Nonlinear Sigma Model for Disordered Media: Replica Trick for Non-Perturbative Results and Interactions

In these lectures, given at the NATO ASI at Windsor (2001), applications of the replicas nonlinear sigma model to disordered systems are reviewed. A particular attention is given to two sets of issues. First, obtaining non-perturbative results in the replica limit is discussed, using as examples (i) an oscillatory behaviour of the two-level correlation function and (ii) long-tail asymptotes of different mesoscopic distributions. Second, a new variant of the sigma model for interacting electrons in disordered normal and superconducting systems is presented, with demonstrating how to reduce it, under certain controlled approximations, to known ``phase-only'' actions, including that of the ``dirty bosons'' model.Comment: 25 pages, Proceedings of the NATO ASI "Field Theory of Strongly Correlated Fermions and Bosons in Low - Dimensional Disordered Systems", Windsor, August, 2001; to be published by Kluwe

Prognostic Value of the PRAME Gene Expression in T-Cell Lymphoproliferative Disorders

Background. T-cell lymphomas (T-CL) represent a heterogeneous group of malignant lymphoproliferative disorders characterized by unfavorable prognosis. The cancer-testis PRAME gene is notable for its spontaneous expression in transformed cells as observed in solid tumors, B-cell lymphoproliferative and chronic myeloproliferative diseases. Activity and clinical significance of PRAME in T-CL was not studied before, which determines the relevance and provides ground for the present trial. Aim. To assess the clinical significance of the PRAME gene expression in T-CL. Materials & Methods. PRAME gene expression level was measured in samples of lymph nodes, blood, and bone marrow from 35 T-CL patients. Among them 3 patients received allogeneic hematopoietic stem cell transplantation, and 6 patients received autologous hematopoietic stem cell transplantation. A correlation was established between the PRAME expression in bone marrow and peripheral blood with morphological markers of disseminated disease with bone marrow lesions and leukemic blood. PRAME expression level was correlated with survival parameters and tumor proliferative activity (Ki-67). Results. PRAME activity was observed in 21 (60 %) patients. PRAME hyperexpression is associated with advanced stages of disease (p = 0.0734), bone marrow lesions (p = 0.0289), leukemic blood (p = 0.0187), worsening of the overall survival (OS) (p = 0.0787) and event-free survival (EFS) (p = 0.7185), also after hematopoietic stem cell transplantation (p = 0.2661 for OS and p = 0.0452 for EFS), and with a high Ki-67 expression level (p = 0.0155). Conclusion. PRAME expression in T-CL is often observed and related with unfavorable clinical prognosis

A search for the decay modes B+/- to h+/- tau l

We present a search for the lepton flavor violating decay modes B+/- to h+/- tau l (h= K,pi; l= e,mu) using the BaBar data sample, which corresponds to 472 million BBbar pairs. The search uses events where one B meson is fully reconstructed in one of several hadronic final states. Using the momenta of the reconstructed B, h, and l candidates, we are able to fully determine the tau four-momentum. The resulting tau candidate mass is our main discriminant against combinatorial background. We see no evidence for B+/- to h+/- tau l decays and set a 90% confidence level upper limit on each branching fraction at the level of a few times 10^-5.Comment: 15 pages, 7 figures, submitted to Phys. Rev.

The Static Maxwell System in Three Dimensional Axially Symmetric Inhomogeneous Media and Axially Symmetric Generalization of the Cauchy–Riemann System

In this paper we discuss different generalizations of the Cauchy–Riemann system and their connection with the static Maxwell system. In particular, this allows us to present relations between slice-monogenic functions and hypermonogenic functions, as well as to provide a physical interpretation of slice-monogenic functions. Furthermore, we present an explicit and complete set of basic solutions of a new class of axial-hypermonogenic functions in R^3. In the end we determine the symmetry operators for the class of axial-hypermonogenic functions