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A 3+1 decomposition of the twistor and valence-2 Killing spinor equation is made using the space spinor formalism. Conditions on initial data sets for the Einstein vacuum equations are given so that their developments contain solutions to…
We study the peeling on Kerr spacetime for fields satisfying conformally invariant linear and nonlinear scalar wave equations. We follow an approach initiated by L.J. Mason and the first author for the Schwarzschild metric, based on a…
Near-Kerr black hole initial datasets are constructed by applying either the parabolic-hyperbolic or the algebraic-hyperbolic form of the constraints. In both cases, strongly and weakly asymptotically flat initial datasets with desirable…
We prove the wellposedness of scalar wave equations on spatially flat universe as a background with nonminimal coupling with the scalar potential turned on by introducing the $k$-order linear energy and the corresponding energy norm. In the…
When using the black hole exclusion (horizon boundary condition) technique, $K$ is usually nonzero and spatially variable, so none of the special cases of York's conformal-decomposition algorithm apply, and the full 4-vector nonlinear York…
The Hilbert Schmidt Independence Criterion (HSIC) is a kernel dependence measure that has applications in various aspects of machine learning. Conveniently, the objectives of different dimensionality reduction applications using HSIC often…
In numerical relativity simulations with non-trivial matter configurations, one must solve the Hamiltonian and momentum constraints of the ADM formulation for the metric variables in the initial data. We introduce a new scheme based on the…
We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
Kernel methods are fundamental tools in machine learning that allow detection of non-linear dependencies between data without explicitly constructing feature vectors in high dimensional spaces. A major disadvantage of kernel methods is…
We consider initial boundary value problems with the homogeneous Neumann boundary condition. Given an initial value, we establish the uniqueness in determining a spatially varying coefficient of zeroth-order term by a single measurement of…
We present a non-perturbative quantization of gravitational null initial data. Our starting point is the characteristic null initial problem for tetradic gravity with a parity-odd Holst term in the bulk. After a basic review about the…
The original Kerr theorem provides the foundation for Kerr-Schild transformations by classifying all shear-free and geodesic null congruences in flat spacetime; the key ingredient of the Kerr-Schild ansatz. However, due to the high level of…
We introduce the notion of angular values for deterministic linear difference equations and random linear cocycles. We measure the principal angles between subspaces of fixed dimension as they evolve under nonautonomous or random linear…
We discuss the existence of asymptotically Euclidean initial data sets to the vacuum Einstein field equations which would give rise (modulo an existence result for the evolution equations near spatial infinity) to developments with a past…
We study the local equivalence problem for Riemannian submersions under fiber-preserving isometries using differential invariants. After briefly recalling the vertical--horizontal splitting, the O'Neill tensors $A$ and $T$, and the mean…
This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the…
An IDEAL characterization of a particular spacetime metric, $g_0$, consists of a set of tensorial equations $T[g] = 0$ arising from expressions constructed from the metric, $g$, its curvature tensor and its covariant derivatives and which…
Stationary, axisymmetric, vacuum, solutions of Einstein's equations are obtained as critical points of the total mass among all axisymmetric and $(t,\phi)$ symmetric initial data with fixed angular momentum. In this variational principle…
This paper addresses several geometric inverse problems for some linear parabolic systems where the initial data (and sometimes also the coefficients of the equations) are unknown. The goal is to identify a subdomain within a…