Simple extractors via constructions of cryptographic pseudo-random generators

Trevisan has shown that constructions of pseudo-random generators from hard functions (the Nisan-Wigderson approach) also produce extractors. We show that constructions of pseudo-random generators from one-way permutations (the Blum-Micali-Yao approach) can be used for building extractors as well. Using this new technique we build extractors that do not use designs and polynomial-based error-correcting codes and that are very simple and efficient. For example, one extractor produces each output bit separately in $O(\log^2 n)$ time. These extractors work for weak sources with min entropy $\lambda n$, for arbitrary constant $\lambda > 0$, have seed length $O(\log^2 n)$, and their output length is $\approx n^{\lambda/3}$.Comment: 21 pages, an extended abstract will appear in Proc. ICALP 2005; small corrections, some comments and references adde

Deep Chandra Observations of HCG 16 - I. Active Nuclei, Star formation and Galactic Winds

We present new, deep Chandra X-ray and Giant Metrewave Radio Telescope 610~MHz observations of the spiral-galaxy-rich compact group HCG 16, which we use to examine nuclear activity, star formation and the high luminosity X-ray binary populations in the major galaxies. We confirm the presence of obscured active nuclei in NGC 833 and NGC 835, and identify a previously unrecognized nuclear source in NGC 838. All three nuclei are variable on timescales of months to years, and for NGC 833 and NGC 835 this is most likely caused by changes in accretion rate. The deep Chandra observations allow us to detect for the first time an Fe-K$\alpha$ emission line in the spectrum of the Seyfert 2 nucleus of NGC 835. We find that NGC 838 and NGC 839 are both starburst-dominated systems, with only weak nuclear activity, in agreement with previous optical studies. We estimate the star formation rates in the two galaxies from their X-ray and radio emission, and compare these results with estimates from the infra-red and ultra-violet bands to confirm that star formation in both galaxies is probably declining after galaxy-wide starbursts were triggered ~400-500 Myr ago. We examine the physical properties of their galactic superwinds, and find that both have temperatures of ~0.8 keV. We also examine the X-ray and radio properties of NGC 848, the fifth largest galaxy in the group, and show that it is dominated by emission from its starburst.Comment: 18 pages, 11 figures, 11 tables, accepted for publication in ApJ; updated references and fixed typos identified at proof stag

Nuclear phytochrome a signaling promotes phototropism in Arabidopsis.

Phototropin photoreceptors (phot1 and phot2 in Arabidopsis thaliana) enable responses to directional light cues (e.g., positive phototropism in the hypocotyl). In Arabidopsis, phot1 is essential for phototropism in response to low light, a response that is also modulated by phytochrome A (phyA), representing a classical example of photoreceptor coaction. The molecular mechanisms underlying promotion of phototropism by phyA remain unclear. Most phyA responses require nuclear accumulation of the photoreceptor, but interestingly, it has been proposed that cytosolic phyA promotes phototropism. By comparing the kinetics of phototropism in seedlings with different subcellular localizations of phyA, we show that nuclear phyA accelerates the phototropic response, whereas in the fhy1 fhl mutant, in which phyA remains in the cytosol, phototropic bending is slower than in the wild type. Consistent with this data, we find that transcription factors needed for full phyA responses are needed for normal phototropism. Moreover, we show that phyA is the primary photoreceptor promoting the expression of phototropism regulators in low light (e.g., PHYTOCHROME KINASE SUBSTRATE1 [PKS1] and ROOT PHOTO TROPISM2 [RPT2]). Although phyA remains cytosolic in fhy1 fhl, induction of PKS1 and RPT2 expression still occurs in fhy1 fhl, indicating that a low level of nuclear phyA signaling is still present in fhy1 fhl

Rank deficiency of Kalman error covariance matrices in linear time-varying system with deterministic evolution

We prove that for-linear, discrete, time-varying, deterministic system (perfect-model) with noisy outputs, the Riccati transformation in the Kalman filter asymptotically bounds the rank of the forecast and the analysis error covariance matrices to be less than or equal to the number of nonnegative Lyapunov exponents of the system. Further, the support of these error covariance matrices is shown to be confined to the space spanned by the unstable-neutral backward Lyapunov vectors, providing the theoretical justification for the methodology of the algorithms that perform assimilation only in the unstable-neutral subspace. The equivalent property of the autonomous system is investigated as a special case

The Origin of Massive Compact Galaxies: Lessons from IllustrisTNG

We investigate the formation and evolution of z=0 massive compact galaxies (MCGs) in the IllustrisTNG cosmological simulation. We found that, as in observations, MCGs are mainly old (median age $\sim 10.8$ Gyr), have super-solar metallicities (median $\log Z/Z_{\odot}\sim0.35$) and are $\alpha$-enhanced (median $[\alpha/Fe]\sim0.25$). The age distribution extends to younger ages, however, and a few MCGs are as young as $\sim7$ Gyr. In general, MCGs assemble their mass early and accrete low angular momentum gas, significantly increasing their mass while growing their size much slower. A small fraction of MCGs follow another evolutionary path, going through a compaction event, with their sizes shrinking by 40% or more. The accretion of low angular momentum gas leads to enhanced SMBH growth, and MCGs reach the threshold SMBH mass of $\log M_\mathrm{BH}\sim10^{8.5} M_\odot$ - when kinetic AGN feedback kicks in and quenches the galaxy - earlier than non-compact galaxies. Comparing MCGs to a sample of median-sized quiescent galaxies matched in effective velocity dispersion, we find that their accretion histories are very different. 71% of MCGs do not merge after quenching compared to 37% of median-sized quiescent galaxies. Moreover, tracing these populations back in time, we find that at least a third of median-sized quiescent galaxies do not have a compact progenitor, underscoring that both dry mergers and progenitor bias effects are responsible for the differences in the kinematics and stellar population properties of MCGs and median-sized quiescent galaxies.Comment: 15 pages, 15 figures (not including appendices). Accepted for publication in the Monthly Notices of the Royal Astronomical Societ

A Hypergraph Dictatorship Test with Perfect Completeness

A hypergraph dictatorship test is first introduced by Samorodnitsky and Trevisan and serves as a key component in their unique games based \PCP construction. Such a test has oracle access to a collection of functions and determines whether all the functions are the same dictatorship, or all their low degree influences are $o(1).$ Their test makes $q\geq3$ queries and has amortized query complexity $1+O(\frac{\log q}{q})$ but has an inherent loss of perfect completeness. In this paper we give an adaptive hypergraph dictatorship test that achieves both perfect completeness and amortized query complexity $1+O(\frac{\log q}{q})$.Comment: Some minor correction

Elastic electron scattering from 3-hydroxytetrahydrofuran: experimental and theoretical studies

We report the results of measurements and calculations for elastic electron scattering from 3-hydroxytetrahydrofuran (C4H8O2). The measurements are performed with a crossed electron-target beam apparatus and the absolute cross-sections are determined using the relative flow technique. The calculations are carried out using the Schwinger multichannel method in the static-exchange plus polarization (SEP) approximation. A set of angular differential cross-sections (DCS) is provided at five incident energies (6.5, 8, 10, 15 and 20 eV) over an angular range of 20–130°, and the energy dependence of the elastic DCS at a scattering angle of 120° is also presented. Integral elastic and elastic momentum transfer cross-sections have also been derived and calculated. The results are compared with those of recent measurements and calculations for the structurally similar molecule tetrahydrofuran (C4H8O)

Nutraceutical Profiles of Two Hydroponically Grown Sweet Basil Cultivars as Affected by the Composition of the Nutrient Solution and the Inoculation With Azospirillum brasilense

Sweet basil (Ocimum basilicum L.) is one of the most produced aromatic herbs in the world, exploiting hydroponic systems. It has been widely assessed that macronutrients, like nitrogen (N) and sulfur (S), can strongly affect the organoleptic qualities of agricultural products, thus influencing their nutraceutical value. In addition, plant-growth-promoting rhizobacteria (PGPR) have been shown to affect plant growth and quality. Azospirillum brasilense is a PGPR able to colonize the root system of different crops, promoting their growth and development and influencing the acquisition of mineral nutrients. On the bases of these observations, we aimed at investigating the impact of both mineral nutrients supply and rhizobacteria inoculation on the nutraceutical value on two different sweet basil varieties, i.e., Genovese and Red Rubin. To these objectives, basil plants have been grown in hydroponics, with nutrient solutions fortified for the concentration of either S or N, supplied as SO42\u2013 or NO3\u2013, respectively. In addition, plants were either non-inoculated or inoculated with A. brasilense. At harvest, basil plants were assessed for the yield and the nutraceutical properties of the edible parts. The cultivation of basil plants in the fortified nutrient solutions showed a general increasing trend in the accumulation of the fresh biomass, albeit the inoculation with A. brasilense did not further promote the growth. The metabolomic analyses disclosed a strong effect of treatments on the differential accumulation of metabolites in basil leaves, producing the modulation of more than 400 compounds belonging to the secondary metabolism, as phenylpropanoids, isoprenoids, alkaloids, several flavonoids, and terpenoids. The primary metabolism that resulted was also influenced by the treatments showing changes in the fatty acid, carbohydrates, and amino acids metabolism. The amino acid analysis revealed that the treatments induced an increase in arginine (Arg) content in the leaves, which has been shown to have beneficial effects on human health. In conclusion, between the two cultivars studied, Red Rubin displayed the most positive effect in terms of nutritional value, which was further enhanced following A. brasilense inoculation