Seven-fluorochrome mouse M-FISH for high-resolution analysis of interchromosomal rearrangements

The mouse has evolved to be the primary mammalian genetic model organism. Important applications include the modeling of human cancer and cloning experiments. In both settings, a detailed analysis of the mouse genome is essential. Multicolor karyotyping technologies have emerged to be invaluable tools for the identification of mouse chromosomes and for the deciphering of complex rearrangements. With the increasing use of these multicolor technologies resolution limits are critical. However, the traditionally used probe sets, which employ 5 different fluorochromes, have significant limitations. Here, we introduce an improved labeling strategy. Using 7 fluorochromes we increased the sensitivity for the detection of small interchromosomal rearrangements (700 kb or less) to virtually 100%. Our approach should be important to unravel small interchromosomal rearrangements in mouse models for DNA repair defects and chromosomal instability. Copyright (C) 2003 S. Karger AG, Basel

Random matrix theory for CPA: Generalization of Wegner's nn--orbital model

We introduce a generalization of Wegner's $n$-orbital model for the description of randomly disordered systems by replacing his ensemble of Gaussian random matrices by an ensemble of randomly rotated matrices. We calculate the one- and two-particle Green's functions and the conductivity exactly in the limit $n\to\infty$. Our solution solves the CPA-equation of the $(n=1)$-Anderson model for arbitrarily distributed disorder. We show how the Lloyd model is included in our model.Comment: 3 pages, Rev-Te

Rigorous mean field model for CPA: Anderson model with free random variables

A model of a randomly disordered system with site-diagonal random energy fluctuations is introduced. It is an extension of Wegner's $n$-orbital model to arbitrary eigenvalue distribution in the electronic level space. The new feature is that the random energy values are not assumed to be independent at different sites but free. Freeness of random variables is an analogue of the concept of independence for non-commuting random operators. A possible realization is the ensemble of at different lattice-sites randomly rotated matrices. The one- and two-particle Green functions of the proposed hamiltonian are calculated exactly. The eigenstates are extended and the conductivity is nonvanishing everywhere inside the band. The long-range behaviour and the zero-frequency limit of the two-particle Green function are universal with respect to the eigenvalue distribution in the electronic level space. The solutions solve the CPA-equation for the one- and two-particle Green function of the corresponding Anderson model. Thus our (multi-site) model is a rigorous mean field model for the (single-site) CPA. We show how the Llyod model is included in our model and treat various kinds of noises.Comment: 24 pages, 2 diagrams, Rev-Tex. Diagrams are available from the authors upon reques

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Semigroups of distributions with linear Jacobi parameters

We show that a convolution semigroup of measures has Jacobi parameters polynomial in the convolution parameter $t$ if and only if the measures come from the Meixner class. Moreover, we prove the parallel result, in a more explicit way, for the free convolution and the free Meixner class. We then construct the class of measures satisfying the same property for the two-state free convolution. This class of two-state free convolution semigroups has not been considered explicitly before. We show that it also has Meixner-type properties. Specifically, it contains the analogs of the normal, Poisson, and binomial distributions, has a Laha-Lukacs-type characterization, and is related to the $q=0$ case of quadratic harnesses.Comment: v3: the article is merged back together with arXiv:1003.4025. A significant revision following suggestions by the referee. 2 pdf figure

Lowering and raising operators for the free Meixner class of orthogonal polynomials

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line

Towards many colors in FISH on 3D-preserved interphase nuclei

The article reviews the existing methods of multicolor FISH on nuclear targets, first of all, interphase chromosomes. FISH proper and image acquisition are considered as two related components of a single process. We discuss (1) M-FISH (combinatorial labeling + deconvolution + widefield microscopy); (2) multicolor labeling + SIM (structured illumination microscopy); (3) the standard approach to multicolor FISH + CLSM (confocal laser scanning microscopy; one fluorochrome - one color channel); (4) combinatorial labeling + CLSM; (5) non-combinatorial labeling + CLSM + linear unmixing. Two related issues, deconvolution of images acquired with CLSM and correction of data for chromatic Z-shift, are also discussed. All methods are illustrated with practical examples. Finally, several rules of thumb helping to choose an optimal labeling + microscopy combination for the planned experiment are suggested. Copyright (c) 2006 S. Karger AG, Basel

Applications of Automata and Graphs: Labeling-Operators in Hilbert Space I

We show that certain representations of graphs by operators on Hilbert space have uses in signal processing and in symbolic dynamics. Our main result is that graphs built on automata have fractal characteristics. We make this precise with the use of Representation Theory and of Spectral Theory of a certain family of Hecke operators. Let G be a directed graph. We begin by building the graph groupoid G induced by G, and representations of G. Our main application is to the groupoids defined from automata. By assigning weights to the edges of a fixed graph G, we give conditions for G to acquire fractal-like properties, and hence we can have fractaloids or G-fractals. Our standing assumption on G is that it is locally finite and connected, and our labeling of G is determined by the "out-degrees of vertices". From our labeling, we arrive at a family of Hecke-type operators whose spectrum is computed. As applications, we are able to build representations by operators on Hilbert spaces (including the Hecke operators); and we further show that automata built on a finite alphabet generate fractaloids. Our Hecke-type operators, or labeling operators, come from an amalgamated free probability construction, and we compute the corresponding amalgamated free moments. We show that the free moments are completely determined by certain scalar-valued functions.Comment: 69 page

The Index of (White) Noises and their Product Systems

(See detailed abstract in the article.) We single out the correct class of spatial product systems (and the spatial endomorphism semigroups with which the product systems are associated) that allows the most far reaching analogy in their classifiaction when compared with Arveson systems. The main differences are that mere existence of a unit is not it sufficient: The unit must be CENTRAL. And the tensor product under which the index is additive is not available for product systems of Hilbert modules. It must be replaced by a new product that even for Arveson systems need not coincide with the tensor product