28 research outputs found

    New coins from old, smoothly

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    Given a (known) function f:[0,1]→(0,1)f:[0,1] \to (0,1), we consider the problem of simulating a coin with probability of heads f(p)f(p) by tossing a coin with unknown heads probability pp, as well as a fair coin, NN times each, where NN may be random. The work of Keane and O'Brien (1994) implies that such a simulation scheme with the probability ¶p(N<∞)\P_p(N<\infty) equal to 1 exists iff ff is continuous. Nacu and Peres (2005) proved that ff is real analytic in an open set S⊂(0,1)S \subset (0,1) iff such a simulation scheme exists with the probability ¶p(N>n)\P_p(N>n) decaying exponentially in nn for every p∈Sp \in S. We prove that for α>0\alpha>0 non-integer, ff is in the space Cα[0,1]C^\alpha [0,1] if and only if a simulation scheme as above exists with ¶p(N>n)≀C(Δn(p))α\P_p(N>n) \le C (\Delta_n(p))^\alpha, where \Delta_n(x)\eqbd \max \{\sqrt{x(1-x)/n},1/n \}. The key to the proof is a new result in approximation theory: Let \B_n be the cone of univariate polynomials with nonnegative Bernstein coefficients of degree nn. We show that a function f:[0,1]→(0,1)f:[0,1] \to (0,1) is in Cα[0,1]C^\alpha [0,1] if and only if ff has a series representation ∑n=1∞Fn\sum_{n=1}^\infty F_n with F_n \in \B_n and ∑k>nFk(x)≀C(Δn(x))α\sum_{k>n} F_k(x) \le C(\Delta_n(x))^\alpha for all x∈[0,1] x \in [0,1] and n≄1n \ge 1. We also provide a counterexample to a theorem stated without proof by Lorentz (1963), who claimed that if some \phi_n \in \B_n satisfy ∣f(x)−ϕn(x)âˆŁâ‰€C(Δn(x))α|f(x)-\phi_n(x)| \le C (\Delta_n(x))^\alpha for all x∈[0,1] x \in [0,1] and n≄1n \ge 1, then f∈Cα[0,1]f \in C^\alpha [0,1].Comment: 29 pages; final version; to appear in Constructive Approximatio

    Quantum measures for density correlations in optical lattices

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    The density-density correlation profiles obtained superimposing absorption images from atomic clouds freely expanding after the release of the confining optical lattice can be theoretically described in terms of a generalized quantum measure based on coherent-like states. We show that the corresponding density patterns differ in a testable way from those computed using standard many-body mean values, usually adopted in fitting experimental data.Comment: LaTeX, 14 page

    Supernova Neutrinos and the LSND Evidence for Neutrino Oscillations

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    The observation of the Μˉe\bar{\nu}_e energy spectrum from a supernova burst can provide constraints on neutrino oscillations. We derive formulas for adiabatic oscillations of supernova antineutrinos for a variety of 3- and 4-neutrino mixing schemes and mass hierarchies which are consistent with the LSND evidence for ΜˉΌ→Μˉe\bar{\nu}_{\mu}\to \bar{\nu}_e oscillations. Finally, we explore the constraints on these models and LSND given by the supernova SN1987A Μˉe\bar{\nu}_e's observed by the Kamiokande-2 and IMB-3 detectors.Comment: 8 pages, 3 figures. Changes with respect to original version: appendix added; minor changes in text, figures, reference

    On the massless "just-so" solution to the solar neutrino problem

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    We study the effect of the non-resonant, vacuum oscillation-like neutrino flavor conversion induced by non-standard flavor changing and non-universal flavor diagonal neutrino interactions with electrons in the sun. We have found an acceptable fit for the combined analysis for the solar experiments total rates, the Super-Kamiokande (SK) energy spectrum and zenith angle dependence. Phenomenological constraints on non-standard flavor changing and non-universal flavor diagonal neutrino interactions are considered.Comment: 4 pages, Latex, uses eps

    Three-generation flavor transitions and decays of supernova relic neutrinos

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    If neutrinos have mass, they can also decay. Decay lifetimes of cosmological interest can be probed, in principle, through the detection of the redshifted, diffuse neutrino flux produced by all past supernovae--the so-called supernova relic neutrino (SRN) flux. In this work, we solve the SRN kinetic equations in the general case of three-generation flavor transitions followed by invisible (nonradiative) two-body decays. We then use the general solution to calculate observable SRN spectra in some representative decay scenarios. It is shown that, in the presence of decay, the SRN event rate can basically span the whole range below the current experimental upper bound--a range accessible to future experimental projects. Radiative SRN decays are also briefly discussed.Comment: 25 pages, including 7 figure

    NEOTROPICAL XENARTHRANS: a data set of occurrence of xenarthran species in the Neotropics

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    Xenarthrans – anteaters, sloths, and armadillos – have essential functions for ecosystem maintenance, such as insect control and nutrient cycling, playing key roles as ecosystem engineers. Because of habitat loss and fragmentation, hunting pressure, and conflicts with 24 domestic dogs, these species have been threatened locally, regionally, or even across their full distribution ranges. The Neotropics harbor 21 species of armadillos, ten anteaters, and six sloths. Our dataset includes the families Chlamyphoridae (13), Dasypodidae (7), Myrmecophagidae (3), Bradypodidae (4), and Megalonychidae (2). We have no occurrence data on Dasypus pilosus (Dasypodidae). Regarding Cyclopedidae, until recently, only one species was recognized, but new genetic studies have revealed that the group is represented by seven species. In this data-paper, we compiled a total of 42,528 records of 31 species, represented by occurrence and quantitative data, totaling 24,847 unique georeferenced records. The geographic range is from the south of the USA, Mexico, and Caribbean countries at the northern portion of the Neotropics, to its austral distribution in Argentina, Paraguay, Chile, and Uruguay. Regarding anteaters, Myrmecophaga tridactyla has the most records (n=5,941), and Cyclopes sp. has the fewest (n=240). The armadillo species with the most data is Dasypus novemcinctus (n=11,588), and the least recorded for Calyptophractus retusus (n=33). With regards to sloth species, Bradypus variegatus has the most records (n=962), and Bradypus pygmaeus has the fewest (n=12). Our main objective with Neotropical Xenarthrans is to make occurrence and quantitative data available to facilitate more ecological research, particularly if we integrate the xenarthran data with other datasets of Neotropical Series which will become available very soon (i.e. Neotropical Carnivores, Neotropical Invasive Mammals, and Neotropical Hunters and Dogs). Therefore, studies on trophic cascades, hunting pressure, habitat loss, fragmentation effects, species invasion, and climate change effects will be possible with the Neotropical Xenarthrans dataset

    Pervasive gaps in Amazonian ecological research

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    Biodiversity loss is one of the main challenges of our time, and attempts to address it require a clear understanding of how ecological communities respond to environmental change across time and space. While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes, vast areas of the tropics remain understudied. In the American tropics, Amazonia stands out as the world's most diverse rainforest and the primary source of Neotropical biodiversity, but it remains among the least known forests in America and is often underrepresented in biodiversity databases. To worsen this situation, human-induced modifications may eliminate pieces of the Amazon's biodiversity puzzle before we can use them to understand how ecological communities are responding. To increase generalization and applicability of biodiversity knowledge, it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple organism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region's vulnerability to environmental change. 15%–18% of the most neglected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lost
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