60,585 research outputs found

    Cell-Probe Bounds for Online Edit Distance and Other Pattern Matching Problems

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    We give cell-probe bounds for the computation of edit distance, Hamming distance, convolution and longest common subsequence in a stream. In this model, a fixed string of nn symbols is given and one δ\delta-bit symbol arrives at a time in a stream. After each symbol arrives, the distance between the fixed string and a suffix of most recent symbols of the stream is reported. The cell-probe model is perhaps the strongest model of computation for showing data structure lower bounds, subsuming in particular the popular word-RAM model. * We first give an Ω((δlogn)/(w+loglogn))\Omega((\delta \log n)/(w+\log\log n)) lower bound for the time to give each output for both online Hamming distance and convolution, where ww is the word size. This bound relies on a new encoding scheme and for the first time holds even when ww is as small as a single bit. * We then consider the online edit distance and longest common subsequence problems in the bit-probe model (w=1w=1) with a constant sized input alphabet. We give a lower bound of Ω(logn/(loglogn)3/2)\Omega(\sqrt{\log n}/(\log\log n)^{3/2}) which applies for both problems. This second set of results relies both on our new encoding scheme as well as a carefully constructed hard distribution. * Finally, for the online edit distance problem we show that there is an O((logn)2/w)O((\log n)^2/w) upper bound in the cell-probe model. This bound gives a contrast to our new lower bound and also establishes an exponential gap between the known cell-probe and RAM model complexities.Comment: 32 pages, 4 figure

    Joint Structure Learning of Multiple Non-Exchangeable Networks

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    Several methods have recently been developed for joint structure learning of multiple (related) graphical models or networks. These methods treat individual networks as exchangeable, such that each pair of networks are equally encouraged to have similar structures. However, in many practical applications, exchangeability in this sense may not hold, as some pairs of networks may be more closely related than others, for example due to group and sub-group structure in the data. Here we present a novel Bayesian formulation that generalises joint structure learning beyond the exchangeable case. In addition to a general framework for joint learning, we (i) provide a novel default prior over the joint structure space that requires no user input; (ii) allow for latent networks; (iii) give an efficient, exact algorithm for the case of time series data and dynamic Bayesian networks. We present empirical results on non-exchangeable populations, including a real data example from biology, where cell-line-specific networks are related according to genomic features.Comment: To appear in Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics (AISTATS

    A Theory of a Spot

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    We present a simple inflationary scenario that can produce arbitrarily large spherical underdense or overdense regions embedded in a standard Lambda cold dark matter paradigm, which we refer to as bubbles. We analyze the effect such bubbles would have on the Cosmic Microwave Background (CMB). For super-horizon sized bubble in the vicinity of the last scattering surface, a signal is imprinted onto CMB via a combination of Sach-Wolfe and an early integrated Sach-Wolfe (ISW) effects. Smaller, sub-horizon sized bubbles at lower redshifts (during matter domination and later) can imprint secondary anisotropies on the CMB via Rees-Sciama, late-time ISW and Ostriker-Vishniac effects. Our scenario, and arguably most similar inflationary models, produce bubbles which are over/underdense in potential: in density such bubbles are characterized by having a distinct wall with the interior staying at the cosmic mean density. We show that such models can potentially, with only moderate fine tuning, explain the \emph{cold spot}, a non-Gaussian feature identified in the Wilkinson Microwave Anisotropy Probe (WMAP) data by several authors. However, more detailed comparisons with current and future CMB data are necessary to confirm (or rule out) this scenario.Comment: 19 pages, 19 figures, added references and explanations, JCAP in pres

    Spanish banking sector: past, present and future

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    Evento: 15th Annual European Financials Conference. Organizado por: Goldman Sach
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