96,003 research outputs found

    Junctures: An Abecedum

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    Editor\u27s Note: Alfred Lubran\u27s article was inspired by the note on page 164 of David Crystal\u27s The Cambridge Encyclopedia of Language (reviewed in the November 1991 Word Ways); his examples of A, I, N, and T are reproduced below. All words can be found in Chambers English Dictionary

    Life and Quantum Biology, an Interdisciplinary Approach

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    The rapidly increasing interest in the quantum properties of living matter stimulates a discussion of the fundamental properties of life as well as quantum mechanics. In this discussion often concepts are used that originate in philosophy and ask for a philosophical analysis. In the present work the classic philosophical tradition based on Aristotle and Aquinas is employed which surprisingly is able to shed light on important aspects. Especially one could mention the high degree of unity in living objects and the occurrence of thorough qualitative changes. The latter are outside the scope of classical physics where changes are restricted to geometrical rearrangement of microscopic particles. A challenging approach is used in the philosophical analysis as the empirical evidence is not taken from everyday life but from 20th century science (quantum mechanics) and recent results in the field of quantum biology. In the discussion it is argued that quantum entanglement is possibly related to the occurrence of life. Finally it is recommended that scientists and philosophers should be open for dialogue that could enrich both. Scientists could redirect their investigation, as paradigm shifts like the one originating from philosophical evaluation of quantum mechanics give new insight about the relation between the whole en the parts. Whereas philosophers could use scientific results as a consistency check for their philosophical framework for understanding reality.Comment: 13 page

    Foundational principles for large scale inference: Illustrations through correlation mining

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    When can reliable inference be drawn in the "Big Data" context? This paper presents a framework for answering this fundamental question in the context of correlation mining, with implications for general large scale inference. In large scale data applications like genomics, connectomics, and eco-informatics the dataset is often variable-rich but sample-starved: a regime where the number nn of acquired samples (statistical replicates) is far fewer than the number pp of observed variables (genes, neurons, voxels, or chemical constituents). Much of recent work has focused on understanding the computational complexity of proposed methods for "Big Data." Sample complexity however has received relatively less attention, especially in the setting when the sample size nn is fixed, and the dimension pp grows without bound. To address this gap, we develop a unified statistical framework that explicitly quantifies the sample complexity of various inferential tasks. Sampling regimes can be divided into several categories: 1) the classical asymptotic regime where the variable dimension is fixed and the sample size goes to infinity; 2) the mixed asymptotic regime where both variable dimension and sample size go to infinity at comparable rates; 3) the purely high dimensional asymptotic regime where the variable dimension goes to infinity and the sample size is fixed. Each regime has its niche but only the latter regime applies to exa-scale data dimension. We illustrate this high dimensional framework for the problem of correlation mining, where it is the matrix of pairwise and partial correlations among the variables that are of interest. We demonstrate various regimes of correlation mining based on the unifying perspective of high dimensional learning rates and sample complexity for different structured covariance models and different inference tasks
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