Small eigenvalues of the staggered Dirac operator in the adjoint representation and Random Matrix Theory

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and symplectic ensemble. Lattice gauge theory with staggered fermions has verified two of the cases so far, unitary and symplectic, with staggered fermions in the fundamental representation of SU(3) and SU(2). We verify the missing case here, namely orthogonal, with staggered fermions in the adjoint representation of SU(N_c), N_c=2, 3.Comment: 3 pages, revtex, 2 postscript figure

Determinantal process starting from an orthogonal symmetry is a Pfaffian process

When the number of particles $N$ is finite, the noncolliding Brownian motion (BM) and the noncolliding squared Bessel process with index $\nu > -1$ (BESQ$^{(\nu)}$) are determinantal processes for arbitrary fixed initial configurations. In the present paper we prove that, if initial configurations are distributed with orthogonal symmetry, they are Pfaffian processes in the sense that any multitime correlation functions are expressed by Pfaffians. The $2 \times 2$ skew-symmetric matrix-valued correlation kernels of the Pfaffians processes are explicitly obtained by the equivalence between the noncolliding BM and an appropriate dilatation of a time reversal of the temporally inhomogeneous version of noncolliding BM with finite duration in which all particles start from the origin, $N \delta_0$, and by the equivalence between the noncolliding BESQ$^{(\nu)}$ and that of the noncolliding squared generalized meander starting from $N \delta_0$.Comment: v2: AMS-LaTeX, 17 pages, no figure, corrections made for publication in J.Stat.Phy

Infinite systems of non-colliding generalized meanders and Riemann-Liouville differintegrals

Yor's generalized meander is a temporally inhomogeneous modification of the $2(\nu+1)$-dimensional Bessel process with $\nu > -1$, in which the inhomogeneity is indexed by $\kappa \in [0, 2(\nu+1))$. We introduce the non-colliding particle systems of the generalized meanders and prove that they are the Pfaffian processes, in the sense that any multitime correlation function is given by a Pfaffian. In the infinite particle limit, we show that the elements of matrix kernels of the obtained infinite Pfaffian processes are generally expressed by the Riemann-Liouville differintegrals of functions comprising the Bessel functions $J_{\nu}$ used in the fractional calculus, where orders of differintegration are determined by $\nu-\kappa$. As special cases of the two parameters $(\nu, \kappa)$, the present infinite systems include the quaternion determinantal processes studied by Forrester, Nagao and Honner and by Nagao, which exhibit the temporal transitions between the universality classes of random matrix theory.Comment: LaTeX, 35 pages, v3: The argument given in Section 3.2 was simplified. Minor corrections were mad

Vicious walk with a wall, noncolliding meanders, and chiral and Bogoliubov-deGennes random matrices

Spatially and temporally inhomogeneous evolution of one-dimensional vicious walkers with wall restriction is studied. We show that its continuum version is equivalent with a noncolliding system of stochastic processes called Brownian meanders. Here the Brownian meander is a temporally inhomogeneous process introduced by Yor as a transform of the Bessel process that is a motion of radial coordinate of the three-dimensional Brownian motion represented in the spherical coordinates. It is proved that the spatial distribution of vicious walkers with a wall at the origin can be described by the eigenvalue-statistics of Gaussian ensembles of Bogoliubov-deGennes Hamiltonians of the mean-field theory of superconductivity, which have the particle-hole symmetry. We report that the time evolution of the present stochastic process is fully characterized by the change of symmetry classes from the type $C$ to the type $C$I in the nonstandard classes of random matrix theory of Altland and Zirnbauer. The relation between the non-colliding systems of the generalized meanders of Yor, which are associated with the even-dimensional Bessel processes, and the chiral random matrix theory is also clarified.Comment: REVTeX4, 16 pages, 4 figures. v2: some additions and correction

Synthesis and characterization of poly{2-[3-(1H-pyrrol-2-yl)phenyl]-1H- pyrrole} and its copolymer with EDOT1

A pyrrole-functionalized monomer 2-[3-(1H-pyrrol-2-yl)phenyl]-1H-pyrrole (PyPhPy) was synthesized. The structure of monomer was investigated by Nuclear Magnetic Resonance ( 1H NMR) and Fourier Transform Infrared (FTIR) spectroscopy. The chemical polymerization of PyPhPy (CPyPhPy) was realized using FeCl3 as the oxidant. The electrochemical oxidative polymerization of polymer P(PyPhPy) and its copolymer with 3,4-ethylenedioxythiophene poly(2-[3-(1H- pyrrol-2-yl)phenyl]-1H-pyrrole-co-3,4- ethylenedioxythiophene) [P(PyPhPy-co-EDOT)] were achieved via potentiodynamic method by using NaClO 4/ LiClO 4 as the supporting electrolyte in CH 3CN. Characterizations of the resulting polymers were performed by cyclic voltammetry (CV), FTIR, scanning electron microscopy (SEM), UV-Visible spectrophotometry (UV- Vis) and thermogravimetry analyses (TGA). Electrical conductivity of CPyPhPy, P(PyPhPy), and P(PyPhPyco- EDOT) were measured by four-probe technique. © Pleiades Publishing, Ltd., 2011

Mutant adenosine deaminase 2 in a polyarteritis nodosa vasculopathy.

BACKGROUND: Polyarteritis nodosa is a systemic necrotizing vasculitis with a pathogenesis that is poorly understood. We identified six families with multiple cases of systemic and cutaneous polyarteritis nodosa, consistent with autosomal recessive inheritance. In most cases, onset of the disease occurred during childhood. METHODS: We carried out exome sequencing in persons from multiply affected families of Georgian Jewish or German ancestry. We performed targeted sequencing in additional family members and in unrelated affected persons, 3 of Georgian Jewish ancestry and 14 of Turkish ancestry. Mutations were assessed by testing their effect on enzymatic activity in serum specimens from patients, analysis of protein structure, expression in mammalian cells, and biophysical analysis of purified protein. RESULTS: In all the families, vasculitis was caused by recessive mutations in CECR1, the gene encoding adenosine deaminase 2 (ADA2). All the Georgian Jewish patients were homozygous for a mutation encoding a Gly47Arg substitution, the German patients were compound heterozygous for Arg169Gln and Pro251Leu mutations, and one Turkish patient was compound heterozygous for Gly47Val and Trp264Ser mutations. In the endogamous Georgian Jewish population, the Gly47Arg carrier frequency was 0.102, which is consistent with the high prevalence of disease. The other mutations either were found in only one family member or patient or were extremely rare. ADA2 activity was significantly reduced in serum specimens from patients. Expression in human embryonic kidney 293T cells revealed low amounts of mutant secreted protein. CONCLUSIONS: Recessive loss-of-function mutations of ADA2, a growth factor that is the major extracellular adenosine deaminase, can cause polyarteritis nodosa vasculopathy with highly varied clinical expression. (Funded by the Shaare Zedek Medical Center and others.)