A Survey on the Krein-von Neumann Extension, the corresponding Abstract Buckling Problem, and Weyl-Type Spectral Asymptotics for Perturbed Krein Laplacians in Nonsmooth Domains

In the first (and abstract) part of this survey we prove the unitary equivalence of the inverse of the Krein--von Neumann extension (on the orthogonal complement of its kernel) of a densely defined, closed, strictly positive operator, $S\geq \varepsilon I_{\mathcal{H}}$ for some $\varepsilon >0$ in a Hilbert space $\mathcal{H}$ to an abstract buckling problem operator. This establishes the Krein extension as a natural object in elasticity theory (in analogy to the Friedrichs extension, which found natural applications in quantum mechanics, elasticity, etc.). In the second, and principal part of this survey, we study spectral properties for $H_{K,\Omega}$, the Krein--von Neumann extension of the perturbed Laplacian $-\Delta+V$ (in short, the perturbed Krein Laplacian) defined on $C^\infty_0(\Omega)$, where $V$ is measurable, bounded and nonnegative, in a bounded open set $\Omega\subset\mathbb{R}^n$ belonging to a class of nonsmooth domains which contains all convex domains, along with all domains of class $C^{1,r}$, $r>1/2$.Comment: 68 pages. arXiv admin note: extreme text overlap with arXiv:0907.144

Association between serum keptin concentrations and insulin resistance: A population-based study from China

BACKGROUND Insulin resistance contributes to the cardio-metabolic risk. The effect of leptin in obese and overweight population on insulin resistance was seldom reported. METHODS A total of 1234 subjects (572 men and 662 women) aged ≥18 y was sampled by the procedure. Adiposity measures included BMI, waist circumference, hip circumference, WHR, upper arm circumference, triceps skinfold and body fat percentage. Serum leptin concentrations were measured by an ELISA method. The homeostasis model (HOMA-IR) was applied to estimate insulin resistance. RESULTS In men, BMI was the variable which was most strongly correlated with leptin, whereas triceps skinfold was most sensitive for women. More importantly, serum leptin levels among insulin resistant subjects were almost double compared to the subjects who had normal insulin sensitivity at the same level of adiposity in both men and women, after controlling for potential confounders. In addition, HOMA-IR increased significantly across leptin quintiles after adjustment for age, BMI, total energy intake, physical activity and smoking status in both men and women (p for trend <0.0001). CONCLUSIONS There was a significant association between HOMA-IR and serum leptin concentrations in Chinese men and women, independently of adiposity levels. This may suggest that serum leptin concentration is an important predictor of insulin resistance and other metabolic risks irrespective of obesity levels. Furthermore, leptin levels may be used to identify the cardio-metabolic risk in obese and overweight population.Hui Zuo, Zumin Shi, Baojun Yuan, Yue Dai, Gaolin Wu, Akhtar Hussai

Gene products of chromosome 11q and their association with CCND1 gene amplification and tamoxifen resistance in premenopausal breast cancer

Introduction: The amplification event occurring at chromosome locus 11q13, reported in several different cancers, includes a number of potential oncogenes. We have previously reported amplification of one such oncogene, namely CCND1, to be correlated with an adverse effect of tamoxifen in premenopausal breast cancer patients. Over-expression of cyclin D-1 protein, however, confers tamoxifen resistance but not a tamoxifen-induced adverse effect. Potentially, co-amplification of an additional 11q13 gene, with a resulting protein over-expression, is required to cause an agonistic effect. Moreover, during 11q13 amplification a deletion of the distal 11q region has been described. In order to assess the potential impact of the deletion we examined a selected marker for this event. Method: Array comparative genomic hybridization analysis was employed to identify and confirm changes in the gene expression of a number of different genes mapping to the 11q chromosomal region, associated with CCND1 amplification. The subsequent protein expression of these candidate genes was then examined in a clinical material of 500 primary breast cancers from premenopausal patients who were randomly assigned to either tamoxifen or no adjuvant treatment. The protein expression was also compared with gene expression data in a subset of 56 breast cancer samples. Results: Cortactin and FADD (Fas-associated death domain) over-expression was linked to CCND1 amplification, determined by fluorescence in situ hybridization, but was not associated with a diminished effect of tamoxifen. However, deletion of distal chromosome 11q, defined as downregulation of the marker Chk1 (checkpoint kinase 1), was associated with an impaired tamoxifen response, and interestingly with low proliferative breast cancer of low grade. For Pak1 (p21-activated kinase 1) and cyclin D-1 the protein expression corresponded to the gene expression data. Conclusions: The results indicate that many 11q13 associated gene products are over-expressed in conjunction with cyclin D-1 but not linked to an agonistic effect of tamoxifen. Finally, the deletion of distal 11q, linked to 11q13 amplification, might be an important event affecting breast cancer outcome and tamoxifen response

Trigger finger: etiology, evaluation, and treatment

Trigger finger is a common finger aliment, thought to be caused by inflammation and subsequent narrowing of the A1 pulley, which causes pain, clicking, catching, and loss of motion of the affected finger. Although it can occur in anyone, it is seen more frequently in the diabetic population and in women, typically in the fifth to sixth decade of life. The diagnosis is usually fairly straightforward, as most patients complain of clicking or locking of the finger, but other pathological processes such as fracture, tumor, or other traumatic soft tissue injuries must be excluded. Treatment modalities, including splinting, corticosteroid injection, or surgical release, are very effective and are tailored to the severity and duration of symptoms

Phylogeny in Aid of the Present and Novel Microbial Lineages: Diversity in Bacillus

Bacillus represents microbes of high economic, medical and biodefense importance. Bacillus strain identification based on 16S rRNA sequence analyses is invariably limited to species level. Secondly, certain discrepancies exist in the segregation of Bacillus subtilis strains. In the RDP/NCBI databases, out of a total of 2611 individual 16S rDNA sequences belonging to the 175 different species of the genus Bacillus, only 1586 have been identified up to species level. 16S rRNA sequences of Bacillus anthracis (153 strains), B. cereus (211 strains), B. thuringiensis (108 strains), B. subtilis (271 strains), B. licheniformis (131 strains), B. pumilus (83 strains), B. megaterium (47 strains), B. sphaericus (42 strains), B. clausii (39 strains) and B. halodurans (36 strains) were considered for generating species-specific framework and probes as tools for their rapid identification. Phylogenetic segregation of 1121, 16S rDNA sequences of 10 different Bacillus species in to 89 clusters enabled us to develop a phylogenetic frame work of 34 representative sequences. Using this phylogenetic framework, 305 out of 1025, 16S rDNA sequences presently classified as Bacillus sp. could be identified up to species level. This identification was supported by 20 to 30 nucleotides long signature sequences and in silico restriction enzyme analysis specific to the 10 Bacillus species. This integrated approach resulted in identifying around 30% of Bacillus sp. up to species level and revealed that B. subtilis strains can be segregated into two phylogenetically distinct groups, such that one of them may be renamed

Geometry and field theory in multi-fractional spacetime

We construct a theory of fields living on continuous geometries with fractional Hausdorff and spectral dimensions, focussing on a flat background analogous to Minkowski spacetime. After reviewing the properties of fractional spaces with fixed dimension, presented in a companion paper, we generalize to a multi-fractional scenario inspired by multi-fractal geometry, where the dimension changes with the scale. This is related to the renormalization group properties of fractional field theories, illustrated by the example of a scalar field. Depending on the symmetries of the Lagrangian, one can define two models. In one of them, the effective dimension flows from 2 in the ultraviolet (UV) and geometry constrains the infrared limit to be four-dimensional. At the UV critical value, the model is rendered power-counting renormalizable. However, this is not the most fundamental regime. Compelling arguments of fractal geometry require an extension of the fractional action measure to complex order. In doing so, we obtain a hierarchy of scales characterizing different geometric regimes. At very small scales, discrete symmetries emerge and the notion of a continuous spacetime begins to blur, until one reaches a fundamental scale and an ultra-microscopic fractal structure. This fine hierarchy of geometries has implications for non-commutative theories and discrete quantum gravity. In the latter case, the present model can be viewed as a top-down realization of a quantum-discrete to classical-continuum transition.Comment: 1+82 pages, 1 figure, 2 tables. v2-3: discussions clarified and improved (especially section 4.5), typos corrected, references added; v4: further typos correcte

Topographical body fat distribution links to amino acid and lipid metabolism in healthy non-obese women.

Visceral adiposity is increasingly recognized as a key condition for the development of obesity related disorders, with the ratio between visceral adipose tissue (VAT) and subcutaneous adipose tissue (SAT) reported as the best correlate of cardiometabolic risk. In this study, using a cohort of 40 obese females (age: 25-45 y, BMI: 28-40 kg/m(2)) under healthy clinical conditions and monitored over a 2 weeks period we examined the relationships between different body composition parameters, estimates of visceral adiposity and blood/urine metabolic profiles. Metabonomics and lipidomics analysis of blood plasma and urine were employed in combination with in vivo quantitation of body composition and abdominal fat distribution using iDXA and computerized tomography. Of the various visceral fat estimates, VAT/SAT and VAT/total abdominal fat ratios exhibited significant associations with regio-specific body lean and fat composition. The integration of these visceral fat estimates with metabolic profiles of blood and urine described a distinct amino acid, diacyl and ether phospholipid phenotype in women with higher visceral fat. Metabolites important in predicting visceral fat adiposity as assessed by Random forest analysis highlighted 7 most robust markers, including tyrosine, glutamine, PC-O 44∶6, PC-O 44∶4, PC-O 42∶4, PC-O 40∶4, and PC-O 40∶3 lipid species. Unexpectedly, the visceral fat associated inflammatory profiles were shown to be highly influenced by inter-days and between-subject variations. Nevertheless, the visceral fat associated amino acid and lipid signature is proposed to be further validated for future patient stratification and cardiometabolic health diagnostics