This article deals with the two-group classification problem, where the class conditional probability π(z) = P{Y = 1 | Z = z} belongs to a known class of functions F which is totally bounded with respect to the supremum norm. Given an -cover F of F , we consider kernel regression methods for constructing classifiers using members of F . A Horvitz-Thompsontype inverse weighting approach will be ...

We deterministically construct quasi-polynomial weights in quasi-polynomial time, such that in a given polytope with totally unimodular constraints, one vertex is isolated, i.e., there is a unique minimum weight vertex. More precisely, the property that we need is that every face of the polytope lies in an affine space defined by a totally unimodular matrix. This derandomizes the famous Isolati...

The (tree) amplituhedron An,k,m is the image in the Grassmannian Grk,k+m of the totally nonnegative part of Grk,n, under a (map induced by a) linear map which is totally positive. It was introduced by Arkani-Hamed and Trnka in 2013 in order to give a geometric basis for the computation of scattering amplitudes in N = 4 supersymmetric Yang-Mills theory. When k + m = n, the amplituhedron is isomo...

P is the class of pseudocompact Hausdorff topological groups, and P′ is the class of groups which admit a topology T such that (G,T ) ∈ P. It is known that every G= (G,T ) ∈ P is totally bounded, so for G ∈ P′ the supremum T ∨(G) of all pseudocompact group topologies on G and the supremum T #(G) of all totally bounded group topologies on G satisfy T ∨ ⊆ T #. The authors conjecture for abelian G...

We prove that, for totally irregular measures ? on R d with ? 3 , the ( ? 1 ) -dimensional Riesz transform T A V f x = ? ? E y adapted to Schrödinger operator L div + fundamental solution is not bounded 2 . This generalises recent results obtained by Conde-Alonso, Mourgoglou and Tolsa free-space elliptic operators Hölder continuous coefficients since it allows presence of potentials in reverse ...

The dynamics of linear positive systems map the orthant to itself. In other words, it maps a set vectors with zero sign variations This raises following question: what $k$ itself? We address this question using tools from theory cooperative dynamical and totally matrices. yields generalization called $k$-positive systems, that reduces for $k=1$. describe applications new type analysis nonlinear...

This paper presents an improved and time-optimal self-stabilizing algorithm for a major task in distributed computinga rooted spanning tree construction. Our solution is decentralized (“truly distributed”), uses a bounded memory and is not based on the assumption that either n (the number of nodes), or diam (the actual diameter of the network), or an existence of cycles in the network are known...