Laplacian Distribution and Domination

Let $m_G(I)$ denote the number of Laplacian eigenvalues of a graph $G$ in an interval $I$, and let $\gamma(G)$ denote its domination number. We extend the recent result $m_G[0,1) \leq \gamma(G)$, and show that isolate-free graphs also satisfy $\gamma(G) \leq m_G[2,n]$. In pursuit of better understanding Laplacian eigenvalue distribution, we find applications for these inequalities. We relate these spectral parameters with the approximability of $\gamma(G)$, showing that $\frac{\gamma(G)}{m_G[0,1)} \not\in O(\log n)$. However, $\gamma(G) \leq m_G[2, n] \leq (c + 1) \gamma(G)$ for $c$-cyclic graphs, $c \geq 1$. For trees $T$, $\gamma(T) \leq m_T[2, n] \leq 2 \gamma(G)$

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

Lateralization as a symmetry breaking process in birdsong

Journal ArticleThe singing by songbirds is a most convincing example in the animal kingdom of functional lateralization of the brain, a feature usually associated with human language. Lateralization is expressed as one or both of the bird's sound sources being active during the vocalization. Normal songs require high coordination between the vocal organ and respiratory activity, which is bilaterally symmetric

Conditional Involvement of CONSTITUTIVE PHOTOMORPHOGENIC1 in the Degradation of Phytochrome A.

All higher plants possess multiple phytochrome photoreceptors, with phytochrome A (phyA) being light labile and other members of the family being relatively light stable (phyB-phyE in Arabidopsis [Arabidopsis thaliana]). phyA also differs from other members of the family because it enables plants to deetiolate in far-red light-rich environments typical of dense vegetational cover. Later in development, phyA counteracts the shade avoidance syndrome. Light-induced degradation of phyA favors the establishment of a robust shade avoidance syndrome and was proposed to be important for phyA-mediated deetiolation in far-red light. phyA is ubiquitylated and targeted for proteasome-mediated degradation in response to light. Cullin1 and the ubiquitin E3 ligase CONSTITUTIVE PHOTOMORPHOGENIC1 (COP1) have been implicated in this process. Here, we systematically analyze the requirement of cullins in this process and show that only CULLIN1 plays an important role in light-induced phyA degradation. In addition, the role of COP1 in this process is conditional and depends on the presence of metabolizable sugar in the growth medium. COP1 acts with SUPPRESSOR OF PHYTOCHROME A (SPA) proteins. Unexpectedly, the light-induced decline of phyA levels is reduced in spa mutants irrespective of the growth medium, suggesting a COP1-independent role for SPA proteins

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

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