2,815 research outputs found
Assessing the painful, uninflamed eye in primary care
We acknowledge the important contributions of Professor Amada J Lee, University of Aberdeen, Division of Statistics, for assistance with analysing the data from the patient survey. We thank Kamran Khan, Oliver Chadwick, and Paul Chua, trainee ophthalmologists, NHS Grampian, for providing the clinical images. Contributors: LK contributed to the design of the study, the survey of patients, and writing the paper. JVF contributed to the design of the study and writing the paper. ADD contributed to the design of the study, the survey of the patients, and writing the paper. JVF is guarantor for the paper.Peer reviewedPublisher PD
Autoimmunity, Autoinflammation, and Infection in Uveitis
Funding/Support: No funding or grant support. Financial Disclosures: John V. Forrester has received an honorarium for lecturing from Janssen (London, UK). Lucia Kuffova has undertaken consultancy work for Abbvie (London, UK). Andrew D. Dick has undertaken consultancy work for Abbvie (London, UK), Roche (London, UK), and Genentech (London, UK) and has received honoraria from Janssen (London, UK) and Abbvie (London, UK). The authors attest that they meet the current ICMJE criteria for authorship.Peer reviewedPublisher PD
Derivation of an eigenvalue probability density function relating to the Poincare disk
A result of Zyczkowski and Sommers [J.Phys.A, 33, 2045--2057 (2000)] gives
the eigenvalue probability density function for the top N x N sub-block of a
Haar distributed matrix from U(N+n). In the case n \ge N, we rederive this
result, starting from knowledge of the distribution of the sub-blocks,
introducing the Schur decomposition, and integrating over all variables except
the eigenvalues. The integration is done by identifying a recursive structure
which reduces the dimension. This approach is inspired by an analogous approach
which has been recently applied to determine the eigenvalue probability density
function for random matrices A^{-1} B, where A and B are random matrices with
entries standard complex normals. We relate the eigenvalue distribution of the
sub-blocks to a many body quantum state, and to the one-component plasma, on
the pseudosphere.Comment: 11 pages; To appear in J.Phys
Analytic solutions of the 1D finite coupling delta function Bose gas
An intensive study for both the weak coupling and strong coupling limits of
the ground state properties of this classic system is presented. Detailed
results for specific values of finite are given and from them results for
general are determined. We focus on the density matrix and concomitantly
its Fourier transform, the occupation numbers, along with the pair correlation
function and concomitantly its Fourier transform, the structure factor. These
are the signature quantities of the Bose gas. One specific result is that for
weak coupling a rational polynomial structure holds despite the transcendental
nature of the Bethe equations. All these new results are predicated on the
Bethe ansatz and are built upon the seminal works of the past.Comment: 23 pages, 0 figures, uses rotate.sty. A few lines added. Accepted by
Phys. Rev.
Growth models, random matrices and Painleve transcendents
The Hammersley process relates to the statistical properties of the maximum
length of all up/right paths connecting random points of a given density in the
unit square from (0,0) to (1,1). This process can also be interpreted in terms
of the height of the polynuclear growth model, or the length of the longest
increasing subsequence in a random permutation. The cumulative distribution of
the longest path length can be written in terms of an average over the unitary
group. Versions of the Hammersley process in which the points are constrained
to have certain symmetries of the square allow similar formulas. The derivation
of these formulas is reviewed. Generalizing the original model to have point
sources along two boundaries of the square, and appropriately scaling the
parameters gives a model in the KPZ universality class. Following works of Baik
and Rains, and Pr\"ahofer and Spohn, we review the calculation of the scaled
cumulative distribution, in which a particular Painlev\'e II transcendent plays
a prominent role.Comment: 27 pages, 5 figure
The Emergence of Superconducting Systems in Anti-de Sitter Space
In this article, we investigate the mathematical relationship between a (3+1)
dimensional gravity model inside Anti-de Sitter space , and a (2+1)
dimensional superconducting system on the asymptotically flat boundary of (in the absence of gravity). We consider a simple case of the Type II
superconducting model (in terms of Ginzburg-Landau theory) with an external
perpendicular magnetic field . An interaction potential is introduced
within the Lagrangian system. This provides more flexibility within the model,
when the superconducting system is close to the transition temperature .
Overall, our result demonstrates that the two Ginzburg-Landau differential
equations can be directly deduced from Einstein's theory of general relativity.Comment: 10 pages, 2 figure
Random Matrix Theory and the Sixth Painlev\'e Equation
A feature of certain ensembles of random matrices is that the corresponding
measure is invariant under conjugation by unitary matrices. Study of such
ensembles realised by matrices with Gaussian entries leads to statistical
quantities related to the eigenspectrum, such as the distribution of the
largest eigenvalue, which can be expressed as multidimensional integrals or
equivalently as determinants. These distributions are well known to be
-functions for Painlev\'e systems, allowing for the former to be
characterised as the solution of certain nonlinear equations. We consider the
random matrix ensembles for which the nonlinear equation is the form
of \PVI. Known results are reviewed, as is their implication by way of series
expansions for the distributions. New results are given for the boundary
conditions in the neighbourhood of the fixed singularities at of
\PVI displayed by a generalisation of the generating function for the
distributions. The structure of these expansions is related to Jimbo's general
expansions for the -function of \PVI in the neighbourhood of its
fixed singularities, and this theory is itself put in its context of the linear
isomonodromy problem relating to \PVI.Comment: Dedicated to the centenary of the publication of the Painlev\'e VI
equation in the Comptes Rendus de l'Academie des Sciences de Paris by Richard
Fuchs in 190
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