Complexity of pattern classes and Lipschitz property

Rademacher and Gaussian complexities are successfully used in learning theory for measuring the capacity of the class of functions to be learned. One of the most important properties for these complexities is their Lipschitz property: a composition of a class of functions with a fixed Lipschitz function may increase its complexity by at most twice the Lipschitz constant. The proof of this property is non-trivial (in contrast to the other properties) and it is believed that the proof in the Gaussian case is conceptually more difficult then the one for the Rademacher case. In this paper we give a detailed prove of the Lipschitz property for the Rademacher case and generalize the same idea to an arbitrary complexity (including the Gaussian). We also discuss a related topic about the Rademacher complexity of a class consisting of all the Lipschitz functions with a given Lipschitz constant. We show that the complexity is surprisingly low in the one-dimensional case. The question for higher dimensions remains open

Compilation, design tests: Energetic particles Satellite S-3 including design tests for S-3A, S-3B and S-3C

A compilation of engineering design tests which were conducted in support of the Energetic Particle Satellite S-3, S-3A, and S-3b programs. The purpose for conducting the tests was to determine the adequacy and reliability of the Energetic Particles Series of satellites designs. The various tests consisted of: (1) moments of inertia, (2) functional reliability, (3) component and structural integrity, (4) initiators and explosives tests, and (5) acceptance tests

Multiphase Plasma in Sub-Damped Lyman Alpha Systems: A Hidden Metal Reservoir

We present a VLT/UVES spectrum of a proximate sub-damped Lyman-alpha (sub-DLA) system at z=2.65618 toward the quasar Q0331-4505 (z_qso=2.6785+/-0.0030). Absorption lines of O I, Si II, Si III, Si IV, C II, C III, C IV, Fe II, Al II, and O VI are seen in the sub-DLA, which has a neutral hydrogen column density log N(H I)=19.82+/-0.05. The absorber is at a velocity of 1820+/-250 km/s from the quasar; however, its low metallicity [O/H]=-1.64+/-0.07, lack of partial coverage, lack of temporal variations between observations taken in 2003 and 2006, and non-detection of N V imply the absorber is not a genuine intrinsic system. By measuring the O VI column density and assuming equal metallicities in the neutral and ionized gas, we determine the column density of hot ionized hydrogen in this sub-DLA, and in two other sub-DLAs with O VI drawn from the literature. Coupling this with determinations of the typical amount of warm ionized hydrogen in sub-DLAs, we confirm that sub-DLAs are a more important metal reservoir than DLAs, in total comprising at least 6-22% of the metal budget at z~2.5.Comment: 5 pages, 3 color figures, accepted for publication in ApJ

Outflowing material in the z<SUB>em</SUB> = 4.92 BAL QSO SDSS J160501.21-011220.0

We present the analysis of broad absorption lines (BALs) seen in the spectrum of the Zem &#x22CD; 4.92 QSO SDSS J160501.21-011220.0. Our high spectral resolution UVES spectrum shows two well-detached absorption line systems at Zabs = 4.685 and 4.855. The system at Zabs = 4.855 covers the background source completely, suggesting that the gas is located outside the broad emission line region. On the contrary, the system at Zabs = 4.685, which occults only the continuum source, has a covering factor of the order of 0.9. Physical conditions are investigated in the BAL system at Zabs = 4.855 using detailed photoionization models. The observed H I absorption line together with the limits on C II and Si II absorptions suggest that 16 &lt; log N(H I) (cm -2) &lt; 17 in this system. Comparison with models show that the observed column densities of N V , Si IV and C IV in this system require that nitrogen is underabundant by more than a factor of 3 compared to silicon if the ionizing radiation is similar to a typical QSO spectrum. This is contrary to what is usually derived for the emission line gas in QSOs. We show that the relative suppression in the N V column density can be explained for Solar abundance ratios or abundance ratios typical of Starburst abundances if an ionizing spectrum devoid of X-rays is used instead. Thus, if the composition of BAL is like that of the emission line regions it is most likely that the cloud sees a spectrum devoid of X-rays similar to what we observe from this QSO. This is consistent with the fact that none of our models have high Compton optical depths to remove X-rays from the QSO. Similar arguments lead to the conclusion that the system at Zabs = 4.685 as well is not Compton thick. Using simple Eddington arguments we show that the mass of the central black hole is &#8764; 7.1 &#215; M&#920;. This suggests that the accretion onto a seed black hole must have started as early as z &#8764; 11

Effect of phytase on phytate P utilization by turkeys

An in vitro method was developed for poultry to predict inorganic phosphorus release from maize-soya bean feeds containing supplemental phytase (E.C. 3.1.3.8), and to quantify the effect of acid phosphatase (E.C. 3.1,3.2.), fungal protease (E.C. 3.4.23.6) and Aspergillus niger cellulase (E.C. 3.2.1.4.) on phytate dephosphorylation. Pepsin and pancreatin digestion periods were preceded by a 30 min preincubation at pH 5.25 to simulate digestion in the crop of poultry. Pancreatin digestion was carried out in dialysis tubings, with a ratio of about 1:25 (v/v) between the digesta and dialyzing medium, to simulate gradient absorption from the duodenum. The feed/water ratio was kept within physiological limits and a constant feed weight to digestive enzymes was maintained. There was a linear response to increasing dosages of phytase up to 1000 FTU/kg feed, and to increasing phosphate concentration in feeds. In vivo validation was performed with growing turkeys (1-3 wk) fed diets containing 12 g/kg of calcium; 0, 500, 1000 FTU/kg of phytase in a factorial arrangement with 0, 1, 2, 3 g/kg of supplemental phosphate (from KH2PO4). After a simple transformation (variable/in vitro phosphorus = f (in vitro phosphorus)) amounts of phosphorus hydrolyzed from feed samples by in vitro digestions correlated with the 3 week body weight gains (R= 0.986 P [less than] 0.0001), toe ash (R=0.952 P [less than] 0.0001), feed intake (R=0.994 P [less than] 0.0001) and feed efficiency (R=0.992 P [less than] 0.0001). The dephosphorylating ability of phytase in vitro was significantly enhanced (P [less than] 0.05) by the addition of acid phosphatase. Fungal acid protease and Aspergillus niger cellulase also enhanced the dephosphorylation process in vitro.Project # G-2029-01 Agreement # 14-08-0001-G-2029-0

Pulsating magneto-dipole radiation of a quaking neutron star powered by energy of Alfven seismic vibrations

We compute the characteristic parameters of magnetic dipole radiation of a neutron star undergoing torsional seismic vibrations under the action of Lorentz restoring force about axis of a dipolar magnetic field experiencing decay. After brief outline of general theoretical background of the model of vibration powered neutron star, we present numerical estimates of basic vibration and radiation characteristics, such as the oscillation frequency, lifetime, luminosity of radiation, and investigate their time dependence upon magnetic field decay. The presented analysis suggests that gradual decrease in frequencies of pulsating high-energy emission detected from a handful of currently monitored AXP/SGR-like X-ray sources can be explained as being produced by vibration powered magneto-dipole radiation of quaking magnetars. \keywords{neutron stars, torsion Alfv\'en vibrations, vibration powered radiation, magnetic field decay, magnetars}Comment: Preprint of article accepted for publication in "Research in Astronomy and Astrophysics" [RAA-Vol.11-No9-(2011)-p.1074

On Hastings' counterexamples to the minimum output entropy additivity conjecture

Hastings recently reported a randomized construction of channels violating the minimum output entropy additivity conjecture. Here we revisit his argument, presenting a simplified proof. In particular, we do not resort to the exact probability distribution of the Schmidt coefficients of a random bipartite pure state, as in the original proof, but rather derive the necessary large deviation bounds by a concentration of measure argument. Furthermore, we prove non-additivity for the overwhelming majority of channels consisting of a Haar random isometry followed by partial trace over the environment, for an environment dimension much bigger than the output dimension. This makes Hastings' original reasoning clearer and extends the class of channels for which additivity can be shown to be violated.Comment: 17 pages + 1 lin

Silicon nanoparticles and interstellar extinction

To examine a recently proposed hypothesis that silicon nanoparticles are the source of extended red emission (ERE) in the interstellar medium, we performed a detailed modeling of the mean Galactic extinction in the presence of silicon nanoparticles. For this goal we used the appropriate optical constants of nanosized Si, essentially different from those of bulk Si due to quantum confinement. It was found that a dust mixture of silicon nanoparticles, bare graphite grains, silicate core-organic refractory mantle grains and three-layer silicate-water ice-organic refractory grains works well in explaining the extinction and, in addition, results in the acceptable fractions of UV/visible photons absorbed by silicon nanoparticles: 0.071-0.081. Since these fractions barely agree with the fraction of UV/visible photons needed to excite the observed ERE, we conclude that the intrinsic photon conversion efficiency of the photoluminescence by silicon nanoparticles must be near 100%, if they are the source of the ERE.Comment: Latex2e, uses emulateapj.sty (included), multicol.sty, epsf.sty, 6 pages, 3 figures (8 Postscript files), accepted for publication in ApJ Letters, complete Postscript file is also available at http://physics.technion.ac.il/~zubko/eb.html#SNP

Detection of 21-cm, H2 and Deuterium absorption at z>3 along the line-of-sight to J1337+3152

We report the detection of 21-cm and H2 absorption lines in the same DLA system (log N(HI)=21.36+-0.10) at zabs=3.17447 towards SDSSJ133724+315254 (z=3.174). We estimate the spin temperature of the gas to be, Ts~600 K, intermediate between the expected values for cold and warm neutral media. This suggests that the HI absorption originates from a mixture of different phases. The total molecular fraction is low, f=10^-7, and H2 rotational level populations are not in equilibrium. The average abundance of the alpha-elements is, [S/H]=-1.45. N and Fe are found underabundant with respect to alpha-elements by ~1.0 dex and ~0.5 dex respectively. Using photoionization models we conclude that the gas is located more than 270 kpc away from the QSO. While the position of 21-cm absorption line coincides with the H2 velocity profile, their centroid are shifted by 2.7+-1.0 km/s from each other. However, the position of the strongest metal absorption component matches the position of the 21-cm absorption line within 0.5 km/s. From this, we constrain the variation of the combination of fundamental constants x=alpha^2 Gp/mu, Delta x/x=-(1.7+-1.7)x10^-6. This system is unique as we can at the same time have an independent constrain on mu using H2 lines. However only Werner band absorption lines are seen and the range of sensitivity coefficients is too narrow to provide a stringent constraint: Delta mu/mu <= 4.0x10^-4. The VLT/UVES spectrum reveals another DLA at zabs=3.16768 with log N(HI)=20.41+-0.15 and low metallicity, [Si/H]=-2.68+-0.11. We derive log N(DI)/N(HI)=-(4.93+-0.15) in this system. This is a factor of two smaller than the value expected from the best fitted value of Omega_b from the WMAP 5 yr data. This confirms the presence of astration of deuterium even at very low metallicity. [abridged]Comment: 14 pages, 11 figures, 4 tables, accepted for publication in MNRA

Determining the fraction of reddened quasars in COSMOS with multiple selection techniques from X-ray to radio wavelengths

The sub-population of quasars reddened by intrinsic or intervening clouds of dust are known to be underrepresented in optical quasar surveys. By defining a complete parent sample of the brightest and spatially unresolved quasars in the COSMOS field, we quantify to which extent this sub-population is fundamental to our understanding of the true population of quasars. By using the available multiwavelength data of various surveys in the COSMOS field, we built a parent sample of 33 quasars brighter than $J=20$ mag, identified by reliable X-ray to radio wavelength selection techniques. Spectroscopic follow-up with the NOT/ALFOSC was carried out for four candidate quasars that had not been targeted previously to obtain a 100\% redshift completeness of the sample. The population of high $A_V$ quasars (HAQs), a specific sub-population of quasars selected from optical/near-infrared photometry, is found to contribute $21\%^{+9}_{-5}$ of the parent sample. The full population of bright spatially unresolved quasars represented by our parent sample consists of $39\%^{+9}_{-8}$ reddened quasars defined by having $A_V>0.1$, and $21\%^{+9}_{-5}$ of the sample having $E(B-V)>0.1$ assuming the extinction curve of the Small Magellanic Cloud. We show that the HAQ selection works well for selecting reddened quasars, but some are missed because their optical spectra are too blue to pass the $g-r$ color cut in the HAQ selection. This is either due to a low degree of dust reddening or anomalous spectra. We find that the fraction of quasars with contributing light from the host galaxy is most dominant at $z \lesssim 1$. At higher redshifts the population of spatially unresolved quasars selected by our parent sample is found to be representative of the full population at $J<20$ mag. This work quantifies the bias against reddened quasars in studies that are based solely on optical surveys.Comment: 22 pages, 10 figures, accepted for publication in A&A. The ArXiv abstract has been shortened for it to be printabl