Related papers: Extremal Polarization Configurations for Integrabl…

We present sufficient condition for a family of positive definite kernels on a compact two-point homogeneous space to be strictly positive definite based on their representation as a series of spherical harmonics. The family analyzed is a…

Non-local correlations between a fully characterised quantum system and an untrusted black box device are described by an assemblage of conditional quantum states. These assemblages form a convex set, whose extremal points are relevant in…

We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…

We study alternating minimization for matrix completion in the simplest possible setting: completing a rank-one matrix from a revealed subset of the entries. We bound the asymptotic convergence rate by the variational characterization of…

A nearly optimal explicitly-sparse representation for oscillatory kernels is presented in this work by developing a curvelet based method. Multilevel curvelet-like functions are constructed as the transform of the original nodal basis. Then…

This paper addresses the problem of finding an asymptotic solution for first and second order integro-differential equations containing an arbitrary kernel, by evaluating the corresponding inverse Laplace and Fourier transforms. The aim of…

This paper presents the Planck 2015 likelihoods, statistical descriptions of the 2-point correlations of CMB data, using the hybrid approach employed previously: pixel-based at $\ell<30$ and a Gaussian approximation to the distribution of…

Partial Bergman kernels $\Pi_{k, E}$ are kernels of orthogonal projections onto subspaces $\mathcal{k} \subset H^0(M, L^k)$ of holomorphic sections of the $k$th power of an ample line bundle over a Kahler manifold $(M, \omega)$. The…

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of…

We refine the asymptotic estimates for minimizers of a class of nonlocal energy functionals of the form \[ \frac{1}{4} \iint_{\R^{2n} \setminus (\R^n \setminus \Omega)^2} \snr{u(x) - u(y)}^2 K(x - y) \,dx\,dy + \int_\Omega W(u(x)) \,dx, \]…

Projected kernel calibration is a newly proposed frequentist calibration method, which is asymptotic normal and semi-parametric. Its loss function is usually referred to as the PK loss function. In this work, we prove the uniform…

Let $X$ be an abstract orientable not necessarily compact CR manifold of dimension $2n+1$, $n\geq1$, and let $L^k$ be the $k$-th tensor power of a CR complex line bundle $L$ over $X$. Suppose that condition $Y(q)$ holds at each point of…

The theoretical minimum emittance cells are the optimal configurations for achieving the absolute minimum emittance, if specific optics constraints are satisfied at the middle of the cell's dipole. Linear lattice design options based on an…

Despite their success, kernel methods suffer from a massive computational cost in practice. In this paper, in lieu of commonly used kernel expansion with respect to $N$ inputs, we develop a novel optimal design maximizing the entropy among…

We prove that for any infinite-dimensional quantum channel the entropic disturbance (defined as difference between the $\chi$-quantity of a generalized ensemble and that of the image of the ensemble under the channel) is lower…

In the absence of explicit regularization, Kernel "Ridgeless" Regression with nonlinear kernels has the potential to fit the training data perfectly. It has been observed empirically, however, that such interpolated solutions can still…

In this thesis we study the relationship between the existence of canonical metrics on a complex manifold and stability in the sense of geometric invariant theory. We introduce a modification of K-stability of a polarised variety which we…

This paper presents a new perspective on the identification at infinity for the intercept of the sample selection model as identification at the boundary via a transformation of the selection index. This perspective suggests generalizations…

The rates of quantum cryptographic protocols are usually expressed in terms of a conditional entropy minimized over a certain set of quantum states. In particular, in the device-independent setting, the minimization is over all the quantum…

Kernel-based clustering algorithms have the ability to capture the non-linear structure in real world data. Among various kernel-based clustering algorithms, kernel k-means has gained popularity due to its simple iterative nature and ease…