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.
Study axisymmetric waves on extremal Kerr spacetime using physical-space estimates.
Carter tensor analysis aids wave equation on Kerr-Newman spacetime.
This paper proposes grid cells encode position via a conformal isometric embedding of 2D physical space.
New method finds precise late-time behavior of wave equations.
Global existence and decay for quasilinear wave equations on various spacetimes, including Kerr black holes.
Physics-informed neural operator learns from coarse to fine discretized data.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
We develop a cross-sectional research design to identify causal effects in the presence of unobservable heterogeneity without instruments. When units are dense in physical space, it may be sufficient to regress the "spatial first differences" (SFD) of the outcome on the treatment and omit all covariates. The identifyin…
The fundamental group and rational cohomology of the configuration spaces of the Skyrme and Faddeev-Hopf models are computed. Physical space is taken to be a compact oriented 3-manifold, either with or without a marked point representing an end at infinity. For the Skyrme model, the codomain is any Lie group, while for…
A collaborative convex framework for factoring a data matrix into a non-negative product , with a sparse coefficient matrix , is proposed. We restrict the columns of the dictionary matrix to coincide with certain columns of the data matrix , thereby guaranteeing a physically meaningful dictionary and …
The paper proves boundedness and decay of Teukolsky equations on Kerr backgrounds.
We present a variational renormalization group (RG) approach using a deep generative model based on normalizing flows. The model performs hierarchical change-of-variables transformations from the physical space to a latent space with reduced mutual information. Conversely, the neural net directly maps independent Gauss…
Scattering theory developed for linearised gravity near Schwarzschild black hole.
The paper explores Kaluza-Klein theories without assuming a fibration structure.
4-dim intrinsic (material) Riemannian metric of the material 4-D space-time continuum is utilized as the characteristic of the aging processes developing in the material. Manifested through variation of basic material characteristics such as density, moduli of elasticity, yield stress, strength, and toughness.,…
The paper tackles drift identification in Lévy α-stable stochastic systems, proposing a Fourier space approach.
New method reduces high-dimensional data to key features.
New insights into data geometry reveal manifold structure in grid-cell activity.
We prove boundedness and polynomial decay statements for solutions to the spin Teukolsky-type equation projected to the spherical harmonic on Reissner-Nordström spacetime. The equation is verified by a gauge-invariant quantity which we identify and which involves the electromagnetic and curvature tensor…
We prove in this paper the linear stability of the celebrated Schwarzschild family of black holes in general relativity: Solutions to the linearisation of the Einstein vacuum equations around a Schwarzschild metric arising from regular initial data remain globally bounded on the black hole exterior and in fact decay to…
Second part of series studying charged scalar fields on Reissner--Nordström spacetimes.
A geometric string solution has background fields in overlapping coordinate patches related by diffeomorphisms and gauge transformations, while for a non-geometric background this is generalised to allow transition functions involving duality transformations. Non-geometric string backgrounds arise from T-duals and mirr…
In the historical literature there has been an extended discussion on the question, whether the report of Sartorius von Waltershausen about C. F. Gauss checking the largest triangle of the geodetical measurement campaign in the kingdom of Hannover as a kind of ``test'' for the Euclididean nature of physical space can b…
We focus in this paper on high-dimensional regression problems where each regressor can be associated to a location in a physical space, or more generally a generic geometric space. Such problems often employ sparse priors, which promote models using a small subset of regressors. To increase statistical power, the so-c…
Motivated by the sigma model limit of multicomponent Ginzburg-Landau theory, a version of the Faddeev-Skyrme model is considered in which the scalar field is coupled dynamically to a one-form field called the supercurrent. This coupled model is investigated in the general setting where physical space is an oriented Rie…
Hexagon grid patterns emerge from conformal isometry in grid cell neural networks.
The paper studies how grid cell patterns emerge in neural networks.
A new method optimizes Fourier pricing for multi-asset options using adaptive quadrature.
Proves stability of Schwarzschild black holes without symmetry assumptions.
New methods estimate multivariate shortfall risk more efficiently.
New method reconstructs Black-Scholes option prices from current profiles.
We develop a definitive physical-space scattering theory for the scalar wave equation on Kerr exterior backgrounds in the general subextremal case |a|<M. In particular, we prove results corresponding to "existence and uniqueness of scattering states" and "asymptotic completeness" and we show moreover that the resulting…
This paper contains the first two parts (I-II) of a three-part series concerning the scalar wave equation \Box_gψ = 0 on a fixed Kerr background. We here restrict to two cases: (II1) |a| \ll M, general ψ or (II2) |a| < M, ψ axisymmetric. In either case, we prove a version of 'integrated local energy decay', specificall…
Global existence and boundedness proved for quasilinear wave equations on Kerr black holes.