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.
Wave propagation framework using cone structures and observers' vector fields.
A new model uses Lorentz-Finsler geometry to predict wave propagation.
In this paper, we investigate the geometric propagation and diffraction of singularities of solutions to the wave equation on manifolds with edge singularities.
Graph algorithms are key tools in many fields of science and technology. Some of these algorithms depend on propagating information between distant nodes in a graph. Recently, there have been a number of deep learning architectures proposed to learn on undirected graphs. However, most of these architectures aggregate i…
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…
Ultrasonic guided waves are commonly used to localize structural damage in infrastructures such as buildings, airplanes, bridges. Damage localization can be viewed as an inverse problem. Physical model based techniques are popular for guided wave based damage localization. The performance of these techniques depend on …
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should seek alternatives. Fortunately, many of the laws of behaviour of the physical wor…
Analyzes properties of stiffness tensors for elastic wave imaging.
Generalizes Fermat's principle for wave propagation in cone structures.
In this paper two zero-dimensional compact sets with equal topological and fractal dimensions but embedded in Euclidean space by different ways are under study. Diffraction of plane electromagnetic wave propagated and reflected by fractal surfaces is considered for each of these compact sets placed in vacuum. It is obt…
We review recent work on the Einstein equations of general relativity when the curvature is defined in a weak sense. Weakly regular spacetimes are constructed, in which impulsive gravitational waves, as well as shock waves, propagate.
New metrics link Kähler and pp-wave spacetimes.
We discuss positivity properties of `distinguished propagators', i.e. distinguished inverses of operators that frequently occur in scattering theory and wave propagation. We relate this to the work of Duistermaat and Hörmander on distinguished parametrices (approximate inverses), which has played a major role in quantu…
We study the propagator of the wave equation on a closed Riemannian manifold . We propose a geometric approach to the construction of the propagator as a single oscillatory integral global both in space and in time with a distinguished complex-valued phase function. This enables us to provide a global invariant defi…
Machine learning predicts dam-break flood wave behavior accurately.
In this paper we prove the propagation of singularities for the wave equation on differential forms with natural (i.e. relative or absolute) boundary conditions on Lorentzian manifolds with corners, which in particular includes a formulation of Maxwell's equations. These results are analogous to those obtained by the a…
We study inverse problems consisting on determining medium properties using the responses to probing waves from the machine learning point of view. Based on the understanding of propagation of waves and their nonlinear interactions, we construct a deep convolutional neural network in which the parameters are used to cl…
MetaNOR learns common nonlocal kernels for efficient metamaterial modeling.
It is well known that Lagrangian dynamical systems naturally arise in describing wave front dynamics in the limit of short waves (which is called pseudoclassical limit or limit of geometrical optics). Wave fronts are the surfaces of constant phase, their points move along lines which are called rays. In non-homogeneous…
Inhomogeneous plasmas filaments instabilities are investigated by using the techniques of classical differential geometry of curves where Frenet torsion and curvature describe completely the motion of curves. In our case the Frenet frame changes in time and also depends upon the other coordinates taking into account th…
Study proves interaction of three impulsive gravitational waves, showing local solution and Lipschitz continuity.
A Global Navigation Satellite System (GNSS) uses a constellation of satellites around the earth for accurate navigation, timing, and positioning. Natural phenomena like space weather introduce irregularities in the Earth's ionosphere, disrupting the propagation of the radio signals that GNSS relies upon. Such disruptio…
Probabilistic graphical models compactly represent joint distributions by decomposing them into factors over subsets of random variables. In Bayesian networks, the factors are conditional probability distributions. For many problems, common information exists among those factors. Adding similarity restrictions can be v…
We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularitie…
Study traveling waves in hyperbolic space for Fisher-KPP equations.
Geometric focusing affects dispersive estimates for Schrödinger and wave equations.
Study reconstructs Riemannian metric from Cherenkov radiation in complex media.
DistillKac generates images quickly using damped wave equations.
Study examines wave equation decay and Strichartz estimates on conic manifolds.
We find ways to make physical signals misclassified by computer vision models.
We investigate shock-wave solutions of the Einstein equations in the case when the speed of propagation is equal to the speed of light. The work extends the shock matching theory of Smoller and Temple, which characterizes solutions of the Einstein equations when the spacetime metric is only Lipschitz continuous across …
Study dispersive estimates for Schrödinger and wave equations on a cone with specific metric.
Novel approach to wave equations near null infinity in flat spacetimes.
Describes links between Finsler and Lorentz geometries for Riemannian geometers.
Full Wave Inversion (FWI) imaging scheme has many applications in engineering, geoscience and medical sciences. In this paper, a surrogate deep learning FWI approach is presented to quantify properties of materials using stress waves. Such inverse problems, in general, are ill-posed and nonconvex, especially in cases w…
DISTANA predicts and denoises spatial wave dynamics.
Proposes a wave-constrained matrix factorization for signal learning.
Accurate forward modeling is important for solving inverse problems. An inaccurate wave-equation simulation, as a forward operator, will offset the results obtained via inversion. In this work, we consider the case where we deal with incomplete physics. One proxy of incomplete physics is an inaccurate discretization of…
Develops support theorem for analytic transforms in tomography.
Dynamical systems can be modelled by partial differential equations and numerical computations are used everywhere in science and engineering. In this work, we investigate the performance of recurrent and convolutional deep neural network architectures to predict the surface waves. The system is governed by the Saint-V…
Unified geometry for relativity and beyond.
We introduce economic models based on Boolean Delay Equations: this formalism makes easier to take into account the complexity of the interactions between firms and is particularly appropriate for studying the propagation of an initial damage due to a catastrophe. Here we concentrate on simple cases, which allow to und…
New approach simplifies proof of wave equations on black holes.
We consider the wave equation on a product cone and find a joint asymptotic expansion for solutions near null and future infinities. The rates of decay seen in the expansion at future infinity are the resonances of a hyperbolic cone and were computed by the authors in a previous paper. The expansion treats an asymptoti…
Researchers reconstruct simple Riemannian manifolds from boundary wave arrival times.
Two wave fronts and that originated at some points of the manifold are said to be causally related if one of them passed through the origin of the other before the other appeared. We define the causality relation invariant to be the algebraic number of times the earlier born front pass…
New method learns kernels in nonlocal operators robustly.
We prove several relations between spectrum and dynamics including wave trace expansion, sharp/improved Weyl laws, propagation of singularities and quantum ergodicity for the sub-Riemannian (sR) Laplacian in the four dimensional quasi-contact case. A key role in all results is played by the presence of abnormal geodesi…