Related papers: Kernel(J) warns of false vacua

In this paper we show that the strictly positive definite matrix valued isotropic kernels in the circle and the real dot product kernels in Euclidean spaces are not well behaved with respect to its scalar valued projections. We generalize…

We provide a holomorphic description of the Hilbert space H(j_1,..,j_n) of SU(2)-invariant tensors (intertwiners) and establish a holomorphically factorized formula for the decomposition of identity in H(j_1,..,j_n). Interestingly, the…

For any integer $ p \geq 2 $, we construct a compact Riemannian manifold $ \mathcal{N} $ such that if $ \dim \mathcal{M} > p $, there is a map in the Sobolev space of mappings $ W^{1,p} (\mathcal{M}, \mathcal{N})$ which is not a weak limit…

Given a topological space $X$, a thickening kernel is a monoidal presheaf on $(\mathbb{R}_{\geq0},+)$ with values in the monoidal category of derived kernels on $X$. A bi-thickening kernel is defined on $(\mathbb{R},+)$. To such a…

We study the pseudoduality transformations in two dimensional N = (2, 2) sigma models on K\"ahler manifolds. We show that structures on the target space can be transformed into the pseudodual manifolds by means of (anti)holomorphic…

A cap of spherical radius $\alpha$ on a unit $d$-sphere $S$ is the set of points within spherical distance $\alpha$ from a given point on the sphere. Let $\mathcal F$ be a finite set of caps lying on $S$. We prove that if no hyperplane…

We study several aspects of the quantum structure of the minimal potentially realistic renormalizable $\mathrm{SO}(10)$ Higgs model in which the $\mathbf{45}\oplus \mathbf{126}$ scalars spontaneously break the symmetry down to the Standard…

The space of Fredholm operators of fixed index is stratified by submanifolds according to the dimension of the kernel. Geometric considerations often lead to questions about the intersections of concrete families of elliptic operators with…

Quantum vacua are characterized by the topological structure of their fermion zero modes. The vacua are distributed into universality classes protected by topology in momentum space. The vacua whose manifold of fermion zero modes has…

This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…

Given an m x n rectangular mesh, its adjacency matrix A, having only integer entries, may be interpreted as a map between vector spaces over an arbitrary field K. We describe the kernel of A: it is a direct sum of two natural subspaces…

Kernel methods approximate nonlinear maps in a data-driven manner by projecting the target map onto a finite-dimensional Hilbert space called the solution space. Traditionally, this space is a subspace of a fixed ambient reproducing kernel…

The kernel method is an essential tool for the study of generating series of walks in the quarter plane. This method involves equating to zero a certain polynomial, the kernel polynomial, and using properties of the curve, the kernel curve,…

We study spherical charged black holes in the presence of a cosmological constant with corrections motivated by the theory of loop quantum gravity. The effective theory is constructed at the Hamiltonian level by introducing certain…

We propose a framework for 2D shape analysis using positive definite kernels defined on Kendall's shape manifold. Different representations of 2D shapes are known to generate different nonlinear spaces. Due to the nonlinearity of these…

The seminal theorem of I.J. Schoenberg characterizes positive definite (p.d.) kernels on the unit sphere $S^{n-1}$ invariant under the automorphisms of the sphere. We obtain two generalizations of this theorem for p.d. kernels on fiber…

Let $\sigma : \mathbb C^d \rightarrow \mathbb C^d$ be an affine-linear involution such that $J_\sigma = -1$ and let $U, V$ be two domains in $\mathbb C^d.$ Let $\phi : U \rightarrow V$ be a $\sigma$-invariant $2$-proper map such that…

Starting from a subinvariant positive definite kernel under a branching pullback, we attach to the resulting kernel tower a canonical electrical network on the word tree whose edge weights are the diagonal increments. This converts diagonal…

We investigate the validity of the hyperhoop conjecture, which claims to determine a necessary and sufficient condition for the formation of black hole horizons in higher-dimensional space-times. Here we consider momentarily static,…

In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…