Almost-Euclidean subspaces of ℓ1N\ell_1^N via tensor products: a simple approach to randomness reduction

It has been known since 1970's that the N-dimensional $\ell_1$-space contains nearly Euclidean subspaces whose dimension is $\Omega(N)$. However, proofs of existence of such subspaces were probabilistic, hence non-constructive, which made the results not-quite-suitable for subsequently discovered applications to high-dimensional nearest neighbor search, error-correcting codes over the reals, compressive sensing and other computational problems. In this paper we present a "low-tech" scheme which, for any $a > 0$, allows to exhibit nearly Euclidean $\Omega(N)$-dimensional subspaces of $\ell_1^N$ while using only $N^a$ random bits. Our results extend and complement (particularly) recent work by Guruswami-Lee-Wigderson. Characteristic features of our approach include (1) simplicity (we use only tensor products) and (2) yielding "almost Euclidean" subspaces with arbitrarily small distortions.Comment: 11 pages; title change, abstract and references added, other minor change

Amenability of algebras of approximable operators

We give a necessary and sufficient condition for amenability of the Banach algebra of approximable operators on a Banach space. We further investigate the relationship between amenability of this algebra and factorization of operators, strengthening known results and developing new techniques to determine whether or not a given Banach space carries an amenable algebra of approximable operators. Using these techniques, we are able to show, among other things, the non-amenability of the algebra of approximable operators on Tsirelson's space.Comment: 20 pages, to appear in Israel Journal of Mathematic

Gold substrate-induced single-mode lasing of GaN nanowires

We demonstrate a method for mode-selection by coupling a GaN nanowire laser to an underlying gold substrate. Multimode lasing of GaN nanowires is converted to single-mode behavior following placement onto a gold film. A mode-dependent loss is generated by the absorbing substrate to suppress multiple transverse-mode operation with a concomitant increase in lasing threshold of only ∼13%. This method provides greater flexibility in realizing practical single-mode nanowire lasers and offers insight into the design of metal-contacted nanoscale optoelectronics

Hastings' additivity counterexample via Dvoretzky's theorem

The goal of this note is to show that Hastings' counterexample to the additivity of minimal output von Neumann entropy can be readily deduced from a sharp version of Dvoretzky's theorem on almost spherical sections of convex bodies.Comment: 12 pages; v.2: added references, Appendix A expanded to make the paper essentially self-containe

In-situ uniaxial drawing of poly-L-lactic acid (PLLA): Following the crystalline morphology development using time-resolved SAXS/WAXS

Simultaneous synchrotron small- and wide-angle X-ray scattering (SAXS/WAXS) was used to follow the crystalline morphology evolution of poly-L- lactic acid (PLLA) during uniaxial deformation at various draw temperatures (Td). The mechanical behaviour of PLLA, was found to be strongly dependent on Td. 2D SAXS/WAXS data taken during the draw showed that at low Tds cavitation and voiding occurred and the initial crystallites underwent ‘overdrawing’ where they slip and are partially destroyed. SEM confirmed that surface voiding and cavitation had occurred at Td = 60 and 65 °C but was absent at higher Tds. During the draw, no long-range macromolecular lamellar structure was seen in the SAXS, but small crystallites of the disordered α′ crystal form of PLLA were observed in the WAXS at all Tds. The PLLA samples were then step annealed in a second processing stage (post-draw) to develop the oriented crystalline lamellar structure and increase the amount of the stable α crystalline form. SAXS/WAXS data showed that a highly oriented lamellar stack macrostructure developed on annealing, with increased crystallite size and crystallinity at all Tds. Furthermore, step annealing drove the crystalline transition in all samples from the disordered α′ crystal form to the stable α crystal form. Therefore, varying pre- and post-processing parameters can significantly influence the mechanical properties, orientation, crystalline morphology and crystal phase transition of the final PLLA material

Exponential and moment inequalities for U-statistics

A Bernstein-type exponential inequality for (generalized) canonical U-statistics of order 2 is obtained and the Rosenthal and Hoffmann-J{\o}rgensen inequalities for sums of independent random variables are extended to (generalized) U-statistics of any order whose kernels are either nonnegative or canonicalComment: 22 page

Annular-shaped emission from gallium nitride nanotube lasers

Annular-shaped lasing emission is demonstrated from gallium nitride nanotubes fabricated using a two-step top-down technique. By optically pumping, we observe a clear threshold of 1055 kW/cm2, a narrow spectral linewidth of 0.19 nm, and guided emission from the nanotubes. Lasing is also demonstrated in a liquid environment, with an approximate doubling in threshold observed. The nanotube lasers could be of interest for optical nanofluidic applications or applications benefiting from a hollow beam shape. More generally, the results indicate that cross-sectional shape control can be employed to manipulate the properties of nanolasers

Measurement of the Luminosity in the ZEUS Experiment at HERA II

The luminosity in the ZEUS detector was measured using photons from electron bremsstrahlung. In 2001 the HERA collider was upgraded for operation at higher luminosity. At the same time the luminosity-measuring system of the ZEUS experiment was modified to tackle the expected higher photon rate and synchrotron radiation. The existing lead-scintillator calorimeter was equipped with radiation hard scintillator tiles and shielded against synchrotron radiation. In addition, a magnetic spectrometer was installed to measure the luminosity independently using photons converted in the beam-pipe exit window. The redundancy provided a reliable and robust luminosity determination with a systematic uncertainty of 1.7%. The experimental setup, the techniques used for luminosity determination and the estimate of the systematic uncertainty are reported.Comment: 25 pages, 11 figure

Polarization control in GaN nanowire lasers

We demonstrate polarization control in optically-pumped single GaN nanowire lasers fabricated by a top-down method. By placing the GaN nanowires onto gold substrates, the naturally occurring randomly orientated elliptical polarization of nanowire lasers is converted to a linear polarization that is oriented parallel to the substrate surface. Confirmed by simulation results, this polarization control is attributed to a polarization-dependent loss induced by the gold substrate, which breaks the mode degeneracy of the nanowire and forms two orthogonally polarized modes with largely different cavity losses

Nonlinear spectral calculus and super-expanders

Nonlinear spectral gaps with respect to uniformly convex normed spaces are shown to satisfy a spectral calculus inequality that establishes their decay along Cesaro averages. Nonlinear spectral gaps of graphs are also shown to behave sub-multiplicatively under zigzag products. These results yield a combinatorial construction of super-expanders, i.e., a sequence of 3-regular graphs that does not admit a coarse embedding into any uniformly convex normed space.Comment: Typos fixed based on referee comments. Some of the results of this paper were announced in arXiv:0910.2041. The corresponding parts of arXiv:0910.2041 are subsumed by the current pape