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...
We are interested in computing a simple eigenpair $(λ,{\bf x})$ of a large non-Hermitian matrix $A$, by a general harmonic Rayleigh-Ritz projection method. Given a search subspace $\mathcal{K}$ and a target point $τ$, we focus on the convergence of...
For a given subspace, the Rayleigh-Ritz method projects the large quadratic eigenvalue problem (QEP) onto it and produces a small sized dense QEP. Similar to the Rayleigh-Ritz method for the linear eigenvalue problem, the Rayleigh-Ritz method defines...
For an arbitrary self-adjoint operator $B$ in a Hilbert space $H$, we present direct and inverse theorems establishing the relationship between the degree of smoothness of a vector $x \in H$ with respect to the operator $B$, the rate of convergence...
A simple tool to extract motion vectors from h264 encoded videos. (⭐ 122)
Brain fiber tracts are widely used in studying brain diseases, which may lead to a better understanding of how disease affects the brain. The segmentation of brain fiber tracts assumed enormous importance in disease analysis. In this paper, we propos...
This paper proves a linear algebra result that has to do with the geometry of "widgets". For us a widget is a collection of n pairs of points in a vector space. (The pairs represent the different possible spin states of a particle.) We investigate li...
A Mall bundle on a Hopf manifold H is a holomorphic vector bundle whose pullback to the universal cover of H is trivial. We define resonant and non-resonant Mall bundles, generalizing the notion of the resonance in ODE, and prove that a non-resonant...