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

Constitutive stilbene contents of grapevine cluster stems as potential source of resveratrol in wine

Ripe clusters of 8 Vitis vinifera L. varieties (Cabernet franc, Gewürztraminer, Marzemino, Merlot, Moscato, Pinot gris, Sauvignon, Tocai friulano) were analysed to determine the constitutional levels of trans- and cis-resveratrol, ε-viniferin and pterostilbene. Grape stems were extracted by an hydroalcoholic solution, in order to simulate the resveratrol extraction from stems that might occur during alcoholic fermentation, due to the presence of little pieces of stems in the fermenting must. The average stem concentrations of constitutive trans-, cis-resveratrol and ε-viniferin were 142, 0.30, and 70 mu g.g-1 FW, respectively; pterostilbene was not found. Varieties differed significantly in their stilbene content. The percentage of trans-resveratrol extracted from the stems by a hydroalcoholic solution varied from 2.5 % (Gewürztraminer) to 32.9 % (Marzemino), the contribution of the stems to the trans-resveratrol concentration of the hydroalcoholic solution being, on the average, 34 mu g.l-1

Dynamical analysis of the cluster pair: A3407 + A3408

We carried out a dynamical study of the galaxy cluster pair A3407 \& A3408 based on a spectroscopic survey obtained with the 4 meter Blanco telescope at the CTIO, plus 6dF data, and ROSAT All-Sky-Survey. The sample consists of 122 member galaxies brighter than $m_R=20$. Our main goal is to probe the galaxy dynamics in this field and verify if the sample constitutes a single galaxy system or corresponds to an ongoing merging process. Statistical tests were applied to clusters members showing that both the composite system A3407 + A3408 as well as each individual cluster have Gaussian velocity distribution. A velocity gradient of $\sim 847\pm 114$ $\rm km\;s^{-1}$ was identified around the principal axis of the projected distribution of galaxies, indicating that the global field may be rotating. Applying the KMM algorithm to the distribution of galaxies we found that the solution with two clusters is better than the single unit solution at the 99\% c.l. This is consistent with the X-ray distribution around this field, which shows no common X-ray halo involving A3407 and A3408. We also estimated virial masses and applied a two-body model to probe the dynamics of the pair. The more likely scenario is that in which the pair is gravitationally bound and probably experiences a collapse phase, with the cluster cores crossing in less than $\sim$1 $h^{-1}$ Gyr, a pre-merger scenario. The complex X-ray morphology, the gas temperature, and some signs of galaxy evolution in A3408 suggests a post-merger scenario, with cores having crossed each other $\sim 1.65 h^{-1}$Gyr ago, as an alternative solution.Comment: 17 pages, 12 figures, submitted to MNRAS, accepted 2016 May 9. Received 2016 May 9; in original form 2016 April 1

Fast Distributed Approximation for Max-Cut

Finding a maximum cut is a fundamental task in many computational settings. Surprisingly, it has been insufficiently studied in the classic distributed settings, where vertices communicate by synchronously sending messages to their neighbors according to the underlying graph, known as the $\mathcal{LOCAL}$ or $\mathcal{CONGEST}$ models. We amend this by obtaining almost optimal algorithms for Max-Cut on a wide class of graphs in these models. In particular, for any $\epsilon > 0$, we develop randomized approximation algorithms achieving a ratio of $(1-\epsilon)$ to the optimum for Max-Cut on bipartite graphs in the $\mathcal{CONGEST}$ model, and on general graphs in the $\mathcal{LOCAL}$ model. We further present efficient deterministic algorithms, including a $1/3$-approximation for Max-Dicut in our models, thus improving the best known (randomized) ratio of $1/4$. Our algorithms make non-trivial use of the greedy approach of Buchbinder et al. (SIAM Journal on Computing, 2015) for maximizing an unconstrained (non-monotone) submodular function, which may be of independent interest

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

On the Creation of the Universe out of Nothing

We explain how the Universe was created with no expenditure of energy or initial mass.Comment: To be presented at IWARA 2009 (4th International Workshop on Astronomy and Relativistic Astrophysics), to be held in Brazil, October 200