Exactly solvable potentials of Calogero type for q-deformed Coxeter groups

We establish that by parameterizing the configuration space of a one-dimensional quantum system by polynomial invariants of q-deformed Coxeter groups it is possible to construct exactly solvable models of Calogero type. We adopt the previously introduced notion of solvability which consists of relating the Hamiltonian to finite dimensional representation spaces of a Lie algebra. We present explicitly the $G_2^q$-case for which we construct the potentials by means of suitable gauge transformations.Comment: 22 pages Late

Quantum Calogero-Moser Models: Integrability for all Root Systems

The issues related to the integrability of quantum Calogero-Moser models based on any root systems are addressed. For the models with degenerate potentials, i.e. the rational with/without the harmonic confining force, the hyperbolic and the trigonometric, we demonstrate the following for all the root systems: (i) Construction of a complete set of quantum conserved quantities in terms of a total sum of the Lax matrix (L), i.e. (\sum_{\mu,\nu\in{\cal R}}(L^n)_{\mu\nu}), in which ({\cal R}) is a representation space of the Coxeter group. (ii) Proof of Liouville integrability. (iii) Triangularity of the quantum Hamiltonian and the entire discrete spectrum. Generalised Jack polynomials are defined for all root systems as unique eigenfunctions of the Hamiltonian. (iv) Equivalence of the Lax operator and the Dunkl operator. (v) Algebraic construction of all excited states in terms of creation operators. These are mainly generalisations of the results known for the models based on the (A) series, i.e. (su(N)) type, root systems.Comment: 45 pages, LaTeX2e, no figure

Preliminary results for RR Lyrae stars and Classical Cepheids from the Vista Magellanic Cloud (VMC) Survey

The Vista Magellanic Cloud (VMC, PI M.R. Cioni) survey is collecting $K_S$-band time series photometry of the system formed by the two Magellanic Clouds (MC) and the "bridge" that connects them. These data are used to build $K_S$-band light curves of the MC RR Lyrae stars and Classical Cepheids and determine absolute distances and the 3D geometry of the whole system using the $K$-band period luminosity ($PLK_S$), the period - luminosity - color ($PLC$) and the Wesenhiet relations applicable to these types of variables. As an example of the survey potential we present results from the VMC observations of two fields centered respectively on the South Ecliptic Pole and the 30 Doradus star forming region of the Large Magellanic Cloud. The VMC $K_S$-band light curves of the RR Lyrae stars in these two regions have very good photometric quality with typical errors for the individual data points in the range of $\sim$ 0.02 to 0.05 mag. The Cepheids have excellent light curves (typical errors of $\sim$ 0.01 mag). The average $K_S$ magnitudes derived for both types of variables were used to derive $PLK_S$ relations that are in general good agreement within the errors with the literature data, and show a smaller scatter than previous studies.Comment: 7 pages, 6 figure. Accepted for publication in Astrophysics and Space Science. Following a presentation at the conference "The Fundamental Cosmic Distance Scale: State of the Art and the Gaia Perspective", Naples, May 201

Young and Intermediate-age Distance Indicators

Distance measurements beyond geometrical and semi-geometrical methods, rely mainly on standard candles. As the name suggests, these objects have known luminosities by virtue of their intrinsic proprieties and play a major role in our understanding of modern cosmology. The main caveats associated with standard candles are their absolute calibration, contamination of the sample from other sources and systematic uncertainties. The absolute calibration mainly depends on their chemical composition and age. To understand the impact of these effects on the distance scale, it is essential to develop methods based on different sample of standard candles. Here we review the fundamental properties of young and intermediate-age distance indicators such as Cepheids, Mira variables and Red Clump stars and the recent developments in their application as distance indicators.Comment: Review article, 63 pages (28 figures), Accepted for publication in Space Science Reviews (Chapter 3 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

Toward an internally consistent astronomical distance scale

Accurate astronomical distance determination is crucial for all fields in astrophysics, from Galactic to cosmological scales. Despite, or perhaps because of, significant efforts to determine accurate distances, using a wide range of methods, tracers, and techniques, an internally consistent astronomical distance framework has not yet been established. We review current efforts to homogenize the Local Group's distance framework, with particular emphasis on the potential of RR Lyrae stars as distance indicators, and attempt to extend this in an internally consistent manner to cosmological distances. Calibration based on Type Ia supernovae and distance determinations based on gravitational lensing represent particularly promising approaches. We provide a positive outlook to improvements to the status quo expected from future surveys, missions, and facilities. Astronomical distance determination has clearly reached maturity and near-consistency.Comment: Review article, 59 pages (4 figures); Space Science Reviews, in press (chapter 8 of a special collection resulting from the May 2016 ISSI-BJ workshop on Astronomical Distance Determination in the Space Age

Lymphocyte Subsets Show Different Response Patterns to In Vivo Bound Natalizumab—A Flow Cytometric Study on Patients with Multiple Sclerosis

Natalizumab is an effective monoclonal antibody therapy for the treatment of relapsing- remitting multiple sclerosis (RRMS) and interferes with immune cell migration into the central nervous system by blocking the α4 subunit of very-late activation antigen-4 (VLA-4). Although well tolerated and very effective, some patients still suffer from relapses in spite of natalizumab therapy or from unwanted side effects like progressive multifocal leukoencephalopathy (PML). In search of a routine-qualified biomarker on the effectiveness of natalizumab therapy we applied flow cytometry and analyzed natalizumab binding to α4 and α4 integrin surface levels on T-cells, B-cells, natural killer (NK) cells, and NKT cells from 26 RRMS patients under up to 72 weeks of therapy. Four-weekly infusions of natalizumab resulted in a significant and sustained increase of lymphocyte-bound natalizumab (p<0.001) which was paralleled by a significant decrease in detectability of the α4 integrin subunit on all lymphocyte subsets (p<0.001). We observed pronounced natalizumab accumulations on T and B cells at single measurements in all patients who reported clinical disease activity (n = 4). The natalizumab binding capacity of in vitro saturated lymphocytes collected during therapy was strongly diminished compared to treatment-naive cells indicating a therapy-induced reduction of α4. Summing up, this pilot study shows that flow cytometry is a useful method to monitor natalizumab binding to lymphocytes from RRMS patients under therapy. Investigating natalizumab binding provides an opportunity to evaluate the molecular level of effectiveness of natalizumab therapy in individual patients. In combination with natalizumab saturation experiments, it possibly even provides a means of studying the feasability of patient-tailored infusion intervals. A routine-qualified biomarker on the basis of individual natalizumab saturation on lymphocyte subsets might be an effective tool to improve treatment safety

New near-infrared period-luminosity-metallicity relations for RR Lyrae stars and the outlook for GAIA

We present results of the analysis of 70 RR Lyrae stars located in the bar of the Large Magellanic Cloud (LMC). Combining the spectroscopically determined metallicity of these stars from the literature with precise periods from the OGLE III catalog and multi-epoch Ks photometry from the VISTA survey of the Magellanic Clouds system, we derive a new near-infrared period-luminosity-metallicity (PLKsZ) relation for RR Lyrae variables. In order to fit the relation we use a fitting method developed specifically for this study. The zero-point of the relation is estimated two different ways: by assuming the value of the distance to the LMC and by using Hubble Space Telescope parallaxes of five RR Lyrae stars in the Milky Way (MW). The difference in distance moduli derived by applying these two approaches is ~0.2 mag. To investigate this point further we derive the PLKsZ relation based on 23 MW RR Lyrae stars that had been analyzed in Baade-Wesselink studies. We compared the derived PLKsZ relations for RR Lyrae stars in the MW and LMC. Slopes and zero-points are different, but still consistent within the errors. The shallow slope of the metallicity term is confirmed by both LMC and MW variables. The astrometric space mission Gaia is expected to provide a huge contribution to the determination of the RR Lyrae PLKsZ relation; however, calculating an absolute magnitude from the trigonometric parallax of each star and fitting a PLKsZ relation directly to period and absolute magnitude leads to biased results. We present a tool to achieve an unbiased solution by modeling the data and inferring the slope and zero-point of the relation via statistical methods.Peer reviewedFinal Accepted Versio