272,647 research outputs found

    Localizationof the 5S and 45S rDNA sites and CPDNA sequence analysis in species of the quadrifaria group of Paspalum (Poaceae, Panicae).

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    The Quadrifaria group of Paspalum (Poaceae, Paniceae) comprises species native to the subtropical and temperate regions of South America. The purpose of this research was to characterize the I genomes in five species of this group and to establish phylogenetic relationships among them. Prometaphase chromatin condensation patterns, the physical location of 5S and 45S rDNA sites by fluorescence in situ hybridization (FISH), and sequences of five chloroplast non-coding regions were analysed. The condensation patterns observed were highly conserved among diploid and tetraploid accessions studied and not influenced by the dyes used or by the FISH procedure, allowing the identification of almost all the chromosome pairs that carried the rDNA signals. The FISH analysis of 5S rDNA sites showed the same localization and a correspondence between the number of sites and ploidy level. In contrast, the distribution of 45S rDNA sites was variable. Two general patterns were observed with respect to the location of the 45S rDNA. The species and cytotypes Paspalum haumanii 2x, P. intermedium 2x, P. quadrifarium 4x and P. exaltatum 4x showed proximal sites on chromosome 8 and two to four distal sites in other chromosomes, while P. quarinii 4x and P. quadrifarium 2x showed only distal sites located on a variable number of small chromosomes and on the long arm of chromosome 1. The single most-parsimonious tree found from the phylogenetic analysis showed the Quadrifaria species partitioned in two clades, one of them includes P. haumanii 2x and P. intermedium 2x together with P. quadrifarium 4x and P. exaltatum 4x, while the other contains P. quadrifarium 2x and P. quarinii 4x. The subdivision found with FISH is consistent with the clades recovered with cpDNA data and both analyses suggest that the Quadrifaria group, as presently defined, is not monophyletic and its species belong in at least two clades

    Energy distribution and equation of state of the early Universe: matching the end of inflation and the onset of radiation domination

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    We study the energy distribution and equation of state of the universe between the end of inflation and the onset of radiation domination (RD), considering observationally consistent single-field inflationary scenarios, with a potential 'flattening' at large field values, and a monomial shape V(ϕ)ϕpV(\phi) \propto |\phi|^p around the origin. As a proxy for (p)reheating, we include a quadratic interaction g2ϕ2X2g^2\phi^2X^2 between the inflaton ϕ\phi and a light scalar 'daughter' field XX, with g2>0g^2>0. We capture the non-perturbative and non-linear nature of the system dynamics with lattice simulations, obtaining that: i)i) the final energy transferred to XX depends only on pp, not on g2g^2, ; ii)ii) the final transfer of energy is always negligible for 2p<42 \leq p < 4, and of order 50%\sim 50\% for p4p \geq 4; iii)iii) the system goes at late times to matter-domination for p=2p = 2, and always to RD for p>2p > 2. In the latter case we calculate the number of e-folds until RD, significantly reducing the uncertainty in the inflationary observables nsn_s and rr.Comment: 7 pages + references, 5 figures. It matches published versio

    Largest Prime Factors of Quadratic Polynomials

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    Let p1mod4p\equiv 1 \bmod 4 be a prime number and let x>1x>1 be a large number. This note shows that the largest prime factor of the finite product xn2x(n2+1)\prod_{x\leq n\leq 2x}\left(n^2+1 \right) satisfies the relation px4/3p \geq x^{4/3} as xx tends to infinity. This improves the current estimate px1.279p \geq x^{1.279}.Comment: Seven Pages. Keywords: Prime number; Distribution of prime; Polynomial prime valu

    Accelerating Permutation Testing in Voxel-wise Analysis through Subspace Tracking: A new plugin for SnPM

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    Permutation testing is a non-parametric method for obtaining the max null distribution used to compute corrected pp-values that provide strong control of false positives. In neuroimaging, however, the computational burden of running such an algorithm can be significant. We find that by viewing the permutation testing procedure as the construction of a very large permutation testing matrix, TT, one can exploit structural properties derived from the data and the test statistics to reduce the runtime under certain conditions. In particular, we see that TT is low-rank plus a low-variance residual. This makes TT a good candidate for low-rank matrix completion, where only a very small number of entries of TT (0.35%\sim0.35\% of all entries in our experiments) have to be computed to obtain a good estimate. Based on this observation, we present RapidPT, an algorithm that efficiently recovers the max null distribution commonly obtained through regular permutation testing in voxel-wise analysis. We present an extensive validation on a synthetic dataset and four varying sized datasets against two baselines: Statistical NonParametric Mapping (SnPM13) and a standard permutation testing implementation (referred as NaivePT). We find that RapidPT achieves its best runtime performance on medium sized datasets (50n20050 \leq n \leq 200), with speedups of 1.5x - 38x (vs. SnPM13) and 20x-1000x (vs. NaivePT). For larger datasets (n200n \geq 200) RapidPT outperforms NaivePT (6x - 200x) on all datasets, and provides large speedups over SnPM13 when more than 10000 permutations (2x - 15x) are needed. The implementation is a standalone toolbox and also integrated within SnPM13, able to leverage multi-core architectures when available.Comment: 36 pages, 16 figure

    Heyde theorem on locally compact Abelian groups with the connected component of zero of dimension 1

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    Let XX be a locally compact Abelian group with the connected component of zero of dimension 1. Let ξ1\xi_1 and ξ2\xi_2 be independent random variables with values in XX with nonvanishing characteristic functions. We prove that if a topological automorphism α\alpha of the group XX satisfies the condition Ker(I+α)={0}{{\rm Ker}(I+\alpha)=\{0\}} and the conditional distribution of the linear form L2=ξ1+αξ2{L_2 = \xi_1 + \alpha\xi_2} given L1=ξ1+ξ2{L_1 = \xi_1 + \xi_2} is symmetric, then the distributions of ξj\xi_j are convolutions of Gaussian distributions on XX and distributions supported in the subgroup {xX:2x=0}\{x\in X:2x=0\}. This result can be viewed as a generalization of the well-known Heyde theorem on the characterization of the Gaussian distribution on the real line.Comment: 15 p