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
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...
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...
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...
A geometric version of the Poincaré Lemma is established for the topological vector space of differential chains. In particular, every differential k-cycle with compact support in a contractible open subset U of a smooth n-manifold M is the boundary...
I'm in Linear Algebra right now and we're mostly just working with vector spaces, but they're introducing us to the basic concepts of fields and groups in preparation taking for Abstract Algebra la...
Gather/scatter is a type of memory addressing that at once collects (gathers) from, or stores (scatters) data to, multiple arbitrary memory indices. Examples
A plotter is a machine that produces vector graphics drawings. Plotters draw lines on paper using a pen, or in some applications, use a knife to cut a
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