Consequences of an incorrect model specification on population growth

We consider stochastic differential equations to model the growth of a population ina randomly varying environment. These growth models are usually based on classical deterministic models, such as the logistic or the Gompertz models, taken as approximate models of the "true" (usually unknown) growth rate. We study the effect of the gap between the approximate and the "true" model on model predictions, particularly on asymptotiv behavior and mean and variance of the time to extinction of the population

Neutropenic sepsis in the ICU: Outcome predictors in a two-phase model and microbiology findings

Objective. Patients with neutropenic sepsis have a poor prognosis. We aimed to identify outcome predictors and generate hypotheses how the care for these patients may be improved. Methods. All 12.352 patients admitted between 2006 and 2011 to the medical ICUs of our tertiary university center were screened for neutropenia; out of 558 patients identified, 102 fulfilled the inclusion criteria and were analyzed. Severity markers and outcome predictors were assessed. Results. The overall ICU mortality was 54.9%. The severity of sepsis and the number of organ failures predicted survival of the primary septic episode (APACHE II 22.8 and 29.0; SOFA 7.3 and 10.1, resp.). In the recovery phase, persistent organ damage and higher persistent C-reactive protein levels were associated with a poor outcome. Blood transfusions and CMV infection correlated with an unfavorable prognosis. Ineffective initial antibiotic therapy, fungal infections, and detection of multiresistant bacteria displayed a particularly poor outcome. Infections with coagulase-negative staphylococci and enterococci were associated with a significantly higher mortality and a high degree of systemic inflammation. Conclusion. Patients with persistent organ dysfunction show an increased mortality in the further course of their ICU stay. Early antimicrobial treatment of Gram-positive cocci may improve the outcome of these patients

Deciphering the properties of the medium produced in heavy ion collisions at RHIC by a pQCD analysis of quenched large p⊥p_{\perp} π0\pi^0 spectra

We discuss the question of the relevance of perturbative QCD calculations for analyzing the properties of the dense medium produced in heavy ion collisions. Up to now leading order perturbative estimates have been worked out and confronted with data for quenched large $p_{\perp}$ hadron spectra. Some of them are giving paradoxical results, contradicting the perturbative framework and leading to speculations such as the formation of a strongly interacting quark-gluon plasma. Trying to bypass some drawbacks of these leading order analysis and without performing detailed numerical investigations, we collect evidence in favour of a consistent description of quenching and of the characteristics of the produced medium within the pQCD framework.Comment: 10 pages, 3 figure

Order-alpha_s^2 corrections to one-particle inclusive processes in DIS

We analyze the order-$\alpha_s^2$ QCD corrections to semi-inclusive deep inelastic scattering and present results for processes initiated by a gluon. We focus in the most singular pieces of these corrections in order to obtain the hitherto unknown NLO evolution kernels relevant for the non homogeneous QCD scale dependence of these cross sections, and to check explicitly factorization at this order. In so doing we discuss the prescription of overlapping singularities in more than one variable.Comment: 16 pages, 9 eps figures. Uses revtex4 and feynm

Analytical solutions for two heteronuclear atoms in a ring trap

We consider two heteronuclear atoms interacting with a short-range $\delta$ potential and confined in a ring trap. By taking the Bethe-ansatz-type wavefunction and considering the periodic boundary condition properly, we derive analytical solutions for the heteronuclear system. The eigen-energies represented in terms of quasi-momentums can then be determined by solving a set of coupled equations. We present a number of results, which display different features from the case of identical atoms. Our result can be reduced to the well-known Lieb-Liniger solution when two interacting atoms have the same masses.Comment: 6 pages, 6 figure

Nonlinear analysis of spacecraft thermal models

We study the differential equations of lumped-parameter models of spacecraft thermal control. Firstly, we consider a satellite model consisting of two isothermal parts (nodes): an outer part that absorbs heat from the environment as radiation of various types and radiates heat as a black-body, and an inner part that just dissipates heat at a constant rate. The resulting system of two nonlinear ordinary differential equations for the satellite's temperatures is analyzed with various methods, which prove that the temperatures approach a steady state if the heat input is constant, whereas they approach a limit cycle if it varies periodically. Secondly, we generalize those methods to study a many-node thermal model of a spacecraft: this model also has a stable steady state under constant heat inputs that becomes a limit cycle if the inputs vary periodically. Finally, we propose new numerical analyses of spacecraft thermal models based on our results, to complement the analyses normally carried out with commercial software packages.Comment: 29 pages, 4 figure

Stability of Attractive Bose-Einstein Condensates in a Periodic Potential

Using a standing light wave trap, a stable quasi-one-dimensional attractive dilute-gas Bose-Einstein condensate can be realized. In a mean-field approximation, this phenomenon is modeled by the cubic nonlinear Schr\"odinger equation with attractive nonlinearity and an elliptic function potential of which a standing light wave is a special case. New families of stationary solutions are presented. Some of these solutions have neither an analog in the linear Schr\"odinger equation nor in the integrable nonlinear Schr\"odinger equation. Their stability is examined using analytic and numerical methods. Trivial-phase solutions are experimentally stable provided they have nodes and their density is localized in the troughs of the potential. Stable time-periodic solutions are also examined.Comment: 12 pages, 18 figure

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

Poisson Statistics for the Largest Eigenvalues in Random Matrix Ensemble

The paper studies the spectral properties of large Wigner, band and sample covariance random matrices with heavy tails of the marginal distributions of matrix entries.Comment: This is an extended version of my talk at the QMath 9 conference at Giens, France on September 13-17, 200