15,944 research outputs found
Finite Groebner bases in infinite dimensional polynomial rings and applications
We introduce the theory of monoidal Groebner bases, a concept which
generalizes the familiar notion in a polynomial ring and allows for a
description of Groebner bases of ideals that are stable under the action of a
monoid. The main motivation for developing this theory is to prove finiteness
theorems in commutative algebra and its applications. A major result of this
type is that ideals in infinitely many indeterminates stable under the action
of the symmetric group are finitely generated up to symmetry. We use this
machinery to give new proofs of some classical finiteness theorems in algebraic
statistics as well as a proof of the independent set conjecture of Hosten and
the second author.Comment: 24 pages, adds references to work of Cohen, adds more details in
Section
Watching the hands of the Arabidopsis biological clock
Oligonucleotide and cDNA microarrays have been used to analyse the mRNA levels of 8,000 genes in Arabidopsis thaliana throughout the day/night cycle. Genes involved in signal transduction and in various metabolic pathways were found to be coordinately regulated by circadian rhythms and/or by light
Formation and Evolution of Binary Asteroids
Satellites of asteroids have been discovered in nearly every known small body
population, and a remarkable aspect of the known satellites is the diversity of
their properties. They tell a story of vast differences in formation and
evolution mechanisms that act as a function of size, distance from the Sun, and
the properties of their nebular environment at the beginning of Solar System
history and their dynamical environment over the next 4.5 Gyr. The mere
existence of these systems provides a laboratory to study numerous types of
physical processes acting on asteroids and their dynamics provide a valuable
probe of their physical properties otherwise possible only with spacecraft.
Advances in understanding the formation and evolution of binary systems have
been assisted by: 1) the growing catalog of known systems, increasing from 33
to nearly 250 between the Merline et al. (2002) Asteroids III chapter and now,
2) the detailed study and long-term monitoring of individual systems such as
1999 KW4 and 1996 FG3, 3) the discovery of new binary system morphologies and
triple systems, 4) and the discovery of unbound systems that appear to be
end-states of binary dynamical evolutionary paths.
Specifically for small bodies (diameter smaller than 10 km), these
observations and discoveries have motivated theoretical work finding that
thermal forces can efficiently drive the rotational disruption of small
asteroids. Long-term monitoring has allowed studies to constrain the system's
dynamical evolution by the combination of tides, thermal forces and rigid body
physics. The outliers and split pairs have pushed the theoretical work to
explore a wide range of evolutionary end-states.Comment: 42 pages, 4 figures, contribution to the Asteroids 4 boo
Prospects for computational steering of evolutionary computation
Currently, evolutionary computation (EC) typically takes place in batch mode: algorithms are run autonomously, with the user providing little or no intervention or guidance. Although it is rarely possible to specify in advance, on the basis of EC theory, the optimal evolutionary algorithm for a particular problem, it seems likely that experienced EC practitioners possess considerable tacit knowledge of how evolutionary algorithms work. In situations such as this, computational steering (ongoing, informed user intervention in the execution of an otherwise autonomous computational process) has been profitably exploited to improve performance and generate insights into computational processes. In this short paper, prospects for the computational steering of evolutionary computation are assessed, and a prototype example of computational steering applied to a coevolutionary algorithm is presented
Probabilistic Archetypal Analysis
Archetypal analysis represents a set of observations as convex combinations
of pure patterns, or archetypes. The original geometric formulation of finding
archetypes by approximating the convex hull of the observations assumes them to
be real valued. This, unfortunately, is not compatible with many practical
situations. In this paper we revisit archetypal analysis from the basic
principles, and propose a probabilistic framework that accommodates other
observation types such as integers, binary, and probability vectors. We
corroborate the proposed methodology with convincing real-world applications on
finding archetypal winter tourists based on binary survey data, archetypal
disaster-affected countries based on disaster count data, and document
archetypes based on term-frequency data. We also present an appropriate
visualization tool to summarize archetypal analysis solution better.Comment: 24 pages; added literature review and visualizatio
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