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Junctures: An Abecedum
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
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
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Foundational principles for large scale inference: Illustrations through correlation mining
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 of acquired samples (statistical replicates) is far fewer than the
number 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 is fixed, and the dimension 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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