61,537 research outputs found
Protein sectors: statistical coupling analysis versus conservation
Statistical coupling analysis (SCA) is a method for analyzing multiple
sequence alignments that was used to identify groups of coevolving residues
termed "sectors". The method applies spectral analysis to a matrix obtained by
combining correlation information with sequence conservation. It has been
asserted that the protein sectors identified by SCA are functionally
significant, with different sectors controlling different biochemical
properties of the protein. Here we reconsider the available experimental data
and note that it involves almost exclusively proteins with a single sector. We
show that in this case sequence conservation is the dominating factor in SCA,
and can alone be used to make statistically equivalent functional predictions.
Therefore, we suggest shifting the experimental focus to proteins for which SCA
identifies several sectors. Correlations in protein alignments, which have been
shown to be informative in a number of independent studies, would then be less
dominated by sequence conservation.Comment: 36 pages, 17 figure
Combinatorics and Geometry of Transportation Polytopes: An Update
A transportation polytope consists of all multidimensional arrays or tables
of non-negative real numbers that satisfy certain sum conditions on subsets of
the entries. They arise naturally in optimization and statistics, and also have
interest for discrete mathematics because permutation matrices, latin squares,
and magic squares appear naturally as lattice points of these polytopes.
In this paper we survey advances on the understanding of the combinatorics
and geometry of these polyhedra and include some recent unpublished results on
the diameter of graphs of these polytopes. In particular, this is a thirty-year
update on the status of a list of open questions last visited in the 1984 book
by Yemelichev, Kovalev and Kravtsov and the 1986 survey paper of Vlach.Comment: 35 pages, 13 figure
Multiple perspectives on the concept of conditional probability
Conditional probability is a key to the subjectivist theory of probability; however, it plays a subsidiary role in the usual conception of probability where its counterpart, namely independence is of basic importance. The paper investigates these concepts from various perspectives in order to shed light on their multi-faceted character. We will include the mathematical, philosophical, and educational perspectives. Furthermore, we will inspect conditional probability from the corners of competing ideas and solving strategies. For the comprehension of conditional probability, a wider approach is urgently needed to overcome the well-known problems in learning the concepts, which seem nearly unaffected by teaching
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