Numerical ranges of an operator on an indefinite inner product space

For n x n complex matrices A and an n x n Hermitian matrix S, we consider the S-numerical range of A and the positive S-numerical range of A defined by WS(A) = {〈Av, v〉S/〈v, v〉S : v ∈ ℂn, 〈v, v〉S ≠ 0} and W S + (A) = {〈Av, v〉S : v ∈ ℂn, 〈v, v〉S = 1}, respectively, where 〈u, v〉S = v*Su. These sets generalize the classical numerical range, and they are closely related to the joint numerical range of three Hermitian forms and the cone generated by it. Using some theory of the joint numerical range we can give a detailed description of WS(A) and WS + (A) for arbitrary Hermitian matrices S. In particular, it is shown that WS + (A) is always convex and WS(A) is always p-convex for all S. Similar results are obtained for the sets VS(A) = {〈Av, v〉/〈Sv, v〉: v ∈ ℂn, 〈Sv, v〉 ≠ 0}, VS + (A) = {〈Av, v〉: v ∈ ℂn, 〈Sv, v〉 = 1}, where 〈u, v〉 = v* u. Furthermore, we characterize those linear operators preserving WS(A), WS + (A), V S(A), or VS + (A). Possible generalizations of our results, including their extensions to bounded linear operators on an infinite dimensional Hilbert or Krein space, are discussed.published_or_final_versio

Inhibition of release of inflammatory mediators in primary and cultured cells by a Chinese herbal medicine formula for allergic rhinitis

BACKGROUND: We demonstrated that a Chinese herbal formula, which we refer to as RCM-101, developed from a traditional Chinese medicine formula, reduced nasal and non-nasal symptoms of seasonal allergic rhinitis (SAR). The present study in primary and cultured cells was undertaken to investigate the effects of RCM-101 on the production/release of inflammatory mediators known to be involved in SAR. METHODS: Compound 48/80-induced histamine release was studied in rat peritoneal mast cells. Production of leukotriene B(4 )induced by the calcium ionophore A23187 was studied in porcine neutrophils using an HPLC assay and lipopolysaccharide-stimulated prostaglandin E(2 )production was studied in murine macrophage (Raw 264.7) cells by immune-enzyme assay. Expression of cyclooxygenase-1 (COX-1) and cyclooxygenase-2 (COX-2) was determined in Raw 264.7 cells, using western blotting techniques. RESULTS: RCM-101 (1–100 μg/mL) produced concentration-dependent inhibition of compound 48/80-induced histamine release from rat peritoneal mast cells and of lipopolysaccharide-stimulated prostaglandin E(2 )release from Raw 264.7 cells. Over the range 1 – 10 μg/mL, it inhibited A23187-induced leukotriene B(4 )production in porcine neutrophils. In addition, RCM-101 (100 μg/mL) inhibited the expression of COX-2 protein but did not affect that of COX-1. CONCLUSION: The findings indicate that RCM-101 inhibits the release and/or synthesis of histamine, leukotriene B(4 )and prostaglandin E(2 )in cultured cells. These interactions of RCM-101 with multiple inflammatory mediators are likely to be related to its ability to reduce symptoms of allergic rhinitis

Increased levels of RNA oxidation enhance the reversion frequency in aging pro-apoptotic yeast mutants

Despite recent advances in understanding the complexity of RNA processes, regulation of the metabolism of oxidized cellular RNAs and the mechanisms through which oxidized ribonucleotides affect mRNA translation, and consequently cell viability, are not well characterized. We show here that the level of oxidized RNAs is markedly increased in a yeast decapping Kllsm4Δ1 mutant, which accumulates mRNAs, ages much faster that the wild type strain and undergoes regulated-cell-death. We also found that in Kllsm4Δ1 cells the mutation rate increases during chronological life span indicating that the capacity to han- dle oxidized RNAs in yeast declines with aging. Lowering intracellular ROS levels by antioxidants recovers the wild- type phenotype of mutant cells, including reduced amount of oxidized RNAs and lower mutation rate. Since mRNA oxidation was reported to occur in different neurodegen- erative diseases, decapping-deficient cells may represent a useful tool for deciphering molecular mechanisms of cell response to such conditions, providing new insights into RNA modification-based pathogenesis

Things change: Women’s and men’s marital disruption dynamics in Italy during a time of social transformations, 1970-2003

We study women’s and men’s marital disruption in Italy between 1970 and 2003. By applying an event-history analysis to the 2003 Italian variant of the Generations and Gender Survey we found that the spread of marital disruption started among middle-highly educated women. Then in recent years it appears that less educated women have also been able to dissolve their unhappy unions. Overall we can see the beginning of a reversed educational gradient from positive to negative. In contrast the trend in men’s marital disruption risk appears as a change over time common to all educational groups, although with persisting educational differentials.determinants, educational differences, event history analysis, gender difference, Italy, marital disruption

Accelerated gas-liquid visible light photoredox catalysis with continuous-flow photochemical microreactors

In this protocol, we describe the construction and use of an operationally simple photochemical microreactor for gas-liquid photoredox catalysis using visible light. The general procedure includes details on how to set up the microreactor appropriately with inlets for gaseous reagents and organic starting materials, and it includes examples of how to use it to achieve continuous-flow preparation of disulfides or trifluoromethylated heterocycles and thiols. The reported photomicroreactors are modular, inexpensive and can be prepared rapidly from commercially available parts within 1 h even by nonspecialists. Interestingly, typical reaction times of gas-liquid visible light photocatalytic reactions performed in microflow are lower (in the minute range) than comparable reactions performed as a batch process (in the hour range). This can be attributed to the improved irradiation efficiency of the reaction mixture and the enhanced gas-liquid mass transfer in the segmented gas-liquid flow regime

Displacements analysis of self-excited vibrations in turning

The actual research deals with determining by a new protocol the necessary parameters considering a three-dimensional model to simulate in a realistic way the turning process on machine tool. This paper is dedicated to the experimental displacements analysis of the block tool / block workpiece with self-excited vibrations. In connexion with turning process, the self-excited vibrations domain is obtained starting from spectra of two accelerometers. The existence of a displacements plane attached to the tool edge point is revealed. This plane proves to be inclined compared to the machines tool axes. We establish that the tool tip point describes an ellipse. This ellipse is very small and can be considered as a small straight line segment for the stable cutting process (without vibrations). In unstable mode (with vibrations) the ellipse of displacements is really more visible. A difference in phase occurs between the tool tip displacements on the radial direction and on the cutting one. The feed motion direction and the cutting one are almost in phase. The values of the long and small ellipse axes (and their ratio) shows that these sizes are increasing with the feed rate value. The axis that goes through the stiffness center and the tool tip represents the maximum stiffness direction. The maximum (resp. minimum) stiffness axis of the tool is perpendicular to the large (resp. small) ellipse displacements axis. FFT analysis of the accelerometers signals allows to reach several important parameters and establish coherent correlations between tool tip displacements and the static - elastic characteristics of the machine tool components tested

Evidence of a metabolic memory to early-life dietary restriction in male C57BL/6 mice

<p>Background: Dietary restriction (DR) extends lifespan and induces beneficial metabolic effects in many animals. What is far less clear is whether animals retain a metabolic memory to previous DR exposure, that is, can early-life DR preserve beneficial metabolic effects later in life even after the resumption of ad libitum (AL) feeding. We examined a range of metabolic parameters (body mass, body composition (lean and fat mass), glucose tolerance, fed blood glucose, fasting plasma insulin and insulin-like growth factor 1 (IGF-1), insulin sensitivity) in male C57BL/6 mice dietary switched from DR to AL (DR-AL) at 11 months of age (mid life). The converse switch (AL-DR) was also undertaken at this time. We then compared metabolic parameters of the switched mice to one another and to age-matched mice maintained exclusively on an AL or DR diet from early life (3 months of age) at 1 month, 6 months or 10 months post switch.</p> <p>Results: Male mice dietary switched from AL-DR in mid life adopted the metabolic phenotype of mice exposed to DR from early life, so by the 10-month timepoint the AL-DR mice overlapped significantly with the DR mice in terms of their metabolic phenotype. Those animals switched from DR-AL in mid life showed clear evidence of a glycemic memory, with significantly improved glucose tolerance relative to mice maintained exclusively on AL feeding from early life. This difference in glucose tolerance was still apparent 10 months after the dietary switch, despite body mass, fasting insulin levels and insulin sensitivity all being similar to AL mice at this time.</p> <p>Conclusions: Male C57BL/6 mice retain a long-term glycemic memory of early-life DR, in that glucose tolerance is enhanced in mice switched from DR-AL in mid life, relative to AL mice, even 10 months following the dietary switch. These data therefore indicate that the phenotypic benefits of DR are not completely dissipated following a return to AL feeding. The challenge now is to understand the molecular mechanisms underlying these effects, the time course of these effects and whether similar interventions can confer comparable benefits in humans.</p&gt

Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control

Sampled-data analysis and harmonic balance analysis are applied to analyze switching DC-DC converters under constant on-time control. Design-oriented boundary conditions for the period-doubling bifurcation and the saddle-node bifurcation are derived. The required ramp slope to avoid the bifurcations and the assigned pole locations associated with the ramp are also derived. The derived boundary conditions are more general and accurate than those recently obtained. Those recently obtained boundary conditions become special cases under the general modeling approach presented in this paper. Different analyses give different perspectives on the system dynamics and complement each other. Under the sampled-data analysis, the boundary conditions are expressed in terms of signal slopes and the ramp slope. Under the harmonic balance analysis, the boundary conditions are expressed in terms of signal harmonics. The derived boundary conditions are useful for a designer to design a converter to avoid the occurrence of the period-doubling bifurcation and the saddle-node bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications on August 10, 2011; Manuscript ID: CTA-11-016

Seasonal changes in patterns of gene expression in avian song control brain regions.

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.Photoperiod and hormonal cues drive dramatic seasonal changes in structure and function of the avian song control system. Little is known, however, about the patterns of gene expression associated with seasonal changes. Here we address this issue by altering the hormonal and photoperiodic conditions in seasonally-breeding Gambel's white-crowned sparrows and extracting RNA from the telencephalic song control nuclei HVC and RA across multiple time points that capture different stages of growth and regression. We chose HVC and RA because while both nuclei change in volume across seasons, the cellular mechanisms underlying these changes differ. We thus hypothesized that different genes would be expressed between HVC and RA. We tested this by using the extracted RNA to perform a cDNA microarray hybridization developed by the SoNG initiative. We then validated these results using qRT-PCR. We found that 363 genes varied by more than 1.5 fold (>log(2) 0.585) in expression in HVC and/or RA. Supporting our hypothesis, only 59 of these 363 genes were found to vary in both nuclei, while 132 gene expression changes were HVC specific and 172 were RA specific. We then assigned many of these genes to functional categories relevant to the different mechanisms underlying seasonal change in HVC and RA, including neurogenesis, apoptosis, cell growth, dendrite arborization and axonal growth, angiogenesis, endocrinology, growth factors, and electrophysiology. This revealed categorical differences in the kinds of genes regulated in HVC and RA. These results show that different molecular programs underlie seasonal changes in HVC and RA, and that gene expression is time specific across different reproductive conditions. Our results provide insights into the complex molecular pathways that underlie adult neural plasticity

Targeting the TGF-β1 Pathway to Prevent Normal Tissue Injury After Cancer Therapy

Evidence supporting the critical role of transforming growth factor β1 in the development of normal tissue injury after cancer therapy is reviewed and the results of recent research aimed at preventing normal tissue injury by targeting the transforming growth factor β1 pathway are presented