arXiv research

The paper derives expansions for Green's operators and resolvents using Hadamard methods.

Formula for Hadamard coefficients from Green's operators on spacetimes.

Wave propagator constructed on globally hyperbolic spacetimes.

The paper provides formulas for Hadamard coefficients using Green's operators.

McKernel introduces a framework to use kernel approximates in the mini-batch setting with Stochastic Gradient Descent (SGD) as an alternative to Deep Learning. Based on Random Kitchen Sinks [Rahimi and Recht 2007], we provide a C++ library for Large-scale Machine Learning. It contains a CPU optimized implementation of …

Locally convex compact immersed hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature are considered. We prove that such hypersurfaces are embedded as the boundary of convex body under certain conditions on the normal curvatures

We consider a general Hermitian holomorphic line bundle $L$ on a compact complex manifold $M$ and let ${\Box}^q_p$ be the Kodaira Laplacian on $(0,q)$ forms with values in $L^p$. The main result is a complete asymptotic expansion for the semi-classically scaled heat kernel $\exp(-u{\Box}^q_p/p)(x,x)$ along the diagonal…

Policy gradient converges linearly with Hadamard parameterization in tabular settings.

Proves a synthetic Lorentzian Cartan-Hadamard theorem.

Maps between Hadamard manifolds are quasi-isometric to harmonic maps.

Local isoperimetric inequality holds for balls with nonpositive curvature.

BEGIN network models binary data without parametric assumptions.

In this paper, we investigate submanifolds with locally bounded mean curvature in Hadamard manifolds, product manifolds $N\times\mathbb{R}$, submanifolds with bounded $\varphi$-mean curvature in the hyperbolic space, and successfully give lower bounds for the weighted fundamental tone and the first eigenvalue of the $p…

This book provides a detailed introduction to linear wave equations on Lorentzian manifolds (for vector-bundle valued fields). After a collection of preliminary material in the first chapter one finds in the second chapter the construction of local fundamental solutions together with their Hadamard expansion. The third…

Study fourth order Schrödinger equation on Cartan-Hadamard manifolds, proving existence, scattering, and blow-up results.

We study the problem of nonparametric dependence detection. Many existing methods may suffer severe power loss due to non-uniform consistency, which we illustrate with a paradox. To avoid such power loss, we approach the nonparametric test of independence through the new framework of binary expansion statistics (BEStat…

We generalize Hadamard-Stoker-Currier Theorems for surfaces immersed in a Killing submersion over a strictly Hadamard surface whose fibers are the trajectories of a unit Killing field. We prove that every complete surface whose principal curvatures are greater than a certain function (depending on the ambient manifold)…

Despite their successes, what makes kernel methods difficult to use in many large scale problems is the fact that storing and computing the decision function is typically expensive, especially at prediction time. In this paper, we overcome this difficulty by proposing Fastfood, an approximation that accelerates such co…

Harmonic maps between pinched Hadamard surfaces are quasi-conformal.

New insights into identifying mixtures of product distributions using Hadamard extensions.

We give lower bounds for the first Dirichilet eigenvalues for domains in submanifolds with locally bounded mean curvatures. These bounds depend on the injectivity radius, sectional curvature (upperbound) of the ambient space and on the mean curvature of the submanifold. For submanifolds fo Hadamard manifolds these lowe…

Cyclic projections in Hadamard spaces can be irregular, unlike in Hilbert spaces.

Study shows spectrum properties for specific Hadamard manifolds.

Sharp curvature inequality extends Euclidean isoperimetric inequality to Cartan-Hadamard manifolds.

Study local foliations of surfaces with constant mean curvature and constant expansion in space-time.

A new class of harmonic Hadamard manifolds, those spaces called of hypergeometric type, is defined in terms of Gauss hypergeometric equations. Spherical Fourier transform defined on a harmonic Hadamard manifold of hypergeometric type admits an inversion formula. A characterization of harmonic Hadamard manifold being of…

We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. …

New method for CMS derivatives pricing using Watanabe's expansions.

Study local expansions of continuous-time processes using Ito signature properties.

New test for point processes without strong model assumptions.

We prove a theorem of Hadamard-Stoker type: a connected locally convex complete hypersurface immersed in $H^n \times R$ (n>1), where $H^n$ is n-dimensional hyperbolic space, is embedded and homeomorphic either to the n-sphere or to $R^n$. In the latter case it is either a vertical graph over a convex domain in $H^n$ or…

Uniformly extend maps on Hadamard manifolds with curvature constraints.

A new method for creating simpler models from complex ones.

Upper bounds for circumradius in Hadamard surfaces with curvature constraints.

Study geodesic extendibility on metric spaces and map them to a half-space.

Solves Plateau problem for surfaces in pinched curvature manifolds.

Proves Hadamard states for Dirac fields on manifolds with timelike boundaries.

Various results based on some convexity assumptions (involving the exponential map along with affine maps, geodesics and convex hulls) have been recently established on Hadamard manifolds. In this paper we prove that these conditions are mutually equivalent and they hold if and only if the Hadamard manifold is isometri…

Paper computes link determinants using Fourier-Hadamard transforms.

We show that for every quasi-isometric map from a Hadamard manifold of pinched negative curvature to a locally compact, Gromov hyperbolic, ${\rm CAT}(0)$-space there exists an energy minimizing harmonic map at finite distance. This harmonic map is moreover Lipschitz. This generalizes a recent result of Benoist-Hulin.

In this paper we address the problem of studying those Kähler manifolds whose first two coefficients of the associated TYZ expansion vanish and we prove that for a locally Hermitian symmetric space this happens only in the flat case. We also prove that there exist nonflat locally Hermitian symmetric spaces where all th…

We study the asymptotic Dirichlet and Plateau problems on Cartan-Hadamard manifolds satisfying the so-called Strict Convexity (abbr. SC) condition. The main part of the paper consists in studying the SC condition on a manifold whose sectional curvatures are bounded from above and below by certain functions depending on…

New theorem extends Hadamard's to transversely affine geometry.

Paper proposes Walsh-Hadamard Variational Inference for efficient approximate inference in large models.

Study on existence of ground states for free energy on hyperbolic space.

The paper proves Liouville-type theorems on Hadamard manifolds.

We derive asymptotic expansions for the prices of a variety of European and barrier-style claims in a general local-stochastic volatility setting. Our method combines Taylor series expansions of the diffusion coefficients with an expansion in the correlation parameter between the underlying asset and volatility process…

We develop an expansion approach for the pricing of European quanto options written on LIBOR rates (of a foreign currency). We derive the dynamics of the system of foreign LIBOR rates under the domestic forward measure and then consider the price of the quanto option. In order to take the skew/smile effect observed in …