Every graph occurs as an induced subgraph of some hypohamiltonian graph

We prove the titular statement. This settles a problem of Chvátal from 1973 and encompasses earlier results of Thomassen, who showed it for K_3, and Collier and Schmeichel, who proved it for bipartite graphs. We also show that for every outerplanar graph there exists a planar hypohamiltonian graph containing it as an induced subgraph

Spin relaxation in a generic two-dimensional spin-orbit coupled system

We study the relaxation of a spin density injected into a two-dimensional electron system with generic spin-orbit interactions. Our model includes the Rashba as well as linear and cubic Dresselhaus terms. We explicitly derive a general spin-charge coupled diffusion equation. Spin diffusion is characterized by just two independent dimensionless parameters which control the interplay between different spin-orbit couplings. The real-time representation of the diffuson matrix (Green's function of the diffusion equation) is evaluated analytically. The diffuson describes space-time dynamics of the injected spin distribution. We explicitly study two regimes: The first regime corresponds to negligible spin-charge coupling and is characterized by standard charge diffusion decoupled from the spin dynamics. It is shown that there exist several qualitatively different dynamic behaviors of the spin density, which correspond to various domains in the spin-orbit coupling parameter space. We discuss in detail a few interesting phenomena such as an enhancement of the spin relaxation times, real space oscillatory dynamics, and anisotropic transport. In the second regime, we include the effects of spin-charge coupling. It is shown that the spin-charge coupling leads to an enhancement of the effective charge diffusion coefficient. We also find that in the case of strong spin-charge coupling, the relaxation rates formally become complex and the spin/charge dynamics is characterized by real time oscillations. These effects are qualitatively similar to those observed in spin-grating experiments [Weber et al., Nature 437, 1330 (2005)].Comment: 18 pages, 7 figure

Bulk Spin-Hall Effect

We show that a two-dimensional spin-orbit-coupled system in the presence of a charge/spin-density wave with a wave-vector perpendicular to an applied electric field supports bulk manifestations of the direct/inverse spin-Hall effect. We develop a theory of this phenomenon in the framework of the spin diffusion equation formalism and show that, due to the inhomogeneity created by a spin-grating, an anomalous bulk charge-density wave is induced away from sample boundaries. The optimal conditions for the observation of the effect are determined. The main experimental manifestation of the bulk spin-Hall effect, the induced charge/spin-density-wave, is characterized by a pi/2-phase shift relative to the initial non-homogeneous spin/charge-polarization profile and has a non-monotonic time-varying amplitude.Comment: 4 pages, 4 figure

Nanostructured thermoelectric generator for energy harvesting

This paper presents the development processes towards a new generation of nanostructured thermoelectric generators for power harvesting from small temperature gradients by using a combination of traditional silicon microfabrication techniques, electroplating and submicron ion-track nanolithography. Polyimide nanotemplates with pore diameters ranging from 30nm to 120 nm were fabricated. Preliminary results for Bi2Te3 nanowires (50 and 120 nm diameter) electroplated into polycarbonate ion-track commercial membranes are presented. Bi2Te3 nanowires of R ̄ 3m structure, with preferential orientation in the (015) and (110) crystallographic plans with nearly stoichiometric composition were electroplated. The fine-grained observed microstructure (6-10 nm) and (110) crystalline orientation appear extremely promising for improving thermoelectric material properties

Non-equilibrium spin dynamics in a trapped Fermi gas with effective spin-orbit interaction

We consider a trapped atomic system in the presence of spatially varying laser fields. The laser-atom interaction generates a pseudospin degree of freedom (referred to simply as spin) and leads to an effective spin-orbit coupling for the fermions in the trap. Reflections of the fermions from the trap boundaries provide a physical mechanism for effective momentum relaxation and non-trivial spin dynamics due to the emergent spin-orbit coupling. We explicitly consider evolution of an initially spin-polarized Fermi gas in a two-dimensional harmonic trap and derive non-equilibrium behavior of the spin polarization. It shows periodic echoes with a frequency equal to the harmonic trapping frequency. Perturbations, such as an asymmetry of the trap, lead to the suppression of the spin echo amplitudes. We discuss a possible experimental setup to observe spin dynamics and provide numerical estimates of relevant parameters.Comment: 5 pages, 4 figures; published versio

Convergence towards linear combinations of chi-squared random variables: a Malliavin-based approach

We investigate the problem of finding necessary and sufficient conditions for convergence in distribution towards a general finite linear combination of independent chi-squared random variables, within the framework of random objects living on a fixed Gaussian space. Using a recent representation of cumulants in terms of the Malliavin calculus operators $\Gamma_i$ (introduced by Nourdin and Peccati in \cite{n-pe-3}), we provide conditions that apply to random variables living in a finite sum of Wiener chaoses. As an important by-product of our analysis, we shall derive a new proof and a new interpretation of a recent finding by Nourdin and Poly \cite{n-po-1}, concerning the limiting behaviour of random variables living in a Wiener chaos of order two. Our analysis contributes to a fertile line of research, that originates from questions raised by Marc Yor, in the framework of limit theorems for non-linear functionals of Brownian local times

Surface states, Friedel oscillations, and spin accumulation in p-doped semiconductors

We consider a hole-doped semiconductor with a sharp boundary and study the boundary spin accumulation in response to a charge current. First, we solve exactly a single-particle quantum mechanics problem described by the isotropic Luttinger model in half-space and construct an orthonormal basis for the corresponding Hamiltonian. It is shown that the complete basis includes two types of eigenstates. The first class of states contains conventional incident and reflected waves, while the other class includes localized surface states. Second, we consider a many-body system in the presence of a charge current flowing parallel to the boundary. It is shown that the localized states contribute to spin accumulation near the surface. We also show that the spin density exhibits current-induced Friedel oscillations with three different periods determined by the Fermi momenta of the light and heavy holes. We find an exact asymptotic expression for the Friedel oscillations far from the boundary. We also calculate numerically the spin density profile and compute the total spin accumulation, which is defined as the integral of the spin density in the direction perpendicular to the boundary. The total spin accumulation is shown to fit very well the simple formula S ~(1 - m_L/m_H)^2, where m_L and m_H are the light- and heavy-hole masses. The effects of disorder are discussed. We estimate the spin relaxation time in the Luttinger model and argue that spin physics cannot be described within the diffusion approximation.Comment: 22 pages, 8 color figure

Nearest-neighbour Attraction Stabilizes Staggered Currents in the 2D Hubbard Model

Using a strong-coupling approach, we show that staggered current vorticity does not obtain in the repulsive 2D Hubbard model for large on-site Coulomb interactions, as in the case of the copper oxide superconductors. This trend also persists even when nearest-neighbour repulsions are present. However, staggered flux ordering emerges {\bf only} when attractive nearest-neighbour Coulomb interactions are included. Such ordering opens a gap along the $(\pi,0)-(0,\pi)$ direction and persists over a reasonable range of doping.Comment: 5 pages with 5 .eps files (Typos in text are corrected

Prognostic Impact of HOTAIR Expression is Restricted to ER-Negative Breast Cancers

Expression of HOX transcript antisense intergenic RNA (HOTAIR), a large intergenic noncoding RNA (lincRNA), has been described as a metastases-associated lincRNA in various cancers including breast, liver and colon cancer cancers. We sought to determine if expression of HOTAIR could be used as a surrogate for assessing nodal metastases and evaluated RNA in situ hybridization (RNA-ISH) assay in a tissue microarray constructed from 133 breast cancer patients. The prognostic value of HOTAIR was further validated in large cohorts using The Cancer Genome Atlas (TCGA) breast cancer subjects. RNA-ISH analysis was successful in 94 cases (17% cases scored 0, 32.9% scored 1, 30.8% scored 2, and 19.1% scored 3). The expression of HOTAIR did not correlate with nodal metastasis regardless of the scoring intensity or with other study parameters (age, tumor size and grade, expression status). Further analysis of TCGA dataset showed that HOTAIR expression was lower in ductal carcinomas but higher in ER-negative tumors. Overexpression of HOTAIR was not associated with nodal metastases or prognosis in ER-positive patients. Its function as a poor prognostic indicator in ER-negative patients was restricted to node-positive patients. HOTAIR appears to be a marker for lymphatic metastases rather than hematogenous metastases in ER-negative patients