1,123 research outputs found
Feynman graph polynomials
The integrand of any multi-loop integral is characterised after Feynman
parametrisation by two polynomials. In this review we summarise the properties
of these polynomials. Topics covered in this article include among others:
Spanning trees and spanning forests, the all-minors matrix-tree theorem,
recursion relations due to contraction and deletion of edges, Dodgson's
identity and matroids.Comment: 35 pages, references adde
The EBEX Experiment
EBEX is a balloon-borne polarimeter designed to measure the intensity and
polarization of the cosmic microwave background radiation. The measurements
would probe the inflationary epoch that took place shortly after the big bang
and would significantly improve constraints on the values of several
cosmological parameters. EBEX is unique in its broad frequency coverage and in
its ability to provide critical information about the level of polarized
Galactic foregrounds which will be necessary for all future CMB polarization
experiments. EBEX consists of a 1.5 m Dragone-type telescope that provides a
resolution of less than 8 arcminutes over four focal planes each of 4 degree
diffraction limited field of view at frequencies up to 450 GHz. The experiment
is designed to accommodate 330 transition edge bolometric detectors per focal
plane, for a total of up to 1320 detectors. EBEX will operate with frequency
bands centered at 150, 250, 350, and 450 GHz. Polarimetry is achieved with a
rotating achromatic half-wave plate. EBEX is currently in the design and
construction phase, and first light is scheduled for 2008.Comment: 13 pages, 10 figures. Figure 1 is changed from the one which appeared
in the Proceedings of the SPI
Relations between M\"obius and coboundary polynomial
It is known that, in general, the coboundary polynomial and the M\"obius
polynomial of a matroid do not determine each other. Less is known about more
specific cases. In this paper, we will try to answer if it is possible that the
M\"obius polynomial of a matroid, together with the M\"obius polynomial of the
dual matroid, define the coboundary polynomial of the matroid. In some cases,
the answer is affirmative, and we will give two constructions to determine the
coboundary polynomial in these cases.Comment: 12 page
Hamming weights and Betti numbers of Stanley-Reisner rings associated to matroids
To each linear code over a finite field we associate the matroid of its
parity check matrix. We show to what extent one can determine the generalized
Hamming weights of the code (or defined for a matroid in general) from various
sets of Betti numbers of Stanley-Reisner rings of simplicial complexes
associated to the matroid
Topological representations of matroid maps
The Topological Representation Theorem for (oriented) matroids states that
every (oriented) matroid can be realized as the intersection lattice of an
arrangement of codimension one homotopy spheres on a homotopy sphere. In this
paper, we use a construction of Engstr\"om to show that structure-preserving
maps between matroids induce topological mappings between their
representations; a result previously known only in the oriented case.
Specifically, we show that weak maps induce continuous maps and that the
process is a functor from the category of matroids with weak maps to the
homotopy category of topological spaces. We also give a new and conceptual
proof of a result regarding the Whitney numbers of the first kind of a matroid.Comment: Final version, 21 pages, 8 figures; Journal of Algebraic
Combinatorics, 201
Self-avoiding walks crossing a square
We study a restricted class of self-avoiding walks (SAW) which start at the
origin (0, 0), end at , and are entirely contained in the square on the square lattice . The number of distinct
walks is known to grow as . We estimate as well as obtaining strict upper and lower bounds,
We give exact results for the number of SAW of
length for and asymptotic results for .
We also consider the model in which a weight or {\em fugacity} is
associated with each step of the walk. This gives rise to a canonical model of
a phase transition. For the average length of a SAW grows as ,
while for it grows as
. Here is the growth constant of unconstrained SAW in . For we provide numerical evidence, but no proof, that the
average walk length grows as .
We also consider Hamiltonian walks under the same restriction. They are known
to grow as on the same lattice. We give
precise estimates for as well as upper and lower bounds, and prove that
Comment: 27 pages, 9 figures. Paper updated and reorganised following
refereein
Superfield Description of a Self-Dual Supergravity a la MacDowell-Mansouri
Using MacDowell-Mansouri theory, in this work, we investigate a superfield
description of the self-dual supergravity a la Ashtekar. We find that in order
to reproduce previous results on supersymmetric Ashtekar formalism, it is
necessary to properly combine the supersymmetric field-strength in the
Lagrangian. We extend our procedure to the case of supersymmetric Ashtekar
formalism in eight dimensions.Comment: 19 pages, Latex; section 6 improve
Molecular dynamics simulations of oxide memory resistors (memristors)
Reversible bipolar nano-switches that can be set and read electronically in a
solid-state two-terminal device are very promising for applications. We have
performed molecular-dynamics simulations that mimic systems with oxygen
vacancies interacting via realistic potentials and driven by an external bias
voltage. The competing short- and long-range interactions among charged mobile
vacancies lead to density fluctuations and short-range ordering, while
illustrating some aspects of observed experimental behavior, such as memristor
polarity inversion.Comment: 15 pages, 5 figure
Ideal hierarchical secret sharing schemes
Hierarchical secret sharing is among the most natural generalizations of threshold secret sharing, and it has attracted a lot of attention from the invention of secret sharing until nowadays. Several constructions of ideal hierarchical secret sharing schemes have been proposed, but it was not known what access structures admit such a scheme. We solve this problem by providing a natural definition for the family of the hierarchical access structures and, more importantly, by presenting a complete characterization of the ideal hierarchical access structures, that is, the ones admitting an ideal secret sharing scheme. Our characterization deals with the properties of the hierarchically minimal sets of the access structure, which are the minimal qualified sets whose participants are in the lowest possible levels in the hierarchy. By using our characterization, it can be efficiently checked whether any given hierarchical access structure that is defined by its hierarchically minimal sets is ideal. We use the well known connection between ideal secret sharing and matroids and, in particular, the fact that every ideal access structure is a matroid port. In addition, we use recent results on ideal multipartite access structures and the connection between multipartite matroids and integer polymatroids. We prove that every ideal hierarchical access structure is the port of a representable matroid and, more specifically, we prove that every ideal structure in this family admits ideal linear secret sharing schemes over fields of all characteristics. In addition, methods to construct such ideal schemes can be derived from the results in this paper and the aforementioned ones on ideal multipartite secret sharing. Finally, we use our results to find a new proof for the characterization of the ideal weighted threshold access structures that is simpler than the existing one.Peer ReviewedPostprint (author's final draft
Sustainability appraisal: Jack of all trades, master of none?
Sustainable development is a commonly quoted goal for decision making and supports a large number of other discourses. Sustainability appraisal has a stated goal of supporting decision making for sustainable development. We suggest that the inherent flexibility of sustainability appraisal facilitates outcomes that often do not adhere to the three goals enshrined in most definitions of sustainable development: economic growth, environmental protection and enhancement, and the wellbeing of the human population. Current practice is for sustainable development to be disenfranchised through the interpretation of sustainability, whereby the best alternative is good enough even when unsustainable. Practitioners must carefully and transparently review the frameworks applied during sustainability appraisal to ensure that outcomes will meet the three goals, rather than focusing on a discourse that emphasises one or more goals at the expense of the other(s)
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