Ergodic Jacobi matrices and conformal maps

We study structural properties of the Lyapunov exponent $\gamma$ and the density of states $k$ for ergodic (or just invariant) Jacobi matrices in a general framework. In this analysis, a central role is played by the function $w=-\gamma+i\pi k$ as a conformal map between certain domains. This idea goes back to Marchenko and Ostrovskii, who used this device in their analysis of the periodic problem

The absolutely continuous spectrum of one-dimensional Schr"odinger operators

This paper deals with general structural properties of one-dimensional Schr"odinger operators with some absolutely continuous spectrum. The basic result says that the omega limit points of the potential under the shift map are reflectionless on the support of the absolutely continuous part of the spectral measure. This implies an Oracle Theorem for such potentials and Denisov-Rakhmanov type theorems. In the discrete case, for Jacobi operators, these issues were discussed in my recent paper [19]. The treatment of the continuous case in the present paper depends on the same basic ideas.Comment: references added; a few very minor change

De Branges spaces and Krein's theory of entire operators

This work presents a contemporary treatment of Krein's entire operators with deficiency indices $(1,1)$ and de Branges' Hilbert spaces of entire functions. Each of these theories played a central role in the research of both renown mathematicians. Remarkably, entire operators and de Branges spaces are intimately connected and the interplay between them has had an impact in both spectral theory and the theory of functions. This work exhibits the interrelation between Krein's and de Branges' theories by means of a functional model and discusses recent developments, giving illustrations of the main objects and applications to the spectral theory of difference and differential operators.Comment: 37 pages, no figures. The abstract was extended. Typographical errors were corrected. The bibliography style was change

Response of the solar atmosphere to magnetic field evolution in a coronal hole region

Methods. We study an equatorial CH observed simultaneously by HINODE and STEREO on July 27, 2007. The HINODE/SP maps are adopted to derive the physical parameters of the photosphere and to research the magnetic field evolution and distribution. The G band and Ca II H images with high tempo-spatial resolution from HINODE/BFI and the multi-wavelength data from STEREO/EUVI are utilized to study the corresponding atmospheric response of different overlying layers. Results. We explore an emerging dipole locating at the CH boundary. Mini-scale arch filaments (AFs) accompanying the emerging dipole were observed with the Ca II H line. During the separation of the dipolar footpoints, three AFs appeared and expanded in turn. The first AF divided into two segments in its late stage, while the second and third AFs erupted in their late stages. The lifetimes of these three AFs are 4, 6, 10 minutes, and the two intervals between the three divisions or eruptions are 18 and 12 minutes, respectively. We display an example of mixed-polarity flux emergence of IN fields within the CH and present the corresponding chromospheric response. With the increase of the integrated magnetic flux, the brightness of the Ca II H images exhibits an increasing trend. We also study magnetic flux cancellations of NT fields locating at the CH boundary and present the obvious chromospheric and coronal response. We notice that the brighter regions seen in the 171 A images are relevant to the interacting magnetic elements. By examining the magnetic NT and IN elements and the response of different atmospheric layers, we obtain good positive linear correlations between the NT magnetic flux densities and the brightness of both G band (correlation coefficient 0.85) and Ca II H (correlation coefficient 0.58).Comment: 9 pages, 9 figures. A&A, in pres

Multimodal analysis of drug transporter expression in gastrointestinal tissue

Objectives: Drug transporters affect antiretroviral therapy (ART) tissue disposition, but quantitative measures of drug transporter protein expression across preclinical species are not available. Our objective was to use proteomics to obtain absolute transporter concentrations and assess agreement with corresponding gene and immunometric protein data. Design: In order to make interspecies comparisons, two humanized mouse [hu-HSC-Rag (n = 41); bone marrow-liver-thymus (n = 13)] and one primate [rhesus macaque (nonhuman primate, n = 12)] models were dosed to steady state with combination ART. Ileum and rectum were collected at necropsy and snap frozen for analysis. Methods: Tissues were analyzed for gene (quantitative PCR) and protein [liquid chromatography-mass spectrometry (LC-MS) proteomics and western blot] expression and localization (immunohistochemistry) of ART efflux and uptake transporters. Drug concentrations were measured by LC-MS/MS. Multivariable regression was used to determine the ability of transporter data to predict tissue ART penetration. Results: Analytical methods did not agree, with different trends observed for gene and protein expression. For example, quantitative PCR analysis showed a two-fold increase in permeability glycoprotein expression in nonhuman primates versus mice; however, proteomics showed a 200-fold difference in the opposite direction. Proteomics results were supported by immunohistochemistry staining showing extensive efflux transporter localization on the luminal surface of these tissues. ART tissue concentration was variable between species, and multivariable regression showed poor predictive power of transporter data. Conclusion: Lack of agreement between analytical techniques suggests that resources should be focused on generating downstream measures of protein expression to predict drug exposure. Taken together, these data inform the use of preclinical models for studying ART distribution and the design of targeted therapies for HIV eradication

Humanized Rag1−/−γc−/− Mice Support Multilineage Hematopoiesis and Are Susceptible to HIV-1 Infection via Systemic and Vaginal Routes

Several new immunodeficient mouse models for human cell engraftment have recently been introduced that include the Rag2−/−γc−/−, NOD/SCID, NOD/SCIDγc−/− and NOD/SCIDβ2m−/− strains. Transplantation of these mice with CD34+ human hematopoietic stem cells leads to prolonged engraftment, multilineage hematopoiesis and the capacity to generate human immune responses against a variety of antigens. However, the various mouse strains used and different methods of engrafting human cells are beginning to illustrate strain specific variations in engraftment levels, duration and longevity of mouse life span. In these proof-of-concept studies we evaluated the Balb/c-Rag1−/−γ−/− strain for engraftment by human fetal liver derived CD34+ hematopoietic cells using the same protocol found to be effective for Balb/c-Rag2−/−γc−/− mice. We demonstrate that these mice can be efficiently engrafted and show multilineage human hematopoiesis with human cells populating different lymphoid organs. Generation of human cells continues beyond a year and production of human immunoglobulins is noted. Infection with HIV-1 leads to chronic viremia with a resultant CD4 T cell loss. To mimic the predominant sexual viral transmission, we challenged humanized Rag1−/−γc−/− mice with HIV-1 via vaginal route which also resulted in chronic viremia and helper T cell loss. Thus these mice can be further exploited for studying human pathogens that infect the human hematopoietic system in an in vivo setting