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.
Developed a new symmetric hyperbolic formulation for Einstein-Yang-Mills system.
The paper solves the Cauchy problem for Friedrichs systems on specific spacetime manifolds.
We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its development. In doing so, we demonstrate the viability of hyperbolic geometry f…
A Backlund transformation between two hyperbolic Monge-Ampere systems may be described as a certain type of exterior differential system on a 6-dimensional manifold B. The transformation is homogeneous if the group of symmetries of the system acts transitively on B. We give a complete classification of homogeneous Back…
Geometric operators link solutions on different spacetimes.
Hyperbolicity proven for a specific type of group extension.
It is unknown whether an unknotting tunnel is always isotopic to a geodesic in a finite volume hyperbolic 3-manifold. In this paper, we address the generalization of this problem to hyperbolic 3-manifolds admitting tunnel systems. We show that there exist finite volume hyperbolic 3-manifolds with a single cusp, with a …
Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.
Proves rigidity of 3D partially hyperbolic systems via autonomous dynamics.
Hyperbolic geometry reveals financial network structure and systemic importance.
The paper defines conditions for a free-by-free group to be hyperbolic.
Given a sub-hyperbolic semi-rational branched covering which is not CLH-equivalent a rational map, it must have the non-empty canonical Thurston obstruction. By using this canonical Thurston obstruction, we decompose this dynamical system in this paper into several sub-dynamical systems. Each of these sub-dynamical sys…
New classification of hyperbolic Monge-Ampère systems with .
Minimal crossing number found in arithmetic curve systems.
This paper extends, to a class of systems of semi-linear hyperbolic second order PDEs in three variables, the geometric study of a single nonlinear hyperbolic PDE in the plane as presented in [Anderson I.M., Kamran N., Duke Math. J. 87 (1997), 265-319]. The constrained variational bi-complex is introduced and used to d…
Study shows non-wandering, partially hyperbolic systems are ergodic.
A uniqueness result in the inverse problem for an inhomogeneous hyperbolic system on a real vector bundle over a smooth compact manifold, based on energy measurements for improperly known sources, is established.
We show the existence of a family of manifolds on which all (pointwise or absolutely) partially hyperbolic systems are dynamically coherent. This family is the set of 3-manifolds with nilpotent, non-abelian fundamental group. We further classify the partially hyperbolic systems on these manifolds up to leaf conjugacy. …
Researchers classify and characterize Bäcklund transformations for hyperbolic Monge-Ampère systems.
Study on symmetric hyperbolic systems with nonlocal potentials, proving well-posedness and existence of solutions.
Study of pulleys and gears in spherical and hyperbolic geometries.
This article is concerned with the question: For which pairs of hyperbolic Euler-Lagrange systems in the plane does there exist a rank- Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler-Lagrange systems. In addition, we discover a clas…
Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of ga…
Paper proves stability of solutions for specific hyperbolic systems.
Anosov flow found in specific partially hyperbolic systems.
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
Extensions (entropies) play a central role in the theory of hyperbolic conservation laws by providing intrinsic selection criteria for weak solutions. For a given hyperbolic system u_t+f(u)_x=0, a standard approach is to analyze directly the second order PDE system for the extensions. Instead we find it advantageous to…
This paper investigates the notion of learning user and item representations in non-Euclidean space. Specifically, we study the connection between metric learning in hyperbolic space and collaborative filtering by exploring Mobius gyrovector spaces where the formalism of the spaces could be utilized to generalize the m…
The two main theorems of this paper provide a characterization of hyperbolic affine iterated function systems defined on Rm. Atsushi Kameyama (Distances on Topological Self-Similar Sets, Proceedings of Symposia in Pure Mathematics, Volume 72.1, 2004) asked the following fundamental question: given a topological self-si…
New patterns on spheres and hyperbolic planes described by integrable systems.
One-parameter hyperbolic planar motion was first studied by S. Yce and N. Kuruolu. Moreover, they analyzed the relationships between the absolute, relative and sliding velocities of one-parameter hyperbolic planar motion as well as the related pole curves, \cite{Yuc}. One-paramete…
The paper studies hyperbolic equations in a spacetime foliation, proving existence and uniqueness.
Classifies 3D partially hyperbolic systems, proving ergodicity.
New formula for torsion function in 3-manifolds with torus boundaries.
Method constructs orthogonal curvilinear coordinates in constant curvature spaces.
The curvature and the reduced curvature are basic differential invariants of the pair (Hamiltonian system, Lagrange distribution) on the symplectic manifold. It is shown that the negativity of the reduced curvature implies the hyperbolicity of any compact invariant set of the Hamiltonian flow restricted to a prescribed…
A steady state (or equilibrium point) of a dynamical system is hyperbolic if the Jacobian at the steady state has no eigenvalues with zero real parts. In this case, the linearized system does qualitatively capture the dynamics in a small neighborhood of the hyperbolic steady state. However, one is often forced to consi…
In integrable hydrodynamic systems, coordinates exist where generators and symmetries are simple.
We consider a natural mechanical system on a Finsler manifold and study its \emph{curvature} using the intrinsic Jacobi equations (called \emph{Jacobi curves}) along the extremals of the least action of the system. The curvature for such a system is expressed in terms of the Riemann curvature and the Chern curvature (i…
In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomol…
We study the problem of constructing systems of hyperbolic conservation laws in one space dimension with prescribed eigencurves, i.e. the eigenvector fields of the Jacobian of the flux are given. We formulate this as a typically overdetermined system of equations for the eigenvalues-to-be. Equivalent formulations in te…
The notion of limit roots of a Coxeter group W was recently introduced (see arXiv:1112.5415 and arXiv:1303.6710): they are the accumulation points of directions of roots of a root system for W. In the case where the root system lives in a Lorentzian space W admits a faithful representation as a discrete reflection grou…
New dynamical approach defines symmedian as hyperbolic barycenter.
We consider hyperbolic and partially hyperbolic diffeomorphisms on compact manifolds. Associated with invariant foliation of these systems, we define some topological invariants and show certain relationships between these topological invariants and the geometric and Lyapunov growths of these foliations. As an applicat…
In this paper we introduce the hyperbolic mean curvature flow and prove that the corresponding system of partial differential equations are strictly hyperbolic, and based on this, we show that this flow admits a unique short-time smooth solution and possesses the nonlinear stability defined on the Euclidean space with …
We prove that for certain sequences of hyperbolic three--manifolds with cusps which converge to hyperbolic three--space in a weak ("Benjamini-Schramm") sense and certain coefficient systems the regularized analytic torsion approximates the -torsion of the universal cover under an additional hypothesis. We also pro…
In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles…
Twisted local systems on surfaces of finite type appear often in geometry and physics. Most of them arise geometrically as local systems of charts for pleated hyperbolic structures. Bonahon and Thurston's "shear-bend coordinates" parameterize these local systems of charts. On a surface …