Block Coordinate Descent for Sparse NMF

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets

Highly Quantum-Confined InAs Nanoscale Membranes

Nanoscale size-effects drastically alter the fundamental properties of semiconductors. Here, we investigate the dominant role of quantum confinement in the field-effect device properties of free-standing InAs nanomembranes with varied thicknesses of 5-50 nm. First, optical absorption studies are performed by transferring InAs "quantum membranes" (QMs) onto transparent substrates, from which the quantized sub-bands are directly visualized. These sub-bands determine the contact resistance of the system with the experimental values consistent with the expected number of quantum transport modes available for a given thickness. Finally, the effective electron mobility of InAs QMs is shown to exhibit anomalous field- and thickness-dependences that are in distinct contrast to the conventional MOSFET models, arising from the strong quantum confinement of carriers. The results provide an important advance towards establishing the fundamental device physics of 2-D semiconductors

Integral Equation Methods for Electrostatics, Acoustics, and Electromagnetics in Smoothly Varying, Anisotropic Media

[EN] We present a collection of well-conditioned integral equation methods for the solution of electrostatic, acoustic, or electromagnetic scattering problems involving anisotropic, inhomogeneous media. In the electromagnetic case, our approach involves a minor modification of a classical formulation. In the electrostatic or acoustic setting, we introduce a new vector partial differential equation, from which the desired solution is easily obtained. It is the vector equation for which we derive a well-conditioned integral equation. In addition to providing a unified framework for these solvers, we illustrate their performance using iterative solution methods coupled with the FFT-based technique of [F. Vico, L. Greengard, M. Ferrando, J. Comput. Phys., 323 (2016), pp. 191-203] to discretize and apply the relevant integral operators.The work of the authors was partially supported by the Spanish Ministry of Science and Innovation under project TEC2016-78028-C3-3-P and the U.S. Department of Energy under grant DE-FG02-86ER53223.Imbert-Gérard, L.; Vico Bondía, F.; Greengard, L.; Ferrando Bataller, M. (2019). Integral Equation Methods for Electrostatics, Acoustics, and Electromagnetics in Smoothly Varying, Anisotropic Media. SIAM Journal on Numerical Analysis. 57(3):1020-1035. https://doi.org/10.1137/18M1187039S1020103557

Single spin asymmetry measurements for π0\pi^0 inclusive productions in p+p↑→π0+Xp+p_{\uparrow} \to \pi^0 + X and \pi^-+\p_{\uparrow}\to \pi^0+X reactions at 70 and 40 GeV respectively

The inclusive $\pi^0$ asymmetries were measured in reactions $p+p\uparrow \to \pi^0+X$ and $\pi^-+p\uparrow \to \pi^0+X$ at 70 and 40 GeV/c respectively. The measurements were made at the central region (for the first reaction) and asymmetry is compatible with zero in the entire measured $p_T$ region. For the second reaction the asymmetry is zero for small $x_F$ region ($-0.4<x_F<-0.1, 0.5<p_T(GeV/c) <1.5$) and increases with growth of $\mid x_F\mid$. Averaged over the interval $-0.8<x_F<-0.4, 1<p_T(GeV/c)<2$ the asymmetry was $-(13.8\pm 3.8)$.Comment: 4 pages, 2 figures; Presented at SPIN-2004 at Trieste, October 10-16,200