753 research outputs found

    Number of distinct sites visited by N random walkers on a Euclidean lattice

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    The evaluation of the average number S_N(t) of distinct sites visited up to time t by N independent random walkers all starting from the same origin on an Euclidean lattice is addressed. We find that, for the nontrivial time regime and for large N, S_N(t) \approx \hat S_N(t) (1-\Delta), where \hat S_N(t) is the volume of a hypersphere of radius (4Dt \ln N)^{1/2}, \Delta={1/2}\sum_{n=1}^\infty \ln^{-n} N \sum_{m=0}^n s_m^{(n)} \ln^{m} \ln N, d is the dimension of the lattice, and the coefficients s_m^{(n)} depend on the dimension and time. The first three terms of these series are calculated explicitly and the resulting expressions are compared with other approximations and with simulation results for dimensions 1, 2, and 3. Some implications of these results on the geometry of the set of visited sites are discussed.Comment: 15 pages (RevTex), 4 figures (eps); to appear in Phys. Rev.

    Corrections to the Central Limit Theorem for Heavy-Tailed Probability Densities

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    Classical Edgeworth expansions provide asymptotic correction terms to the Central Limit Theorem (CLT) up to an order that depends on the number of moments available. In this paper, we provide subsequent correction terms beyond those given by a standard Edgeworth expansion in the general case of regularly varying distributions with diverging moments (beyond the second). The subsequent terms can be expressed in a simple closed form in terms of certain special functions (Dawson's integral and parabolic cylinder functions), and there are qualitative differences depending on whether the number of moments available is even, odd or not an integer, and whether the distributions are symmetric or not. If the increments have an even number of moments, then additional logarithmic corrections must also be incorporated in the expansion parameter. An interesting feature of our correction terms for the CLT is that they become dominant outside the central region and blend naturally with known large-deviation asymptotics when these are applied formally to the spatial scales of the CLT

    Gammaherpesvirus infection modulates the temporal and spatial expression of SCGB1A1 (CCSP) and BPIFA1 (SPLUNC1) in the respiratory tract

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    Murine γ-herpesvirus 68 (MHV-68) infection of Mus musculus-derived strains of mice is an established model of γ-herpesvirus infection. We have previously developed an alternative system using a natural host, the wood mouse (Apodemus sylvaticus), and shown that the MHV-68 M3 chemokine-binding protein contributes significantly to MHV-68 pathogenesis. Here we demonstrate in A. sylvaticus using high-density micro-arrays that M3 influences the expression of genes involved in the host response including Scgb1a1 and Bpifa1 that encode potential innate defense proteins secreted into the respiratory tract. Further analysis of MHV-68-infected animals showed that the levels of both protein and RNA for SCGB1A1 and BPIFA1 were decreased at day 7 post infection (p.i.) but increased at day 14 p.i. as compared with M3-deficient and mock-infected animals. The modulation of expression was most pronounced in bronchioles but was also present in the bronchi and trachea. Double staining using RNA in situ hybridization and immunohistology demonstrated that much of the BPIFA1 expression occurs in club cells along with SCGB1A1 and that BPIFA1 is stored within granules in these cells. The increase in SCGB1A1 and BPIFA1 expression at day 14 p.i. was associated with the differentiation of club cells into mucus-secreting cells. Our data highlight the role of club cells and the potential of SCGB1A1 and BPIFA1 as innate defense mediators during respiratory virus infection

    Allometric conservatism in the evolution of bird beaks

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    Evolution can involve periods of rapid divergent adaptation and expansion in the range of diversity, but evolution can also be relatively conservative over certain timescales due to functional, genetic-developmental, and ecological constraints. One way in which evolution may be conservative is in terms of allometry, the scaling relationship between the traits of organisms and body size. Here, we investigate patterns of allometric conservatism in the evolution of bird beaks with beak size and body size data for a representative sample of over 5000 extant bird species within a phylogenetic framework. We identify clades in which the allometric relationship between beak size and body size has remained relatively conserved across species over millions to tens of millions of years. We find that allometric conservatism is nonetheless punctuated by occasional shifts in the slopes and intercepts of allometric relationships. A steady accumulation of such shifts through time has given rise to the tremendous diversity of beak size relative to body size across birds today. Our findings are consistent with the Simpsonian vision of macroevolution, with evolutionary conservatism being the rule but with occasional shifts to new adaptive zones

    Structural Properties of Self-Attracting Walks

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    Self-attracting walks (SATW) with attractive interaction u > 0 display a swelling-collapse transition at a critical u_{\mathrm{c}} for dimensions d >= 2, analogous to the \Theta transition of polymers. We are interested in the structure of the clusters generated by SATW below u_{\mathrm{c}} (swollen walk), above u_{\mathrm{c}} (collapsed walk), and at u_{\mathrm{c}}, which can be characterized by the fractal dimensions of the clusters d_{\mathrm{f}} and their interface d_{\mathrm{I}}. Using scaling arguments and Monte Carlo simulations, we find that for u<u_{\mathrm{c}}, the structures are in the universality class of clusters generated by simple random walks. For u>u_{\mathrm{c}}, the clusters are compact, i.e. d_{\mathrm{f}}=d and d_{\mathrm{I}}=d-1. At u_{\mathrm{c}}, the SATW is in a new universality class. The clusters are compact in both d=2 and d=3, but their interface is fractal: d_{\mathrm{I}}=1.50\pm0.01 and 2.73\pm0.03 in d=2 and d=3, respectively. In d=1, where the walk is collapsed for all u and no swelling-collapse transition exists, we derive analytical expressions for the average number of visited sites and the mean time to visit S sites.Comment: 15 pages, 8 postscript figures, submitted to Phys. Rev.

    Direct en-face, speckle-reduced images using angular-compounded Master-Slave optical coherence tomography

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    In this paper, an angular compounding method to achieve speckle contrast reduction in optical coherence tomography (OCT) imaging is explored in detail. The angular compounding approach involves collecting multiple images at different angles of incidence, registering the images to correct for induced distortions, and then incoherently summing the images to reduce speckle. The method was experimentally demonstrated with a spectrometer-based Master-Slave enhanced OCT instrument capable of directly generating en-face images. We have investigated the impact of the angular range and number of averaged frames on the degree of speckle artefact reduction, as well as the effect on image resolution and sharpness. The minimum angular step necessary to secure a sufficiently small speckle pattern correlation between the images has also been determined, and the method has subsequently been validated on a biological sample (potato cells)

    Innovation and elaboration on the avian tree of life

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    Widely documented, megaevolutionary jumps in phenotypic diversity continue to perplex researchers because it remains unclear whether these marked changes can emerge from microevolutionary processes. Here, we tackle this question using new approaches for modeling multivariate traits to evaluate the magnitude and distribution of elaboration and innovation in the evolution of bird beaks. We find that elaboration, evolution along the major axis of phenotypic change, is common at both macro- and megaevolutionary scales, whereas innovation, evolution away from the major axis of phenotypic change, is more prominent at megaevolutionary scales. The major axis of phenotypic change among species beak shapes at megaevolutionary scales is an emergent property of innovation across clades. Our analyses suggest that the reorientation of phenotypes via innovation is a ubiquitous route for divergence that can arise through gradual change alone, opening up further avenues for evolution to explore

    From Macro to Micro: Autonomous Multiscale Image Fusion for Robotic Surgery

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    In recent years, minimally invasive robotic surgery has shown great promises for enhancing surgical precision and improving patient outcomes. Despite these advances, intraoperative tissue characterisation (such as the identification of cancerous tissue) still relies on traditional biopsy and histology, a process that is time-consuming and often disrupts the normal surgical workflow. In order to provide effective intra-operative decision-making, emerging optical biopsy techniques, such as probe based confocal laser endomicroscopy (pCLE) and optical coherence tomography (OCT), have been developed to provide real-time in vivo, in situ assessment of tissue micro-structures. Clinical deployment of these techniques, however, requires large area surveillance, from macro (mm/cm) to micro (µm) coverage in order to differentiate underlying tissue structures. This article provides a real-time multi-scale fusion scheme for robotic surgery. It demonstrates how the da Vinci surgical robot, used together with the da Vinci Research Kit, can be used for automated 2D scanning of pCLE/OCT probes, providing large area tissue surveillance by image stitching. Open-loop control of the robot provides insufficient precision for probe scanning, and therefore the motion is visually servoed using the live pCLE images (for lateral position) and OCT images (for axial position). The resulting tissue maps can then be fused in real-time with a stereo reconstruction from the laparoscopic video, providing the surgeon with a multi-scale 3D view of the operating site

    Gamma-ray Observations Under Bright Moonlight with VERITAS

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    Imaging atmospheric Cherenkov telescopes (IACTs) are equipped with sensitive photomultiplier tube (PMT) cameras. Exposure to high levels of background illumination degrades the efficiency of and potentially destroys these photo-detectors over time, so IACTs cannot be operated in the same configuration in the presence of bright moonlight as under dark skies. Since September 2012, observations have been carried out with the VERITAS IACTs under bright moonlight (defined as about three times the night-sky-background (NSB) of a dark extragalactic field, typically occurring when Moon illumination > 35%) in two observing modes, firstly by reducing the voltage applied to the PMTs and, secondly, with the addition of ultra-violet (UV) bandpass filters to the cameras. This has allowed observations at up to about 30 times previous NSB levels (around 80% Moon illumination), resulting in 30% more observing time between the two modes over the course of a year. These additional observations have already allowed for the detection of a flare from the 1ES 1727+502 and for an observing program targeting a measurement of the cosmic-ray positron fraction. We provide details of these new observing modes and their performance relative to the standard VERITAS observations
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