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.
Two flat sub-Lorentzian problems on Martinet distribution differ in attainable set intersections.
Researchers found the longest arcs for specific sub-Lorentzian structures.
Proves existence of longest paths in sub-Lorentzian problems.
Optimal transport explored on a specific geometric space.
Researchers found sub-Lorentzian geodesics on a specific Lie subgroup.
Study on extremals in sub-Lorentzian geometry defined by antinorm.
Study on surfaces in Heisenberg group with constant mean curvature.
In this article we develop some elementary aspects of a theory of symmetry in sub-Lorentzian geometry. First of all we construct invariants characterizing isometric classes of sub-Lorentzian contact 3 manifolds. Next we characterize vector fields which generate isometric and conformal symmetries in general sub-Lorentzi…
We provide a classification of -invariant sub-Lorentzian structures on dimensional contact Lie groups. Our approach is based on invariants arising form the construction of a normal Cartan connection.
Study of a series of Lorentzian structures on SL(2,R) with SO(1,1) symmetry.
Sub-Riemannian Geometry is proved to play an important role in many applications, e.g., Mathematical Physics and Control Theory. The simplest example of sub-Riemannian structure is provided by the 3-D Heisenberg group. Sub-Riemannian Geometry enjoys major differences from the Riemannian being a generalisation of the la…
We study sub-Riemannian and sub-Lorentzian geometry on the Lie group $\SU(1,1)$ and on its universal cover $\CSU(1,1)$. In the sub-Riemannian case we find the distance function and completely describe sub-Riemannian geodesics on both $\SU(1,1)$ and $\CSU(1,1)$, connecting two fixed points. In particular, we prove that …
Study on Hausdorff dimension and curvature bounds in sub-Lorentzian Heisenberg group.
This paper classifies holonomy groups of K-contact sub-pseudo-Riemannian manifolds.
It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation function. Both lead to the definition of the Alexandrov topology, which…
We construct normal forms for Lorentzian metrics on Engel distributions under the assumption that abnormal curves are timelike future directed Hamiltonian geodesics. Then we indicate some cases in which the abnormal timelike future directed curve initiating at the origin is geometrically optimal. We also give certain e…
Let E be the Engel group and D be a rank 2 bracket generating left invariant distribution with a Lorentzian metric, which is a nondegenerate metric of index 1. In this paper, we first prove that timelike normal extremals are locally maximizing. Second, we obtain a parametrization of timelike, spacelike, lightlike norma…
We consider the four-dimensional nonholonomic distribution defined by the 4-potential of the electromagnetic field on the manifold. This distribution has a metric tensor with the Lorentzian signature , therefore, the causal structure appears as in the general relativity theory. By means of the Pontryagin's m…
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…
Study proves only origin-centered spheres solve certain curvature problems.
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…
New method solves generalized Minkowski problem for torsional rigidity.
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.
Describes state variables in sequential decision problems, linking them to Markovian and non-Markovian models.
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 …
This paper solves the dual Minkowski problem for q-torsional rigidity.