arXiv research

SWD approximates GP for faster regression.

The two-sphere valued wave map flow on a Lorentzian domain R x Sigma, where Sigma is any flat two-torus, is studied. The Cauchy problem with initial data tangent to the moduli space of holomorphic maps Sigma -> S^2 is considered, in the limit of small initial velocity. It is proved that wave maps, in this limit, conver…

Parsimonious Dynamic Mode Decomposition selects sparse modes robustly.

In this paper, we present two observations about static spherically symmetric solutions of the Einstein-Klein-Gordon equations. The first is a comment extending the well-known result of the existence of static states (i.e. standing wave solutions) of the Einstein-Klein-Gordon equations. The second more important observ…

We consider restrictions placed by geodesic completeness on spacetimes possessing a null parallel vector field, the so-called Brinkmann spacetimes. This class of spacetimes includes important idealized gravitational wave models in General Relativity, namely the plane-fronted waves with parallel rays, or pp-waves, which…

We prove a differential Harnack inequality for the solution of the parabolic Allen-Cahn equation $\frac{\partial f}{\partial t}=\triangle f-(f^3-f)$ on a closed n-dimensional manifold. As a corollary we find a classical Harnack inequality. We also formally compare the standing wave solution to a gradient estimate of M…

Novel method detects spike-and-wave patterns in EEG signals.

In recent work, we have proven uniform decay bounds for solutions of the wave equation $\Box_gφ=0$ on a Schwarzschild exterior, in particular, the uniform pointwise estimate $|φ|\le Cv_+^{-1}$, which holds throughout the domain of outer communications, where $v$ is an advanced Eddington-Finkelstein coordinate, $v_+=\ma…

Study uses DMD to analyze oceanic features in Strait of Gibraltar.

Gravitational wave memory increases faster than Brownian motion in early universe and astrophysical sources.

D-Wave hybrid quantum-classical portfolio optimization shows classical decomposition is key, not quantum sampling.

Extended wMEM approach for MEG inverse problem using wavelet and spatial filters.

The paper analyzes the spectra of compact quotients of the oscillator group.

Machine learning predicts dam-break flood wave behavior accurately.

Develops methods to model and forecast inter-sectoral balance dynamics.

Carter tensor analysis aids wave equation on Kerr-Newman spacetime.

Suppose a given observation matrix can be decomposed as the sum of a low-rank matrix and a sparse matrix (outliers), and the goal is to recover these individual components from the observed sum. Such additive decompositions have applications in a variety of numerical problems including system identification, latent var…

We prove a global Birkhoff decomposition for almost split real forms of loop groups, when an underlying finite dimensional Lie group is compact. Among applications, this shows that the dressing action - by the whole subgroup of loops which extend holomorphically to the exterior disc - on the $U$-hierarchy of the ZS-AKN…

Proves fundamental theorem for singular surfaces with limiting tangent planes.

Global existence and boundedness proved for quasilinear wave equations on Kerr black holes.

LemonadeBench evaluates LLMs' economic intuition through a simulated lemonade stand.

Study linearized Schwarzschild spacetimes, proving decay of master quantities.

Entropy formula for parabolic Allen-Cahn equations on compact manifolds.

Study on variance of Laplace eigenfunctions on manifolds.

Proves energy estimates for tensorial wave equations, decoupling components for stability proof.

Stability of a special spacetime solution is proven under certain symmetries.

Study wave front singularities and their geometric properties.

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.

Analyzes properties of stiffness tensors for elastic wave imaging.

EMG analysis quantifies bipedal standing quality in SCI patients.

Deep learning model predicts wind-wave relationship.

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.

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.

Simple conformally recurrent spaces are identified as pp-waves.

New method detects spike-and-wave epileptiform discharges using Kendall's Tau-b.

Any one-cusped hyperbolic manifold M with an unknotting tunnel tau is obtained by Dehn filling a cusp of a two-cusped hyperbolic manifold. In the case where M is obtained by "generic" Dehn filling, we prove that tau is isotopic to a geodesic, and characterize whether tau is isotopic to an edge in the canonical decompos…

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 $2$-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…