Steklov-type eigenvalues associated with best Sobolev trace constants: domain perturbation and overdetermined systems

We consider a variant of the classic Steklov eigenvalue problem, which arises in the study of the best trace constant for functions in Sobolev space. We prove that the elementary symmetric functions of the eigenvalues depend real-analytically upon variation of the underlying domain and we compute the corresponding Hadamard-type formulas for the shape derivatives. We also consider isovolumetric and isoperimetric domain perturbations and we characterize the corresponding critical domains in terms of appropriate overdetermined systems. Finally, we prove that balls are critical domains for the elementary symmetric functions of the eigenvalues subject to volume or perimeter constraint

On the break in the single-particle energy dispersions and the `universal' nodal Fermi velocity in the high-temperature copper-oxide superconductors

Recent data from angle-resolved photoemission experiments published by Zhou et al. [Nature, Vol. 423, 398 (2003)] concerning a number of hole-doped copper-oxide-based high-temperature superconductors reveal that in the nodal directions of the underlying square Brillouin zones (i.e. the directions along which the d-wave superconducting gap is vanishing) the Fermi velocities for some finite range of k inside the Fermi sea and away from the nodal Fermi wavevector k_F are to within an experimental uncertainty of approximately 20% the same both in all the compounds investigated and over a wide range of doping concentrations and that, in line with earlier experimental observations, at some characteristic wavevector k_* away from k_F the Fermi velocities undergo a sudden change, with this change (roughly speaking, a finite discontinuity) being the greatest (smallest) in the case of underdoped (overdoped) compounds. In this paper we present a rigorous analysis concerning the implications of these observations. [Short abstract]Comment: 29 pages, 4 postscript figures. Brought into conformity with the published versio

Effects of short-term treatment with atorvastatin in smokers with asthma - a randomized controlled trial

<b>Background</b> The immune modulating properties of statins may benefit smokers with asthma. We tested the hypothesis that short-term treatment with atorvastatin improves lung function or indices of asthma control in smokers with asthma.<p></p> <b>Methods</b> Seventy one smokers with mild to moderate asthma were recruited to a randomized double-blind parallel group trial comparing treatment with atorvastatin (40 mg per day) versus placebo for 4 weeks. After 4 weeks treatment inhaled beclometasone (400 ug per day) was added to both treatment arms for a further 4 weeks. The primary outcome was morning peak expiratory flow after 4 weeks treatment. Secondary outcome measures included indices of asthma control and airway inflammation.<p></p> <b>Results</b> At 4 weeks, there was no improvement in the atorvastatin group compared to the placebo group in morning peak expiratory flow [-10.67 L/min, 95% CI -38.70 to 17.37, p=0.449], but there was an improvement with atorvastatin in asthma quality of life score [0.52, 95% CI 0.17 to 0.87 p=0.005]. There was no significant improvement with atorvastatin and inhaled beclometasone compared to inhaled beclometasone alone in outcome measures at 8 weeks.<p></p> <b>Conclusions</b> Short-term treatment with atorvastatin does not alter lung function but may improve asthma quality of life in smokers with mild to moderate asthma. Clinicaltrials.gov identifier: NCT0046382

q-Form fields on p-branes

In this paper, we give one general method for localizing any form (q-form) field on p-branes with one extra dimension, and apply it to some typical p-brane models. It is found that, for the thin and thick Minkowski branes with an infinite extra dimension, the zero mode of the q-form fields with q<(p-1)/2 can be localized on the branes. For the thick Minkowski p-branes with one finite extra dimension, the localizable q-form fields are those with q<p/2, and there are also some massive bound Kaluza-Klein modes for these q-form fields on the branes. For the same q-form field, the number of the bound Kaluza-Klein modes (but except the scalar field (q=0)) increases with the dimension of the p-branes. Moreover, on the same p-brane, the q-form fields with higher q have less number of massive bound KK modes. While for a family of pure geometrical thick p-branes with a compact extra dimension, the q-form fields with q<p/2 always have a localized zero mode. For a special pure geometrical thick p-brane, there also exist some massive bound KK modes of the q-form fields with q<p/2, whose number increases with the dimension of the p-brane.Comment: 14 pages, 2 figures, published versio

Robust Detection of Hierarchical Communities from Escherichia coli Gene Expression Data

Determining the functional structure of biological networks is a central goal of systems biology. One approach is to analyze gene expression data to infer a network of gene interactions on the basis of their correlated responses to environmental and genetic perturbations. The inferred network can then be analyzed to identify functional communities. However, commonly used algorithms can yield unreliable results due to experimental noise, algorithmic stochasticity, and the influence of arbitrarily chosen parameter values. Furthermore, the results obtained typically provide only a simplistic view of the network partitioned into disjoint communities and provide no information of the relationship between communities. Here, we present methods to robustly detect coregulated and functionally enriched gene communities and demonstrate their application and validity for Escherichia coli gene expression data. Applying a recently developed community detection algorithm to the network of interactions identified with the context likelihood of relatedness (CLR) method, we show that a hierarchy of network communities can be identified. These communities significantly enrich for gene ontology (GO) terms, consistent with them representing biologically meaningful groups. Further, analysis of the most significantly enriched communities identified several candidate new regulatory interactions. The robustness of our methods is demonstrated by showing that a core set of functional communities is reliably found when artificial noise, modeling experimental noise, is added to the data. We find that noise mainly acts conservatively, increasing the relatedness required for a network link to be reliably assigned and decreasing the size of the core communities, rather than causing association of genes into new communities.Comment: Due to appear in PLoS Computational Biology. Supplementary Figure S1 was not uploaded but is available by contacting the author. 27 pages, 5 figures, 15 supplementary file

Multiplex PCR technique could be an alternative approach for early detection of leprosy among close contacts - a pilot study from India

<p>Abstract</p> <p>Background</p> <p>Implementation of Multi drug Therapy (MDT) regimen has resulted in the decline of the total number of leprosy cases in the world. Though the prevalence rate has been declining, the incidence rate remains more or less constant and high in South East Asian countries particularly in India, Nepal, Bangladesh, Pakistan and Srilanka. Leprosy, particularly that of multibacillary type spreads silently before it is clinically detected. An early detection and treatment would help to prevent transmission in the community. Multiplex PCR (M-PCR) technique appears to be promising towards early detection among contacts of leprosy cases.</p> <p>Methods</p> <p>A total of 234 paucibacillary (PB) and 205 multibacillary (MB) leprosy cases were studied in a community of an endemic area of Bankura district of West Bengal (Eastern India). They were assessed by smear examination for acid-fast bacilli (AFB) and M-PCR technique. These patients were treated with Multidrug Therapy (MDT) as prescribed by WHO following detection. A total of 110 MB and 72 PB contacts were studied by performing M-PCR in their nasal swab samples.</p> <p>Results</p> <p>83.4% of MB patients were observed to be positive by smear examination for AFB and 89.2% by M-PCR. While 22.2% of PB patients were found to be positive by smear examination for AFB, 80.3% of these patients were positive by M-PCR. Among leprosy contacts (using M-PCR), 10.9% were found to be positive among MB contacts and 1.3% among PB contacts. Interestingly, two contacts of M-PCR positive MB cases developed leprosy during the period of two years follow up.</p> <p>Conclusion</p> <p>The M-PCR technique appears to be an efficient tool for early detection of leprosy cases in community based contact tracing amongst close associates of PB and MB cases. Early contact tracing using a molecular biology tool can be of great help in curbing the incidence of leprosy further.</p

Ferritins: furnishing proteins with iron

Ferritins are a superfamily of iron oxidation, storage and mineralization proteins found throughout the animal, plant, and microbial kingdoms. The majority of ferritins consist of 24 subunits that individually fold into 4-α-helix bundles and assemble in a highly symmetric manner to form an approximately spherical protein coat around a central cavity into which an iron-containing mineral can be formed. Channels through the coat at inter-subunit contact points facilitate passage of iron ions to and from the central cavity, and intrasubunit catalytic sites, called ferroxidase centers, drive Fe2+ oxidation and O2 reduction. Though the different members of the superfamily share a common structure, there is often little amino acid sequence identity between them. Even where there is a high degree of sequence identity between two ferritins there can be major differences in how the proteins handle iron. In this review we describe some of the important structural features of ferritins and their mineralized iron cores and examine in detail how three selected ferritins oxidise Fe2+ in order to explore the mechanistic variations that exist amongst ferritins. We suggest that the mechanistic differences reflect differing evolutionary pressures on amino acid sequences, and that these differing pressures are a consequence of different primary functions for different ferritins

The nuclear receptors of Biomphalaria glabrata and Lottia gigantea: Implications for developing new model organisms

© 2015 Kaur et al. 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 creditedNuclear receptors (NRs) are transcription regulators involved in an array of diverse physiological functions including key roles in endocrine and metabolic function. The aim of this study was to identify nuclear receptors in the fully sequenced genome of the gastropod snail, Biomphalaria glabrata, intermediate host for Schistosoma mansoni and compare these to known vertebrate NRs, with a view to assessing the snail's potential as a invertebrate model organism for endocrine function, both as a prospective new test organism and to elucidate the fundamental genetic and mechanistic causes of disease. For comparative purposes, the genome of a second gastropod, the owl limpet, Lottia gigantea was also investigated for nuclear receptors. Thirty-nine and thirty-three putative NRs were identified from the B. glabrata and L. gigantea genomes respectively, based on the presence of a conserved DNA-binding domain and/or ligand-binding domain. Nuclear receptor transcript expression was confirmed and sequences were subjected to a comparative phylogenetic analysis, which demonstrated that these molluscs have representatives of all the major NR subfamilies (1-6). Many of the identified NRs are conserved between vertebrates and invertebrates, however differences exist, most notably, the absence of receptors of Group 3C, which includes some of the vertebrate endocrine hormone targets. The mollusc genomes also contain NR homologues that are present in insects and nematodes but not in vertebrates, such as Group 1J (HR48/DAF12/HR96). The identification of many shared receptors between humans and molluscs indicates the potential for molluscs as model organisms; however the absence of several steroid hormone receptors indicates snail endocrine systems are fundamentally different.The National Centre for the Replacement, Refinement and Reduction of Animals in Research, Grant Ref:G0900802 to CSJ, LRN, SJ & EJR [www.nc3rs.org.uk]

Spin-related tunneling through a nanostructured electric-magnetic barrier on the surface of a topological insulator

We investigate quantum tunneling through a single electric and/or magnetic barrier on the surface of a three-dimensional topological insulator. We found that (1) the propagating behavior of electrons in such system exhibits a strong dependence on the direction of the incident electron wavevector and incident energy, giving the possibility to construct a wave vector and/or energy filter; (2) the spin orientation can be tuned by changing the magnetic barrier structure as well as the incident angles and energies