This paper addresses the Mountain Pass Theorem for locally Lipschitz functions on finite-dimensional vector spaces in terms of tangencies. Namely, let $f \colon \mathbb R^n \to \mathbb R$ be a locally Lipschitz function with a mountain pass geometry....
We introduce a new function on the set of pairs of cluster variables via $f$-vectors, which we call it the compatibility degree (of cluster complexes). The compatibility degree is a natural generalization of the classical compatibility degree introdu...
We introduce the new algebraic property of Weyl compatibility for symmetric tensors and vectors. It is strictly related to Riemann compatibility, which generalizes the Codazzi condition while preserving much of its geometric implications. In particul...
engineering, a phasor (a portmanteau of phase vector) is a complex number representing a sinusoidal function whose amplitude A and initial phase θ are time-invariant
In mathematics, the Newtonian potential, or Newton potential, is an operator in vector calculus that acts as the inverse to the negative Laplacian on functions
We consider neutral pseudoscalar, $η$, and axial vector, $f_1(1420)$, mesons in the OZI-rule-respecting flavor basis, $\lbrace (\bar s s), {1\over \sqrt{2}}(\bar u u + \bar d d)\rbrace$, and suggest a scenario for their coupling to the nucleon. Wi...
The 160 GeV polarised muon beam available at CERN, with positive or negative charge, makes COMPASS a unique place for GPD studies. The first GPD related COMPASS results come from exclusive vector meson production on transversely polarised protons and...
Web graphs form a family of planar directed graphs with boundary that can be used to model quantum $\mathfrak{sl}_n$-invariant vectors. Standard Young tableaux on an $n \times k$ rectangle naturally index a basis for $\mathfrak{sl}_n$ web graphs. We...
Given an element in a finite-dimensional real vector space, $V$, that is a nonnegative linear combination of basis vectors for some basis $B$, we compute the probability that it is furthermore a nonnegative linear combination of basis vectors for a s...
Spark Arena (also known as Auckland City Arena, and formerly as Vector Arena) is a multipurpose arena in Auckland, New Zealand. The venue is located at
The dispersion relations of carbon nanotubes are often obtained cross-sectioning those of graphene (zone-folding technique) in a rectangular region of the reciprocal space, where it is easier to fold the resulting relations into the nanotube Brillo...
with the Haswell microarchitecture, which shipped in 2013. AVX-512 expands AVX to 512-bit support using a new EVEX prefix encoding proposed by Intel in
We extend recent 256 SSE vector work to 512 AVX giving a four fold speedup. We use MAGPIE (Machine Automated General Performance Improvement via Evolution of software) to speedup a C++ linear genetic programming interpreter. Local search is provided...
We publish an extension of openQCD-1.6 with AVX-512 vector instructions using Intel intrinsics. Recent Intel processors support extended instruction sets with operations on 512-bit wide vectors, increasing both the capacity for floating point operati...
AVX-512 are 512-bit extensions to the 256-bit Advanced Vector Extensions SIMD instructions for x86 instruction set architecture (ISA) proposed by Intel
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a vanishing fr...
This paper explores some applications of a two-moment inequality for the integral of the $r$-th power of a function, where $0 < r< 1$. The first contribution is an upper bound on the Rényi entropy of a random vector in terms of the two different mom...
The field of compressed sensing has shown that a sparse but otherwise arbitrary vector can be recovered exactly from a small number of randomly constructed linear projections (or samples). The question addressed in this paper is whether an even sma...
This paper addresses the question of when projections of a high-dimensional random vector are approximately Gaussian. This problem has been studied previously in the context of high-dimensional data analysis, where the focus is on low-dimensional pro...
For a hyperplane arrangement in a real vector space, the coefficients of its Poincaré polynomial have many interpretations. An interesting one is provided by the Varchenko-Gel'fand ring, which is the ring of functions from the chambers of the arrang...