arXiv research

Paper presents a neural network for estimating wavefronts in direction of arrival scenarios.

Paper finds local normal forms for wavefronts in flat coordinates.

Microlocal analysis provides deep insight into singularity structures and is often crucial for solving inverse problems, predominately, in imaging sciences. Of particular importance is the analysis of wavefront sets and the correct extraction of those. In this paper, we introduce the first algorithmic approach to extra…

Abstract: Characterizes frontals and wavefronts with formulas.

We give a classification of generic bifurcations of intersections of wavefronts generated by different points of a hypersurface with or without boundaries.

Study on curvature invariants near singularities of wavefronts.

We introduce the notion of reticular Legendrian unfoldings in order to investigate stabilities of bifurcations of wavefronts generated by a hypersurface germ with a boundary, a corner, or an r-corner in a smooth n dimensional manifold. We define several stabilities of reticular Legendrian unfoldings and prove that they…

We investigate genericities of reticular Lagrangian maps and reticular Legendrian maps in order to give generic classifications of caustics and wavefronts generated by a hypersurface germ without or with a boundary in a smooth manifold.

We extend the notion of reticular Legendrian unfoldings in order to investigate multi-time bifurcations of wavefronts generated by an r-corner. We give a classification list of generic and stable bifurcations with two time parameter and give all generic figures in the plane and the space.

Motivated by the study of wave fronts in anisotropic media, we propose an incidence geometry of anisotropic spheres in a Finsler-Minkowski space. An anisotropic version of the Laguerre functional is considered. In some circumstances, this functional can be used to determine that two wavefronts observed at distinct time…

Recent advances in twistor theory are applied to geometric optics in ${\Bbb{R}}^3$. The general formulae for reflection of a wavefront in a surface are derived and in three special cases explicit descriptions are provided: when the reflecting surface is a plane, when the incoming wave is a plane and when the incoming w…

Conflict sets are loci of intersecting wavefronts emanating from $l$ different surfaces. We show that generically conflict sets are Legendrian: locally they admit the structure of wavefronts. Simple stable singularities for this problem in $\R^n$ occur when $0 \leq n-l \leq 4$. Other related sets, such as kite curves a…

We introduce a theory of virtual Legendrian knots. A virtual Legendrian knot is a cooriented wavefront on an oriented surface up to Legendrian isotopy of its lift to the unit cotangent bundle and stabilization and destablization of the surface away from the wavefront. We show that the groups of Vassiliev invariants of …

Study of fastest paths in anisotropic media via Finsler geometry.

Study finds rigid submanifolds in spacelike waves under specific conditions.

A new model predicts wildfire spread with wind and slope effects.

Paper approximates backward heat equation using wave equations and Ricci flow.

A systematic geometric theory for the ultradifferentiable (non-quasianalytic and quasianalytic) wavefront set similar to the well-known theory in the classic smooth and analytic setting is developed. In particular an analogue of Bony's Theorem and the invariance of the ultradifferentiable wavefront set under diffeomorp…

Study null surfaces of pseudo-spherical curves in anti-de Sitter space.

We study diffeologies on locally convex spaces and their application to smooth multiplication of distributions.

We consider the four-dimensional nonholonomic distribution defined by the 4-potential of the electromagnetic field on the manifold. This distribution has a metric tensor with the Lorentzian signature $(+,-,-,-)$, therefore, the causal structure appears as in the general relativity theory. By means of the Pontryagin's m…

Transforms uniquely determine Higgs fields on real-analytic manifolds.

Machine learning models predict DM performance for AO systems.

Let $X$ be a compact manifold with boundary. Suppose that the boundary is fibred, $φ:\pa X\longrightarrow Y,$ and let $x\in\CI(X)$ be a boundary defining function. This data fixes the space of `fibred cusp' vector fields, consisting of those vector fields $V$ on $X$ satisfying $Vx=O(x^2)$ and which are tangent to the f…

We extend to the $n$-dimensional case a recent theorem establishing the validity of the Huygens' envelope principle for wavefronts in Finsler spaces. Our results have direct applications in analogue gravity models, for which the Fermat's principle of least time naturally gives origin to an underlying Finslerian geometr…

Study of billiards in sub-Finsler geometry, including unusual orbits.

Wave propagation framework using cone structures and observers' vector fields.

Study on evolutes and focal surfaces of pseudo-spherical framed immersions in anti-de Sitter space.

Study Legendrian surfaces using N-graphs and flag moduli.

We prove that the boundary distance map of a smooth compact Finsler manifold with smooth boundary determines its topological and differentiable structures. We construct the optimal fiberwise open subset of its tangent bundle and show that the boundary distance map determines the Finsler function in this set but not in …

Study of evolutoids and involutoids of convex curves in 2D space forms.

New estimators outperform maximum likelihood without hyper-parameter estimation.

New estimator reduces kernel mean estimation error.

Dual Bayesian Affine Estimators for Wiener-type state-space models

Enhances gradient estimates for Hermitian Monge-Ampère equations.

Paper proposes robust estimators for GANs under Wasserstein contamination.

New framework converts offline to online estimation using black-box offline estimators.

Proposes variational autoencoder for efficient MMSE estimation.

Paper improves Fisher information estimation methods.

Proposes a robust estimator for RD designs.

New estimator reduces variance in discrete random variables.

SCOPE estimator improves covariance and precision matrix estimation.

We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task maximum likelihood estimates. We derive the optimal minimum risk estimator and the minimax estimator, and show t…

Obtaining more accurate equity value estimates is the starting point for stock selection, value-based indexing in a noisy market, and beating benchmark indices through tactical style rotation. Unfortunately, discounted cash flow, method of comparables, and fundamental analysis typically yield discrepant valuation estim…

The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able to efficiently estimate the variance of this estimator is very helpful to vario…

Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuo…

A new copula estimation method using classification.

This paper reviews SDR methods for multivariate response regression.