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

Building resilence against adverse shocks: What are the determinants of vulnerability and resilence?

This paper proposes a simple way to measure livelihood diversification, and uses this measure together with income levels to classify Bolivian households by level of vulnerability. Regression analysis is then carried out to determine the factors and strategies associated with high resilience or high vulnerability. The results show that the single most important strategy for resilience is to have a working and income earning spouse in the household. This is still much too uncommon in Bolivia. A second important factor is the age of the head of household. Young families are considerably more vulnerable than more mature families, as they have not had time to build up assets that can provide alternative sources of livelihood. One of the most surprising results of the study is that urban households are considerably more vulnerable to adverse shocks than rural households, whereas gender and ethnicity are irrelevant. The paper finishes with a comprehensive list of policy recommendations

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