Testing linear hypotheses in high-dimensional regressions

For a multivariate linear model, Wilk's likelihood ratio test (LRT) constitutes one of the cornerstone tools. However, the computation of its quantiles under the null or the alternative requires complex analytic approximations and more importantly, these distributional approximations are feasible only for moderate dimension of the dependent variable, say $p\le 20$. On the other hand, assuming that the data dimension $p$ as well as the number $q$ of regression variables are fixed while the sample size $n$ grows, several asymptotic approximations are proposed in the literature for Wilk's \bLa including the widely used chi-square approximation. In this paper, we consider necessary modifications to Wilk's test in a high-dimensional context, specifically assuming a high data dimension $p$ and a large sample size $n$. Based on recent random matrix theory, the correction we propose to Wilk's test is asymptotically Gaussian under the null and simulations demonstrate that the corrected LRT has very satisfactory size and power, surely in the large $p$ and large $n$ context, but also for moderately large data dimensions like $p=30$ or $p=50$. As a byproduct, we give a reason explaining why the standard chi-square approximation fails for high-dimensional data. We also introduce a new procedure for the classical multiple sample significance test in MANOVA which is valid for high-dimensional data.Comment: Accepted 02/2012 for publication in "Statistics". 20 pages, 2 pages and 2 table

Significantly enhanced critical current densities in MgB2 tapes made by a scaleable, nano-carbon addition route

Nanocarbon-doped Fe-sheathed MgB2 tapes with different doping levels were prepared by the in situ powder-in-tube method. Compared to the undoped tapes, Jc for all the C-doped samples was enhanced by more than an order of magnitude in magnetic fields above 9 T. At 4.2 K, the transport Jc for the 5 at% doped tapes reached 1.85x104 A/cm2 at 10 T and 2.8x103 A/cm2 at 14 T, respectively. Moreover, the critical temperature for the doped tapes decreased slightly. Transmission electron microscopy showed a number of intra-granular dislocations and the dispersed nanoparticles embedded within MgB2 grains induced by the C doping. The mechanism for the enhancement of flux pinning is also discussed. These results indicate that powder-in-tube-processed MgB2 tape is very promising for high-field applications.Comment: 13 pages, 5 figures. to be published soo

Magnetic spin moment reduction in photoexcited ferromagnets through exchange interaction quenching: Beyond the rigid band approximation

The exchange interaction among electrons is one of the most fundamental quantum mechanical interactions in nature and underlies any magnetic phenomena from ferromagnetic ordering to magnetic storage. The current technology is built upon a thermal or magnetic field, but a frontier is emerging to directly control magnetism using ultrashort laser pulses. However, little is known about the fate of the exchange interaction. Here we report unambiguously that photoexcitation is capable of quenching the exchange interaction in all three $3d$ ferromagnetic metals. The entire process starts with a small number of photoexcited electrons which build up a new and self-destructive potential that collapses the system into a new state with a reduced exchange splitting. The spin moment reduction follows a Bloch-like law as $M_z(\Delta E)=M_z(0)(1-{\Delta E}/{\Delta E_0})^{\frac{1}{\beta}}$, where $\Delta E$ is the absorbed photon energy and $\beta$ is a scaling exponent. A good agreement is found between the experimental and our theoretical results. Our findings may have a broader implication for dynamic electron correlation effects in laser-excited iron-based superconductors, iron borate, rare-earth orthoferrites, hematites and rare-earth transition metal alloys.Comment: 16 pages, 3 figures, one supplementary material fil

Sequential nature of damage annealing and activation in implanted GaAs

Rapid thermal processing of implanted GaAs reveals a definitive sequence in the damage annealing and the electrical activation of ions. Removal of implantation-induced damage and restoration of GaAs crystallinity occurs first. Irrespective of implanted species, at this stage the GaAs is n-type and highly resistive with almost ideal values of electron mobility. Electrical activation is achieved next when, in a narrow anneal temperature window, the material becomes n- or p-type, or remains semi-insulating, commensurate to the chemical nature of the implanted ion. Such a two-step sequence in the electrical doping of GaAs by ion implantation may be unique of GaAs and other compound semiconductors

Generating high-order optical and spin harmonics from ferromagnetic monolayers

High-order harmonic generation (HHG) in solids has entered a new phase of intensive research, with envisioned band-structure mapping on an ultrashort time scale. This partly benefits from a flurry of new HHG materials discovered, but so far has missed an important group. HHG in magnetic materials should have profound impact on future magnetic storage technology advances. Here we introduce and demonstrate HHG in ferromagnetic monolayers. We find that HHG carries spin information and sensitively depends on the relativistic spin-orbit coupling; and if they are dispersed into the crystal momentum ${\bf k}$ space, harmonics originating from real transitions can be ${\bf k}$-resolved and carry the band structure information. Geometrically, the HHG signal is sensitive to spatial orientations of monolayers. Different from the optical counterpart, the spin HHG, though probably weak, only appears at even orders, a consequence of SU(2) symmetry. Our findings open an unexplored frontier -- magneto-high-order harmonic generation.Comment: 19 pages, 4 figure

Effect of aging on the reinforcement efficiency of carbon nanotubes in epoxy matrix

The reinforcement efficiency of carbon nanotubes (CNTs) in epoxy matrix was investigated in the elastic regime. Cyclic uniaxial tensile tests were performed at constant strain amplitude and increasing maximum strain. Post-curing of the epoxy and its composite at a temperature close to the glass transition temperature allowed us to explore the effect of aging on the reinforcement efficiency of CNT. It is found that the reinforcement efficiency is compatible with a mean field mixture rule of stress reinforcement by random inclusions. It also diminishes when the maximum strain increased and this effect is amplified by aging. The decrease of elastic modulus with increasing cyclic maximum strain is quite similar to the one observed for filled elastomers with increasing strain amplitude, a phenomenon often referred as the Payne effect

Tunneling dynamics of side chains and defects in proteins, polymer glasses, and OH-doped network glasses

Simulations on a Lennard-Jones computer glass are performed to study effects arising from defects in glasses at low temperatures. The numerical analysis reveals that already a low concentration of defects may dramatically change the low temperature properties by giving rise to extrinsic double-well potentials (DWP's). The main characteristics of these extrinsic DWP's are (i) high barrier heights, (ii) high probability that a defect is indeed connected with an extrinsic DWP, (iii) highly localized dynamics around this defect, and (iv) smaller deformation potential coupling to phonons. Designing an extension of the Standard Tunneling Model (STM) which parametrizes this picture and comparing with ultrasound experiments on the wet network glass $a$-B$_2$O$_3$ shows that effects of OH-impurities are accurately accounted for. This model is then applied to organic polymer glasses and proteins. It is suggested that side groups may act similarly like doped impurities inasmuch as extrinsic DWP's are induced, which possess a distribution of barriers peaked around a high barrier height. This compares with the structurlessly distributed barrier heights of the intrinsic DWP's, which are associated with the backbone dynamics. It is shown that this picture is consistent with elastic measurements on polymers, and can explain anomalous nonlogarithmic line broadening recently observed in hole burning experiments in PMMA.Comment: 34 pages, Revtex, 9 eps-figures, accepted for publication in J. Chem. Phy

Secondary metabolites screening from in-vitro cultured Rauwolfia tetraphylla by HPTLC-MS: A special emphasises on their antimicrobial applications

The current study designed at evaluating the phytochemical, trace metal concentration and antimicrobial properties were screened by the ethanolic extracts of in-vitro cultured medicinal plant Rauwolfia tetraphylla . The In-vitro shoots proliferation from nodal explants of R. tetraphylla using Murashige and Skoog (MS) medium containing 0.1mM of NAA and 0.25mM of BAP was effectively induce the shoot buds. The phytochemical analysis of cultured plant extracts revealed the presence of steroids, reducing sugars, sugars, alkaloids, phenols, flavonoid, saponins, tannins and amino acids. In continuously, we assessed by HPTLC coupled with mass spectrum, based on the mass spectrum were easily identified the major compounds such as 3-isoreserpine, ajmalicine, ajmaline, reserpine and yohimbine from R. tetraphylla . Metal contents of plant samples, Cd, Cr, Cu, Fe, Ni, Pb and Zn concentrations are BDL, BDL, 0.12, 0.68, BDL, BDL and 0.62 mg kg-1, respectively. The ethanol extraction of in-vitro R. tetraphylla inhibits the growth of bacteria and fungi to a greater extent

Design Principles for Sparse Matrix Multiplication on the GPU

We implement two novel algorithms for sparse-matrix dense-matrix multiplication (SpMM) on the GPU. Our algorithms expect the sparse input in the popular compressed-sparse-row (CSR) format and thus do not require expensive format conversion. While previous SpMM work concentrates on thread-level parallelism, we additionally focus on latency hiding with instruction-level parallelism and load-balancing. We show, both theoretically and experimentally, that the proposed SpMM is a better fit for the GPU than previous approaches. We identify a key memory access pattern that allows efficient access into both input and output matrices that is crucial to getting excellent performance on SpMM. By combining these two ingredients---(i) merge-based load-balancing and (ii) row-major coalesced memory access---we demonstrate a 4.1x peak speedup and a 31.7% geomean speedup over state-of-the-art SpMM implementations on real-world datasets.Comment: 16 pages, 7 figures, International European Conference on Parallel and Distributed Computing (Euro-Par) 201