2,132 research outputs found

    Classification of Generalized Multiresolution Analyses

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    We discuss how generalized multiresolution analyses (GMRAs), both classical and those defined on abstract Hilbert spaces, can be classified by their multiplicity functions mm and matrix-valued filter functions HH. Given a natural number valued function mm and a system of functions encoded in a matrix HH satisfying certain conditions, a construction procedure is described that produces an abstract GMRA with multiplicity function mm and filter system HH. An equivalence relation on GMRAs is defined and described in terms of their associated pairs (m,H)(m,H). This classification system is applied to classical examples in L2(Rd)L^2 (\mathbb R^d) as well as to previously studied abstract examples.Comment: 18 pages including bibliograp

    Trial design: how must we move ahead?

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    Scleroderma is clinically heterogeneous and a variety of plausible mechanisms of disease have been hypothesized. Recent years have witnessed a significant improvement in overall survival although all of the gains in management have been therapies for specific organ involvement, e.g. renal crisis and pulmonary arterial hypertension. Future studies will rely on improved clinical science, which involves structured validation of proposed measures of outcome; development of a combined response index; and further refinement of specific subsets of disease expression. Immunoablation with stem cell reconstitution is an example of aggressive therapy chosen as appropriate for a particularly severe disease subset and in whom the pilot data are encouraging. Good science and clinical ethics force continued consideration of equipoise between risk and benefi

    On Algorithmic Statistics for space-bounded algorithms

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    Algorithmic statistics studies explanations of observed data that are good in the algorithmic sense: an explanation should be simple i.e. should have small Kolmogorov complexity and capture all the algorithmically discoverable regularities in the data. However this idea can not be used in practice because Kolmogorov complexity is not computable. In this paper we develop algorithmic statistics using space-bounded Kolmogorov complexity. We prove an analogue of one of the main result of `classic' algorithmic statistics (about the connection between optimality and randomness deficiences). The main tool of our proof is the Nisan-Wigderson generator.Comment: accepted to CSR 2017 conferenc

    Short Duplication in a cDNA Clone of the rbcL Gene from Picea abies

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