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    Preen Gland-Secreted Alkanols Enhance Male Attractiveness in Parrots

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    The skin glands are widely used in pheromone production throughout the vertebrate worlds. Growing evidences show that birds also have chemical communication, but the uropygial (also called preen or oil) glands, serving as only specialized skin glands of birds, have no sex pheromones characterized. Here, by combining GC-MS analysis and bioassay, we show with the budgerigar, Melopsittacus undulatus, that birds can used the preen gland-secreted volatiles (a blend of octadecanol, nonadecanol and eicosanol for male budgerigars) spread over body plumage when preening to convey sex information. Here, we first report the avian pheromones derived from the uropyginal gland and suggests that the gland has broader implications than previously known (e.g. plumage waterproofing and reflectance in sexual behaviour of birds

    Ergodic SDEs on submanifolds and related numerical sampling schemes

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    In many applications, it is often necessary to sample the mean value of certain quantity with respect to a probability measure {\mu} on the level set of a smooth function ξ:RdRk\xi: \mathbb{R}^d\rightarrow \mathbb{R}^k, 1k<d1\le k < d. A specially interesting case is the so-called conditional probability measure, which is useful in the study of free energy calculation and model reduction of diffusion processes. By Birkhoff's ergodic theorem, one approach to estimate the mean value is to compute the time average along an infinitely long trajectory of an ergodic diffusion process on the level set whose invariant measure is {\mu}. Motivated by the previous work of Ciccotti, Leli\`evre, and Vanden-Eijnden [11], as well as the work of Leli\`evre, Rousset, and Stoltz [33], in this paper we construct a family of ergodic diffusion processes on the level set of ξ\xi whose invariant measures coincide with the given one. For the conditional measure, in particular, we show that the corresponding SDEs of the constructed ergodic processes have relatively simple forms, and, moreover, we propose a consistent numerical scheme which samples the conditional measure asymptotically. The numerical scheme doesn't require computing the second derivatives of ξ\xi and the error estimates of its long time sampling efficiency are obtained.Comment: 45 pages. Accepted versio
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