Sho Matsumoto

ABJ fractional brane from ABJM Wilson loop

A bstractWe present a new Fermi gas formalism for the ABJ matrix model. This formulation identifies the effect of the fractional M2-brane in the ABJ matrix model as that of a composite Wilson loop operator in the corresponding ABJM matrix model. Using this formalism, we study the phase part of the ABJ partition function numerically and find a simple expression for it. We further compute a few exact values of the partition function at some coupling constants. Fitting these exact values against the expected form of the grand potential, we can determine the grand potential with exact coefficients. The results at various coupling constants enable us to conjecture an explicit form of the grand potential for general coupling constants. The part of the conjectured grand potential from the perturbative sum, worldsheet instantons and bound states is regarded as a natural generalization of that in the ABJM matrix model, though the membrane instanton part contains a new contribution.

On some properties of orthogonal Weingarten functions

We give a Fourier-type formula for computing the orthogonal Weingarten formula. The Weingarten calculus was introduced as a systematic method to compute integrals of polynomials with respect to Haar measure over classical groups. Although a Fourier-type formula was known in the unitary case, the orthogonal counterpart was not known. It relies on the Jack polynomial generalization of both Schur and zonal polynomials. This formula substantially reduces the complexity involved in the computation of Weingarten formulas. We also describe a few more new properties of the Weingarten formula, state a conjecture, and give a table of values.

Protein O-Mannosyltransferases B and C Support Hyphal Development and Differentiation in Aspergillus nidulans

ABSTRACT Aspergillus nidulans possesses three pmt genes encoding protein O-d-mannosyltransferases (Pmt). Previously, we reported that PmtA, a member of the PMT2 subfamily, is involved in the proper maintenance of fungal morphology and formation of conidia (T. Oka, T. Hamaguchi, Y. Sameshima, M. Goto, and K. Furukawa, Microbiology 150:1973-1982, 2004). In the present paper, we describe the characterization of the pmtA paralogues pmtB and pmtC. PmtB and PmtC were classified as members of the PMT1 and PMT4 subfamilies, respectively. A pmtB disruptant showed wild-type (wt) colony formation at 30°C but slightly repressed growth at 42°C. Conidiation of the pmtB disruptant was reduced to approximately 50% of that of the wt strain; in addition, hyperbranching of hyphae indicated that PmtB is involved in polarity maintenance. A pmtA and pmtB double disruptant was viable but very slow growing, with morphological characteristics that were cumulative with respect to either single disruptant. Of the three single pmt mutants, the pmtC disruptant showed the highest growth repression; the hyphae were swollen and frequently branched, and the ability to form conidia under normal growth conditions was lost. Recovery from the aberrant hyphal structures occurred in the presence of osmotic stabilizer, implying that PmtC is responsible for the maintenance of cell wall integrity. Osmotic stabilization at 42°C further enabled the pmtC disruptant to form conidiophores and conidia, but they were abnormal and much fewer than those of the wt strain. Apart from the different, abnormal phenotypes, the three pmt disruptants exhibited differences in their sensitivities to antifungal reagents, mannosylation activities, and glycoprotein profiles, indicating that PmtA, PmtB, and PmtC perform unique functions during cell growth.

Jucys–Murphy elements, orthogonal matrix integrals, and Jack measures

We study symmetric polynomials whose variables are odd-numbered Jucys–Murphy elements. They define elements of the Hecke algebra associated to the Gelfand pair of the symmetric group with the hyperoctahedral group. We evaluate their expansions in zonal spherical functions and in double coset sums. These evaluations are related to integrals of polynomial functions over orthogonal groups. Furthermore, we give their extension based on Jack polynomials.

General Moments of the Inverse Real Wishart Distribution and Orthogonal Weingarten Functions

We study a random positive definite symmetric matrix distributed according to a real Wishart distribution. We compute general moments of the random matrix and of its inverse explicitly. To do so, we employ the orthogonal Weingarten function, which was recently introduced in the study of Haar-distributed orthogonal matrices. As applications, we give formulas for moments of traces of a Wishart matrix and its inverse.

Multiparticle Correlations in Mesoscopic Scattering: Boson Sampling, Birthday Paradox, and Hong-Ou-Mandel Profiles

The interplay between single-particle interference and quantum indistinguishability leads to signature correlations in many-body scattering. We uncover these with a semiclassical calculation of the transmission probabilities through mesoscopic cavities for systems of noninteracting particles. For chaotic cavities we provide the universal form of the first two moments of the transmission probabilities over ensembles of random unitary matrices, including weak localization and dephasing effects. If the incoming many-body state consists of two macroscopically occupied wave packets, their time delay drives a quantum-classical transition along a boundary determined by the bosonic birthday paradox. Mesoscopic chaotic scattering of Bose-Einstein condensates is, then, a realistic candidate to build a boson sampler and to observe the macroscopic Hong-Ou-Mandel effect.

WEINGARTEN CALCULUS FOR MATRIX ENSEMBLES ASSOCIATED WITH COMPACT SYMMETRIC SPACES

A method for computing integrals of polynomial functions on compact symmetric spaces is given. Those integrals are expressed as sums of functions on symmetric groups.

Integration of invariant matrices and moments of inverses of Ginibre and Wishart matrices

We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool is the Weingarten calculus. As an application, we obtain new formulas for the pseudoinverse of Gaussian matrices and for the inverse of compound Wishart matrices.

Moments of characteristic polynomials for compact symmetric spaces and Jack polynomials

We express the averages of products of characteristic polynomials for random matrix ensembles associated with compact symmetric spaces in terms of Jack polynomials or Heckman and Opdams Jacobi polynomials depending on the root system of the space. We also give explicit expressions for the asymptotic behavior of these averages in the limit as the matrix size goes to infinity.

GENERAL MOMENTS OF MATRIX ELEMENTS FROM CIRCULAR ORTHOGONAL ENSEMBLES

The aim of this paper is to present a systematic method for computing moments of matrix elements taken from circular orthogonal ensembles (COE). The formula is given as a sum of Weingarten functions for orthogonal groups but the technique for its proof involves Weingarten calculus for unitary groups. As an application, explicit expressions for the moments of a single matrix element of a COE matrix are given.