Monomial Testing and Applications

In this paper, we devise two algorithms for the problem of testing $q$-monomials of degree $k$ in any multivariate polynomial represented by a circuit, regardless of the primality of $q$. One is an $O^*(2^k)$ time randomized algorithm. The other is an $O^*(12.8^k)$ time deterministic algorithm for the same $q$-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several applications of $q$-monomial testing are also given, including a deterministic $O^*(12.8^{mk})$ upper bound for the $m$-set $k$-packing problem.Comment: 17 pages, 4 figures, submitted FAW-AAIM 2013. arXiv admin note: substantial text overlap with arXiv:1302.5898; and text overlap with arXiv:1007.2675, arXiv:1007.2678, arXiv:1007.2673 by other author

On The Expected Photon Spectrum in B -> X_s + gamma and Its Uses

Measuring the photon energy spectrum in radiative B decays provides essential help for gaining theoretical control over semileptonic B transitions. The hadronic recoil mass distribution in B -> X_u \ell\nu promises the best environment for determining |V_ub|. The theoretical uncertainties are largest in the domain of low values of the lepton pair mass q^2. Universality relations allow to describe this domain reliably in terms of the photon spectrum in B -> X_s + \gamma. A method is proposed to incorporate 1/m_b corrections into this relation. The low-E_\gamma tail in radiative decays is important in the context of extracting |V_ub|. We argue that CLEO's recent fit to the spectrum underestimates the fraction of the photon spectrum below 2 GeV. Potentially significant uncertainties enter in the theoretical evaluation of the integrated end-point lepton spectrum or the B -> X_u \ell\nu width with a too high value of the lower cut on q^2 in alternative approaches to |V_ub|.Comment: 24 pages, 6 figures, LaTeX. Revised: Complete version. Numerical predictions are improved and the estimate for the decay fraction revised. The theoretical expectations for the decay fraction and the spectrum itself are given on the plot

Maximum a Posteriori Adaptation of Network Parameters in Deep Models

We present a Bayesian approach to adapting parameters of a well-trained context-dependent, deep-neural-network, hidden Markov model (CD-DNN-HMM) to improve automatic speech recognition performance. Given an abundance of DNN parameters but with only a limited amount of data, the effectiveness of the adapted DNN model can often be compromised. We formulate maximum a posteriori (MAP) adaptation of parameters of a specially designed CD-DNN-HMM with an augmented linear hidden networks connected to the output tied states, or senones, and compare it to feature space MAP linear regression previously proposed. Experimental evidences on the 20,000-word open vocabulary Wall Street Journal task demonstrate the feasibility of the proposed framework. In supervised adaptation, the proposed MAP adaptation approach provides more than 10% relative error reduction and consistently outperforms the conventional transformation based methods. Furthermore, we present an initial attempt to generate hierarchical priors to improve adaptation efficiency and effectiveness with limited adaptation data by exploiting similarities among senones

Lifshitz Transition in the Two Dimensional Hubbard Model

Using large-scale dynamical cluster quantum Monte Carlo simulations, we study the Lifshitz transition of the two dimensional Hubbard model with next-nearest-neighbor hopping ($t'$), chemical potential and temperature as control parameters. At $t'\le0$, we identify a line of Lifshitz transition points associated with a change of the Fermi surface topology at zero temperature. In the overdoped region, the Fermi surface is complete and electron-like; across the Lifshitz transition, the Fermi surface becomes hole-like and develops a pseudogap. At (or very close to) the Lifshitz transition points, a van Hove singularity in the density of states crosses the Fermi level. The van Hove singularity occurs at finite doping due to correlation effects, and becomes more singular when $t'$ becomes more negative. The resulting temperature dependence on the bare d-wave pairing susceptibility close to the Lifshitz points is significantly different from that found in the traditional van Hove scenarios. Such unambiguous numerical observation of the Lifshitz transition at $t'\le0$ extends our understanding of the quantum critical region in the phase diagram, and shines lights on future investigations of the nature of the quantum critical point in the two dimensional Hubbard model.Comment: 9 pages, 8 figures, accepted for publication in Physics Review

Electronic Structure of New AFFeAs Prototype of Iron Arsenide Superconductors

This work is provoked by recent discovery of new class prototype systems AFFeAs (A=Sr,Ca) of novel layered ironpnictide High-Tc superconductors (Tc=36K). Here we report ab initio LDA results for electronic structure of the AFFeAs systems. We provide detailed comparison between electronic properties of both new systems and reference LaOFeAs (La111) compound. In the vicinity of the Fermi level all three systems have essentially the same band dispersions. However for iron fluoride systems F(2p) states were found to be separated in energy from As(4p) ones in contrast to La111, where O(2p) states strongly overlaps with As(4p). Thus it should be more plausible to include only Fe(3d) and As(4p) orbitals into a realistic noninteracting model than for La111. Moreover Sr substitution with smaller ionic radius Ca in AFFeAs materials leads to a lattice contruction and stronger Fe(3d)-As(4p) hybridization resulting in smaller value of the density of states at the Fermi level in the case of Ca compound. So to some extend Ca system reminds RE111 with later Rare Earths. However Fermi surface of new fluorides is found to be nearly perfect two-dimensional. Also we do not expect strong dependence of superconducting properties with respect to different types of A substitutes.Comment: 5 pages, 4 figure

Stability of C20 fullerene chains

The stability of (C20)N chains with N = 3 - 7 is analyzed by numerical simulation using a tight-binding potential and molecular dynamics. Various channels of losing the cluster-chain structure of the (C20)N complexes are observed, including the decay of C20 clusters, their coalescence, and the separation of one C20 fullerene from the chain.Comment: To appear in JETP Letter

Numerical Study of the Spin Hall Conductance in the Luttinger Model

We present first numerical studies of the disorder effect on the recently proposed intrinsic spin Hall conductance in a three dimensional (3D) lattice Luttinger model. The results show that the spin Hall conductance remains finite in a wide range of disorder strength, with large fluctuations. The disorder-configuration-averaged spin Hall conductance monotonically decreases with the increase of disorder strength and vanishes before the Anderson localization takes place. The finite-size effect is also discussed.Comment: 4 pages, 4 figures; the final version appearing in PR

Global polarization of QGP in non-central heavy ion collisions at high energies

Due to the presence of a large orbital angular momentum of the parton system produced at the early stage of non-central heavy-ion collisions, quarks and anti-quarks are shown to be polarized in the direction opposite to the reaction plane which is determined by the impact-parameter and the beam momentum. The global quark polarization via elastic scattering was first calculated in an effective static potential model, then using QCD at finite temperature with the hard-thermal-loop re-summed gluon propagator. The measurable consequences are discussed. Global hyperon polarization from the hadronization of polarized quarks are predicted independent of the hadronization scenarios. It has also been shown that the global polarization of quarks and anti-quarks leads also to spin alignment of vector mesons. Dedicated measurements at RHIC are underway and some of the preliminary results are obtained. In this presentation, the basic idea and main results of global quark polarization are presented. The direct consequences such as global hyperon polarization and spin alignment are summarized.Comment: plenary talk at the 19th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions (QM2006), Shanghai, China, November 14-20, 200

Strain relaxation in InGaN/GaN micro-pillars evidenced by high resolution cathodoluminescence hyperspectral imaging

A size-dependent strain relaxation and its effects on the optical properties of InGaN/GaN multiple quantum wells (QWs) in micro-pillars have been investigated through a combination of high spatial resolution cathodoluminescence (CL) hyperspectral imaging and numerical modeling. The pillars have diameters (d) ranging from 2 to 150 μm and were fabricated from a III-nitride light-emitting diode (LED) structure optimized for yellow-green emission at ∼560 nm. The CL mapping enables us to investigate strain relaxation in these pillars on a sub-micron scale and to confirm for the first time that a narrow (≤2 μm) edge blue-shift occurs even for the large InGaN/GaN pillars (d > 10 μm). The observed maximum blue-shift at the pillar edge exceeds 7 nm with respect to the pillar centre for the pillars with diameters in the 2–16 μm range. For the smallest pillar (d = 2 μm), the total blue-shift at the edge is 17.5 nm including an 8.2 nm “global” blue-shift at the pillar centre in comparison with the unetched wafer. By using a finite element method with a boundary condition taking account of a strained GaN buffer layer which was neglected in previous simulation works, the strain distribution in the QWs of these pillars was simulated as a function of pillar diameter. The blue-shift in the QWs emission wavelength was then calculated from the strain-dependent changes in piezoelectric field, and the consequent modification of transition energy in the QWs. The simulation and experimental results agree well, confirming the necessity for considering the strained buffer layer in the strain simulation. These results provide not only significant insights into the mechanism of strain relaxation in these micro-pillars but also practical guidance for design of micro/nano LEDs