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.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
Proves energy estimates for tensorial wave equations, decoupling components for stability proof.
Study proves global existence and decay for complex wave equations.
Develops equivariant connections for Yang-Mills equations, simplifying interactions modeling.
DISTANA predicts and denoises spatial wave dynamics.
We study two inverse problems on a globally hyperbolic Lorentzian manifold . The problems are: 1. Passive observations in spacetime: Consider observations in a neighborhood of a time-like geodesic . Under natural causality conditions, we reconstruct the conformal type of the unknown open, relativ…
Researchers can retrieve Yang-Mills-Higgs fields from Minkowski space measurements.
Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of singularity theory of differentiable mappings, initiated by H. Whitney and…
We study the following problem: Given initial data on a compact Cauchy horizon, does there exist a unique solution to wave equations on the globally hyperbolic region? Our main results apply to any spacetime satisfying the null energy condition and containing a compact Cauchy horizon with surface gravity that can be no…
Starting from a relativistic phenomenology of anyons in crystals, we discuss the concept of relativistic interaction and the need to unify electromagnetism and gravitation within the Spencer cohomology of Lie equations. Then, from the sophisticated non-linear Spencer complex of the Poincaré and conformal Lie pseudogrou…
We establish the full global non-linear stability of the Kerr-de Sitter family of black holes, as solutions of the initial value problem for the Einstein vacuum equations with positive cosmological constant, for small angular momenta, and without any symmetry assumptions on the initial data. We achieve this by extendin…
The study finds solutions to a financial equation related to volatility.
These lecture notes, based on a course given at the Zurich Clay Summer School (June 23-July 18, 2008), review our current mathematical understanding of the global behaviour of waves on black hole exterior backgrounds. Interest in this problem stems from its relationship to the non-linear stability of the black hole spa…
We prove the global non-linear stability, without symmetry assumptions, of slowly rotating charged black holes in de Sitter spacetimes in the context of the initial value problem for the Einstein-Maxwell equations: If one perturbs the initial data of a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole, then in a …
Conservation laws, heirarchies, scattering theory and Bäcklund transformations are known to be the building blocks of integrable partial differential equations. We identify these as facets of a theory of Poisson group actions, and apply the theory to the ZS-AKNS nxn heirarchy (which includes the non-linear Schrödinger …
Proves stability of Minkowski space-time for Einstein-Yang-Mills equations.
Tractable model explains market dynamics using Langevin and SUSY QM.
To every Darboux integrable system there is an associated Lie group which is a fundamental invariant of the system and which we call the Vessiot group. This article shows that solving the Cauchy problem for a Darboux integrable partial differential equation can be reduced to solving an equation of Lie type for the …
It is known that the Schrödinger flow on a complex Grassmann manifold is equivalent to the matrix non-linear Schrödinger equation and the Ferapontov flow on a principal Adjoint U(n)-orbit is equivalent to the -wave equation. In this paper, we give a systematic method to construct integrable geometric curve flows on …
We show that degenerate horizons exhibit a new trapping effect. Specifically, we obtain a non-degenerate Morawetz estimate for the wave equation in the domain of outer communications of extremal Reissner-Nordstrom up to and including the future event horizon. We show that such an estimate requires 1) a higher degree of…
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
New Galilean spacetimes found as pp-wave reductions.
Analyzes Gerstner's trochoidal waves and their geometric properties.
Wave fronts on certain surfaces become dense.
The paper develops a state-space approach to deep Gaussian processes for efficient state estimation.
Stability of Minkowski space-time in Einstein-Yang-Mills system proven.
We adopt a vierbein formalism to study pseudo-Finsler spaces modeled on a pseudo-Minkowski space. We show that it is possible to obtain closed expressions for most of the geometric objects of the theory, including Berwald's curvature, Landsberg's tensor, Douglas' curvature, non-linear connection and Ricci scalar. These…
Analyzes properties of stiffness tensors for elastic wave imaging.
Deep learning model predicts wind-wave relationship.
We give a review of the systematic construction of hierarchies of soliton flows and integrable elliptic equations associated to a complex semi-simple Lie algebra and finite order automorphisms. For example, the non-linear Schrödinger equation, the n-wave equation, and the sigma-model are soliton flows; and the equation…
Impulsive waves contradict a 1962 conjecture about pp-waves.
Extends Penrose limit to Finsler spacetimes.
New findings on plane waves in 3D spacetimes, showing non-unimodular elliptic plane waves are unique.
Classifies solutions to vacuum weighted Einstein equations on pr-waves.
High frequency limit for most of wave phenomena is known as quasiclassical limit or ray optics limit. Propagation of waves in this limit is described in terms of wave fronts and rays. Wave front is a surface of constant phase whose points are moving along rays. As it appears, their motion can be described by Hamilton e…
Study compact plane waves, showing they are essentially standard.
We characterize singularities of focal surfaces of wave fronts in terms of differential geometric properties of the initial wave fronts. Moreover, we study relationships between geometric properties of focal surfaces and geometric invariants of the initial wave fronts.
New method finds precise late-time behavior of wave equations.
Paper explores non-uniqueness and uniqueness class for wave equations on graphs.
The financial rogue waves are reported analytically in the nonlinear option pricing model due to Ivancevic, which is nonlinear wave alternative of the Black-Scholes model. These solutions may be used to describe the possible physical mechanisms for rogue wave phenomenon in financial markets and related fields.
New metrics link Kähler and pp-wave spacetimes.
The accurate characterization of the business cycles in the nonlinear dynamic financial and economic systems in the time of globalization represents a formidable research problem. The central banks and other financial institutions make their decisions on the minimum capital requirements, countercyclical capital buffer …
We show that every n-dimensional locally homogeneous pp-wave is a plane wave, provided it is indecomposable and its curvature operator, when acting on -forms, has rank greater than one. As a consequence we obtain that indecomposable, Ricci-flat locally homogeneous pp-waves are plane waves. This generalises a classic…
In recent years, deep learning has proven to be a viable methodology for surrogate modeling and uncertainty quantification for a vast number of physical systems. However, in their traditional form, such models can require a large amount of training data. This is of particular importance for various engineering and scie…
The paper shows how null hypersurfaces behave in Lorentz-Minkowski space.
New metrics constructed dual to specific wave-like geometries.
In this paper, benefiting from the strong ability of deep neural network in estimating non-linear functions, we propose a discriminative embedding function to be used as a feature extractor for clustering tasks. The trained embedding function transfers knowledge from the domain of a labeled set of morphologically-disti…
Study pp-waves with lightlike parallel spinors in vacuum spacetimes.