On the algebraic structures connected with the linear Poisson brackets of hydrodynamics type

The generalized form of the Kac formula for Verma modules associated with linear brackets of hydrodynamics type is proposed. Second cohomology groups of the generalized Virasoro algebras are calculated. Connection of the central extensions with the problem of quntization of hydrodynamics brackets is demonstrated

Quadratic Poisson brackets compatible with an algebra structure

Quadratic Poisson brackets on a vector space equipped with a bilinear multiplication are studied. A notion of a bracket compatible with the multiplication is introduced and an effective criterion of such compatibility is given. Among compatible brackets, a subclass of coboundary brackets is described, and such brackets are enumerated in a number of examples.Comment: 6 page

Chern-Simons action for zero-mode supporting gauge fields in three dimensions

Recent results on zero modes of the Abelian Dirac operator in three dimensions support to some degree the conjecture that the Chern-Simons action admits only certain quantized values for gauge fields that lead to zero modes of the corresponding Dirac operator. Here we show that this conjecture is wrong by constructing an explicit counter-example.Comment: version as published in PRD, minor change

A simple proof of Hardy-Lieb-Thirring inequalities

We give a short and unified proof of Hardy-Lieb-Thirring inequalities for moments of eigenvalues of fractional Schroedinger operators. The proof covers the optimal parameter range. It is based on a recent inequality by Solovej, Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger constant).Comment: 12 page

Eigenfunctions at the threshold energies of magnetic Dirac operators

Discussed are $\pm m$ modes and $\pm m$ resonances of Dirac operators with vector potentials $H_{\!A}= \alpha \cdot (D - A(x)) + m \beta$. Asymptotic limits of $\pm m$ modes at infinity are derived when $|A(x)| \le C^{-\rho}$, $\rho > 1$, provided that $H_A$ has $\pm m$ modes. In wider classes of vector potentials, sparseness of the vector potentials which give rise to the $\pm m$ modes of $H_A$ are established. It is proved that no $H_A$ has $\pm m$ resonances if $|A(x)|\le C^{-\rho}$, $\rho >3/2$.Comment: 25 pages, New results are adde

Ectodermal Influx and Cell Hypertrophy Provide Early Growth for All Murine Mammary Rudiments, and Are Differentially Regulated among Them by Gli3

Mammary gland development starts in utero with one or several pairs of mammary rudiments (MRs) budding from the surface ectodermal component of the mammalian embryonic skin. Mice develop five pairs, numbered MR1 to MR5 from pectoral to inguinal position. We have previously shown that Gli3Xt-J/Xt-J mutant embryos, which lack the transcription factor Gli3, do not form MR3 and MR5. We show here that two days after the MRs emerge, Gli3Xt-J/Xt-J MR1 is 20% smaller, and Gli3Xt-J/Xt-J MR2 and MR4 are 50% smaller than their wild type (wt) counterparts. Moreover, while wt MRs sink into the underlying dermis, Gli3Xt-J/Xt-J MR4 and MR2 protrude outwardly, to different extents. To understand why each of these five pairs of functionally identical organs has its own, distinct response to the absence of Gli3, we determined which cellular mechanisms regulate growth of the individual MRs, and whether and how Gli3 regulates these mechanisms. We found a 5.5 to 10.7-fold lower cell proliferation rate in wt MRs compared to their adjacent surface ectoderm, indicating that MRs do not emerge or grow via locally enhanced cell proliferation. Cell-tracing experiments showed that surface ectodermal cells are recruited toward the positions where MRs emerge, and contribute to MR growth during at least two days. During the second day of MR development, peripheral cells within the MRs undergo hypertrophy, which also contributes to MR growth. Limited apoptotic cell death counterbalances MR growth. The relative contribution of each of these processes varies among the five MRs. Furthermore, each of these processes is impaired in the absence of Gli3, but to different extents in each MR. This differential involvement of Gli3 explains the variation in phenotype among Gli3Xt-J/Xt-J MRs, and may help to understand the variation in numbers and positions of mammary glands among mammals

Path to Facilitate the Prediction of Functional Amino Acid Substitutions in Red Blood Cell Disorders – A Computational Approach

A major area of effort in current genomics is to distinguish mutations that are functionally neutral from those that contribute to disease. Single Nucleotide Polymorphisms (SNPs) are amino acid substitutions that currently account for approximately half of the known gene lesions responsible for human inherited diseases. As a result, the prediction of non-synonymous SNPs (nsSNPs) that affect protein functions and relate to disease is an important task.In this study, we performed a comprehensive analysis of deleterious SNPs at both functional and structural level in the respective genes associated with red blood cell metabolism disorders using bioinformatics tools. We analyzed the variants in Glucose-6-phosphate dehydrogenase (G6PD) and isoforms of Pyruvate Kinase (PKLR & PKM2) genes responsible for major red blood cell disorders. Deleterious nsSNPs were categorized based on empirical rule and support vector machine based methods to predict the impact on protein functions. Furthermore, we modeled mutant proteins and compared them with the native protein for evaluation of protein structure stability.We argue here that bioinformatics tools can play an important role in addressing the complexity of the underlying genetic basis of Red Blood Cell disorders. Based on our investigation, we report here the potential candidate SNPs, for future studies in human Red Blood Cell disorders. Current study also demonstrates the presence of other deleterious mutations and also endorses with in vivo experimental studies. Our approach will present the application of computational tools in understanding functional variation from the perspective of structure, expression, evolution and phenotype

The experience of living with chronic heart failure: a narrative review of qualitative studies

<p>Abstract</p> <p>Background</p> <p>Chronic heart failure (CHF) is the leading cause of all hospitalisations and readmissions in older people, accounting for a large proportion of developed countries' national health care expenditure. CHF can severely affect people's quality of life by reducing their independence and ability to undertake certain activities of daily living, as well as affecting their psychosocial and economic capacity. This paper reports the findings of a systematic narrative review of qualitative studies concerning people's experience of living with CHF, aiming to develop a wide-ranging understanding of what is known about the patient experience.</p> <p>Methods</p> <p>We searched eight relevant electronic databases using the terms based on the diagnosis of 'chronic heart failure', 'heart failure' and 'congestive heart failure' and qualitative methods, with restrictions to the years 1990-May 2008. We also used snowballing, hand searching and the expert knowledge of the research team to ensure all relevant papers were included in the review. Of 65 papers collected less than half (n = 30) were found relevant for this review. These papers were subsequently summarised and entered into QSR NVivo7 for data management and analysis.</p> <p>Results</p> <p>The review has identified the most prominent impacts of CHF on a person's everyday life including social isolation, living in fear and losing a sense of control. It has also identified common strategies through which patients with CHF manage their illness such as sharing experiences and burdens with others and being flexible to changing circumstances.</p> <p>Finally, there are multiple factors that commonly impact on patients' self care and self-management in the disease trajectory including knowledge, understanding and health service encounters. These health service encounters encompass access, continuity and quality of care, co-morbid conditions, and personal relationships.</p> <p>Conclusions</p> <p>The core and sub-concepts identified within this study provide health professionals, service providers, policy makers and educators with broad insights into common elements of people's experiences of CHF and potential options for improving their health and wellbeing. Future studies should focus on building a comprehensive picture of CHF through examination of differences between genders, and differences within age groups, socioeconomic groups and cultural groups.</p

STAGES IN THE ORIGIN OF VERTEBRATES: ANALYSIS BY MEANS OF SCENARIOS

Vertebrates lack an epidermal nerve plexus. This feature is common to many invertebrates from which vertebrates differ by an extensive set of shared-derived characters (synapomorphies) derived from the neural crest and epidermal neurogenic placodes. Hence, the hypothesis that the developmental precursor of the epidermal nerve plexus may be homologous to the neural crest and epidermal neurogenic placodes. This account attempts to generate a nested set of scenarios for the prevertebrate-vertebrate transition, associating a presumed sequence of behavioural and environmental changes with the observed phenotypic ones. Toward this end, it integrates morphological, developmental, functional (physiological/behavioural) and some ecological data, as many phenotypic shifts apparently involved associated transitions in several aspects of the animals. The scenarios deal with the origin of embryonic and adult tissues and such major organs as the notochord, the CNS, gills and kidneys and propose a sequence of associated changes. Alternative scenarios are stated as the evidence often remains insufficient for decision. The analysis points to gaps in comprehension of the biology of the animals and therefore suggests further research.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/72629/1/j.1469-185X.1989.tb00471.x.pd