Analytic and Asymptotic Methods for Nonlinear Singularity Analysis: a Review and Extensions of Tests for the Painlev\'e Property

The integrability (solvability via an associated single-valued linear problem) of a differential equation is closely related to the singularity structure of its solutions. In particular, there is strong evidence that all integrable equations have the Painlev\'e property, that is, all solutions are single-valued around all movable singularities. In this expository article, we review methods for analysing such singularity structure. In particular, we describe well known techniques of nonlinear regular-singular-type analysis, i.e. the Painlev\'e tests for ordinary and partial differential equations. Then we discuss methods of obtaining sufficiency conditions for the Painlev\'e property. Recently, extensions of \textit{irregular} singularity analysis to nonlinear equations have been achieved. Also, new asymptotic limits of differential equations preserving the Painlev\'e property have been found. We discuss these also.Comment: 40 pages in LaTeX2e. To appear in the Proceedings of the CIMPA Summer School on "Nonlinear Systems," Pondicherry, India, January 1996, (eds) B. Grammaticos and K. Tamizhman

A versatile microarray platform for capturing rare cells

Analyses of rare events occurring at extremely low frequencies in body fluids are still challenging. We established a versatile microarray-based platform able to capture single target cells from large background populations. As use case we chose the challenging application of detecting circulating tumor cells (CTCs) - about one cell in a billion normal blood cells. After incubation with an antibody cocktail, targeted cells are extracted on a microarray in a microfluidic chip. The accessibility of our platform allows for subsequent recovery of targets for further analysis. The microarray facilitates exclusion of false positive capture events by co-localization allowing for detection without fluorescent labelling. Analyzing blood samples from cancer patients with our platform reached and partly outreached gold standard performance, demonstrating feasibility for clinical application. Clinical researchers free choice of antibody cocktail without need for altered chip manufacturing or incubation protocol, allows virtual arbitrary targeting of capture species and therefore wide spread applications in biomedical sciences

Therapy of intracellular Staphylococcus aureus by tigecyclin

Background: In the fields of traumatology and orthopaedics staphylococci are the most frequently isolated pathogens. Staphylococcus aureus and Staphylococcus epidermidis are known to be the major causative agents of osteomyelitis. The increasing number of multiresistant Staphylococcus aureus and resistant coagulase-negative staphylococci as a trigger of complicated osteomyelitis and implant-associated infections is a major problem. Antibiotic therapy fails in 20% of cases. Therefore the development of novel antibiotics becomes necessary. Methods: This study analyses tigecyclin, the first antibiotic of the glycylines, as a potential therapy for osteomyelitis caused by multiresistant Staphylococcus aureus. Therefore its intracellular activity and the potential use in polymethylmetacrylate-bone cement are examined. The intracellular activity of tigecyclin is determined by a human osteoblast infection model. The investigation of the biomechanical characteristics is conducted concerning the ISO 5833-guidelines. Results: Tigecyclin shows in vitro an intracellular activity that ranges between the antimicrobial activity of gentamicin and rifampicin. A significant negative effect on the biomechanical characteristics with an impaired stability is detected after adding tigecyclin to polymethylmetacrylate-bone cement with a percentage of 1.225% per weight. Conclusions: This study shows that tigecyclin might be a potent alternative for the systemic therapy of osteomyelitis and implant-associated infections whereas the local application has to be reconsidered individually.<br

Density functional theory calculations of adsorption-induced surface stress changes

Density functional theory calculations of adsorbate-induced surface stress changes have been performed for a number of adsorbate and overlayer systems for which experimental data exists, namely: oxygen and sulphur adsorption on Ni(1 0 0); oxygen adsorption on W(1 1 0); pseudomorphic growth of Ni on Cu(1 0 0) and of Fe on W(1 1 0); oxygen adsorption on a 5 ML pseudomorphic film of Ni(1 0 0) grown on Cu(1 0 0). The theoretical calculations reproduce all the qualitative features of the experimental data, but there are some significant quantitative differences, most notably for the two atomic adsorbates on the bulk Ni(1 0 0) surface, for which the theoretical stress changes are substantially smaller than the experimental ones, a situation not obviously attributable to experimental error. For the W(1 1 0)/Fe system there is also a marked difference between experiment and theory in the coverage at which key surface stress changes occur

Properties of hyperons in chiral perturbation theory

The development of chiral perturbation theory in hyperon phenomenology has been troubled due to power-counting subtleties and to a possible slow convergence. Furthermore, the presence of baryon-resonances, e.g. the lowest-lying decuplet, complicates the approach, and the inclusion of their effects may become necessary. Recently, we have shown that a fairly good convergence is possible using a renormalization prescription of the loop-divergencies which recovers the power counting, is covariant and consistent with analyticity. Moreover, we have systematically incorporated the decuplet resonances taking care of both power-counting and $consistency$ problems. A model-independent understanding of diferent properties including the magnetic moments of the baryon-octet, the electromagnetic structure of the decuplet resonances and the hyperon vector coupling $f_1(0)$, has been successfully achieved within this approach. We will briefly review these developments and stress the important role they play for an accurate determination of the Cabibbo-Kobayashi-Maskawa matrix element $V_{us}$ from hyperon semileptonic decay data.Comment: To appear in HypX Proceeding

A novel determination of the local dark matter density

We present a novel study on the problem of constructing mass models for the Milky Way, concentrating on features regarding the dark matter halo component. We have considered a variegated sample of dynamical observables for the Galaxy, including several results which have appeared recently, and studied a 7- or 8-dimensional parameter space - defining the Galaxy model - by implementing a Bayesian approach to the parameter estimation based on a Markov Chain Monte Carlo method. The main result of this analysis is a novel determination of the local dark matter halo density which, assuming spherical symmetry and either an Einasto or an NFW density profile is found to be around 0.39 GeV cm$^{-3}$ with a 1-$\sigma$ error bar of about 7%; more precisely we find a $\rho_{DM}(R_0) = 0.385 \pm 0.027 \rm GeV cm^{-3}$ for the Einasto profile and $\rho_{DM}(R_0) = 0.389 \pm 0.025 \rm GeV cm^{-3}$ for the NFW. This is in contrast to the standard assumption that $\rho_{DM}(R_0)$ is about 0.3 GeV cm$^{-3}$ with an uncertainty of a factor of 2 to 3. A very precise determination of the local halo density is very important for interpreting direct dark matter detection experiments. Indeed the results we produced, together with the recent accurate determination of the local circular velocity, should be very useful to considerably narrow astrophysical uncertainties on direct dark matter detection.Comment: 31 pages,11 figures; minor changes in the text; two figures adde

Anisotropy of Vortex-Liquid and Vortex-Solid Phases in Single Crystals of Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}: Violation of the Scaling Law

The vortex-liquid and vortex-solid phases in single crystals of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ placed in tilted magnetic fields are studied by in-plane resistivity measurements using the Corbino geometry to avoid spurious surface barrier effects. It was found that the anisotropy of the vortex-solid phase increases with temperature and exhibits a maximum at $T\approx 0.97 T_c$. In contrast, the anisotropy of the vortex-liquid rises monotonically across the whole measured temperature range. The observed behavior is discussed in the context of dimensional crossover and thermal fluctuations of vortices in the strongly layered system.Comment: 4 pages, 3 figures, submitted to Phys. Rev. Let

Neutrophil extracellular trap formation is independent of de novo gene expression

Neutrophils are essential innate immune cells whose responses are crucial in the clearance of invading pathogens. Neutrophils can respond to infection by releasing neutrophil extracellular traps (NETs). NETs are formed of chromatin and specific granular proteins and are released after execution of a poorly characterized cell death pathway. Here, we show that NET formation induced by PMA or Candida albicans is independent of RNA polymerase II and III-mediated transcription as well as of protein synthesis. Thus, neutrophils contain all the factors required for NET formation when they emerge from the bone marrow as differentiated cells

Propylene Carbonate Reexamined: Mode-Coupling β\beta Scaling without Factorisation ?

The dynamic susceptibility of propylene carbonate in the moderately viscous regime above $T_{\rm c}$ is reinvestigated by incoherent neutron and depolarised light scattering, and compared to dielectric loss and solvation response. Depending on the strength of $\alpha$ relaxation, a more or less extended $\beta$ scaling regime is found. Mode-coupling fits yield consistently $\lambda=0.72$ and $T_{\rm c}=182$K, although different positions of the susceptibility minimum indicate that not all observables have reached the universal asymptotics

A 15.7-minAM CVn binary discovered in K2

We present the discovery of SDSS J135154.46−064309.0, a short-period variable observed using 30-mincadence photometry in K2 Campaign 6. Follow-up spectroscopy and high-speed photometry support a classification as a new member of the rare class of ultracompact accreting binaries known as AM CVn stars. The spectroscopic orbital period of 15.65 ± 0.12 min makes this system the fourth-shortest-period AM CVn known, and the second system of this type to be discovered by the Kepler spacecraft. The K2 data show photometric periods at 15.7306 ± 0.0003 min, 16.1121 ± 0.0004 min, and 664.82 ± 0.06 min, which we identify as the orbital period, superhump period, and disc precession period, respectively. From the superhump and orbital periods we estimate the binary mass ratio q = M2/M1= 0.111 ± 0.005, though this method of mass ratio determination may not be well calibrated for helium-dominated binaries. This system is likely to be a bright foreground source of gravitational waves in the frequency range detectable by Laser Interferometer Space Antenna, and may be of use as a calibration source if future studies are able to constrain the masses of its stellar components