9,041 research outputs found

    Biased tomography schemes: an objective approach

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    We report on an intrinsic relationship between the maximum-likelihood quantum-state estimation and the representation of the signal. A quantum analogy of the transfer function determines the space where the reconstruction should be done without the need for any ad hoc truncations of the Hilbert space. An illustration of this method is provided by a simple yet practically important tomography of an optical signal registered by realistic binary detectors.Comment: 4 pages, 3 figures, accepted in PR

    Upper estimate of martingale dimension for self-similar fractals

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    We study upper estimates of the martingale dimension dmd_m of diffusion processes associated with strong local Dirichlet forms. By applying a general strategy to self-similar Dirichlet forms on self-similar fractals, we prove that dm=1d_m=1 for natural diffusions on post-critically finite self-similar sets and that dmd_m is dominated by the spectral dimension for the Brownian motion on Sierpinski carpets.Comment: 49 pages, 7 figures; minor revision with adding a referenc

    Entropy and information in neural spike trains: Progress on the sampling problem

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    The major problem in information theoretic analysis of neural responses and other biological data is the reliable estimation of entropy--like quantities from small samples. We apply a recently introduced Bayesian entropy estimator to synthetic data inspired by experiments, and to real experimental spike trains. The estimator performs admirably even very deep in the undersampled regime, where other techniques fail. This opens new possibilities for the information theoretic analysis of experiments, and may be of general interest as an example of learning from limited data.Comment: 7 pages, 4 figures; referee suggested changes, accepted versio

    Random walk on the range of random walk

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    We study the random walk X on the range of a simple random walk on ℤ d in dimensions d≥4. When d≥5 we establish quenched and annealed scaling limits for the process X, which show that the intersections of the original simple random walk path are essentially unimportant. For d=4 our results are less precise, but we are able to show that any scaling limit for X will require logarithmic corrections to the polynomial scaling factors seen in higher dimensions. Furthermore, we demonstrate that when d=4 similar logarithmic corrections are necessary in describing the asymptotic behavior of the return probability of X to the origin

    Generalized QR factorization and its applications

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    AbstractThe purpose of this paper is to reintroduce the generalized QR factorization with or without pivoting of two matrices A and B having the same number of rows. When B is square and nonsingular, the factorization implicity gives the orthogonal factorization of B−1A. Continuing the work of Paige and Hammarling, we discuss the different forms of the factorization from the point of view of general-purpose software development. In addition, we demonstrate the applications of the GQR factorization in solving the linear equality-constrained least-squares problem and the generalized linear regression problem, and in estimating the conditioning of these problems

    Mitigating the effect of shipping on freshwater megafauna: the case study of the Yangtze finless porpoise

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    Shipping has increasingly become a major threat to cetaceans due to its direct effect (e.g. ship strikes) and indirect effects (e.g. noise and habitat displacement). Most previous studies have focused on the deleterious effects of shipping traffic on marine species, while the effect of shipping on freshwater cetaceans has received little attention. The Yangtze River is a major trade artery in China, and shipping traffic there caused deaths of the now-extinct Yangtze river dolphin or baiji (Lipotes vexillifer). Here, we examine the distributional overlap of another cetacean species, the critically endangered Yangtze finless porpoise (Neophocoena asiaorientalis asiaorientalis) and cargo ships in a busy section of Yangtze River from Ezhou to Zhenjiang City. We use vessel-based survey data from 2006, 2012, and 2017 to quantify the distribution of porpoise. We use satellite images to quantify the distribution of cargo vessels travelling upstream. Most porpoise were concentrated within 300 m of the river banks. Shipping increased by 65% from 2006 to 2017, and ~ 60% of the upstream vessels was also within 300 m of the banks. This increase in shipping may have caused an observed shift in porpoise distribution away from the banks after 2006. Enhanced enforcement of existing shipping regulations that limit vessels to established shipping lane and set refuges in the side channels could help reduce the distributional overlap of porpoise and ships and aid in porpoise conservation. This could be applied and benefit the cetacean conservation under continued growth of shipping in rivers
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