Semiflow selection and Markov selection theorems

The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential equation are unique, and leads to a semiflow. We prove an abstract result on measurable selection of a semiflow for the situations without uniqueness. We outline applications to ODEs, PDEs, differential inclusions, etc. Our proof of the semiflow selection theorem is motivated by N. V. Krylov's Markov selection theorem. To accentuate this connection, we include a new version of the Markov selection theorem related to more recent papers of Flandoli & Romito and Goldys et al.Comment: In this revised version we have added a new abstract result in Sec. 2. It is used to correct the Navier-Stokes example in application

Anharmonic Self-Energy of Phonons: Ab Initio Calculations and Neutron Spin Echo Measurements

We have calculated (ab initio) and measured (by spin-echo techniques) the anharmonic self-energy of phonons at the X-point of the Brillouin zone for isotopically pure germanium. The real part agrees with former, less accurate, high temperature data obtained by inelastic neutron scattering on natural germanium. For the imaginary part our results provide evidence that transverse acoustic phonons at the X-point are very long lived at low temperatures, i.e. their probability of decay approaches zero, as a consequence of an unusual decay mechanism allowed by energy conservation.Comment: 8 pages, 2 figures, pdf fil

Predictive validity of the CriSTAL tool for short-term mortality in older people presenting at Emergency Departments: a prospective study

© 2018, The Author(s). Abstract: To determine the validity of the Australian clinical prediction tool Criteria for Screening and Triaging to Appropriate aLternative care (CRISTAL) based on objective clinical criteria to accurately identify risk of death within 3 months of admission among older patients. Methods: Prospective study of ≥ 65 year-olds presenting at emergency departments in five Australian (Aus) and four Danish (DK) hospitals. Logistic regression analysis was used to model factors for death prediction; Sensitivity, specificity, area under the ROC curve and calibration with bootstrapping techniques were used to describe predictive accuracy. Results: 2493 patients, with median age 78–80 years (DK–Aus). The deceased had significantly higher mean CriSTAL with Australian mean of 8.1 (95% CI 7.7–8.6 vs. 5.8 95% CI 5.6–5.9) and Danish mean 7.1 (95% CI 6.6–7.5 vs. 5.5 95% CI 5.4–5.6). The model with Fried Frailty score was optimal for the Australian cohort but prediction with the Clinical Frailty Scale (CFS) was also good (AUROC 0.825 and 0.81, respectively). Values for the Danish cohort were AUROC 0.764 with Fried and 0.794 using CFS. The most significant independent predictors of short-term death in both cohorts were advanced malignancy, frailty, male gender and advanced age. CriSTAL’s accuracy was only modest for in-hospital death prediction in either setting. Conclusions: The modified CriSTAL tool (with CFS instead of Fried’s frailty instrument) has good discriminant power to improve prognostic certainty of short-term mortality for ED physicians in both health systems. This shows promise in enhancing clinician’s confidence in initiating earlier end-of-life discussions

Isotope effects on the lattice parameter of cubic SiC

Path-integral molecular dynamics simulations in the isothermal-isobaric (NPT) ensemble have been carried out to study the dependence of the lattice parameter of 3C-SiC upon isotope mass. This computational method allows a quantitative and nonperturbative study of such anharmonic effect. Atomic nuclei were treated as quantum particles interacting via a tight-binding-type potential. At 300 K, the difference Delta a between lattice parameters of 3C-SiC crystals with 12C and 13C amounts to 2.1 x 10^{-4} A. The effect due to Si isotopes is smaller, and amounts to 3.5 x 10^{-5} A when replacing 28Si by 29Si. Results of the PIMD simulations are interpreted in terms of a quasiharmonic approximation for the lattice vibrations.Comment: 4 pages, 3 figure

Health-related quality of life in patients with Gilles de la Tourette syndrome at the transition between adolescence and adulthood

Gilles de la Tourette syndrome (GTS) is a neurodevelopmental condition characterised by tics and comorbid behavioural problems, affecting predominantly male patients. Tic severity typically fluctuates over time, with a consistent pattern showing improvement after adolescence in a considerable proportion of patients. Both tics and behavioural co-morbidities have been shown to have the potential to affect patients’ health-related quality of life (HR-QoL) in children and adults with persisting symptoms. In this study, we present the results of the first investigation of HR-QoL in patients with Gilles de la Tourette syndrome at the transition between adolescence and adulthood using a disease-specific HR-QoL measure, the Gilles de la Tourette Syndrome-Quality of Life-Children and Adolescents scale. Our results showed that patients with GTS and more severe co-morbid anxiety symptoms reported lower HR-QoL across all domains, highlighting the impact of anxiety on patient’s well-being at a critical stage of development. Routine screening for anxiety symptoms is recommended in all patients with GTS seen at transition clinics from paediatric to adult care, to implement effective behavioural and pharmacological interventions as appropriate

Physical requirements for modeling stellar atmospheres according to the different spectral features observed

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