Multidimensional Toda Lattices: Continuous and Discrete Time

In this paper we present multidimensional analogues of both the continuous- and discrete-time Toda lattices. The integrable systems that we consider here have two or more space coordinates. To construct the systems, we generalize the orthogonal polynomial approach for the continuous and discrete Toda lattices to the case of multiple orthogonal polynomials

Actin- and myosin-dependent vesicle loading of presynaptic docking sites prior to exocytosis.

Variance analysis of postsynaptic current amplitudes suggests the presence of distinct docking sites (also called release sites) where vesicles pause before exocytosis. Docked vesicles participate in the readily releasable pool (RRP), but the relation between docking site number and RRP size remains unclear. It is also unclear whether all vesicles of the RRP are equally release competent, and what cellular mechanisms underlie RRP renewal. We address here these questions at single glutamatergic synapses, counting released vesicles using deconvolution. We find a remarkably low variance of cumulative vesicle counts during action potential trains. This, combined with Monte Carlo simulations, indicates that vesicles transit through two successive states before exocytosis, so that the RRP is up to 2-fold higher than the docking site number. The transition to the second state has a very rapid rate constant, and is specifically inhibited by latrunculin B and blebbistatin, suggesting the involvement of actin and myosin

Asymptotic form of two-point correlation function of the XXZ spin chain

Correlation functions of the XXZ spin chain in the critical regime is studied at zero-temperature. They are exactly represented in the Fredholm determinant form and are related with an operator-valued Riemann-Hilbert problem. Analyzing this problem we prove that a two-point correlation function consisting of sufficiently separated spin operators is expressed by power-functions of the distance between those operators.Comment: 9 pages, LaTeX2e (+ amssymb, amsthm); Proof of Lemma 1 is revise

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

The Emerging QCD Frontier: The Electron Ion Collider

The self-interactions of gluons determine all the unique features of QCD and lead to a dominant abundance of gluons inside matter already at moderate $x$. Despite their dominant role, the properties of gluons remain largely unexplored. Tantalizing hints of saturated gluon densities have been found in $e$+p collisions at HERA, and in d+Au and Au+Au collisions at RHIC. Saturation physics will have a profound influence on heavy-ion collisions at the LHC. But unveiling the collective behavior of dense assemblies of gluons under conditions where their self-interactions dominate will require an Electron-Ion Collider (EIC): a new facility with capabilities well beyond those In this paper I outline the compelling physics case for $e$+A collisions at an EIC and discuss briefly the status of machine design concepts. of any existing accelerator.Comment: 11 pages, 9 figures, prepared for 20th International Conference on Ultra-Relativistic Nucleus-Nucleus Collisions: Quark Matter 2008 (QM2008), Jaipur, India, 4-10 Feb. 200

Annihilation poles of a Smirnov-type integral formula for solutions to quantum Knizhnik--Zamolodchikov equation

We consider the recently obtained integral representation of quantum Knizhnik-Zamolodchikov equation of level 0. We obtain the condition for the integral kernel such that these solutions satisfy three axioms for form factor \'{a} la Smirnov. We discuss the relation between this integral representation and the form factor of XXZ spin chain.Comment: 14 pages, latex, no figures

Three DNA polymerases, recruited by different mechanisms, carry out NER repair synthesis in human cells

Nucleotide excision repair (NER) is the most versatile DNA repair system that deals with the major UV photoproducts in DNA, as well as many other DNA adducts. The early steps of NER are well understood, whereas the later steps of repair synthesis and ligation are not. In particular, which polymerases are definitely involved in repair synthesis and how they are recruited to the damaged sites has not yet been established. We report that, in human fibroblasts, approximately half of the repair synthesis requires both polκ and polδ, and both polymerases can be recovered in the same repair complexes. Polκ is recruited to repair sites by ubiquitinated PCNA and XRCC1 and polδ by the classical replication factor complex RFC1-RFC, together with a polymerase accessory factor, p66, and unmodified PCNA. The remaining repair synthesis is dependent on polɛ, recruitment of which is dependent on the alternative clamp loader CTF18-RFC

Die Wirkung des Lichtes auf das trocknende Öl (I)

(1) Es wird der Grundversuch für die Wirkung des Lichtes auf das trocknende Öl beschrieben. (2) Das Leinöl wurde unter Einblasung des Sauerstoffes mit einer konstant brennenden Quecksilberbogenlampe belichtet. Die Belichtung wurde bei 5 °C durchgeführt, um die Wärmereaktion zu verlangsamen. Der Umwandelungsverlauf des Öles liess sich durch Veränderung der Jodzahl ermessen. (3) Im grossen und ganzen verändern sich nur unbedeutend einige Konstanten, d.h. spezifisches Gewicht, Viskosität, Lichtbrechungsvermögen, Säurezahl, Jodzahl u.s.w. sowohl durch 3-stündige als auch 6-stündige Belichtung. (4) Bemerkenswerter ist hierbei das Verhalten des vorbelichteten Öles gegen Erwärmung. Dies oxydiert durch Erwärmung endgültig rascher als das unvorbelichtete Öl. (5) Das Versnchsergebnis spricht dafür, dass der Zwischenstoff bzw. Beschleuniger, dessen Anwesenheit die Verwandelung leichter vor sich gehen lässt, hauptsächlich durch Belichtung gebildet wird. (6) Die Verwandelungsgeschwindigkeit, welche zu Anfang sehr klein ist, vergrössert sich beschleunigend bis zum Maximum, um sich dann ein wenig zu vermindern. Hierbei tritt das Maximum um so früher ein, je länger das Öl vorbelichtet war. (7) Das Ergebnis (6) wird vermöge der kinetischen Darstellung aufgeklärt

Complete integrability of derivative nonlinear Schr\"{o}dinger-type equations

We study matrix generalizations of derivative nonlinear Schr\"{o}dinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are `C-integrable' and the rest of them are `S-integrable' in Calogero's terminology.Comment: 14 pages, LaTeX2e (IOP style), to appear in Inverse Problem