Related papers: On the completely positive kernels for nonuniform …
In this study, we consider the positive cluster complex, a full subcomplex of a cluster complex the vertices of which are all non-initial cluster variables. In particular, we provide a formula for the difference in face vectors of positive…
We propose a kernel-based partial permutation test for checking the equality of functional relationship between response and covariates among different groups. The main idea, which is intuitive and easy to implement, is to keep the…
A modified gamma kernel should not be automatically preferred to the standard gamma kernel, especially for univariate convex densities with a pole at the origin. In the multivariate case, multiple combined gamma kernels, defined as a…
We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic vector bundles and define positivity in view of $L^2$-estimates. Associated with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a certain…
For supervised and unsupervised learning, positive definite kernels allow to use large and potentially infinite dimensional feature spaces with a computational cost that only depends on the number of observations. This is usually done…
We examine homogeneous metrics on spheres and determine which ones have positive sectional curvature. The answer is subtle and surprisingly difficult to prove. In some cases we also determine their pinching constants. This completes the…
We study a spatial asymptotic behaviour at infinity of kernels $p_t(x)$ for convolution semigroups of nonlocal pseudo-differential operators. We give general and sharp sufficient conditions under which the limits $$ \lim_{r \to \infty}…
This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…
We study uniqueness of positive solutions to the conformal scalar curvature equation on complete Riemannian manifolds with constant negative scalar curvature. We apply the results to show that conformal transformations on certain complete…
In this paper we elaborate on the interplay between energy optimization, positive definiteness, and discrepancy. In particular, assuming the existence of a $K$-invariant measure $\mu$ with full support, we show that conditional positive…
This paper provides a method to study the non-negativity of certain linear operators, from other operators with similar spectral properties. If these new operators are formally self-adjoint and non-negative, we can study the complex powers…
A proposal is made for a mathematically unambiguous treatment of evolution in the presence of closed timelike curves. In constrast to other proposals for handling the naively nonunitary evolution that is often present in such situations,…
Positive definite functions are very important in both theory and applications of approximation theory, probability and statistics. In particular, identifying strictly positive definite kernels is of great interest as interpolation problems…
The Gamma kernel is a projection kernel of the form (A(x)B(y)-B(x)A(y))/(x-y), where A and B are certain functions on the one-dimensional lattice expressed through Euler's Gamma function. The Gamma kernel depends on two continuous…
We consider a class of constant-coefficient partial differential operators on a finite-dimensional real vector space which exhibit a natural dilation invariance. Typically, these operators are anisotropic, allowing for different degrees in…
We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of…
The notion of partial fidelities as invented recently by A.Uhlmann for pairs of finite dimensional density matrices will be extended to the vN-algebraic context and is considered and thoroughly discussed in detail from a mathematical point…
In this paper we are concerned with the learnability of nonlocal interaction kernels for first order systems modeling certain social interactions, from observations of realizations of their dynamics. This paper is the first of a series on…
The study of representations invariant to common transformations of the data is important to learning. Most techniques have focused on local approximate invariance implemented within expensive optimization frameworks lacking explicit…
We consider kernels of discrete convolution operators or, equivalently, homogeneous solutions of partial difference operators and show that these solutions always have to be exponential polynomials. The respective polynomial space in…