A new method solves complex control problems with random coefficients.
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For ea…
We present updates to the problems on Hirzebruch's 1954 problem list focussing on open problems, and on those where substantial progress has been made in recent years. We discuss some purely topological problems, as well as geometric problems about (almost) complex structures, both algebraic and non-algebraic, about co…
We present 27 problems encountered in automating the translation of movie/TV show subtitles. We categorize each problem in one of the three categories viz. problems directly related to textual translation, problems related to subtitle creation guidelines, and problems due to adaptability of machine translation (MT) eng…
Solves Brezis' first open problem on ball solutions.
Classical knot recognition problem solved in NP with exponential time algorithm.
Ranking problems, also known as preference learning problems, define a widely spread class of statistical learning problems with many applications, including fraud detection, document ranking, medicine, credit risk screening, image ranking or media memorability. In this article, we systematically review different types…
Paper solves four problems of pseudo-circle envelopes in Minkowski plane.
In this paper, we address the inverse problem, or the statistical machine learning problem, in Markov random fields with a non-parametric pair-wise energy function with continuous variables. The inverse problem is formulated by maximum likelihood estimation. The exact treatment of maximum likelihood estimation is intra…
Conference compiles problems on foliations and diffeomorphisms.
Solves double coset problem for braid group H_n.
In this paper, we discuss the uniqueness in an integral geometry problem in a strongly convex domain. Our problem is related to the problem of finding a Riemannian metric by the distances between all pairs of the boundary points. For the proof, the problem is reduced to an inverse source problem for a kinetic equation …
Study on geometric variational problems for existence, regularity, and uniqueness of solutions.
Solves a discrete logarithmic Minkowski problem for electrostatic p-capacity.
Study on biharmonic Steklov problems with Neumann boundary conditions and eigenvalue estimates.
Machine learning reduces combinatorial optimization problem dimensions.
New reformulations for multiclass classification problems using optimal transport.
In this paper we consider stochastic optimization problems for an ambiguity averse decision maker who is uncertain about the parameters of the underlying process. In a first part we consider problems of optimal stopping under drift ambiguity for one-dimensional diffusion processes. Analogously to the case of ordinary o…