Third order superintegrable systems separating in polar coordinates

A complete classification is presented of quantum and classical superintegrable systems in $E_2$ that allow the separation of variables in polar coordinates and admit an additional integral of motion of order three in the momentum. New quantum superintegrable systems are discovered for which the potential is expressed in terms of the sixth Painlev\'e transcendent or in terms of the Weierstrass elliptic function

An infinite family of superintegrable systems from higher order ladder operators and supersymmetry

We will discuss how we can obtain new quantum superintegrable Hamiltonians allowing the separation of variables in Cartesian coordinates with higher order integrals of motion from ladder operators. We will discuss also how higher order supersymmetric quantum mechanics can be used to obtain systems with higher order ladder operators and their polynomial Heisenberg algebra. We will present a new family of superintegrable systems involving the fifth Painleve transcendent which possess fourth order ladder operators constructed from second order supersymmetric quantum mechanics. We present the polynomial algebra of this family of superintegrable systems.Comment: 8 pages, presented at ICGTMP 28, accepted for j.conf.serie

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

Synoptic Hα Full-Disk Observations of the Sun from Big Bear Solar Observatory – I. Instrumentation, Image Processing, Data Products, and First Results

The Big Bear Solar Observatory (BBSO) has a long tradition of synoptic full-disk observations. Synoptic observations of contrast enhanced full-disk images in the Ca ii K-line have been used with great success to reproduce the H i Lα irradiance variability observed with the Upper Atmosphere Research Satellite (UARS). Recent improvements in data calibration procedures and image- processing techniques enable us now to provide contrast enhanced Hα full-disk images with a spatial resolution of approximately 2′′ and a temporal resolution of up to 3 frames min−1. In this first paper in a series, we describe the instruments, the data calibration procedures, and the image-processing techniques used to obtain our daily Hα full-disk observations. We also present the final data products such as low- and high-contrast images, and Carrington rotation charts. A time series of an erupting mini-filament further illustrates the quality of our Hα full-disk observations and motivate one of the future research projects. This lays a solid foundation for our subsequent studies of solar activity and chromospheric fine structures. The high quality and the sunrise- to-sunset operation of the Hα full-disk observations presented in this paper make them an ideal choice to study statistical properties of mini-filament eruptions, chromospheric differential rotation, and meridional flows within the chromosphere, as well as the evolution of active regions, filaments, flares, and prominences

Superintegrability and higher order polynomial algebras II

In an earlier article, we presented a method to obtain integrals of motion and polynomial algebras for a class of two-dimensional superintegrable systems from creation and annihilation operators. We discuss the general case and present its polynomial algebra. We will show how this polynomial algebra can be directly realized as a deformed oscillator algebra. This particular algebraic structure allows to find the unitary representations and the corresponding energy spectrum. We apply this construction to a family of caged anisotropic oscillators. The method can be used to generate new superintegrable systems with higher order integrals. We obtain new superintegrable systems involving the fourth Painleve transcendent and present their integrals of motion and polynomial algebras.Comment: 11 page

ExELS: an exoplanet legacy science proposal for the ESA Euclid mission. II. Hot exoplanets and sub-stellar systems

The Exoplanet Euclid Legacy Survey (ExELS) proposes to determine the frequency of cold exoplanets down to Earth mass from host separations of ~1 AU out to the free-floating regime by detecting microlensing events in Galactic Bulge. We show that ExELS can also detect large numbers of hot, transiting exoplanets in the same population. The combined microlensing+transit survey would allow the first self-consistent estimate of the relative frequencies of hot and cold sub-stellar companions, reducing biases in comparing "near-field" radial velocity and transiting exoplanets with "far-field" microlensing exoplanets. The age of the Bulge and its spread in metallicity further allows ExELS to better constrain both the variation of companion frequency with metallicity and statistically explore the strength of star-planet tides. We conservatively estimate that ExELS will detect ~4100 sub-stellar objects, with sensitivity typically reaching down to Neptune-mass planets. Of these, ~600 will be detectable in both Euclid's VIS (optical) channel and NISP H-band imager, with ~90% of detections being hot Jupiters. Likely scenarios predict a range of 2900-7000 for VIS and 400-1600 for H-band. Twice as many can be expected in VIS if the cadence can be increased to match the 20-minute H-band cadence. The separation of planets from brown dwarfs via Doppler boosting or ellipsoidal variability will be possible in a handful of cases. Radial velocity confirmation should be possible in some cases, using 30-metre-class telescopes. We expect secondary eclipses, and reflection and emission from planets to be detectable in up to ~100 systems in both VIS and NISP-H. Transits of ~500 planetary-radius companions will be characterised with two-colour photometry and ~40 with four-colour photometry (VIS,YJH), and the albedo of (and emission from) a large sample of hot Jupiters in the H-band can be explored statistically.Comment: 18 pages, 16 figures, accepted MNRA

Disease map-based biomarker selection and pre-validation for bladder cancer diagnostic

YesContext: Urinary biomarkers are promising as simple alternatives to cystoscopy for the diagnosis of de novo and recurrent bladder cancer. Objective: To identify a highly sensitive and specific biomarker candidate set with potential clinical utility in bladder cancer. Materials and methods: Urinary biomarkers concentrations were determined by ELISA. The performance of individual markers and marker combinations was assessed using ROC analysis. Results: A 5-biomarker panel (IL8, MMP9, VEGFA, PTGS2 and EN2) was defined from the candidate set. Discussion and conclusion: This panel showed a better overall performance than the best individual marker. Further validation studies are needed to evaluate its clinical utility in bladder cancer.This work has been supported in part by the European Commission Program DIPROMON - HEALTH-F5-2012-306157-2: Development of an integrated protein- and cell-based device for non-invasive diagnostics in the urogenital tract

ExELS: an exoplanet legacy science proposal for the ESA Euclid mission. II. Hot exoplanets and sub-stellar systems

The Exoplanet Euclid Legacy Survey (ExELS) proposes to determine the frequency of cold exoplanets down to Earth mass from host separations of ~1 AU out to the free-floating regime by detecting microlensing events in Galactic Bulge. We show that ExELS can also detect large numbers of hot, transiting exoplanets in the same population. The combined microlensing+transit survey would allow the first self-consistent estimate of the relative frequencies of hot and cold sub-stellar companions, reducing biases in comparing "near-field" radial velocity and transiting exoplanets with "far-field" microlensing exoplanets. The age of the Bulge and its spread in metallicity further allows ExELS to better constrain both the variation of companion frequency with metallicity and statistically explore the strength of star-planet tides. We conservatively estimate that ExELS will detect ~4100 sub-stellar objects, with sensitivity typically reaching down to Neptune-mass planets. Of these, ~600 will be detectable in both Euclid's VIS (optical) channel and NISP H-band imager, with ~90% of detections being hot Jupiters. Likely scenarios predict a range of 2900-7000 for VIS and 400-1600 for H-band. Twice as many can be expected in VIS if the cadence can be increased to match the 20-minute H-band cadence. The separation of planets from brown dwarfs via Doppler boosting or ellipsoidal variability will be possible in a handful of cases. Radial velocity confirmation should be possible in some cases, using 30-metre-class telescopes. We expect secondary eclipses, and reflection and emission from planets to be detectable in up to ~100 systems in both VIS and NISP-H. Transits of ~500 planetary-radius companions will be characterised with two-colour photometry and ~40 with four-colour photometry (VIS,YJH), and the albedo of (and emission from) a large sample of hot Jupiters in the H-band can be explored statistically.Comment: 18 pages, 16 figures, accepted MNRA

Eclipsing binary stars in the Large Magellanic Cloud : results from the EROS-2, OGLE and VMC surveys

We present a catalogue of 1768 eclipsing binary stars (EBs) detected in the Large Magellanic Cloud (LMC) by the second generation of the EROS survey (hereinafter EROS-2); 493 of them are new discoveries located in outer regions (out of the central bar) of the LMC. These sources were originally included in a list of candidate classical Cepheids (CCs) extracted from the EROS-2 catalogue on the basis of the period (0.89 < 17.82 mag] diagram. After visual inspection of the light curves we reclassified them as eclipsing binaries. They have blue colours (B_EROS - R_EROS < 0.2 mag) hence we classed them as hot eclipsing binaries (HEBs) containing hot massive components: main sequence (MS) stars or blue giants. We present Ks-band light curves for 999 binaries from our sample that have a counterpart in the VISTA near-infrared ESO public survey of the Magellanic Clouds system (VMC). We provide spectral classifications of 13 HEBs with existing spectroscopy. We divided our sample into contact-like binaries and detached/semi-detached systems based on both visual inspection and the parameters of the Fourier decomposition of the light curves and analysed the period-luminosity (PL) relations of the contact-like systems using the R_EROS and Ks magnitudes at maximum light. The contact-like binaries in our sample do not follow PL relations. We analysed the sample of contact binaries from the OGLE III catalogue and confirmed that PL_I and PL_Ks sequences are defined only by eclipsing binaries containing a red giant component.Peer reviewe

Higher Order Quantum Superintegrability: a new "Painlev\'e conjecture"

We review recent results on superintegrable quantum systems in a two-dimensional Euclidean space with the following properties. They are integrable because they allow the separation of variables in Cartesian coordinates and hence allow a specific integral of motion that is a second order polynomial in the momenta. Moreover, they are superintegrable because they allow an additional integral of order $N>2$. Two types of such superintegrable potentials exist. The first type consists of "standard potentials" that satisfy linear differential equations. The second type consists of "exotic potentials" that satisfy nonlinear equations. For $N= 3$, 4 and 5 these equations have the Painlev\'e property. We conjecture that this is true for all $N\geq3$. The two integrals X and Y commute with the Hamiltonian, but not with each other. Together they generate a polynomial algebra (for any $N$) of integrals of motion. We show how this algebra can be used to calculate the energy spectrum and the wave functions.Comment: 23 pages, submitted as a contribution to the monographic volume "Integrability, Supersymmetry and Coherent States", a volume in honour of Professor V\'eronique Hussin. arXiv admin note: text overlap with arXiv:1703.0975