1,686 research outputs found
Density matrix reconstruction from displaced photon number distributions
We consider state reconstruction from the measurement statistics of phase
space observables generated by photon number states. The results are obtained
by inverting certain infinite matrices. In particular, we obtain reconstruction
formulas, each of which involves only a single phase space observable.Comment: 19 page
The structure of typical clusters in large sparse random configurations
The initial purpose of this work is to provide a probabilistic explanation of
a recent result on a version of Smoluchowski's coagulation equations in which
the number of aggregations is limited. The latter models the deterministic
evolution of concentrations of particles in a medium where particles coalesce
pairwise as time passes and each particle can only perform a given number of
aggregations. Under appropriate assumptions, the concentrations of particles
converge as time tends to infinity to some measure which bears a striking
resemblance with the distribution of the total population of a Galton-Watson
process started from two ancestors. Roughly speaking, the configuration model
is a stochastic construction which aims at producing a typical graph on a set
of vertices with pre-described degrees. Specifically, one attaches to each
vertex a certain number of stubs, and then join pairwise the stubs uniformly at
random to create edges between vertices. In this work, we use the configuration
model as the stochastic counterpart of Smoluchowski's coagulation equations
with limited aggregations. We establish a hydrodynamical type limit theorem for
the empirical measure of the shapes of clusters in the configuration model when
the number of vertices tends to . The limit is given in terms of the
distribution of a Galton-Watson process started with two ancestors
Risk, precaution and science: towards a more constructive policy debate. Talking point on the precautionary principle
Few issues in contemporary risk policy are as momentous or contentious as the precautionary principle. Since it first emerged in German environmental policy, it has been championed by environmentalists and consumer protection groups, and resisted by the industries they oppose (Raffensperger & Tickner, 1999). Various versions of the principle now proliferate across different national and international jurisdictions and policy areas (Fisher, 2002). From a guiding theme in European Commission (EC) environmental policy, it has become a general principle of EC law (CEC, 2000; Vos & Wendler, 2006). Its influence has extended from the regulation of environmental, technological and health risks to the wider governance of science, innovation and trade (O'Riordan & Cameron, 1994)
Representations of sport in the revolutionary socialist press in Britain, 1988–2012
This paper considers how sport presents a dualism to those on the far left of the political spectrum. A long-standing, passionate debate has existed on the contradictory role played by sport, polarised between those who reject it as a bourgeois capitalist plague and those who argue for its reclamation and reformation. A case study is offered of a political party that has consistently used revolutionary Marxism as the basis for its activity and how this party, the largest in Britain, addresses sport in its publications. The study draws on empirical data to illustrate this debate by reporting findings from three socialist publications. When sport did feature it was often in relation to high profile sporting events with a critical tone adopted and typically focused on issues of commodification, exploitation and alienation of athletes and supporters. However, readers’ letters, printed in the same publications, revealed how this interpretation was not universally accepted, thus illustrating the contradictory nature of sport for those on the far left
Exact eigenspectrum of the symmetric simple exclusion process on the complete, complete bipartite, and related graphs
We show that the infinitesimal generator of the symmetric simple exclusion
process, recast as a quantum spin-1/2 ferromagnetic Heisenberg model, can be
solved by elementary techniques on the complete, complete bipartite, and
related multipartite graphs. Some of the resulting infinitesimal generators are
formally identical to homogeneous as well as mixed higher spins models. The
degeneracies of the eigenspectra are described in detail, and the
Clebsch-Gordan machinery needed to deal with arbitrary spin-s representations
of the SU(2) is briefly developed. We mention in passing how our results fit
within the related questions of a ferromagnetic ordering of energy levels and a
conjecture according to which the spectral gaps of the random walk and the
interchange process on finite simple graphs must be equal.Comment: Final version as published, 19 pages, 4 figures, 40 references given
in full forma
The Pure Virtual Braid Group Is Quadratic
If an augmented algebra K over Q is filtered by powers of its augmentation
ideal I, the associated graded algebra grK need not in general be quadratic:
although it is generated in degree 1, its relations may not be generated by
homogeneous relations of degree 2. In this paper we give a sufficient criterion
(called the PVH Criterion) for grK to be quadratic. When K is the group algebra
of a group G, quadraticity is known to be equivalent to the existence of a (not
necessarily homomorphic) universal finite type invariant for G. Thus the PVH
Criterion also implies the existence of such a universal finite type invariant
for the group G. We apply the PVH Criterion to the group algebra of the pure
virtual braid group (also known as the quasi-triangular group), and show that
the corresponding associated graded algebra is quadratic, and hence that these
groups have a (not necessarily homomorphic) universal finite type invariant.Comment: 53 pages, 15 figures. Some clarifications added and inaccuracies
corrected, reflecting suggestions made by the referee of the published
version of the pape
The information sources and journals consulted or read by UK paediatricians to inform their clinical practice and those which they consider important: a questionnaire survey
Background: Implementation of health research findings is important for medicine to be
evidence-based. Previous studies have found variation in the information sources thought to be of greatest importance to clinicians but publication in peer-reviewed journals is the traditional route for dissemination of research findings. There is debate about whether the impact made on clinicians should be considered as part of the evaluation of research outputs. We aimed to determine first which information sources are generally most consulted by paediatricians to inform their clinical practice, and which sources they considered most important, and second, how many and which peer-reviewed journals they read.
Methods: We enquired, by questionnaire survey, about the information sources and academic
journals that UK medical paediatric specialists generally consulted, attended or read and
considered important to their clinical practice.
Results: The same three information sources – professional meetings & conferences, peerreviewed
journals and medical colleagues – were, overall, the most consulted or attended and ranked the most important. No one information source was found to be of greatest importance to all groups of paediatricians. Journals were widely read by all groups, but the proportion ranking them first in importance as an information source ranged from 10% to 46%. The number of journals read varied between the groups, but Archives of Disease in Childhood and BMJ were the most read
journals in all groups. Six out of the seven journals previously identified as containing best paediatric evidence are the most widely read overall by UK paediatricians, however, only the two most prominent are widely read by those based in the community.
Conclusion: No one information source is dominant, therefore a variety of approaches to
Continuing Professional Development and the dissemination of research findings to paediatricians should be used. Journals are an important information source. A small number of key ones can be identified and such analysis could provide valuable additional input into the evaluation of clinical research outputs
Crossover effects in a discrete deposition model with Kardar-Parisi-Zhang scaling
We simulated a growth model in 1+1 dimensions in which particles are
aggregated according to the rules of ballistic deposition with probability p or
according to the rules of random deposition with surface relaxation (Family
model) with probability 1-p. For any p>0, this system is in the
Kardar-Parisi-Zhang (KPZ) universality class, but it presents a slow crossover
from the Edwards-Wilkinson class (EW) for small p. From the scaling of the
growth velocity, the parameter p is connected to the coefficient of the
nonlinear term of the KPZ equation, lambda, giving lambda ~ p^gamma, with gamma
= 2.1 +- 0.2. Our numerical results confirm the interface width scaling in the
growth regime as W ~ lambda^beta t^beta, and the scaling of the saturation time
as tau ~ lambda^(-1) L^z, with the expected exponents beta =1/3 and z=3/2 and
strong corrections to scaling for small lambda. This picture is consistent with
a crossover time from EW to KPZ growth in the form t_c ~ lambda^(-4) ~ p^(-8),
in agreement with scaling theories and renormalization group analysis. Some
consequences of the slow crossover in this problem are discussed and may help
investigations of more complex models.Comment: 16 pages, 7 figures; to appear in Phys. Rev.
Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals
Yor's generalized meander is a temporally inhomogeneous modification of the
-dimensional Bessel process with , in which the
inhomogeneity is indexed by . We introduce the
non-colliding particle systems of the generalized meanders and prove that they
are the Pfaffian processes, in the sense that any multitime correlation
function is given by a Pfaffian. In the infinite particle limit, we show that
the elements of matrix kernels of the obtained infinite Pfaffian processes are
generally expressed by the Riemann-Liouville differintegrals of functions
comprising the Bessel functions used in the fractional calculus,
where orders of differintegration are determined by . As special
cases of the two parameters , the present infinite systems
include the quaternion determinantal processes studied by Forrester, Nagao and
Honner and by Nagao, which exhibit the temporal transitions between the
universality classes of random matrix theory.Comment: LaTeX, 35 pages, v3: The argument given in Section 3.2 was
simplified. Minor corrections were mad
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