7,656 research outputs found

    A stochastic epidemiological model and a deterministic limit for BitTorrent-like peer-to-peer file-sharing networks

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    In this paper, we propose a stochastic model for a file-sharing peer-to-peer network which resembles the popular BitTorrent system: large files are split into chunks and a peer can download or swap from another peer only one chunk at a time. We prove that the fluid limits of a scaled Markov model of this system are of the coagulation form, special cases of which are well-known epidemiological (SIR) models. In addition, Lyapunov stability and settling-time results are explored. We derive conditions under which the BitTorrent incentives under consideration result in shorter mean file-acquisition times for peers compared to client-server (single chunk) systems. Finally, a diffusion approximation is given and some open questions are discussed.Comment: 25 pages, 6 figure

    The Pathologic Affinities of Beriberi and Scurvy

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    Baseline Scotland : groundwater chemistry of the Carboniferous sedimentary aquifers of the Midland Valley

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    This report describes the baseline groundwater chemistry of the sedimentary aquifers of Carboniferous age in the Midland Valley of Scotland. Groundwater is an important resource in the Midland Valley, largely for agriculture, but also for industry – including food and drink processing and mineral water bottling, and for domestic use. A large but unquantified volume of groundwater is also still pumped from former mine workings, largely coal mines, in order to maintain water levels and for quality treatment. Analyses for 62 groundwater samples were interpreted for the purposes of this study. Of these, 36 samples were collected for the Baseline Scotland project between September and December 2008. These were augmented with a further 25 samples collected during separate BGS projects since 2001. The sites were chosen largely to be representative of groundwater in the area, and sources that were very poorly constructed were avoided. A small number of samples were deliberately targeted from mines, either from adits, shafts or boreholes. The data were classed in one of five different hydrogeological units (or aquifer groups): four chronostratigraphic groups, which in decreasing order of age are the Inverclyde, Strathclyde, Clackmannan and Coal Measures groups; and a fifth group incorporating waters sampled from mine discharges. An estimate of the baseline groundwater chemistry conditions in the four chronostratigraphic hydrogeological units is presented, based on a statistical summary of the chemical data, which represents values between the 10th and 90th A summary of the conclusions arising from this study follows. percentiles of the full dataset range. This statistical approach to estimating baseline compositions was complemented by selecting 11 analyses of groundwater from sources where there is little or no indication of direct contamination, including likely impact from mining. The chemistry of these samples represents the typical groundwater conditions in the four non-mine hydrogeological units in the sedimentary Carboniferous aquifers of the Midland Valley

    Hidden breakpoints in genome alignments

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    During the course of evolution, an organism's genome can undergo changes that affect the large-scale structure of the genome. These changes include gene gain, loss, duplication, chromosome fusion, fission, and rearrangement. When gene gain and loss occurs in addition to other types of rearrangement, breakpoints of rearrangement can exist that are only detectable by comparison of three or more genomes. An arbitrarily large number of these "hidden" breakpoints can exist among genomes that exhibit no rearrangements in pairwise comparisons. We present an extension of the multichromosomal breakpoint median problem to genomes that have undergone gene gain and loss. We then demonstrate that the median distance among three genomes can be used to calculate a lower bound on the number of hidden breakpoints present. We provide an implementation of this calculation including the median distance, along with some practical improvements on the time complexity of the underlying algorithm. We apply our approach to measure the abundance of hidden breakpoints in simulated data sets under a wide range of evolutionary scenarios. We demonstrate that in simulations the hidden breakpoint counts depend strongly on relative rates of inversion and gene gain/loss. Finally we apply current multiple genome aligners to the simulated genomes, and show that all aligners introduce a high degree of error in hidden breakpoint counts, and that this error grows with evolutionary distance in the simulation. Our results suggest that hidden breakpoint error may be pervasive in genome alignments.Comment: 13 pages, 4 figure
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