Infinite families of superintegrable systems separable in subgroup coordinates

A method is presented that makes it possible to embed a subgroup separable superintegrable system into an infinite family of systems that are integrable and exactly-solvable. It is shown that in two dimensional Euclidean or pseudo-Euclidean spaces the method also preserves superintegrability. Two infinite families of classical and quantum superintegrable systems are obtained in two-dimensional pseudo-Euclidean space whose classical trajectories and quantum eigenfunctions are investigated. In particular, the wave-functions are expressed in terms of Laguerre and generalized Bessel polynomials.Comment: 19 pages, 6 figure

An infinite family of superintegrable Hamiltonians with reflection in the plane

We introduce a new infinite class of superintegrable quantum systems in the plane. Their Hamiltonians involve reflection operators. The associated Schr\"odinger equations admit separation of variables in polar coordinates and are exactly solvable. The angular part of the wave function is expressed in terms of little -1 Jacobi polynomials. The spectra exhibit "accidental" degeneracies. The superintegrability of the model is proved using the recurrence relation approach. The (higher-order) constants of motion are constructed and the structure equations of the symmetry algebra obtained.Comment: 19 page

A superintegrable finite oscillator in two dimensions with SU(2) symmetry

A superintegrable finite model of the quantum isotropic oscillator in two dimensions is introduced. It is defined on a uniform lattice of triangular shape. The constants of the motion for the model form an SU(2) symmetry algebra. It is found that the dynamical difference eigenvalue equation can be written in terms of creation and annihilation operators. The wavefunctions of the Hamiltonian are expressed in terms of two known families of bivariate Krawtchouk polynomials; those of Rahman and those of Tratnik. These polynomials form bases for SU(2) irreducible representations. It is further shown that the pair of eigenvalue equations for each of these families are related to each other by an SU(2) automorphism. A finite model of the anisotropic oscillator that has wavefunctions expressed in terms of the same Rahman polynomials is also introduced. In the continuum limit, when the number of grid points goes to infinity, standard two-dimensional harmonic oscillators are obtained. The analysis provides the $N\rightarrow \infty$ limit of the bivariate Krawtchouk polynomials as a product of one-variable Hermite polynomials

Families of superintegrable Hamiltonians constructed from exceptional polynomials

We introduce a family of exactly-solvable two-dimensional Hamiltonians whose wave functions are given in terms of Laguerre and exceptional Jacobi polynomials. The Hamiltonians contain purely quantum terms which vanish in the classical limit leaving only a previously known family of superintegrable systems. Additional, higher-order integrals of motion are constructed from ladder operators for the considered orthogonal polynomials proving the quantum system to be superintegrable

TgPRELID, a Mitochondrial Protein Linked to Multidrug Resistance in the Parasite Toxoplasma gondii

New drugs to control infection with the protozoan parasite Toxoplasma gondii are needed as current treatments exert toxic side effects on patients. Approaches to develop novel compounds for drug development include screening of compound libraries and targeted inhibition of essential cellular pathways. We identified two distinct compounds that display inhibitory activity against the parasite's replicative stage: F3215-0002, which we previously identified during a compound library screen, and I-BET151, an inhibitor of bromodomains, the "reader" module of acetylated lysines. In independent studies, we sought to determine the targets of these two compounds using forward genetics, generating resistant mutants and identifying the determinants of resistance with comparative genome sequencing. Despite the dissimilarity of the two compounds, we recovered resistant mutants with nonsynonymous mutations in the same domain of the same gene, TGGT1_254250, which we found encodes a protein that localizes to the parasite mitochondrion (designated TgPRELID after the name of said domain). We found that mutants selected with one compound were cross resistant to the other compound, suggesting a common mechanism of resistance. To further support our hypothesis that TgPRELID mutations facilitate resistance to both I-BET151 and F3215-0002, CRISPR (clustered regularly interspaced short palindromic repeat)/CAS9-mediated mutation of TgPRELID directly led to increased F3215-0002 resistance. Finally, all resistance mutations clustered in the same subdomain of TgPRELID. These findings suggest that TgPRELID may encode a multidrug resistance factor or that I-BET151 and F3215-0002 have the same target(s) despite their distinct chemical structures. IMPORTANCE We report the discovery of TgPRELID, a previously uncharacterized mitochondrial protein linked to multidrug resistance in the parasite Toxoplasma gondii. Drug resistance remains a major problem in the battle against parasitic infection, and understanding how TgPRELID mutations augment resistance to multiple, distinct compounds will reveal needed insights into the development of new therapies for toxoplasmosis and other related parasitic diseases

Disease-associated genotypes of the commensal skin bacterium Staphylococcus epidermidis

Some of the most common infectious diseases are caused by bacteria that naturally colonise humans asymptomatically. Combating these opportunistic pathogens requires an understanding of the traits that differentiate infecting strains from harmless relatives. Staphylococcus epidermidis is carried asymptomatically on the skin and mucous membranes of virtually all humans but is a major cause of nosocomial infection associated with invasive procedures. Here we address the underlying evolutionary mechanisms of opportunistic pathogenicity by combining pangenome-wide association studies and laboratory microbiology to compare S. epidermidis from bloodstream and wound infections and asymptomatic carriage. We identify 61 genes containing infection-associated genetic elements (k-mers) that correlate with in vitro variation in known pathogenicity traits (biofilm formation, cell toxicity, interleukin-8 production, methicillin resistance). Horizontal gene transfer spreads these elements, allowing divergent clones to cause infection. Finally, Random Forest model prediction of disease status (carriage vs. infection) identifies pathogenicity elements in 415 S. epidermidis isolates with 80% accuracy, demonstrating the potential for identifying risk genotypes pre-operatively.Peer reviewe

Supersymmetric Quantum Mechanics with Reflections

We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its eigenfunctions are given in terms of little -1 Jacobi polynomials which obey an eigenvalue equation of Dunkl type and arise as a q-> -1 limit of the little q-Jacobi polynomials. Intertwining operators connecting the wave functions of extended Scarf I potentials with different parameters are presented.Comment: 17 page

Thyroid-stimulating hormone and free thyroxine fail to predict the severity and clinical course of hyperemesis gravidarum : A prospective cohort study

Funding information: This prospective cohort study was supported by a research grant from North West Hospital Group, Alkmaar, the Netherlands (Grant number: 2013T085) and by a research grant from the Amsterdam Reproduction and Development (AR&D) Research Institute, Amsterdam UMC, the Netherlands (Project number: 23346). ACKNOWLEDGMENTS We thank Dr. J.P. Bestwick (employed at Queen Mary University of London, London, UK) and Professor Dr. J.H. Lazarus (employed at Cardiff School of Medicine, Cardiff, UK) for providing TSH medians from their study in the UK. Dr. J.P. Bestwick and Professor Dr. Lazarus have nothing to disclose.Peer reviewedPublisher PD

Recommendations for defining preventable HIV-related mortality for public health monitoring in the era of Getting to Zero: an expert consensus

Getting to Zero is a commonly cited strategic aim to reduce mortality due to both HIV and avoidable deaths among people with HIV. However, no clear definitions are attached to these aims with regard to what constitutes HIV-related or preventable mortality, and their ambition is limited. This Position Paper presents consensus recommendations to define preventable HIV-related mortality for a pragmatic approach to public health monitoring by use of national HIV surveillance data. These recommendations were informed by a comprehensive literature review and agreed by 42 international experts, including clinicians, public health professionals, researchers, commissioners, and community representatives. By applying the recommendations to 2019 national HIV surveillance data from the UK, we show that 30% of deaths among people with HIV were HIV-related or possibly HIV-related, and at least 63% of these deaths were preventable or potentially preventable. The application of these recommendations by health authorities will ensure consistent monitoring of HIV elimination targets and allow for the identification of inequalities and areas for intervention

Genetic association study of QT interval highlights role for calcium signaling pathways in myocardial repolarization.

The QT interval, an electrocardiographic measure reflecting myocardial repolarization, is a heritable trait. QT prolongation is a risk factor for ventricular arrhythmias and sudden cardiac death (SCD) and could indicate the presence of the potentially lethal mendelian long-QT syndrome (LQTS). Using a genome-wide association and replication study in up to 100,000 individuals, we identified 35 common variant loci associated with QT interval that collectively explain ∼8-10% of QT-interval variation and highlight the importance of calcium regulation in myocardial repolarization. Rare variant analysis of 6 new QT interval-associated loci in 298 unrelated probands with LQTS identified coding variants not found in controls but of uncertain causality and therefore requiring validation. Several newly identified loci encode proteins that physically interact with other recognized repolarization proteins. Our integration of common variant association, expression and orthogonal protein-protein interaction screens provides new insights into cardiac electrophysiology and identifies new candidate genes for ventricular arrhythmias, LQTS and SCD