Search results for "factorization"

Atomic Decomposition of Weighted Besov Spaces

1996

We find the atomic decomposition of functions in the weighted Besov spaces under certain factorization conditions on the weight. Introduction. After achieving the atomic decomposition of Hardy spaces (see [8,22, 33]), many of the function saces have been shown to admit similar decompositions. Let us mention the decomposition of B.M.O. (see [32, 25]), Bergman spaces (see [9, 23]), the predual of Bloch space (see [ 11]), Besov spaces (see [15, 4, 10]), Lipschitz spaces (see [18]), Triebel-Lizorkin spaces (see [16, 31]),... They are obtained by quite different methods, but there is a unified and beautiful approach to get the decomposition for most of the spaces. This is the use of a formula du…

Iterative sparse matrix-vector multiplication for accelerating the block Wiedemann algorithm over GF(2) on multi-graphics processing unit systems

2012

SUMMARY The block Wiedemann (BW) algorithm is frequently used to solve sparse linear systems over GF(2). Iterative sparse matrix–vector multiplication is the most time-consuming operation. The necessity to accelerate this step is motivated by the application of BW to very large matrices used in the linear algebra step of the number field sieve (NFS) for integer factorization. In this paper, we derive an efficient CUDA implementation of this operation by using a newly designed hybrid sparse matrix format. This leads to speedups between 4 and 8 on a single graphics processing unit (GPU) for a number of tested NFS matrices compared with an optimized multicore implementation. We further present…

Discrete and Conservative Factorizations in Fib(B)

2021

AbstractWe focus on the transfer of some known orthogonal factorization systems from$$\mathsf {Cat}$$Catto the 2-category$${\mathsf {Fib}}(B)$$Fib(B)of fibrations over a fixed base categoryB: the internal version of thecomprehensive factorization, and the factorization systems given by (sequence of coidentifiers, discrete morphism) and (sequence of coinverters, conservative morphism) respectively. For the class of fibrewise opfibrations in$${\mathsf {Fib}}(B)$$Fib(B), the construction of the latter two simplify to a single coidentifier (respectively coinverter) followed by an internal discrete opfibration (resp. fibrewise opfibration in groupoids). We show how these results follow from thei…

On the number of prime divisors of the order of elliptic curves modulo p

2005

Nilpotent-like fitting formations of finite soluble groups

2000

[EN] In this paper the subnormal subgroup closed saturated formations of finite soluble groups containing nilpotent groups are fully characterised by means of extensions of well-known properties enjoyed by the formation of all nilpotent groups.

Identification of small inhomogeneities: Asymptotic factorization

2007

We consider the boundary value problem of calculating the electrostatic potential for a homogeneous conductor containing finitely many small insulating inclusions. We give a new proof of the asymptotic expansion of the electrostatic potential in terms of the background potential, the location of the inhomogeneities and their geometry, as the size of the inhomogeneities tends to zero. Such asymptotic expansions have already been used to design direct (i.e. noniterative) reconstruction algorithms for the determination of the location of the small inclusions from electrostatic measurements on the boundary, e.g. MUSIC-type methods. Our derivation of the asymptotic formulas is based on integral …

Group Nonnegative Matrix Factorization with Sparse Regularization in Multi-set Data

2021

Constrained joint analysis of data from multiple sources has received widespread attention for that it allows us to explore potential connections and extract meaningful hidden components. In this paper, we formulate a flexible joint source separation model termed as group nonnegative matrix factorization with sparse regularization (GNMF-SR), which aims to jointly analyze the partially coupled multi-set data. In the GNMF-SR model, common and individual patterns of particular underlying factors can be extracted simultaneously with imposing nonnegative constraint and sparse penalty. Alternating optimization and alternating direction method of multipliers (ADMM) are combined to solve the GNMF-S…

Quantitative evaluation of muscle synergy models: a single-trial task decoding approach.

2012

Delis, Ioannis | Berret, Bastien | Pozzo, Thierry | Panzeri, Stefano; International audience; ''Muscle synergies, i.e., invariant coordinated activations of groups of muscles, have been proposed as building blocks that the central nervous system (CNS) uses to construct the patterns of muscle activity utilized for executing movements . Several efficient dimensionality reduction algorithms that extract putative synergies from electromyographic (EMG) signals have been developed. Typically, the quality of synergy decompositions is assessed by computing the Variance Accounted For (VAF). Yet, little is known about the extent to which the combination of those synergies en codes task discriminating…

''Investigating reduction of dimensionality during single-joint elbow movements: a case study on muscle synergies''

2013

Chiovetto, Enrico | Berret, Bastien | Delis, Ioannis | Panzeri, Stefano | Pozzo, Thierry; International audience; ''A long standing hypothesis in the neuroscience community is that the central nervous system (CNS) generates the muscle activities to accomplish movements by combining a relatively small number of stereotyped patterns of muscle activations, often referred to as" muscle synergies." Different definitions of synergies have been given in the literature. The most well-known are those of synchronous, time-varying and temporal muscle synergies. Each one of them is based on a different mathematical model used to factor some EMG array recordings collected during the execution of variety…

Listwise Recommendation Approach with Non-negative Matrix Factorization

2018

Matrix factorization (MF) is one of the most effective categories of recommendation algorithms, which makes predictions based on the user-item rating matrix. Nowadays many studies reveal that the ultimate goal of recommendations is to predict correct rankings of these unrated items. However, most of the pioneering efforts on ranking-oriented MF predict users’ item ranking based on the original rating matrix, which fails to explicitly present users’ preference ranking on items and thus might result in some accuracy loss. In this paper, we formulate a novel listwise user-ranking probability prediction problem for recommendations, that aims to utilize a user-ranking probability matrix to predi…