Soft matrix models and Chern-Simons partition functions

We study the properties of matrix models with soft confining potentials. Their precise mathematical characterization is that their weight function is not determined by its moments. We mainly rely on simple considerations based on orthogonal polynomials and the moment problem. In addition, some of these models are equivalent, by a simple mapping, to matrix models that appear in Chern-Simons theory. The models can be solved with q deformed orthogonal polynomials (Stieltjes-Wigert polynomials), and the deformation parameter turns out to be the usual $q$ parameter in Chern-Simons theory. In this way, we give a matrix model computation of the Chern-Simons partition function on $S^{3}$ and show that there are infinitely many matrix models with this partition function.Comment: 13 pages, 3 figure

Polynomial Solutions of Shcrodinger Equation with the Generalized Woods Saxon Potential

The bound state energy eigenvalues and the corresponding eigenfunctions of the generalized Woods Saxon potential are obtained in terms of the Jacobi polynomials. Nikiforov Uvarov method is used in the calculations. It is shown that the results are in a good agreement with the ones obtained before.Comment: 14 pages, 2 figures, submitted to Physical Review

Solution of a Generalized Stieltjes Problem

We present the exact solution for a set of nonlinear algebraic equations $\frac{1}{z_l}= \pi d + \frac{2 d}{n} \sum_{m \neq l} \frac{1}{z_l-z_m}$. These were encountered by us in a recent study of the low energy spectrum of the Heisenberg ferromagnetic chain \cite{dhar}. These equations are low $d$ (density) ``degenerations'' of more complicated transcendental equation of Bethe's Ansatz for a ferromagnet, but are interesting in themselves. They generalize, through a single parameter, the equations of Stieltjes, $x_l = \sum_{m \neq l} 1/(x_l-x_m)$, familiar from Random Matrix theory. It is shown that the solutions of these set of equations is given by the zeros of generalized associated Laguerre polynomials. These zeros are interesting, since they provide one of the few known cases where the location is along a nontrivial curve in the complex plane that is determined in this work. Using a ``Green's function'' and a saddle point technique we determine the asymptotic distribution of zeros.Comment: 19 pages, 4 figure

The defect variance of random spherical harmonics

The defect of a function $f:M\rightarrow \mathbb{R}$ is defined as the difference between the measure of the positive and negative regions. In this paper, we begin the analysis of the distribution of defect of random Gaussian spherical harmonics. By an easy argument, the defect is non-trivial only for even degree and the expected value always vanishes. Our principal result is obtaining the asymptotic shape of the defect variance, in the high frequency limit. As other geometric functionals of random eigenfunctions, the defect may be used as a tool to probe the statistical properties of spherical random fields, a topic of great interest for modern Cosmological data analysis.Comment: 19 page

Preliminary interpretation of Titan plasma interaction as observed by the Cassini Plasma Spectrometer: Comparisons with Voyager 1

The Cassini Plasma Spectrometer (CAPS) instrument observed the plasma environment at Titan during the Cassini orbiter's TA encounter on October 26, 2004. Titan was in Saturn's magnetosphere during the Voyager 1 flyby and also during the TA encounter. CAPS measurements from this encounter are compared with measurements made by the Voyager 1 Plasma Science Instrument (PLS). The comparisons focus on the composition and nature of ambient and pickup ions. They lead to: A) the major ion components of Saturn's magnetosphere in the vicinity of Titan are H+, H-2(+) and O+/CH4+ ions; B) finite gyroradius effects are apparent in ambient O+ ions as the result of their absorption by Titan's extended atmosphere; C) the principal pickup ions are composed of H+, H-2(+), N+/CH2+, CH4+, and N-2(+); D) the pickup ions are in narrow energy ranges; and E) there is clear evidence of the slowing down of background ions due to pickup ion mass loading

Operator product expansion of higher rank Wilson loops from D-branes and matrix models

In this paper we study correlation functions of circular Wilson loops in higher dimensional representations with chiral primary operators of N=4 super Yang-Mills theory. This is done using the recently established relation between higher rank Wilson loops in gauge theory and D-branes with electric fluxes in supergravity. We verify our results with a matrix model computation, finding perfect agreement in both the symmetric and the antisymmetric case.Comment: 28 pages, latex; v2: minor misprints corrected, references adde

Direct and inverse spectral transform for the relativistic Toda lattice and the connection with Laurent orthogonal polynomials

We introduce a spectral transform for the finite relativistic Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a non-symmetric generalized eigenvalue problem for a pair of bidiagonal matrices (L,M) to define the spectral transform for the RTL. The inverse spectral transform is described in terms of a terminating T-fraction. The generalized eigenvalues are constants of motion and the auxiliary spectral data have explicit time evolution. Using the connection with the theory of Laurent orthogonal polynomials, we study the long-time behaviour of the RTL. As in the case of the Toda lattice the matrix entries have asymptotic limits. We show that L tends to an upper Hessenberg matrix with the generalized eigenvalues sorted on the diagonal, while M tends to the identity matrix.Comment: 24 pages, 9 figure

Systematical Approach to the Exact Solution of the Dirac Equation for A Special Form of the Woods-Saxon Potential

Exact solution of the Dirac equation for a special form of the Woods-Saxon potential is obtained for the s-states. The energy eigenvalues and two-component spinor wave functions are derived by using a systematical method which is called as Nikiforov-Uvarov. It is seen that the energy eigenvalues strongly depend on the potential parameters. In addition, it is also shown that the non-relativistic limit can be reached easily and directly.Comment: 10 pages, no figures, submitted for Publicatio

Parental Access to Children's Raw Genomic Data in Canada: Legal Rights and Professional Responsibility

Children with rare and common diseases now undergo whole genome sequencing (WGS) in clinical and research contexts. Parents sometimes request access to their child's raw genomic data, to pursue their own analyses or for onward sharing with health professionals and researchers. These requests raise legal, ethical, and practical issues for professionals and parents alike. The advent of widespread WGS in pediatrics occurs in a context where privacy and data protection law remains focused on giving individuals control-oriented rights with respect to their personal information. Acting in their child's stead and in their best interests, parents are generally the ones who will be exercising these informational rights on behalf of the child. In this paper, we map the contours of parental authority to access their child's raw genomic data. We consider three use cases: hospital-based researchers, healthcare professionals acting in a clinical-diagnostic capacity, and “pure” academic researchers at a public institution. Our research seeks to answer two principal questions: Do parents have a right of access to their child's raw WGS data? If so, what are the limits of this right? Primarily focused on the laws of Ontario, Canada's most populous province, with a secondary focus on Canada's three other most populous provinces (Quebec, British Columbia, and Alberta) and the European Union, our principal findings include (1) parents have a general right of access to information about their children, but that the access right is more capacious in the clinical context than in the research context; (2) the right of access extends to personal data in raw form; (3) a consideration of the best interests of the child may materially limit the legal rights of parents to access data about their child; (4) the ability to exercise rights of access are transferred from parents to children when they gain decision-making capacity in both the clinical and research contexts, but with more nuance in the former. With these findings in mind, we argue that professional guidelines, which are concerned with obligations to interpret and return results, may assist in furthering a child's best interests in the context of legal access rights. We conclude by crafting recommendations for healthcare professionals in the clinical and research contexts when faced with a parental request for a child's raw genomic data

Solar-Wind Bulk Velocity Throughout the Inner Heliosphere from Multi-Spacecraft Measurements

We extrapolate solar-wind bulk velocity measurements for different in-ecliptic heliospheric positions by calculating the theoretical time lag between the locations. The solar-wind bulk velocity dataset is obtained from in-situ plasma measurements by STEREO A and B, SOHO, Venus Express, and Mars Express. During their simultaneous measurements between 2007 and 2009 we find typical solar activity minimum conditions. In order to validate our extrapolations of the STEREO A and B data, we compare them with simultaneous in-situ observations from the other spacecraft. This way of cross-calibration we obtain a measure for the goodness of our extrapolations over different heliospheric distances. We find that a reliable solar-wind dataset can be provided in case of a longitudinal separation less than 65 degrees. Moreover, we find that the time lag method assuming constant velocity is a good basis to extrapolate from measurements in Earth orbit to Venus or to Mars. These extrapolations might serve as a good solar-wind input information for planetary studies of magnetospheric and ionospheric processes. We additionally show how the stream-stream interactions in the ecliptic alter the bulk velocity during radial propagation