Rank properties of exposed positive maps

Let \cK and \cH be finite dimensional Hilbert spaces and let \fP denote the cone of all positive linear maps acting from \fB(\cK) into \fB(\cH). We show that each map of the form $\phi(X)=AXA^*$ or $\phi(X)=AX^TA^*$ is an exposed point of \fP. We also show that if a map $\phi$ is an exposed point of \fP then either $\phi$ is rank 1 non-increasing or \rank\phi(P)>1 for any one-dimensional projection P\in\fB(\cK).Comment: 6 pages, last section removed - it will be a part of another pape

From St\"{a}ckel systems to integrable hierarchies of PDE's: Benenti class of separation relations

We propose a general scheme of constructing of soliton hierarchies from finite dimensional St\"{a}ckel systems and related separation relations. In particular, we concentrate on the simplest class of separation relations, called Benenti class, i.e. certain St\"{a}ckel systems with quadratic in momenta integrals of motion.Comment: 24 page

Finite Matrix Groups over Nilpotent Group Rings

AbstractWe study groups of matricesSGLn(ZΓ) of augmentation one over the integral group ring ZΓ of a nilpotent group Γ. We relate the torsion ofSGLn(ZΓ) to the torsion of Γ. We prove that all abelianp-subgroups ofSGLn(ZΓ) can be stably diagonalized. Also, all finite subgroups ofSGLn(ZΓ) can be embedded into the diagonal Γn<SGLn(ZΓ). We apply matrix results to show that if Γ is nilpotent-by-(Π′-finite) then all finite Π-groups of normalized units in ZΓ can be embedded into Γ

DSC Study of Collagen in Disc Disease

Differential scanning calorimetry (DSC) has been used to estimate the effect of disc disease on the collagen helix-coil transition and morphology for tissue extracted from patients during surgical operation. Forty discs were obtained from patients with degenerative disc disease undergoing surgery for low back pain. The patients were in the age between 20 and 70 years old. The specimens were kept wet during DSC experiment. The data allow the comparison between thermal stability of collagen tissue from healthy patients and from patients suffering from disc disease. In the paper the comparison between thermal helix-coil transition for collagen fibers from patients suffering from disc disease and collagen fibers from healthy organisms has been discussed. The heating rate has an influence on the position on denaturation temperatures of collagen in disc tissues. Higher helix-coil transition temperature of collagen in degenerated disc suggests that additional intermolecular cross linking of collagen fibers occurs. Denaturation temperatures of collagen in degenerated male disc possess smaller values than in female ones. Disc disease induces changes in collagen structure and leads to formation of additional crosslinks between collagen fibers

Femtosecond Covariance Spectroscopy

The success of non-linear optics relies largely on pulse-to-pulse consistency. In contrast, covariance based techniques used in photoionization electron spectroscopy and mass spectrometry have shown that wealth of information can be extracted from noise that is lost when averaging multiple measurements. Here, we apply covariance based detection to nonlinear optical spectroscopy, and show that noise in a femtosecond laser is not necessarily a liability to be mitigated, but can act as a unique and powerful asset. As a proof of principle we apply this approach to the process of stimulated Raman scattering in alpha-quartz. Our results demonstrate how nonlinear processes in the sample can encode correlations between the spectral components of ultrashort pulses with uncorrelated stochastic fluctuations. This in turn provides richer information compared to the standard non-linear optics techniques that are based on averages over many repetitions with well-behaved laser pulses. These proof-of-principle results suggest that covariance based nonlinear spectroscopy will improve the applicability of fs non-linear spectroscopy in wavelength ranges where stable, transform limited pulses are not available such as, for example, x-ray free electron lasers which naturally have spectrally noisy pulses ideally suited for this approach

Staeckel systems generating coupled KdV hierarchies and their finite-gap and rational solutions

We show how to generate coupled KdV hierarchies from Staeckel separable systems of Benenti type. We further show that solutions of these Staeckel systems generate a large class of finite-gap and rational solutions of cKdV hierarchies. Most of these solutions are new.Comment: 15 page

The integrated stress response in lung disease.

Lungs are repeatedly exposed to inhaled toxic insults, such as smoke, diesel exhaust, and microbes, which elicit cellular stress responses. The phosphorylation of eukaryotic translation initiation factor 2α by one of four stress-sensing kinases triggers a pathway called the integrated stress response that helps protect cellular reserves of nutrients and prevents the accumulation of toxic proteins. In this review, we discuss how activation of the integrated stress response has been shown to play an important role in pulmonary pathology, and how its study may help in the development of novel therapies for diverse conditions, from hypoxia to cancer

Tissue expression of lactate transporters (MCT1 and MCT4) and prognosis of malignant pleural mesothelioma (brief report)

Background: Malignant pleural mesothelioma (MPM) is an aggressive neoplasm of the pleura, mainly related to asbestos exposure. As in other solid tumors, malignant cells exhibit high glucose uptake and glycolytic rates with increased lactic acid efflux into the interstitial space. Lactate transport into and out of cells, crucial to maintaining intracellular pH homeostasis and glycolysis, is carried out by monocarboxylate transporters (MCTs) and the chaperone basigin (CD147). We set out to examine the clinical significance of basigin, MCT1 and MCT4 in the context of MPM and to evaluate their expression in relation to the evolution of the disease. Methods: We used immunohistochemistry to measure the expression of basigin, MCT1 and MCT4 in a cohort of 135 individuals with MPM compared to a series of 15 non-MPM pleura specimens. Moreover, by Kaplan-Meier and Cox analyses we evaluated whether an expression over the average of these markers could be associated with the patients' overall survival (OS). Results: We detected positive staining of basigin, MCT1, and MCT4 in most MPM specimens. In particular, MCT4 was always positive in malignant tissues but undetectable in the 4 normal pleural specimens incorporated within the tissue microarray. This was confirmed in the additional series of 15 normal pleural samples. Moreover, MCT4 expression was significantly associated with reduced OS. Conclusion: In this study, the tissue expression of basigin did not prove to be exploitable as a diagnostic or prognostic marker for MPM patients. The expression of MCT1 was not informative either, being tightly correlated with that of basigin. However, the expression of MCT4 showed promise as a diagnostic/therapeutic and prognostic biomarker