9,949 research outputs found
Centralizers of maximal regular subgroups in simple Lie groups and relative congruence classes of representations
In the paper we present a new, uniform and comprehensive description of
centralizers of the maximal regular subgroups in compact simple Lie groups of
all types and ranks. The centralizer is either a direct product of finite
cyclic groups, a continuous group of rank 1, or a product, not necessarily
direct, of a continuous group of rank 1 with a finite cyclic group. Explicit
formulas for the action of such centralizers on irreducible representations of
the simple Lie algebras are given.Comment: 27 page
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Getting creative in everyday life: Investigating arts and crafts hobbyists' information behavior
While there has been increasing interest in how creative professionals find information to drive creative outputs, previous information behavior research has largely ignored how arts and crafts hobbyists look for information sources in their everyday lives. To fill this literature gap, we conducted interviews and observations with arts and crafts hobbyists to find out how they conceive potential DIY projects. The findings highlight three themes: the dearth of human sources, the prevalence of domain-specific information, and the use of self-curated information. In addition to empirical results, this work also broadens the understanding of information behavior in an arts and crafts context by studying populations beyond professional artists
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On Birthing Dancing Stars: The Need for Bounded Chaos in Information Interaction
While computers causing chaos is acommon social trope, nearly the entirety of the history of computing is dedicated to generating order. Typical interactive information retrieval tasks ask computers to support the traversal and exploration of large, complex information spaces. The implicit assumption is that they are to support users in simplifying the complexity (i.e. in creating order from chaos). But for some types of task, particularly those that involve the creative application or synthesis of knowledge or the creation of new knowledge, this assumption may be incorrect. It is increasingly evident that perfect order—and the systems we create with it—support highly-structured information tasks well, but provide poor support for less-structured tasks.We need digital information environments that help create a little more chaos from order to spark creative thinking and knowledge creation. This paper argues for the need for information systems that offerwhat we term ‘bounded chaos’, and offers research directions that may support the creation of such interface
Shape computations without compositions
Parametric CAD supports design explorations through generative methods which compose and transform geometric elements. This paper argues that elementary shape computations do not always correspond to valid compositional shape structures. In many design cases generative rules correspond to compositional structures, but for relatively simple shapes and rules it is not always possible to assign a corresponding compositional structure of parts which account for all operations of the computation. This problem is brought into strong relief when design processes generate multiple compositions according to purpose, such as product structure, assembly, manufacture, etc. Is it possible to specify shape computations which generate just these compositions of parts or are there additional emergent shapes and features? In parallel, combining two compositions would require the associated combined computations to yield a valid composition. Simple examples are presented which throw light on the issues in integrating different product descriptions (i.e. compositions) within parametric CAD
The Evolving Activity of the Dynamically Young Comet C/2009 P1 (Garradd)
We used the UltraViolet-Optical Telescope on board Swift to observe the
dynamically young comet C/2009 P1 (Garradd) from a heliocentric distance of 3.5
AU pre-perihelion until 4.0 AU outbound. At 3.5 AU pre-perihelion, comet
Garradd had one of the highest dust-to-gas ratios ever observed, matched only
by comet Hale-Bopp. The evolving morphology of the dust in its coma suggests an
outburst that ended around 2.2 AU pre-perihelion. Comparing slit-based
measurements and observations acquired with larger fields of view indicated
that between 3 AU and 2 AU pre-perihelion a significant extended source started
producing water in the coma. We demonstrate that this source, which could be
due to icy grains, disappeared quickly around perihelion. Water production by
the nucleus may be attributed to a constantly active source of at least 75
km, estimated to be more than 20 percent of the surface. Based on our
measurements, the comet lost kg of ice and dust during this
apparition, corresponding to at most a few meters of its surface.Even though
this was likely not Garradd's first passage through the inner solar system, the
activity of the comet was complex and changed significantly during the time it
was observed
Direct imaging of a digital-micromirror device for configurable microscopic optical potentials
Programable spatial light modulators (SLMs) have significantly advanced the
configurable optical trapping of particles. Typically, these devices are
utilized in the Fourier plane of an optical system, but direct imaging of an
amplitude pattern can potentially result in increased simplicity and
computational speed. Here we demonstrate high-resolution direct imaging of a
digital micromirror device (DMD) at high numerical apertures (NA), which we
apply to the optical trapping of a Bose-Einstein condensate (BEC). We utilise a
(1200 x 1920) pixel DMD and commercially available 0.45 NA microscope
objectives, finding that atoms confined in a hybrid optical/magnetic or
all-optical potential can be patterned using repulsive blue-detuned (532 nm)
light with 630(10) nm full-width at half-maximum (FWHM) resolution, within 5%
of the diffraction limit. The result is near arbitrary control of the density
the BEC without the need for expensive custom optics. We also introduce the
technique of time-averaged DMD potentials, demonstrating the ability to produce
multiple grayscale levels with minimal heating of the atomic cloud, by
utilising the high switching speed (20 kHz maximum) of the DMD. These
techniques will enable the realization and control of diverse optical
potentials for superfluid dynamics and atomtronics applications with quantum
gases. The performance of this system in a direct imaging configuration has
wider application for optical trapping at non-trivial NAs.Comment: 9 page
Large Networks of Diameter Two Based on Cayley Graphs
In this contribution we present a construction of large networks of diameter
two and of order for every degree , based on Cayley
graphs with surprisingly simple underlying groups. For several small degrees we
construct Cayley graphs of diameter two and of order greater than of
Moore bound and we show that Cayley graphs of degrees
constructed in this paper are the largest
currently known vertex-transitive graphs of diameter two.Comment: 9 pages, Published in Cybernetics and Mathematics Applications in
Intelligent System
An adaptive prefix-assignment technique for symmetry reduction
This paper presents a technique for symmetry reduction that adaptively
assigns a prefix of variables in a system of constraints so that the generated
prefix-assignments are pairwise nonisomorphic under the action of the symmetry
group of the system. The technique is based on McKay's canonical extension
framework [J.~Algorithms 26 (1998), no.~2, 306--324]. Among key features of the
technique are (i) adaptability---the prefix sequence can be user-prescribed and
truncated for compatibility with the group of symmetries; (ii)
parallelizability---prefix-assignments can be processed in parallel
independently of each other; (iii) versatility---the method is applicable
whenever the group of symmetries can be concisely represented as the
automorphism group of a vertex-colored graph; and (iv) implementability---the
method can be implemented relying on a canonical labeling map for
vertex-colored graphs as the only nontrivial subroutine. To demonstrate the
practical applicability of our technique, we have prepared an experimental
open-source implementation of the technique and carry out a set of experiments
that demonstrate ability to reduce symmetry on hard instances. Furthermore, we
demonstrate that the implementation effectively parallelizes to compute
clusters with multiple nodes via a message-passing interface.Comment: Updated manuscript submitted for revie
Quantum affine Cartan matrices, Poincare series of binary polyhedral groups, and reflection representations
We first review some invariant theoretic results about the finite subgroups
of SU(2) in a quick algebraic way by using the McKay correspondence and quantum
affine Cartan matrices. By the way it turns out that some parameters
(a,b,h;p,q,r) that one usually associates with such a group and hence with a
simply-laced Coxeter-Dynkin diagram have a meaningful definition for the
non-simply-laced diagrams, too, and as a byproduct we extend Saito's formula
for the determinant of the Cartan matrix to all cases. Returning to invariant
theory we show that for each irreducible representation i of a binary
tetrahedral, octahedral, or icosahedral group one can find a homomorphism into
a finite complex reflection group whose defining reflection representation
restricts to i.Comment: 19 page
The Antarctic dry valley lakes: Relevance to Mars
The similarity of the early environments of Mars and Earth, and the biological evolution which occurred on early Earth, motivates exobiologists to seriously consider the possiblity of an early Martian biota. Environments are being identified which could contain Martian life and areas which may presently contain evidence of this former life. Sediments which were thought to be deposited in large ice-covered lakes are present on Mars. Such localities were identified within some of the canyons of the Valles Marineris and more recently in the ancient terrain in the Southern Hemisphere. Perennially ice-covered Antarctic lakes are being studied in order to develop quantitative models that relate environmental factors to the nature of the biological community and sediment forming processes. These models will be applied to the Martian paleolakes to establish the scientific rationale for the exobiological study of ancient Martian sediments
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