Existence and uniqueness of limit cycles in a class of second order ODE's with inseparable mixed terms

We prove a uniqueness result for limit cycles of the second order ODE $\ddot x + \dot x \phi(x,\dot x) + g(x) = 0$. Under mild additional conditions, we show that such a limit cycle attracts every non-constant solution. As a special case, we prove limit cycle's uniqueness for an ODE studied in \cite{ETA} as a model of pedestrians' walk. This paper is an extension to equations with a non-linear $g(x)$ of the results presented in \cite{S}

Spin-dependent direct gap emission in tensile-strained Ge films on Si substrates

The circular polarization of direct gap emission of Ge is studied in optically-excited tensile-strained Ge-on-Si heterostructures as a function of doping and temperature. Owing to the spin-dependent optical selection rules, the radiative recombinations involving strain-split light (cG-LH) and heavy hole (cG-HH) bands are unambiguously resolved. The fundamental cG-LH transition is found to have a low temperature circular polarization degree of about 85% despite an off-resonance excitation of more than 300 meV. By photoluminescence (PL) measurements and tight binding calculations we show that this exceptionally high value is due to the peculiar energy dependence of the optically-induced electron spin population. Finally, our observation of the direct gap doublet clarifies that the light hole contribution, previously considered to be negligible, can dominate the room temperature PL even at low tensile strain values of about 0.2%

Scalar fields on SL(2,R) and H^2 x R geometric spacetimes and linear perturbations

Using appropriate harmonics, we study the future asymptotic behavior of massless scalar fields on a class of cosmological vacuum spacetimes. The spatial manifold is assumed to be a circle bundle over a higher genus surface with a locally homogeneous metric. Such a manifold corresponds to the SL(2,R)-geometry (Bianchi VIII type) or the H^2 x R-geometry (Bianchi III type). After a technical preparation including an introduction of suitable harmonics for the circle-fibered Bianchi VIII to separate variables, we derive systems of ordinary differential equations for the scalar field. We present future asymptotic solutions for these equations in a special case, and find that there is a close similarity with those on the circle-fibered Bianchi III spacetime. We discuss implications of this similarity, especially to (gravitational) linear perturbations. We also point out that this similarity can be explained by the "fiber term dominated behavior" of the two models.Comment: 23 pages, no figures, to be published in Class. Quant. Gravi

Mean first passage time analysis reveals rate-limiting steps, parallel pathways and dead ends in a simple model of protein folding

We have analyzed dynamics on the complex free energy landscape of protein folding in the FOLD-X model, by calculating for each state of the system the mean first passage time to the folded state. The resulting kinetic map of the folding process shows that it proceeds in jumps between well-defined, local free energy minima. Closer analysis of the different local minima allows us to reveal secondary, parallel pathways as well as dead ends.Comment: 7 page

Frailty Index and incident mortality, hospitalization and institutionalization in Alzheimer's disease: data from the ICTUS study.

BACKGROUND: The identification of an objective evaluation of frailty capable of predicting adverse outcomes in Alzheimer's disease is increasingly discussed. The purpose of this study was to investigate whether the Frailty Index (FI) predicts hospitalization, institutionalization, and mortality in Alzheimer's disease patients. METHODS: A prospective multicenter cohort study (follow-up = 2 years) that included 1,191 participants with Alzheimer's disease was carried out. The outcomes of interest were incident hospitalization, institutionalization, and mortality. The FI was calculated as the ratio of actual to thirty potential deficits, that is, deficits presented by the participant divided by 30. Severity of dementia was assessed using the Clinical Dementia Rating score. Cox proportional hazard models were performed. RESULTS: Mean age of the study sample was 76.2 (SD = 7.6) years. A quadratic relationship of the FI with age was reported at baseline (R 2 = .045, p < .001). The FI showed a statistically significant association with mortality (age- and gender-adjusted hazard ratio [HR] = 1.019, 95% confidence interval [CI] = 1.002-1.037, p = .031) and hospitalization (age- and gender-adjusted HR = 1.017, 95% CI = 1.006-1.029, p = .004) and a borderline significance with institutionalization. When the Clinical Dementia Rating score was simultaneously included in the age- and gender-adjusted models, the FI confirmed its predictive capacity for hospitalization (HR = 1.019, 95% CI = 1.006-1.032, p = .004), whereas the Clinical Dementia Rating score was the strongest predictor for mortality (HR = 1.922, 95% CI = 1.256-2.941, p = .003) and institutionalization (HR = 1.955, 95%CI = 1.427-2.679, p < .001). CONCLUSIONS: The FI is a robust predictor of adverse outcomes even after the stage of the underlying dementia is considered. Future work should evaluate the clinical implementation of the FI in the assessment of demented individuals in order to improve the personalization of care

A formal approach to autonomic systems programming: the SCEL Language

The autonomic computing paradigm has been proposed to cope with size, complexity and dynamism of contemporary software-intensive systems. The challenge for language designers is to devise appropriate abstractions and linguistic primitives to deal with the large dimension of systems, and with their need to adapt to the changes of the working environment and to the evolving requirements. We propose a set of programming abstractions that permit to represent behaviors, knowledge and aggregations according to specific policies, and to support programming context-awareness, self-awareness and adaptation. Based on these abstractions, we define SCEL (Software Component Ensemble Language), a kernel language whose solid semantic foundations lay also the basis for formal reasoning on autonomic systems behavior. To show expressiveness and effectiveness of SCEL’s design, we present a Java implementation of the proposed abstractions and show how it can be exploited for programming a robotics scenario that is used as a running example for describing features and potentials of our approac

General behaviour of Bianchi VI_0 solutions with an exponential-potential scalar field

The solutions to the Einstein-Klein-Gordon equations without a cosmological constant are investigated for an exponential potential in a Bianchi VI_0 metric. There exists a two-parameter family of solutions which have a power-law inflationary behaviour when the exponent of the potential, k, satisfies k^2<2. In addition, there exists a two-parameter family of singular solutions for all k^2 values. A simple anisotropic exact solution is found to be stable when 2<k^2.Comment: 10 pages, no figures. To be published in General Relativity and Gravitatio

Optimal control strategies for tuberculosis treatment: a case study in Angola

We apply optimal control theory to a tuberculosis model given by a system of ordinary differential equations. Optimal control strategies are proposed to minimize the cost of interventions. Numerical simulations are given using data from Angola.Comment: This is a preprint of a paper whose final and definite form will appear in the international journal Numerical Algebra, Control and Optimization (NACO). Paper accepted for publication 15-March-201