Undirected Graphs of Entanglement Two

Entanglement is a complexity measure of directed graphs that origins in fixed point theory. This measure has shown its use in designing efficient algorithms to verify logical properties of transition systems. We are interested in the problem of deciding whether a graph has entanglement at most k. As this measure is defined by means of games, game theoretic ideas naturally lead to design polynomial algorithms that, for fixed k, decide the problem. Known characterizations of directed graphs of entanglement at most 1 lead, for k = 1, to design even faster algorithms. In this paper we present an explicit characterization of undirected graphs of entanglement at most 2. With such a characterization at hand, we devise a linear time algorithm to decide whether an undirected graph has this property

Changes in antibiotic use in Dutch hospitals over a six-year period: 1997 to 2002

OBJECTIVE: To analyse trends in antibiotic use in Dutch hospitals over the period 1997 to 2002. METHODS: Data on the use of antibiotics and hospital resource indicators were obtained by distributing a questionnaire to all Dutch hospital pharmacies. Antibiotic use was expressed as the number of defined daily doses (DDD) per 100 patient-days and as DDD per 100 admissions. RESULTS: Between 1997 and 2002, the mean length of stay decreased by 18%. The mean number of admissions remained almost constant. Total antibiotic use significantly increased by 24%, from 47.2 in 1997 to 58.5 DDD per 100 patient-days in 2002 (p<0.01), whereas expressed as DDD per admissions it remained constant. Antibiotic use varied greatly between the hospitals. Moreover, the mean number of DDD per hospital of amoxicillin with clavulanic acid, clarithromycin, cefazolin, clindamycin and ciprofloxacin increased by 16, 38, 39, 50 and 52%, respectively. Total antibiotic use was higher in university hospitals than in general hospitals. CONCLUSIONS: Between 1997 and 2002, patients hospitalised in the Netherlands did not receive more antibiotics but, since they remained in the hospital for fewer days, the number of DDD per 100 patient-days increased. For macrolides, lincosamides and fluoroquinolones increases in both DDD per 100 patient-days and in DDD per 100 admissions were observed. It is arguable whether these trends result in an increase in selection pressure towards resistance in the hospitals. Continuous surveillance of antibiotic use and resistance is warranted to maintain efficacy and safety of antibiotic treatment

Microthyriaceae sp., an endophytic fungus

In screening for natural products with antiparasitic activity, an endophytic fungus, strain F2611, isolated from above-ground tissue of the tropical grass Paspalum conjugatum (Poaceae) in Panama, was chosen for bioactive principle elucidation. Cultivation on malt extract agar (MEA) followed by bioassayguided chromatographic fractionation of the extract led to the isolation of the new polyketide integrasone B (1) and two known mycotoxins, sterigmatocystin (2) and secosterigmatocystin (3). Sterigmatocystin (2) was found to be the main antiparasitic compound in the fermentation extract of this fungus, possessing potent and selective antiparasitic activity against Trypanosoma cruzi, the cause of Chagas disease, with an IC50 value of 0 13 lmol l 1. Compounds 2 and 3 showed high cytotoxicity against Vero cells (IC50 of 0 06 and 0 97 lmol l 1, respectively). The new natural product integrasone B (1), which was co-purified from the active fractions, constitutes the second report of a natural product possessing an epoxyquinone with a lactone ring and exhibited no significant biological activity. Strain F2611 represents a previously undescribed taxon within the Microthyriaceae (Dothideomycetes, AscomycotaIn screening for natural products with antiparasitic activity, an endophytic fungus, strain F2611, isolated from above-ground tissue of the tropical grass Paspalum conjugatum (Poaceae) in Panama, was chosen for bioactive principle elucidation. Cultivation on malt extract agar (MEA) followed by bioassayguided chromatographic fractionation of the extract led to the isolation of the new polyketide integrasone B (1) and two known mycotoxins, sterigmatocystin (2) and secosterigmatocystin (3). Sterigmatocystin (2) was found to be the main antiparasitic compound in the fermentation extract of this fungus, possessing potent and selective antiparasitic activity against Trypanosoma cruzi, the cause of Chagas disease, with an IC50 value of 0 13 lmol l 1. Compounds 2 and 3 showed high cytotoxicity against Vero cells (IC50 of 0 06 and 0 97 lmol l 1, respectively). The new natural product integrasone B (1), which was co-purified from the active fractions, constitutes the second report of a natural product possessing an epoxyquinone with a lactone ring and exhibited no significant biological activity. Strain F2611 represents a previously undescribed taxon within the Microthyriaceae (Dothideomycetes, AscomycotaLaboratory of Tropical Bioorganic Chemistry, Faculty of Natural Exact Sciences and Technology, University of Panama, Panama City, Republic of Panama Smithsonian Tropical Research Institute, Balboa, Panama City, Republic of Panama Centro de Biodiversidade, Gen omica Integrativa e Funcional (BioFIG), Universidade de Lisboa, Faculdade de Ci^encias, Edif ıcio ICAT/TecLabs, Campus da FCUL, Campo Grande, Lisboa, Portugal Institute for Advanced Scientific Investigation and High Technology Services, National Secretariat of Science, Technology, and Innovation, City of Knowledge, Panama City, Republic of Panama School of Plant Sciences, The University of Arizona, Tucson, AZ, USA Department of Biology, University of Utah, Salt Lake City, UT, USA Center for Marine Biotechnology and Biomedicine, Scripps Institution of Oceanography and Skaggs School of Pharmacy and Pharmaceutical Sciences, University of California San Diego, La Jolla, CA, US

Superfluid toroidal currents in atomic condensates

The dynamics of toroidal condensates in the presence of condensate flow and dipole perturbation have been investigated. The Bogoliubov spectrum of condensate is calculated for an oblate torus using a discrete-variable representation and a spectral method to high accuracy. The transition from spheroidal to toroidal geometry of the trap displaces the energy levels into narrow bands. The lowest-order acoustic modes are quantized with the dispersion relation $\omega \sim |m| \omega_s$ with $m=0,\pm 1,\pm 2, ...$. A condensate with toroidal current $\kappa$ splits the $|m|$ co-rotating and counter-rotating pair by the amount: $\Delta E \approx 2 |m|\hbar^2 \kappa < r^{-2}>$. Radial dipole excitations are the lowest energy dissipation modes. For highly occupied condensates the nonlinearity creates an asymmetric mix of dipole circulation and nonlinear shifts in the spectrum of excitations so that the center of mass circulates around the axis of symmetry of the trap. We outline an experimental method to study these excitations.Comment: 8 pages, 8 figure

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least $k$ column vectors, where $k$ is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension $k$. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where $k$ is much smaller than the matrix dimension. We also give an extension of the method to the case where $k$ is larger than the matrix dimension. The quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours. Using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

GG-Strands

A $G$-strand is a map $g(t,{s}):\,\mathbb{R}\times\mathbb{R}\to G$ for a Lie group $G$ that follows from Hamilton's principle for a certain class of $G$-invariant Lagrangians. The SO(3)-strand is the $G$-strand version of the rigid body equation and it may be regarded physically as a continuous spin chain. Here, $SO(3)_K$-strand dynamics for ellipsoidal rotations is derived as an Euler-Poincar\'e system for a certain class of variations and recast as a Lie-Poisson system for coadjoint flow with the same Hamiltonian structure as for a perfect complex fluid. For a special Hamiltonian, the $SO(3)_K$-strand is mapped into a completely integrable generalization of the classical chiral model for the SO(3)-strand. Analogous results are obtained for the $Sp(2)$-strand. The $Sp(2)$-strand is the $G$-strand version of the $Sp(2)$ Bloch-Iserles ordinary differential equation, whose solutions exhibit dynamical sorting. Numerical solutions show nonlinear interactions of coherent wave-like solutions in both cases. ${\rm Diff}(\mathbb{R})$-strand equations on the diffeomorphism group $G={\rm Diff}(\mathbb{R})$ are also introduced and shown to admit solutions with singular support (e.g., peakons).Comment: 35 pages, 5 figures, 3rd version. To appear in J Nonlin Sc

Orbital stability: analysis meets geometry

We present an introduction to the orbital stability of relative equilibria of Hamiltonian dynamical systems on (finite and infinite dimensional) Banach spaces. A convenient formulation of the theory of Hamiltonian dynamics with symmetry and the corresponding momentum maps is proposed that allows us to highlight the interplay between (symplectic) geometry and (functional) analysis in the proofs of orbital stability of relative equilibria via the so-called energy-momentum method. The theory is illustrated with examples from finite dimensional systems, as well as from Hamiltonian PDE's, such as solitons, standing and plane waves for the nonlinear Schr{\"o}dinger equation, for the wave equation, and for the Manakov system

Neutrinoless double-beta decay and seesaw mechanism

From the standard seesaw mechanism of neutrino mass generation, which is based on the assumption that the lepton number is violated at a large (~10exp(+15) GeV) scale, follows that the neutrinoless double-beta decay is ruled by the Majorana neutrino mass mechanism. Within this notion, for the inverted neutrino-mass hierarchy we derive allowed ranges of half-lives of the neutrinoless double-beta decay for nuclei of experimental interest with different sets of nuclear matrix elements. The present-day results of the calculation of the neutrinoless double-beta decay nuclear matrix elements are briefly discussed. We argue that if neutrinoless double-beta decay will be observed in future experiments sensitive to the effective Majorana mass in the inverted mass hierarchy region, a comparison of the derived ranges with measured half-lives will allow us to probe the standard seesaw mechanism assuming that future cosmological data will establish the sum of neutrino masses to be about 0.2 eV.Comment: Some changes in sections I, II, IV, and V; two new figures; additional reference

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Critical exponents and equation of state of the three-dimensional Heisenberg universality class

We improve the theoretical estimates of the critical exponents for the three-dimensional Heisenberg universality class. We find gamma=1.3960(9), nu=0.7112(5), eta=0.0375(5), alpha=-0.1336(15), beta=0.3689(3), and delta=4.783(3). We consider an improved lattice phi^4 Hamiltonian with suppressed leading scaling corrections. Our results are obtained by combining Monte Carlo simulations based on finite-size scaling methods and high-temperature expansions. The critical exponents are computed from high-temperature expansions specialized to the phi^4 improved model. By the same technique we determine the coefficients of the small-magnetization expansion of the equation of state. This expansion is extended analytically by means of approximate parametric representations, obtaining the equation of state in the whole critical region. We also determine a number of universal amplitude ratios.Comment: 40 pages, final version. In publication in Phys. Rev.