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

Chromosomal Gains and Losses in Uveal Melanomas Detected by Comparative Genomic Hybridization

Eleven uveal melanomas were analyzed using comparative genomic hybridization (CGH). The most abundant genetic changes were loss of chromosome 3, overrepresentation of 6p, loss of 6q, and multiplication of 8q. The smallest overrepresented regions on 6p and 8q were 6pterp21 and 8q24qter, respectively. Several additional gains and losses of chromosome segments were repeatedly observed, the most frequent one being loss of 9p (three cases). Monosomy 3 appeared to be a marker for ciliary body involvement. CGH data were compared with the results of chromosome banding. Some alterations, e.g., gains of 6p and losses of 6q, were observed with higher frequencies after CGH, while others, e.g., 9p deletions, were detected only by CGH. The data suggest some similarities of cytogenetic alterations between cutaneous and uveal melanoma. In particular, the 9p deletions are of interest due to recent reports about the location of a putative tumor-suppressor gene for cutaneous malignant melanoma in this region

Molecular cytogenetic analysis of formalin-fixed, paraffin-embedded solid tumors by comparative genomic hybridization after universal DNA-amplification

We present a technique which allows the detection and chromosomal localization of DNA sequence copy number changes in solid tumor genomes from frozen sections and paraffin embedded, formalin fixed specimens. Based on comparative genomic hybridization and on universal DNA amplification procedures this technique is possible even if only a few tumor cells are available. We demonstrate the feasibility of this method to visualize complete and partial chromosome gains and losses and gene amplifications In archived solid tumor samples

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.Comment: 26 pages, REVTeX, 10 ps figures; changed conten

Superheavy nuclei in relativistic effective Lagrangian model

Isotopic and isotonic chains of superheavy nuclei are analyzed to search for spherical double shell closures beyond Z=82 and N=126 within the new effective field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear many-body problem. We take into account several indicators to identify the occurrence of possible shell closures, such as two-nucleon separation energies, two-nucleon shell gaps, average pairing gaps, and the shell correction energy. The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some magic character depending on the parameter set. The magicity of a particular neutron (proton) number in the analyzed mass region is found to depend on the number of protons (neutrons) present in the nucleus.Comment: 26 pages, REVTeX, 10 ps figures; changed conten

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

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

High resolution array-CGH analysis of single cells

Heterogeneity in the genome copy number of tissues is of particular importance in solid tumor biology. Furthermore, many clinical applications such as pre-implantation and non-invasive prenatal diagnosis would benefit from the ability to characterize individual single cells. As the amount of DNA from single cells is so small, several PCR protocols have been developed in an attempt to achieve unbiased amplification. Many of these approaches are suitable for subsequent cytogenetic analyses using conventional methodologies such as comparative genomic hybridization (CGH) to metaphase spreads. However, attempts to harness array-CGH for single-cell analysis to provide improved resolution have been disappointing. Here we describe a strategy that combines single-cell amplification using GenomePlex library technology (GenomePlex(®) Single Cell Whole Genome Amplification Kit, Sigma-Aldrich, UK) and detailed analysis of genomic copy number changes by high-resolution array-CGH. We show that single copy changes as small as 8.3 Mb in single cells are detected reliably with single cells derived from various tumor cell lines as well as patients presenting with trisomy 21 and Prader–Willi syndrome. Our results demonstrate the potential of this technology for studies of tumor biology and for clinical diagnostics

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