2008
Quotients, reciprocals, square roots and square root reciprocals all have the property that infinitely precise Ô-bit rounded results for Ô-bit input operands can be obtained from approximate results of bounded accuracy. We investigate lower bounds on the number of bits of an approximation accurate to a unit in the last place sufficient to guarantee that correct round and sticky bits can be determined. Known lower bounds for quotients and square roots are given and/or sharpened, and a new lower bound for root reciprocals is proved. Specifically for reciprocals, quotients and square roots, tight bounds of order Ô Ç are presented. For infinitely precise rounding of the root reciprocal a lower bound can be found at Ô Ç, but exhaustive testing for small sizes of the operand suggests that in practice ¯ Ô for small ¯ is usually sufficient. Algorithms can be designed for obtaining the round and sticky bits based on the bit pattern of an approximation computed to the required accuracy. We show that some improvement of the known lower bound for reciprocals and division is achievable at the cost of somewhat more complex hardware for rounding. Tests for the exactness of the quotient and square root are also provided.
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Daisy DeCoster · 2018
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Michael D. Hirschhorn · 2010
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Aynat Rubinstein · 2006
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Olga Chernoloz · 2016
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National Cancer Institute · Definitions · 2020
Ope n Pe e r v ie w on Qe ios
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2021
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Americanae (AECID Library) · 2018
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Parhamovich, Adrian · Digital Collections (East Carolina University) · 2012
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Jason T. Huff, Alex M. Plocik, Christine Guthrie et al. · 2016
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Jingtao Lilue, Urs Benedikt Müller, Tobias Steinfeldt et al. · 2016
virulence and resistance polymorphism in the relationship between Toxoplasma gondii and the house mouse
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Václava Kettnerová, Markéta Lopatková · Journal of Linguistics/Jazykovedný casopis · 2019
Abstract Reciprocal verbs are widely debated in the current linguistics. However, other parts of speech can be characterized by reciprocity as well – in contrast to verbs, their analysis is underdeveloped so far. In this paper, we make an attempt to fill this gap, applying results of the description of Czech reciprocal verbs to nouns derived from these verbs. We show that many aspects characteristic of reciprocal verbs hold for reciprocal nouns as well.
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Edmund Gurney, Frederic William Henry Myers, Frank Podmore · Cambridge University Press eBooks · 2011
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Rahaim, Meg · Archive of research processes and output produced by RCA (Royal College of Art) · 2018
Reciprocal Space is a series of 15 blind-embossed prints of crocheted textiles produced in residency at the Wellcome Centre for Human Genetics (WHG), University of Oxford. This body of work explores an epistemological affinity in art and scientific imaging through the construction of printed images. In blind embossing, I explore indexical impression in paper in relation to the “reciprocal” space of diffraction images in x-ray crystallography—in structural biology, an intermediary, inverse representation used to derive molecular shape. This work transposes material or scientific processes as conceptual frameworks that structure making as thinking. Crocheting embodies multidimensional complexity in strand, surface, fold, time. Embossing, as reciprocal inversion of its referent, transposes an aspect of a scientific imaging process onto an artistic one, revealing an affinity in printed artwork and scientific imaging toward the anticipation of knowledge. The work was exhibited at University Church of St Mary’s for Oxford Festival of Science and Ideas, at St Ann’s College, Oxford, and in the 2018 Douro Print Biennial, and led to public workshops on Genes and Crochet at Science Gallery London.
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Hinkle, John E., Rayens, William S. · RePEc: Research Papers in Economics
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The COCOON platform (University of Paris)
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Julian Rodemann, Christoph Jansen, Georg Schollmeyer · arXiv (Cornell University) · 2024
We demonstrate that a wide array of machine learning algorithms are specific instances of one single paradigm: reciprocal learning. These instances range from active learning over multi-armed bandits to self-training. We show that all these algorithms do not only learn parameters from data but also vice versa: They iteratively alter training data in a way that depends on the current model fit. We introduce reciprocal learning as a generalization of these algorithms using the language of decision theory. This allows us to study under what conditions they converge. The key is to guarantee that reciprocal learning contracts such that the Banach fixed-point theorem applies. In this way, we find that reciprocal learning algorithms converge at linear rates to an approximately optimal model under relatively mild assumptions on the loss function, if their predictions are probabilistic and the sample adaption is both non-greedy and either randomized or regularized. We interpret these findings and provide corollaries that relate them to specific active learning, self-training, and bandit algorithms.
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2021
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Wiley StatsRef: Statistics Reference Online · 2014
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gamapvitor · 2023
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