A model for the continuous q-ultraspherical polynomials

We provide an algebraic interpretation for two classes of continuous $q$-polynomials. Rogers' continuous $q$-Hermite polynomials and continuous $q$-ultraspherical polynomials are shown to realize, respectively, bases for representation spaces of the $q$-Heisenberg algebra and a $q$-deformation of the Euclidean algebra in these dimensions. A generating function for the continuous $q$-Hermite polynomials and a $q$-analog of the Fourier-Gegenbauer expansion are naturally obtained from these models

Dipolar Dark Matter and Dark Energy

In previous work [L. Blanchet and A. Le Tiec, Phys. Rev. D 78, 024031 (2008)], a model of dark matter and dark energy based on the concept of gravitational polarization was investigated. This model was shown to recover the concordance cosmological scenario (Lambda-CDM) at cosmological scales, and the phenomenology of the modified Newtonian dynamics (MOND) at galactic scales. In this article we prove that the model can be formulated with a simple and physically meaningful matter action in general relativity. We also provide alternative derivations of the main results of the model, and some details on the variation of the action.Comment: 11 pages, 2 figures; minor stylistic corrections, added references, added appendix; to appear in Phys. Rev.

Building Data-Driven Pathways From Routinely Collected Hospital Data:A Case Study on Prostate Cancer

Background: Routinely collected data in hospitals is complex, typically heterogeneous, and scattered across multiple Hospital Information Systems (HIS). This big data, created as a byproduct of health care activities, has the potential to provide a better understanding of diseases, unearth hidden patterns, and improve services and cost. The extent and uses of such data rely on its quality, which is not consistently checked, nor fully understood. Nevertheless, using routine data for the construction of data-driven clinical pathways, describing processes and trends, is a key topic receiving increasing attention in the literature. Traditional algorithms do not cope well with unstructured processes or data, and do not produce clinically meaningful visualizations. Supporting systems that provide additional information, context, and quality assurance inspection are needed. Objective: The objective of the study is to explore how routine hospital data can be used to develop data-driven pathways that describe the journeys that patients take through care, and their potential uses in biomedical research; it proposes a framework for the construction, quality assessment, and visualization of patient pathways for clinical studies and decision support using a case study on prostate cancer. Methods: Data pertaining to prostate cancer patients were extracted from a large UK hospital from eight different HIS, validated, and complemented with information from the local cancer registry. Data-driven pathways were built for each of the 1904 patients and an expert knowledge base, containing rules on the prostate cancer biomarker, was used to assess the completeness and utility of the pathways for a specific clinical study. Software components were built to provide meaningful visualizations for the constructed pathways. Results: The proposed framework and pathway formalism enable the summarization, visualization, and querying of complex patient-centric clinical information, as well as the computation of quality indicators and dimensions. A novel graphical representation of the pathways allows the synthesis of such information. Conclusions: Clinical pathways built from routinely collected hospital data can unearth information about patients and diseases that may otherwise be unavailable or overlooked in hospitals. Data-driven clinical pathways allow for heterogeneous data (ie, semistructured and unstructured data) to be collated over a unified data model and for data quality dimensions to be assessed. This work has enabled further research on prostate cancer and its biomarkers, and on the development and application of methods to mine, compare, analyze, and visualize pathways constructed from routine data. This is an important development for the reuse of big data in hospitals

Uniqueness results for an ODE related to a generalized Ginzburg-Landau model for liquid crystals

We study a singular nonlinear ordinary differential equation on intervals {[}0, R) with R <= +infinity, motivated by the Ginzburg-Landau models in superconductivity and Landau-de Gennes models in liquid crystals. We prove existence and uniqueness of positive solutions under general assumptions on the nonlinearity. Further uniqueness results for sign-changing solutions are obtained for a physically relevant class of nonlinearities. Moreover, we prove a number of fine qualitative properties of the solution that are important for the study of energetic stability

A unified electrostatic and cavitation model for first-principles molecular dynamics in solution

The electrostatic continuum solvent model developed by Fattebert and Gygi is combined with a first-principles formulation of the cavitation energy based on a natural quantum-mechanical definition for the surface of a solute. Despite its simplicity, the cavitation contribution calculated by this approach is found to be in remarkable agreement with that obtained by more complex algorithms relying on a large set of parameters. Our model allows for very efficient Car-Parrinello simulations of finite or extended systems in solution, and demonstrates a level of accuracy as good as that of established quantum-chemistry continuum solvent methods. We apply this approach to the study of tetracyanoethylene dimers in dichloromethane, providing valuable structural and dynamical insights on the dimerization phenomenon

Nonlinear dynamics of phase separation in thin films

We present a long-wavelength approximation to the Navier-Stokes Cahn-Hilliard equations to describe phase separation in thin films. The equations we derive underscore the coupled behaviour of free-surface variations and phase separation. We introduce a repulsive substrate-film interaction potential and analyse the resulting fourth-order equations by constructing a Lyapunov functional, which, combined with the regularizing repulsive potential, gives rise to a positive lower bound for the free-surface height. The value of this lower bound depends on the parameters of the problem, a result which we compare with numerical simulations. While the theoretical lower bound is an obstacle to the rupture of a film that initially is everywhere of finite height, it is not sufficiently sharp to represent accurately the parametric dependence of the observed dips or `valleys' in free-surface height. We observe these valleys across zones where the concentration of the binary mixture changes sharply, indicating the formation of bubbles. Finally, we carry out numerical simulations without the repulsive interaction, and find that the film ruptures in finite time, while the gradient of the Cahn--Hilliard concentration develops a singularity.Comment: 26 pages, 20 figures, PDFLaTeX with RevTeX4 macros. A thorough analysis of the equations is presented in arXiv:0805.103

Genomic prediction and quantitative trait locus discovery in a cassava training population constructed from multiple breeding stages

Open Access Article; Published online: 11 Dec 2019Assembly of a training population (TP) is an important component of effective genomic selection‐based breeding programs. In this study, we examined the power of diverse germplasm assembled from two cassava (Manihot esculenta Crantz) breeding programs in Tanzania at different breeding stages to predict traits and discover quantitative trait loci (QTL). This is the first genomic selection and genome‐wide association study (GWAS) on Tanzanian cassava data. We detected QTL associated with cassava mosaic disease (CMD) resistance on chromosomes 12 and 16; QTL conferring resistance to cassava brown streak disease (CBSD) on chromosomes 9 and 11; and QTL on chromosomes 2, 3, 8, and 10 associated with resistance to CBSD for root necrosis. We detected a QTL on chromosome 4 and two QTL on chromosome 12 conferring dual resistance to CMD and CBSD. The use of clones in the same stage to construct TPs provided higher trait prediction accuracy than TPs with a mixture of clones from multiple breeding stages. Moreover, clones in the early breeding stage provided more reliable trait prediction accuracy and are better candidates for constructing a TP. Although larger TP sizes have been associated with improved accuracy, in this study, adding clones from Kibaha to those from Ukiriguru and vice versa did not improve the prediction accuracy of either population. Including the Ugandan TP in either population did not improve trait prediction accuracy. This study applied genomic prediction to understand the implications of constructing TP from clones at different breeding stages pooled from different locations on trait accuracy

Higher-order spin effects in the dynamics of compact binaries II. Radiation field

Motivated by the search for gravitational waves emitted by binary black holes, we investigate the gravitational radiation field of point particles with spins within the framework of the multipolar-post-Newtonian wave generation formalism. We compute: (i) the spin-orbit (SO) coupling effects in the binary's mass and current quadrupole moments one post-Newtonian (1PN) order beyond the dominant effect, (ii) the SO contributions in the gravitational-wave energy flux and (iii) the secular evolution of the binary's orbital phase up to 2.5PN order. Crucial ingredients for obtaining the 2.5PN contribution in the orbital phase are the binary's energy and the spin precession equations, derived in paper I of this series. These results provide more accurate gravitational-wave templates to be used in the data analysis of rapidly rotating Kerr-type black-hole binaries with the ground-based detectors LIGO, Virgo, GEO 600 and TAMA300, and the space-based detector LISA.Comment: includes the correction of an erratum to be published in Phys. Rev.

A discrete invitation to quantum filtering and feedback control

The engineering and control of devices at the quantum-mechanical level--such as those consisting of small numbers of atoms and photons--is a delicate business. The fundamental uncertainty that is inherently present at this scale manifests itself in the unavoidable presence of noise, making this a novel field of application for stochastic estimation and control theory. In this expository paper we demonstrate estimation and feedback control of quantum mechanical systems in what is essentially a noncommutative version of the binomial model that is popular in mathematical finance. The model is extremely rich and allows a full development of the theory, while remaining completely within the setting of finite-dimensional Hilbert spaces (thus avoiding the technical complications of the continuous theory). We introduce discretized models of an atom in interaction with the electromagnetic field, obtain filtering equations for photon counting and homodyne detection, and solve a stochastic control problem using dynamic programming and Lyapunov function methods.Comment: 76 pages, 12 figures. A PDF file with high resolution figures can be found at http://minty.caltech.edu/papers.ph