20,067 research outputs found
Spacetime algebraic skeleton
The cosmological constant Lambda, which has seemingly dominated the primaeval
Universe evolution and to which recent data attribute a significant
present-time value, is shown to have an algebraic content: it is essentially an
eigenvalue of a Casimir invariant of the Lorentz group which acts on every
tangent space. This is found in the context of de Sitter spacetimes but, as
every spacetime is a 4-manifold with Minkowski tangent spaces, the result
suggests the existence of a "skeleton" algebraic structure underlying the
geometry of general physical spacetimes. Different spacetimes come from the
"fleshening" of that structure by different tetrad fields. Tetrad fields, which
provide the interface between spacetime proper and its tangent spaces, exhibit
to the most the fundamental role of the Lorentz group in Riemannian spacetimes,
a role which is obscured in the more usual metric formalism.Comment: 13 page
Directed cycles and related structures in random graphs: II--Dynamic properties
We study directed random graphs (random graphs whose edges are directed) as
they evolve in discrete time by the addition of nodes and edges. For two
distinct evolution strategies, one that forces the graph to a condition of near
acyclicity at all times and another that allows the appearance of nontrivial
directed cycles, we provide analytic and simulation results related to the
distributions of degrees. Within the latter strategy, in particular, we
investigate the appearance and behavior of the strong components that were our
subject in the first part of this study.Comment: submitted to Physica
Network conduciveness with application to the graph-coloring and independent-set optimization transitions
We introduce the notion of a network's conduciveness, a probabilistically
interpretable measure of how the network's structure allows it to be conducive
to roaming agents, in certain conditions, from one portion of the network to
another. We exemplify its use through an application to the two problems in
combinatorial optimization that, given an undirected graph, ask that its
so-called chromatic and independence numbers be found. Though NP-hard, when
solved on sequences of expanding random graphs there appear marked transitions
at which optimal solutions can be obtained substantially more easily than right
before them. We demonstrate that these phenomena can be understood by resorting
to the network that represents the solution space of the problems for each
graph and examining its conduciveness between the non-optimal solutions and the
optimal ones. At the said transitions, this network becomes strikingly more
conducive in the direction of the optimal solutions than it was just before
them, while at the same time becoming less conducive in the opposite direction.
We believe that, besides becoming useful also in other areas in which network
theory has a role to play, network conduciveness may become instrumental in
helping clarify further issues related to NP-hardness that remain poorly
understood
A Statistical Strategy for the Sunyaev-Zel'dovich Effect's Cluster Data
We present a statistical strategy for the efficient determination of the
cluster luminosity function from the Sunyaev-Zel'dovich (SZ) effects survey. To
determine the cluster luminosity function from the noise contaminated SZ map,
we first define the zeroth-order cluster luminosity function as a discrepancy
between the measured peak number density of the SZ map and the mean number
density of noise. Then we demonstrate that the noise contamination effects can
be removed by the stabilized deconvolution of the zeroth-order cluster
luminosity function with the one-dimensional Gaussian distribution. We test
this analysis technique against Monte-Carlo simulations, and find that it works
quite well especially in the medium amplitude range where the conventional
cluster identification method based on the threshold cut-off usually fails.Comment: final version, accepted by ApJ Letter
Fundamental Plane of Sunyaev-Zeldovich clusters
Sunyaev-Zel'dovich (SZ) cluster surveys are considered among the most
promising methods for probing dark energy up to large redshifts. However, their
premise is hinged upon an accurate mass-observable relationship, which could be
affected by the (rather poorly understood) physics of the intracluster gas. In
this letter, using a semi-analytic model of the intracluster gas that
accommodates various theoretical uncertainties, I develop a Fundamental Plane
relationship between the observed size, thermal energy, and mass of galaxy
clusters. In particular, I find that M ~ (Y_{SZ}/R_{SZ,2})^{3/4}, where M is
the mass, Y_{SZ} is the total SZ flux or thermal energy, and R_{SZ,2} is the SZ
half-light radius of the cluster. I first show that, within this model, using
the Fundamental Plane relationship reduces the (systematic+random) errors in
mass estimates to 14%, from 22% for a simple mass-flux relationship. Since
measurement of the cluster sizes is an inevitable part of observing the SZ
clusters, the Fundamental Plane relationship can be used to reduce the error of
the cluster mass estimates by ~ 34%, improving the accuracy of the resulting
cosmological constraints without any extra cost. I then argue why our
Fundamental Plane is distinctly different from the virial relationship that one
may naively expect between the cluster parameters. Finally, I argue that while
including more details of the observed SZ profile cannot significantly improve
the accuracy of mass estimates, a better understanding of the impact of
non-gravitational heating/cooling processes on the outskirts of the
intracluster medium (apart from external calibrations) might be the best way to
reduce these errors.Comment: 5 pages, 1 figure, added an analytic derivation of the Fundametal
Plane relation (which is distinctly different from the virial relation),
submitted to Ap
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