7,308 research outputs found

    Some extremal functions in Fourier analysis, II

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    We obtain extremal majorants and minorants of exponential type for a class of even functions on R\R which includes logx\log |x| and xα|x|^\alpha, where 1<α<1-1 < \alpha < 1. We also give periodic versions of these results in which the majorants and minorants are trigonometric polynomials of bounded degree. As applications we obtain optimal estimates for certain Hermitian forms, which include discrete analogues of the one dimensional Hardy-Littlewood-Sobolev inequalities. A further application provides an Erd\"{o}s-Tur\'{a}n-type inequality that estimates the sup norm of algebraic polynomials on the unit disc in terms of power sums in the roots of the polynomials.Comment: 40 pages. Accepted for publication in Trans. Amer. Math. So

    Gaussian Subordination for the Beurling-Selberg Extremal Problem

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    We determine extremal entire functions for the problem of majorizing, minorizing, and approximating the Gaussian function eπλx2e^{-\pi\lambda x^2} by entire functions of exponential type. This leads to the solution of analogous extremal problems for a wide class of even functions that includes most of the previously known examples (for instance \cite{CV2}, \cite{CV3}, \cite{GV} and \cite{Lit}), plus a variety of new interesting functions such as xα|x|^{\alpha} for 1<α-1 < \alpha; \,log((x2+α2)/(x2+β2))\log \,\bigl((x^2 + \alpha^2)/(x^2 + \beta^2)\bigr), for 0α<β0 \leq \alpha < \beta;\, log(x2+α2)\log\bigl(x^2 + \alpha^2\bigr); and x2nlogx2x^{2n} \log x^2\,, for nNn \in \N. Further applications to number theory include optimal approximations of theta functions by trigonometric polynomials and optimal bounds for certain Hilbert-type inequalities related to the discrete Hardy-Littlewood-Sobolev inequality in dimension one

    Tunable pinning of a superconducting vortex a by a magnetic vortex

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    The interaction between a straight vortex line in a superconducting film and a soft magnetic nanodisk in the magnetic vortex state in the presence of a magnetic field applied parallel to the film surfaces is studied theoretically. The superconductor is described by London theory and the nanodisk by the Landau-Lifshitz continuum theory of magnetism, using the approximation known as the rigid vortex model. Pinning of the vortex line by the nanodisk is found to result, predominantly, from the interaction between the vortex line and the changes in the nanodisk magnetization induced by the magnetic field of the vortex line and applied field. In the context of the rigid vortex model, these changes result from the displacement of the magnetic vortex. This displacement is calculated analytically by minimizing the energy, and the pinning potential is obtained. The applied field can tune the pinning potential by controlling the displacement of the magnetic vortex. The nanodisk magnetization curve is predicted to change in the presence of the vortex lineComment: 9 pages, 8 figures. Submitted to Phys. Rev.

    A Note on Tachyon Moduli and Closed Strings

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    The collective behavior of the SL(2,R) covariant brane states of non-critical c=1 string theory found in a previous work, is studied in the Fermi liquid approximation. It is found that such states mimick the coset WZW model, whereas only by further restrictions one recovers the double-scaling limit which was purported to be equivalent to closed string models. Another limit is proposed, inspired by the tachyon condensation ideas, where the spectrum is the same of two-dimensional string theory. We close by noting some strange connections between vacuum states of the theory in their different interpretations.Comment: PDFLaTeX, 17 pages, 2 figures; Section 2 rewritten, several fixes throughout the text to improve clarit

    Implications of Salinity and Acidic Environments on Fitness and Oxidative Stress Parameters in Early Developing Seahorses Hippocampus reidi

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    Water acidification affects aquatic species, both in natural environmental conditions and in ex situ rearing production systems. The chronic effects of acidic conditions (pH 6.5 vs. pH 8.0) in seahorses (Hippocampus spp.) are not well known, especially when coupled with salinity interaction. This study investigated the implications of pH on the growth and oxidative stress in the seahorse Hippocampus reidi (Ginsburg, 1933), one of the most important seahorse species in the ornamental trade. Two trials were carried out in juveniles (0–21 and 21–50 DAR—days after the male’s pouch release) reared under acid (6.5) and control (8.0) pH, both in brackish water (BW—salinity 11) and seawater (SW—salinity 33). In the first trial (0–21 DAR), there was no effect of pH on the growth of seahorses reared in SW, but the survival rate was higher for juveniles raised in SW at pH 6.5. However, the growth and survival of juveniles reared in BW were impaired at pH 6.5. Compared to SW conditions, the levels of superoxide dismutase and DT-diaphorase, as well as the oxidative stress index, increased for juveniles reared in BW. In the second trial, seahorse juveniles were reared in SW at pH 8.0, and subsequently kept for four weeks (from 21 to 50 DAR) at pH 6.5 and 8.0. The final survival rates and condition index were similar in both treatments. However, the growth under acidic conditions was higher than at pH 8.0. In conclusion, this study highlights that survival, growth, and oxidative status condition was enhanced in seahorse juveniles reared in SW under acidic conditions (pH = 6.5). The concurrent conditions of acidic pH (6.5) and BW should be avoided due to harmful effects on the fitness and development of seahorse juveniles.Fundacao Coordenacao de Aperfeicoamento de Pessoal de Nivel Superior-CAPES (Ministerio da Educacao-MEC, Brazil) PDSE 88881.187275/2018-01Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPQ) 307445/2016-

    Quantification of reachable attractors in asynchronous discrete dynamics

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    Motivation: Models of discrete concurrent systems often lead to huge and complex state transition graphs that represent their dynamics. This makes difficult to analyse dynamical properties. In particular, for logical models of biological regulatory networks, it is of real interest to study attractors and their reachability from specific initial conditions, i.e. to assess the potential asymptotical behaviours of the system. Beyond the identification of the reachable attractors, we propose to quantify this reachability. Results: Relying on the structure of the state transition graph, we estimate the probability of each attractor reachable from a given initial condition or from a portion of the state space. First, we present a quasi-exact solution with an original algorithm called Firefront, based on the exhaustive exploration of the reachable state space. Then, we introduce an adapted version of Monte Carlo simulation algorithm, termed Avatar, better suited to larger models. Firefront and Avatar methods are validated and compared to other related approaches, using as test cases logical models of synthetic and biological networks. Availability: Both algorithms are implemented as Perl scripts that can be freely downloaded from http://compbio.igc.gulbenkian.pt/nmd/node/59 along with Supplementary Material.Comment: 19 pages, 2 figures, 2 algorithms and 2 table

    Toward in vitro fertilization in Brachiaria spp.

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    Brachiaria are forage grasses widely cultivated in tropical areas. In vitro pollination was applied to accessions of Brachiaria spp. by placing pollen of non-dehiscent anthers on a solid medium near isolated ovaries. Viability and in vitro germination were tested in order to establish good conditions for pollen development. Comparing sexual to apomictic plants, apomictic pollen has more abortion after meiosis during the microspore stage and a lower viability and, of both types, only some plants have sufficient germination in a high sugar concentration. Using in vitro pollination with the sexual plant, the pollen tube penetrates into the nucellus and micropyle, but the embryo sac degenerates and collapses. In the apomictic B. decumbens, in vitro pollination leads to the transfer of the sperm nuclei into the egg cell and the central cell. The results are discussed according to normal fertilization and barriers in sexual and apomictic plants

    Developing intelligent environments with OSGi and JADE

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    Series: IFIP International Federation for Information ProcessingThe development of intelligent environments poses complex challenges, namely at the level of device heterogeneity and environment dynamics. In fact, we still lack supporting technologies and development approaches that can efficiently integrate different devices and technologies. In this paper we present how a recent integration of two important technologies, OSGi and Jade, can be used to significantly improve the development process, making it a more dynamic, modular and configurable one. We also focus on the main advantages that this integration provides to developers, from the Ambient Intelligence point of view. This work results from the development of two intelligent environments: VirtualECare, which is an intelligent environment for the monitorization of elderly in their homes and UMCourt, a virtual environment for dispute resolution.The work described in this paper is included in TIARAC - Telematics and Artificial Intelligence in Alternative Conflict Resolution Project (PTDC/JUR/71354/2006), which is a research project supported by FCT (Science & Technology Foundation), Portugal

    Width Parameterizations for Knot-Free Vertex Deletion on Digraphs

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    A knot in a directed graph G is a strongly connected subgraph Q of G with at least two vertices, such that no vertex in V(Q) is an in-neighbor of a vertex in V(G)V(Q). Knots are important graph structures, because they characterize the existence of deadlocks in a classical distributed computation model, the so-called OR-model. Deadlock detection is correlated with the recognition of knot-free graphs as well as deadlock resolution is closely related to the Knot-Free Vertex Deletion (KFVD) problem, which consists of determining whether an input graph G has a subset S subseteq V(G) of size at most k such that G[VS] contains no knot. Because of natural applications in deadlock resolution, KFVD is closely related to Directed Feedback Vertex Set. In this paper we focus on graph width measure parameterizations for KFVD. First, we show that: (i) KFVD parameterized by the size of the solution k is W[1]-hard even when p, the length of a longest directed path of the input graph, as well as kappa, its Kenny-width, are bounded by constants, and we remark that KFVD is para-NP-hard even considering many directed width measures as parameters, but in FPT when parameterized by clique-width; (ii) KFVD can be solved in time 2^{O(tw)} x n, but assuming ETH it cannot be solved in 2^{o(tw)} x n^{O(1)}, where tw is the treewidth of the underlying undirected graph. Finally, since the size of a minimum directed feedback vertex set (dfv) is an upper bound for the size of a minimum knot-free vertex deletion set, we investigate parameterization by dfv and we show that (iii) KFVD can be solved in FPT-time parameterized by either dfv+kappa or dfv+p. Results of (iii) cannot be improved when replacing dfv by k due to (i)
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