Difference L operators and a Casorati determinant solution to the T-system for twisted quantum affine algebras

We propose factorized difference operators L(u) associated with the twisted quantum affine algebras U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}), U_{q}(D^{(2)}_{n+1}),U_{q}(D^{(3)}_{4}). These operators are shown to be annihilated by a screening operator. Based on a basis of the solutions of the difference equation L(u)w(u)=0, we also construct a Casorati determinant solution to the T-system for U_{q}(A^{(2)}_{2n}),U_{q}(A^{(2)}_{2n-1}).Comment: 15 page

Nonlinear integral equations for thermodynamics of the sl(r+1) Uimin-Sutherland model

We derive traditional thermodynamic Bethe ansatz (TBA) equations for the sl(r+1) Uimin-Sutherland model from the T-system of the quantum transfer matrix. These TBA equations are identical to the ones from the string hypothesis. Next we derive a new family of nonlinear integral equations (NLIE). In particular, a subset of these NLIE forms a system of NLIE which contains only a finite number of unknown functions. For r=1, this subset of NLIE reduces to Takahashi's NLIE for the XXX spin chain. A relation between the traditional TBA equations and our new NLIE is clarified. Based on our new NLIE, we also calculate the high temperature expansion of the free energy.Comment: 24 pages, 4 figures, to appear in J. Phys. A: Math. Ge

Phenotypic integration of brain size and head morphology in Lake Tanganyika Cichlids

[Background] Phenotypic integration among different anatomical parts of the head is a common phenomenon across vertebrates. Interestingly, despite centuries of research into the factors that contribute to the existing variation in brain size among vertebrates, little is known about the role of phenotypic integration in brain size diversification. Here we used geometric morphometrics on the morphologically diverse Tanganyikan cichlids to investigate phenotypic integration across key morphological aspects of the head. Then, while taking the effect of shared ancestry into account, we tested if head shape was associated with brain size while controlling for the potentially confounding effect of feeding strategy.[Results] The shapes of the anterior and posterior parts of the head were strongly correlated, indicating that the head represents an integrated morphological unit in Lake Tanganyika cichlids. After controlling for phylogenetic non-independence, we also found evolutionary associations between head shape, brain size and feeding ecology.[Conclusions] Geometric morphometrics and phylogenetic comparative analyses revealed that the anterior and posterior parts of the head are integrated, and that head morphology is associated with brain size and feeding ecology in Tanganyikan cichlid fishes. In light of previous results on mammals, our results suggest that the influence of phenotypic integration on brain diversification is a general process.This study was funded through the student exchange support program (scholarship for long-term study abroad) from the Japanese Student Services Organization (JASSO) to M. Tsuboi, a JAE-Doc postdoctoral fellowship from the Consejo Superior de Investigaciones Científicas to A. Gonzalez-Voyer and a Swedish Research Council grant to N. Kolm.Peer Reviewe

From the quantum Jacobi-Trudi and Giambelli formula to a nonlinear integral equation for thermodynamics of the higher spin Heisenberg model

We propose a nonlinear integral equation (NLIE) with only one unknown function, which gives the free energy of the integrable one dimensional Heisenberg model with arbitrary spin. In deriving the NLIE, the quantum Jacobi-Trudi and Giambelli formula (Bazhanov-Reshetikhin formula), which gives the solution of the T-system, plays an important role. In addition, we also calculate the high temperature expansion of the specific heat and the magnetic susceptibility.Comment: 18 pages, LaTeX; some explanations, 2 figures, one reference added; typos corrected; to appear in J. Phys. A: Math. Ge

The Massive Star Forming Region Cygnus OB2. I. Chandra catalogue of association members

We present a catalogue of 1696 X-ray sources detected in the massive star forming region (SFR) Cygnus OB2 and extracted from two archival Chandra observations of the center of the region. A deep source extraction routine, exploiting the low background rates of Chandra observations was employed to maximize the number of sources extracted. Observations at other wavelengths were used to identify low count-rate sources and remove likely spurious sources. Monte Carlo simulations were also used to assess the authenticity of these sources. We used a Bayesian technique to identify optical or near-IR counterparts for 1501 (89%) of our sources, using deep observations from the INT Photometric H-alpha Survey, the Two Micron All Sky Survey, and the UKIRT Infrared Deep Sky Survey-Galactic plane Survey. 755 (45%) of these objects have six-band r', H-alpha, i', J, H, and K optical and near-IR photometry. From an analysis of the Poisson false-source probabilities for each source we estimate that our X-ray catalogue includes < 1% of false sources, and an even lower fraction when only sources with optical or near-IR associations are considered. A Monte Carlo simulation of the Bayesian matching scheme allows this method to be compared to more simplified matching techniques and enables the various sources of error to be quantified. The catalogue of 1696 objects presented here includes X-ray broad band fluxes, model fits, and optical and near-IR photometry in what is one of the largest X-ray catalogue of a single SFR to date. The high number of stellar X-ray sources detected from relatively shallow observations confirms the status and importance of Cygnus OB2 as one of our Galaxy's most massive SFRs.Comment: Accepted for publication in ApJS. 39 pages, 5 figures, 5 tables (full tables available in the published version or on request to the author