On the spectra of the quantized action-variables of the compactified Ruijsenaars-Schneider system

A simple derivation of the spectra of the action-variables of the quantized compactified Ruijsenaars-Schneider system is presented. The spectra are obtained by combining Kahler quantization with the identification of the classical action-variables as a standard toric moment map on the complex projective space. The result is consistent with the Schrodinger quantization of the system worked out previously by van Diejen and Vinet.Comment: Based on talk at the workshop CQIS-2011 (Protvino, Russia, January 2011), 12 page

Conserved quantities in non-abelian monopole fields

Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopole-like field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. It generalizes the fine-tuned inverse-square plus Coulomb potential, found before by McIntosh and Cisneros, and by Zwanziger, for a charged particle in the field of a Dirac monopole. Following Feh\'er, the result is interpreted as describing motion in the asymptotic field of a self-dual Prasad-Sommerfield monopole. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere and Wilczek, a conserved angular momentum is constructed, despite the non-conservation of the electric charge. No Runge-Lenz vector has been found.Comment: 8 pages, RevTex no figures. An error corrected and a new Section adde

Self-duality of the compactified Ruijsenaars-Schneider system from quasi-Hamiltonian reduction

The Delzant theorem of symplectic topology is used to derive the completely integrable compactified Ruijsenaars-Schneider III(b) system from a quasi-Hamiltonian reduction of the internally fused double SU(n) x SU(n). In particular, the reduced spectral functions depending respectively on the first and second SU(n) factor of the double engender two toric moment maps on the III(b) phase space CP(n-1) that play the roles of action-variables and particle-positions. A suitable central extension of the SL(2,Z) mapping class group of the torus with one boundary component is shown to act on the quasi-Hamiltonian double by automorphisms and, upon reduction, the standard generator S of the mapping class group is proved to descend to the Ruijsenaars self-duality symplectomorphism that exchanges the toric moment maps. We give also two new presentations of this duality map: one as the composition of two Delzant symplectomorphisms and the other as the composition of three Dehn twist symplectomorphisms realized by Goldman twist flows. Through the well-known relation between quasi-Hamiltonian manifolds and moduli spaces, our results rigorously establish the validity of the interpretation [going back to Gorsky and Nekrasov] of the III(b) system in terms of flat SU(n) connections on the one-holed torus.Comment: Final version to appear in Nuclear Physics B, with simplified proof of Theorem 1, 56 page

Interferometric view of the circumstellar envelopes of northern FU Orionis-type stars

FU Orionis-type objects are young, low-mass stars with large outbursts in visible light that last for several years or decades. They are thought to represent an evolutionary phase during the life of every young star when accretion from the circumstellar disk is enhanced during recurring time periods. These outbursts are able to rapidly build up the star while affecting the circumstellar disk and thus the ongoing or future planet formation. In many models infall from a circumstellar envelope seems to be necessary to trigger the outbursts. We observed the J=1$-$0 rotational transition of $^{13}$CO and C$^{18}$O towards eight northern FU Orionis-type stars (V1057 Cyg, V1515 Cyg, V2492 Cyg, V2493 Cyg, V1735 Cyg, V733 Cep, RNO 1B and RNO 1C) and derive temperatures and envelope masses and discuss the morphology and kinematics of the circumstellar material. We detected extended CO emission associated with all our targets. Smaller scale CO clumps were found to be associated with five objects with radii of 2000$-$5000 AU and masses of 0.02$-$0.5 $M_{\odot}$; these are clearly heated by the central stars. Three of these envelopes are also strongly detected in the 2.7 mm continuum. No central CO clumps were detected around V733 Cep and V710 Cas but there are many other clumps in their environments. Traces of outflow activity were observed towards V1735 Cyg, V733 Cep and V710 Cas. The diversity of the observed envelopes enables us to set up an evolutionary sequence between the objects. We find their evolutionary state to range from early, embedded Class I stage to late, Class II-type objects with very low-mass circumstellar material. The results reinforce the idea of FU Orionis-type stars as representatives of a transitory stage between embedded Class I young stellar objects and classical T-Tauri stars.Comment: 17 pages, 11 figures; accepted for publication in A&

Multiple imputation approach for interval-censored time to HIV RNA viral rebound within a mixed effects Cox model

This is the peer reviewed version of the following article: “Alarcón-Soto, Y, Langohr K., Fehér, C., García, F., and Gómez, G. (2018) Multiple imputation approach for interval-censored time to HIV RNA viral rebound within a mixed effects Cox Model.Biometrical journal, December 13th ”which has been published in final form at [doi: 10.1002/bimj.201700291]. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.We present a method to fit a mixed effects Cox model with interval-censored data. Our proposal is based on a multiple imputation approach that uses the truncated Weibull distribution to replace the interval-censored data by imputed survival times and then uses established mixed effects Cox methods for right-censored data. Interval-censored data were encountered in a database corresponding to a recompilation of retrospective data from eight analytical treatment interruption (ATI) studies in 158 human immunodeficiency virus (HIV) positive combination antiretroviral treatment (cART) suppressed individuals. The main variable of interest is the time to viral rebound, which is defined as the increase of serum viral load (VL) to detectable levels in a patient with previously undetectable VL, as a consequence of the interruption of cART. Another aspect of interest of the analysis is to consider the fact that the data come from different studies based on different grounds and that we have several assessments on the same patient. In order to handle this extra variability, we frame the problem into a mixed effects Cox model that considers a random intercept per subject as well as correlated random intercept and slope for pre-cART VL per study. Our procedure has been implemented in R using two packages: truncdist and coxme, and can be applied to any data set that presents both interval-censored survival times and a grouped data structure that could be treated as a random effect in a regression model. The properties of the parameter estimators obtained with our proposed method are addressed through a simulation study.Peer ReviewedPostprint (author's final draft

On the duality between the hyperbolic Sutherland and the rational Ruijsenaars-Schneider models

We consider two families of commuting Hamiltonians on the cotangent bundle of the group GL(n,C), and show that upon an appropriate single symplectic reduction they descend to the spectral invariants of the hyperbolic Sutherland and of the rational Ruijsenaars-Schneider Lax matrices, respectively. The duality symplectomorphism between these two integrable models, that was constructed by Ruijsenaars using direct methods, can be then interpreted geometrically simply as a gauge transformation connecting two cross sections of the orbits of the reduction group.Comment: 16 pages, v2: comments and references added at the end of the tex

On dynamical r-matrices obtained from Dirac reduction and their generalizations to affine Lie algebras

According to Etingof and Varchenko, the classical dynamical Yang-Baxter equation is a guarantee for the consistency of the Poisson bracket on certain Poisson-Lie groupoids. Here it is noticed that Dirac reductions of these Poisson manifolds give rise to a mapping from dynamical r-matrices on a pair \L\subset \A to those on another pair \K\subset \A, where \K\subset \L\subset \A is a chain of Lie algebras for which \L admits a reductive decomposition as \L=\K+\M. Several known dynamical r-matrices appear naturally in this setting, and its application provides new r-matrices, too. In particular, we exhibit a family of r-matrices for which the dynamical variable lies in the grade zero subalgebra of an extended affine Lie algebra obtained from a twisted loop algebra based on an arbitrary finite dimensional self-dual Lie algebra.Comment: 19 pages, LaTeX, added a reference and a footnote and removed some typo

The Arabidopsis ROP-activated receptor-like cytoplasmic kinase RLCK VI_A3 is involved in control of basal resistance to powdery mildew and trichome branching.

KEY MESSAGE: The Arabidopsis receptor-like cytoplasmic kinase AtRLCK VI_A3 is activated by AtROPs and is involved in trichome branching and pathogen interaction. Receptor-like cytoplasmic kinases (RLCKs) belong to the large superfamily of receptor-like kinases, which are involved in a variety of cellular processes like plant growth, development and immune responses. Recent studies suggest that RLCKs of the VI_A subfamily are possible downstream effectors of the small monomeric G proteins of the plant-specific Rho family, called 'Rho of plants' (RAC/ROPs). Here, we describe Arabidopsis thaliana AtRLCK VI_A3 as a molecular interactor of AtROPs. In Arabidopsis epidermal cells, transient co-expression of plasma membrane located constitutively activated (CA) AtROP4 or CA AtROP6 resulting in the recruitment of green fluorescent protein-tagged AtRLCK VI_A3 to the cell periphery. Intrinsic kinase activity of AtRLCK VI_A3 was enhanced in the presence of CA AtROP6 in vitro and further suggested a functional interaction between the proteins. In the interaction of the biotrophic powdery mildew fungus Erysiphe cruciferarum (E. cruciferarum) and its host plant Arabidopsis, Atrlck VI_A3 mutant lines supported enhanced fungal reproduction. Furthermore Atrlck VI_A3 mutant lines showed slightly reduced size and an increase in trichome branch number compared to wild-type plants. In summary, our data suggest a role of the AtROP-regulated AtRLCK VI_A3 in basal resistance to E. cruciferarum as well as in plant growth and cellular differentiation during trichome morphogenesis. Results are discussed in the context of literature suggesting a function of RAC/ROPs in both resistance and susceptibility to pathogen infection