Singular solutions of fully nonlinear elliptic equations and applications

We study the properties of solutions of fully nonlinear, positively homogeneous elliptic equations near boundary points of Lipschitz domains at which the solution may be singular. We show that these equations have two positive solutions in each cone of $\mathbb{R}^n$, and the solutions are unique in an appropriate sense. We introduce a new method for analyzing the behavior of solutions near certain Lipschitz boundary points, which permits us to classify isolated boundary singularities of solutions which are bounded from either above or below. We also obtain a sharp Phragm\'en-Lindel\"of result as well as a principle of positive singularities in certain Lipschitz domains.Comment: 41 pages, 2 figure

Convexity criteria and uniqueness of absolutely minimizing functions

We show that absolutely minimizing functions relative to a convex Hamiltonian $H:\mathbb{R}^n \to \mathbb{R}$ are uniquely determined by their boundary values under minimal assumptions on $H.$ Along the way, we extend the known equivalences between comparison with cones, convexity criteria, and absolutely minimizing properties, to this generality. These results perfect a long development in the uniqueness/existence theory of the archetypal problem of the calculus of variations in $L^\infty.$Comment: 34 page

Homogenization of weakly coupled systems of Hamilton--Jacobi equations with fast switching rates

We consider homogenization for weakly coupled systems of Hamilton--Jacobi equations with fast switching rates. The fast switching rate terms force the solutions converge to the same limit, which is a solution of the effective equation. We discover the appearance of the initial layers, which appear naturally when we consider the systems with different initial data and analyze them rigorously. In particular, we obtain matched asymptotic solutions of the systems and rate of convergence. We also investigate properties of the effective Hamiltonian of weakly coupled systems and show some examples which do not appear in the context of single equations.Comment: final version, to appear in Arch. Ration. Mech. Ana

The Hyperfine Spin Splittings In Heavy Quarkonia

The hyperfine spin splittings in heavy quarkonia are studied using the recently developed renormalization group improved spin-spin potential which is independent of the scale parameter $\mu$. The calculated energy difference between the $J/\psi$ and the $\eta_c$ fits the experimental data well, while the predicted energy difference $\Delta M_p$ between the center of the gravity of $1^3P_{0,1,2}$ states and the $1^1P_1$ state of charmonium has the correct sign but is somewhat larger than the experimental data. This is not surprising since there are several other contributions to $\Delta M_p$, which we discuss, that are of comparable size ($\sim 1$ MeV) that should be included, before precise agreement with the data can be expected. The mass differences of the $\psi'-\eta_c'$, $\Upsilon(1S)-\eta_b$, $\Upsilon(2S)-\eta_b'$, and $B_c^*-B_c$ are also predicted.Comment: 17 page

Properties of heavy quarkonia and B_c mesons in the relativistic quark model

The mass spectra and electromagnetic decay rates of charmonium, bottomonium and B_c mesons are comprehensively investigated in the relativistic quark model. The presence of only heavy quarks allows the expansion in powers of their velocities. All relativistic corrections of order v^2/c^2, including retardation effects and one-loop radiative corrections, are systematically taken into account in the computations of the mass spectra. The obtained wave functions are used for the calculation of radiative magnetic dipole (M1) and electric dipole (E1) transitions. It is found that relativistic effects play a substantial role. Their account and the proper choice of the Lorentz structure of the quark-antiquark interaction in a meson is crucial for bringing theoretical predictions in accord with experimental data. A detailed comparison of the calculated decay rates and branching fractions with available experimental data for radiative decays of charmonium and bottomonium is presented. The possibilities to observe the currently missing spin-singlet S and P states as well as D states in bottomonium are discussed. The results for B_c masses and decays are compared with other quark model predictions.Comment: 31 pages, 2 figures, minor correction

SeHCAT [tauroselcholic (selenium-75) acid] for the investigation of bile acid malabsorption and measurement of bile acid pool loss

Background The principal diagnosis/indication for this assessment is chronic diarrhoea due to bile acid malabsorption (BAM). Diarrhoea can be defined as the abnormal passage of loose or liquid stools more than three times daily and/or a daily stool weight > 200 g per day and is considered to be chronic if it persists for more than 4 weeks. The cause of chronic diarrhoea in adults is often difficult to ascertain and patients may undergo several investigations without a definitive cause being identified. BAM is one of several causes of chronic diarrhoea and results from failure to absorb bile acids (which are required for the absorption of dietary fats and sterols in the intestine) in the distal ileum. Objective For people with chronic diarrhoea with unknown cause and in people with Crohn's disease and chronic diarrhoea with unknown cause (i.e. before resection): (1) What are the effects of selenium-75-homocholic acid taurine (SeHCAT) compared with no SeHCAT in terms of chronic diarrhoea, other health outcomes and costs? (2) What are the effects of bile acid sequestrants (BASs) compared with no BASs in people with a positive or negative SeHCAT test? (3) Does a positive or negative SeHCAT test predict improvement in terms of chronic diarrhoea, other health outcomes and costs? Data sources A systematic review was conducted to summarise the evidence on the clinical effectiveness of SeHCAT for the assessment of BAM and the measurement of bile acid pool loss. Search strategies were based on target condition and intervention, as recommended in the Centre for Reviews and Dissemination (CRD) guidance for undertaking reviews in health care and the Cochrane Handbook for Diagnostic Test Accuracy Reviews. The following databases were searched up to April 2012: MEDLINE; MEDLINE In-Process & Other Non-Indexed Citations; EMBASE; the Cochrane Databases; Database of Abstracts of Reviews of Effects; Health Technology Assessment (HTA) Database; and Science Citation Index. Research registers and conference proceedings were also searched. Review methods Systematic review methods followed the principle

Self-optimization, community stability, and fluctuations in two individual-based models of biological coevolution

We compare and contrast the long-time dynamical properties of two individual-based models of biological coevolution. Selection occurs via multispecies, stochastic population dynamics with reproduction probabilities that depend nonlinearly on the population densities of all species resident in the community. New species are introduced through mutation. Both models are amenable to exact linear stability analysis, and we compare the analytic results with large-scale kinetic Monte Carlo simulations, obtaining the population size as a function of an average interspecies interaction strength. Over time, the models self-optimize through mutation and selection to approximately maximize a community fitness function, subject only to constraints internal to the particular model. If the interspecies interactions are randomly distributed on an interval including positive values, the system evolves toward self-sustaining, mutualistic communities. In contrast, for the predator-prey case the matrix of interactions is antisymmetric, and a nonzero population size must be sustained by an external resource. Time series of the diversity and population size for both models show approximate 1/f noise and power-law distributions for the lifetimes of communities and species. For the mutualistic model, these two lifetime distributions have the same exponent, while their exponents are different for the predator-prey model. The difference is probably due to greater resilience toward mass extinctions in the food-web like communities produced by the predator-prey model.Comment: 26 pages, 12 figures. Discussion of early-time dynamics added. J. Math. Biol., in pres

Surface antigen profiles of leukocytes and melanoma cells in lymph node metastases are associated with survival in AJCC stage III melanoma patients

There is an urgent need to identify more accurate prognostic biomarkers in melanoma patients, particularly in those with metastatic disease. This study aimed to identify melanoma and leukocyte surface antigens predictive of survival in a prospective series of AJCC stage IIIb/c melanoma patients (n = 29). Live cell suspensions were prepared from melanoma metastases within lymph nodes (LN). The suspensions were immuno-magnetically separated into CD45+ (leukocyte) and CD45− (non-hematopoietic, enriched melanoma cell) fractions. Surface antigens on CD45− and CD45+ cell populations were profiled using DotScan™ microarrays (Medsaic Pty. Ltd.) and showed differential abundance levels for 52 and 78 antigens respectively. Associations of the surface profiles with clinicopathologic and outcome data (median follow-up 35.4 months post LN resection) were sought using univariate (log-rank test) and multivariate (Wald’s test; modelled with patient’s age, gender and AJCC staging at LN recurrence) survival models. CD9 (p = 0.036), CD39 (p = 0.004) and CD55 (p = 0.005) on CD45+ leukocytes were independently associated with distant metastasis-free survival using multivariate analysis. Leukocytes with high CD39 levels were also significantly associated with increased overall survival (OS) in multivariate analysis (p = 0.016). LNs containing leukocytes expressing CD11b (p = 0.025), CD49d (p = 0.043) and CD79b (p = 0.044) were associated with reduced OS on univariate analysis. For enriched melanoma cells (CD45− cell populations), 11 surface antigens were significantly correlated with the disease-free interval (DFI) between diagnosis of culprit primary melanoma and LN metastasis resection. Nine antigens on CD45+ leukocytes also correlated with DFI. Following validation in independent datasets, surface markers identified here should enable more accurate determination of prognosis in stage III melanoma patients and provide better risk stratification of patients entering clinical trials

A diagnostic PCR assay for the detection of an Australian epidemic strain of Pseudomonas aeruginosa

Background Chronic lung infection with the bacterium Pseudomonas aeruginosa is one of the hallmarks of cystic fibrosis (CF) and is associated with worsening lung function, increased hospitalisation and reduced life expectancy. A virulent clonal strain of P. aeruginosa (Australian epidemic strain I; AES-I) has been found to be widespread in CF patients in eastern Australia. Methods Suppression subtractive hybridization (SSH) was employed to identify genetic sequences that are present in the AES-I strain but absent from the sequenced reference strain PAO1. We used PCR to evaluate the distribution of several of the AES-I loci amongst a collection of 188 P. aeruginosa isolates which was comprised of 35 AES-I isolates (as determined by PFGE), 78 non-AES-I CF isolates including other epidemic CF strains as well as 69 P. aeruginosa isolates from other clinical and environmental sources. Results We have identified a unique AES-I genetic locus that is present in all 35 AES-I isolates tested and not present in any of the other 153 P. aeruginosa strains examined. We have used this unique AES-I locus to develop a diagnostic PCR and a real-time PCR assay to detect the presence of P. aeruginosa and AES-I in patient sputum samples

Carotenoid content and reflectance of yellow and red nuptial plumages in widowbirds (Euplectes spp.)

1. Ornamental carotenoid coloration is commonly based on several different pigments with different nutritional and metabolic constraints. The identification and quantification of carotenoid pigments is therefore crucial to the understanding of signal content and signal evolution. 2. In male widowbirds (Euplectes spp.), the striking yellow and red carotenoid colours have been measured by reflectance spectrometry and studied with respect to sexual selection through male contest competition, but their biochemical mechanisms have not been analysed. 3. Here we use reflectance analysis and high performance liquid chromatography (HPLC) to describe the species-specific colours and plumage carotenoids in three widowbird species: yellow-mantled widowbird (YMW) Euplectes macrourus, red-shouldered widowbird (RSW) E. axillaris and red-collared widowbird (RCW) E. ardens. 4. YMW yellow (‘hue’ colorimetric λR50 = 522 nm) derives from the two ‘dietary yellow’ xanthophylls lutein and zeaxanthin, together with small amounts of ‘derived yellow’ pigments (3′-dehydrolutein and canary xanthophylls). 5. RCW red (λR50 = 574 nm) is achieved by the addition of low concentrations of ‘derived red ’ 4-keto-carotenoids, notably α- and β-doradexanthin and canthaxanthin. 6. RSW red (λR50 = 589 nm) is, in contrast, created by high concentrations of ‘dietary yellow ’ pigments (lutein, zeaxanthin) and ‘derived yellow ’ anhydrolutein, the latter only recently described in birds. 7. The two different mechanisms of producing red plumage are compared with other bird species and discussed with regard to costs and signal ‘honesty’