Energy radiated from a fluctuating selfdual string

We compute the energy that is radiated from a fluctuating selfdual string in the large $N$ limit of $A_{N-1}$ theory using the AdS-CFT correspondence. We find that the radiated energy is given by a non-local expression integrated over the string world-sheet. We also make the corresponding computation for a charged string in six-dimensional classical electrodynamics, thereby generalizing the Larmor formula for the radiated energy from an accelerated point particle.Comment: 12 page

Computing topological invariants with one and two-matrix models

A generalization of the Kontsevich Airy-model allows one to compute the intersection numbers of the moduli space of p-spin curves. These models are deduced from averages of characteristic polynomials over Gaussian ensembles of random matrices in an external matrix source. After use of a duality, and of an appropriate tuning of the source, we obtain in a double scaling limit these intersection numbers as polynomials in p. One can then take the limit p to -1 which yields a matrix model for orbifold Euler characteristics. The generalization to a time-dependent matrix model, which is equivalent to a two-matrix model, may be treated along the same lines ; it also yields a logarithmic potential with additional vertices for general p.Comment: 30 pages, added references, changed conten

Kinetic Limit for Wave Propagation in a Random Medium

We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of order epsilon^(1/2). The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit epsilon to 0 the disorder averaged Wigner function on the kinetic scale, time and space of order epsilon^(-1), is governed by a linear Boltzmann equation.Comment: 71 pages, 3 figure

Development and validation of an algorithm to accurately identify atopic eczema patients in primary care electronic health records from the UK

Electronic health records hold great promise for clinical and epidemiologic research. Undertaking atopic eczema (AE) research using such data is challenging due to its episodic and heterogeneous nature. We sought to develop and validate a diagnostic algorithm that identifies AE cases based on codes used for electronic records used in the UK Health Improvement Network (THIN). We found that at least one of 5 diagnosis codes plus two treatment codes for any skin-directed therapy were likely to accurately identify patients with AE. To validate this algorithm, a questionnaire was sent to the physicians of 200 randomly selected children and adults. The primary outcome, the positive predictive value (PPV) for a physician-confirmed diagnosis of AE, was 86% (95%CI 80-91%). Additional criteria increased the PPV up to 95% but would miss up to 89% of individuals with physician-confirmed AE. The first and last entered diagnosis codes for individuals showed good agreement with the physician-confirmed age at onset and last disease activity; the mean difference was 0.8 years (95% CI -0.3,1.9) and -1.3 years respectively (95%CI -2.5, -0.1). A combination of diagnostic and prescription codes can be used to reliably estimate the diagnosis and duration of AE from the THIN primary care electronic health records in the UK

Multifractal characterisation of length sequences of coding and noncoding segments in a complete genome

The coding and noncoding length sequences constructed from a complete genome are characterised by multifractal analysis. The dimension spectrum $D_{q}$ and its derivative, the 'analogous' specific heat $C_{q}$, are calculated for the coding and noncoding length sequences of bacteria, where $q$ is the moment order of the partition sum of the sequences. From the shape of the $$ and $C_{q}$ curves, it is seen that there exists a clear difference between the coding/noncoding length sequences of all organisms considered and a completely random sequence. The complexity of noncoding length sequences is higher than that of coding length sequences for bacteria. Almost all $D_{q}$ curves for coding length sequences are flat, so their multifractality is small whereas almost all $D_{q}$ curves for noncoding length sequences are multifractal-like. We propose to characterise the bacteria according to the types of the $C_{q}$ curves of their noncoding length sequences.Comment: 15 pages with 5 figures, Latex, Accepted for publication in Physica

The partition function of interfaces from the Nambu-Goto effective string theory

We consider the Nambu-Goto bosonic string model as a description of the physics of interfaces. By using the standard covariant quantization of the bosonic string, we derive an exact expression for the partition function in dependence of the geometry of the interface. Our expression, obtained by operatorial methods, resums the loop expansion of the NG model in the "physical gauge" computed perturbatively by functional integral methods in the literature. Recently, very accurate Monte Carlo data for the interface free energy in the 3d Ising model became avaliable. Our proposed expression compares very well to the data for values of the area sufficiently large in terms of the inverse string tension. This pattern is expected on theoretical grounds and agrees with previous analyses of other observables in the Ising model.Comment: 28 pages, 4 figure

Electron correlation effects in a wide channel from the ν=1\nu =1 quantum Hall edge states

The spatial behavior of Landau levels (LLs) for the $nu=1$ quantum Hall regime at the edge of a wide channel is studied in a self-consistent way by using a generalized local density approximation proposed here. Both exchange interaction and strong electron correlations, due to edge states, are taken into account. They essentially modify the spatial behavior of the occupied lowest spin-up LL in comparison with that of the lowest spin-down LL, which is totally empty. The contrast in the spatial behavior can be attributed to a different effective one-electron lateral confining potentials for the spin-split LLs. Many-body effects on the spatially inhomogeneous spin-splitting are calculated within the screened Hartree-Fock approximation. It is shown that, far from the edges, the maximum activation energy is dominated by the gap between the Fermi level and the bottom of the spin-down LL, because the gap between the Fermi level and the spin-up LL is much larger. In other words, the maximum activation energy in the bulk of the channel corresponds to a highly asymmetric position of the Fermi level within the gap between spin-down and spin-up LLs in the bulk. We have also studied the renormalization of the edge-state group velocity due to electron correlations. The results of the present theory are in line with those suggested and reported by experiments on high quality samples.Comment: 9 pages, 4 figure

Algebraic analysis of a model of two-dimensional gravity

An algebraic analysis of the Hamiltonian formulation of the model two-dimensional gravity is performed. The crucial fact is an exact coincidence of the Poisson brackets algebra of the secondary constraints of this Hamiltonian formulation with the SO(2,1)-algebra. The eigenvectors of the canonical Hamiltonian $H_{c}$ are obtained and explicitly written in closed form.Comment: 21 pages, to appear in General Relativity and Gravitatio

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

High precision Monte Carlo simulations of interfaces in the three-dimensional Ising model: a comparison with the Nambu-Goto effective string model

Motivated by the recent progress in the effective string description of the interquark potential in lattice gauge theory, we study interfaces with periodic boundary conditions in the three-dimensional Ising model. Our Monte Carlo results for the associated free energy are compared with the next-to-leading order (NLO) approximation of the Nambu-Goto string model. We find clear evidence for the validity of the effective string model at the level of the NLO truncation.Comment: 20 pages, 1 figur