4,466 research outputs found
Characterizing the universal rigidity of generic frameworks
A framework is a graph and a map from its vertices to E^d (for some d). A
framework is universally rigid if any framework in any dimension with the same
graph and edge lengths is a Euclidean image of it. We show that a generic
universally rigid framework has a positive semi-definite stress matrix of
maximal rank. Connelly showed that the existence of such a positive
semi-definite stress matrix is sufficient for universal rigidity, so this
provides a characterization of universal rigidity for generic frameworks. We
also extend our argument to give a new result on the genericity of strict
complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio
The orbit rigidity matrix of a symmetric framework
A number of recent papers have studied when symmetry causes frameworks on a
graph to become infinitesimally flexible, or stressed, and when it has no
impact. A number of other recent papers have studied special classes of
frameworks on generically rigid graphs which are finite mechanisms. Here we
introduce a new tool, the orbit matrix, which connects these two areas and
provides a matrix representation for fully symmetric infinitesimal flexes, and
fully symmetric stresses of symmetric frameworks. The orbit matrix is a true
analog of the standard rigidity matrix for general frameworks, and its analysis
gives important insights into questions about the flexibility and rigidity of
classes of symmetric frameworks, in all dimensions.
With this narrower focus on fully symmetric infinitesimal motions, comes the
power to predict symmetry-preserving finite mechanisms - giving a simplified
analysis which covers a wide range of the known mechanisms, and generalizes the
classes of known mechanisms. This initial exploration of the properties of the
orbit matrix also opens up a number of new questions and possible extensions of
the previous results, including transfer of symmetry based results from
Euclidean space to spherical, hyperbolic, and some other metrics with shared
symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure
A Pluralistic Theory of Wordhood
What are words and how should we individuate them? There are two main answers on the philosophical market. For some, words are bundles of structural-functional features defining a unique performance profile. For others, words are non-eternal continuants individuated by their causal-historical ancestry. These conceptions offer competing views of the nature of words, and it seems natural to assume that at most one of them can capture the essence of wordhood. This paper makes a case for pluralism about wordhood: the view that there is a plurality of acceptable conceptions of the nature of words, none of which is uniquely entitled to inform us as to what wordhood consists in
X-Ray Groups of Galaxies in the Aegis Deep and Wide Fields
We present the results of a search for extended X-ray sources and their
corresponding galaxy groups from 800-ks Chandra coverage of the All-wavelength
Extended Groth Strip International Survey (AEGIS). This yields one of the
largest X-ray selected galaxy group catalogs from a blind survey to date. The
red-sequence technique and spectroscopic redshifts allow us to identify 100
of reliable sources, leading to a catalog of 52 galaxy groups. The groups span
the redshift range and virial mass range
. For the 49 extended
sources which lie within DEEP2 and DEEP3 Galaxy Redshift Survey coverage, we
identify spectroscopic counterparts and determine velocity dispersions. We
select member galaxies by applying different cuts along the line of sight or in
projected spatial coordinates. A constant cut along the line of sight can cause
a large scatter in scaling relations in low-mass or high-mass systems depending
on the size of cut. A velocity dispersion based virial radius can more
overestimate velocity dispersion in comparison to X-ray based virial radius for
low mass systems. There is no significant difference between these two radial
cuts for more massive systems. Independent of radial cut, overestimation of
velocity dispersion can be created in case of existence of significant
substructure and also compactness in X-ray emission which mostly occur in low
mass systems. We also present a comparison between X-ray galaxy groups and
optical galaxy groups detected using the Voronoi-Delaunay method (VDM) for
DEEP2 data in this field.Comment: Accepted for publication in AP
Short-range correlations in low-lying nuclear excited states
The electromagnetic transitions to various low-lying excited states of 16O,
48Ca and 208Pb are calculated within a model which considers the short-range
correlations. In general the effects of the correlations are small and do not
explain the required quenching to describe the data.Comment: 6 pages, 2 postscript figures, 1 tabl
Internal states of model isotropic granular packings. I. Assembling process, geometry and contact networks
This is the first paper of a series of three, reporting on numerical
simulation studies of geometric and mechanical properties of static assemblies
of spherical beads under an isotropic pressure. Frictionless systems assemble
in the unique random close packing (RCP) state in the low pressure limit if the
compression process is fast enough, slower processes inducing traces of
crystallization, and exhibit specific properties directly related to
isostaticity of the force-carrying structure. The different structures of
frictional packings assembled by various methods cannot be classified by the
sole density. While lubricated systems approach RCP densities and coordination
number z^*~=6 on the backbone in the rigid limit, an idealized "vibration"
procedure results in equally dense configurations with z^*~=4.5. Near neighbor
correlations on various scales are computed and compared to available
laboratory data, although z^* values remain experimentally inaccessible. Low
coordination packings have many rattlers (more than 10% of the grains carry no
force), which should be accounted for on studying position correlations, and a
small proportion of harmless "floppy modes" associated with divalent grains.
Frictional packings, however slowly assembled under low pressure, retain a
finite level of force indeterminacy, except in the limit of infinite friction.Comment: 29 pages. Published in Physical Review
Gene Expression Response to Stony Coral Tissue Loss Disease Transmission in M. cavernosa and O. faveolata From Florida
Since 2014, corals within Florida’s Coral Reef have been dying at an unprecedented rate due to stony coral tissue loss disease (SCTLD). Here we describe the transcriptomic outcomes of three different SCTLD transmission experiments performed at the Smithsonian Marine Station and Mote Marine Laboratory between 2019 and 2020 on the corals Orbicella faveolata and Montastraea cavernosa. Overall, diseased O. faveolata had 2194 differentially expressed genes (DEGs) compared with healthy colonies, whereas diseased M. cavernosa had 582 DEGs compared with healthy colonies. Many significant DEGs were implicated in immunity, extracellular matrix rearrangement, and apoptosis. These included, but not limited to, peroxidases, collagens, Bax-like, fibrinogen-like, protein tyrosine kinase, and transforming growth factor beta. A gene module was identified that was significantly correlated to disease transmission. This module possessed many apoptosis and immune genes with high module membership indicating that a complex apoptosis and immune response is occurring in corals during SCTLD transmission. Overall, we found that O. faveolata and M. cavernosa exhibit an immune, apoptosis, and tissue rearrangement response to SCTLD. We propose that future studies should focus on examining early time points of infection, before the presence of lesions, to understand the activating mechanisms involved in SCTLD
Working with Young People Who Offend : An Examination of the Literature Regarding Violence, Substance Misuse and Harmful Sexual Behaviour
This paper presents a review of the recent literature relating to effective practice with young people displaying harmful sexual behaviour (HSB), violence or risky substance misuse. The intention is to build upon and update the 2007 literature review Research and practice in risk assessment and risk management of children and young people engaging in offending behaviour, funded by the Risk Management Authority (RMA) and carried out by the Scottish Centre for Crime and Justice Research (SCCJR)
Small grid embeddings of 3-polytopes
We introduce an algorithm that embeds a given 3-connected planar graph as a
convex 3-polytope with integer coordinates. The size of the coordinates is
bounded by . If the graph contains a triangle we can
bound the integer coordinates by . If the graph contains a
quadrilateral we can bound the integer coordinates by . The
crucial part of the algorithm is to find a convex plane embedding whose edges
can be weighted such that the sum of the weighted edges, seen as vectors,
cancel at every point. It is well known that this can be guaranteed for the
interior vertices by applying a technique of Tutte. We show how to extend
Tutte's ideas to construct a plane embedding where the weighted vector sums
cancel also on the vertices of the boundary face
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