Exponential stability of the wave equation with memory and time delay

We study the asymptotic behaviour of the wave equation with viscoelastic damping in presence of a time-delayed damping. We prove exponential stability if the amplitude of the time delay term is small enough

Motivic Serre invariants, ramification, and the analytic Milnor fiber

We show how formal and rigid geometry can be used in the theory of complex singularities, and in particular in the study of the Milnor fibration and the motivic zeta function. We introduce the so-called analytic Milnor fiber associated to the germ of a morphism f from a smooth complex algebraic variety X to the affine line. This analytic Milnor fiber is a smooth rigid variety over the field of Laurent series C((t)). Its etale cohomology coincides with the singular cohomology of the classical topological Milnor fiber of f; the monodromy transformation is given by the Galois action. Moreover, the points on the analytic Milnor fiber are closely related to the motivic zeta function of f, and the arc space of X. We show how the motivic zeta function can be recovered as some kind of Weil zeta function of the formal completion of X along the special fiber of f, and we establish a corresponding Grothendieck trace formula, which relates, in particular, the rational points on the analytic Milnor fiber over finite extensions of C((t)), to the Galois action on its etale cohomology. The general observation is that the arithmetic properties of the analytic Milnor fiber reflect the structure of the singularity of the germ f.Comment: Some minor errors corrected. The original publication is available at http://www.springerlink.co

Well-Posedness and Symmetries of Strongly Coupled Network Equations

We consider a diffusion process on the edges of a finite network and allow for feedback effects between different, possibly non-adjacent edges. This generalizes the setting that is common in the literature, where the only considered interactions take place at the boundary, i. e., in the nodes of the network. We discuss well-posedness of the associated initial value problem as well as contractivity and positivity properties of its solutions. Finally, we discuss qualitative properties that can be formulated in terms of invariance of linear subspaces of the state space, i. e., of symmetries of the associated physical system. Applications to a neurobiological model as well as to a system of linear Schroedinger equations on a quantum graph are discussed.Comment: 25 pages. Corrected typos and minor change

Quantum ergodicity for graphs related to interval maps

We prove quantum ergodicity for a family of graphs that are obtained from ergodic one-dimensional maps of an interval using a procedure introduced by Pakonski et al (J. Phys. A, v. 34, 9303-9317 (2001)). As observables we take the L^2 functions on the interval. The proof is based on the periodic orbit expansion of a majorant of the quantum variance. Specifically, given a one-dimensional, Lebesgue-measure-preserving map of an interval, we consider an increasingly refined sequence of partitions of the interval. To this sequence we associate a sequence of graphs, whose directed edges correspond to elements of the partitions and on which the classical dynamics approximates the Perron-Frobenius operator corresponding to the map. We show that, except possibly for subsequences of density 0, the eigenstates of the quantum graphs equidistribute in the limit of large graphs. For a smaller class of observables we also show that the Egorov property, a correspondence between classical and quantum evolution in the semiclassical limit, holds for the quantum graphs in question.Comment: 20 pages, 1 figur

Service provision and barriers to care for homeless people with mental health problems across 14 European capital cities

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

The same or different psychiatrists for in- and out-patient treatment? A multi-country natural experiment - ADDENDUM.

ADDENDU

Predictors of personal continuity of care of patients with severe mental illness: A comparison across five European countries.

BACKGROUND: In Europe, at discharge from a psychiatric hospital, patients with severe mental illness may be exposed to one of two main care approaches: personal continuity, where one clinician is responsible for in- and outpatient care, and specialisation, where various clinicians are. Such exposure is decided through patient-clinician agreement or at the organisational level, depending on the country's health system. Since personal continuity would be more suitable for patients with complex psychosocial needs, the aim of this study was to identify predictors of patients' exposure to care approaches in different European countries. METHODS: Data were collected on 7302 psychiatric hospitalised patients in 2015 in Germany, Poland, and Belgium (patient-level exposure); and in the UK and Italy (organisational-level exposure). At discharge, patients were exposed to one of the care approaches according to usual practice. Putative predictors of exposure at patients' discharge were assessed in both groups of countries. RESULTS: Socially disadvantaged patients were significantly more exposed to personal continuity. In all countries, the main predictor of exposure was the admission hospital, except in Germany, where having a diagnosis of psychosis and a higher education status were predictors of exposure to personal continuity. In the UK, hospitals practising personal continuity had a more socially disadvantaged patient population. CONCLUSION: Even in countries where exposure is decided through patient-clinician agreement, it was the admission hospital, not patient characteristics, that predicted exposure to care approaches. Nevertheless, organisational decisions in hospitals tend to expose socially disadvantaged patients to personal continuity.European Commission’s 7th Framework Programm.e Grant agreement number 602645

The same or different psychiatrists for in- and out-patient treatment? A multi-country natural experiment.

AimsA core question in the debate about how to organise mental healthcare is whether in- and out-patient treatment should be provided by the same (personal continuity) or different psychiatrists (specialisation). The controversial debate drives costly organisational changes in several European countries, which have gone in opposing directions. The existing evidence is based on small and low-quality studies which tend to favour whatever the new experimental organisation is.We compared 1-year clinical outcomes of personal continuity and specialisation in routine care in a large scale study across five European countries. METHODS: This is a 1-year prospective natural experiment conducted in Belgium, England, Germany, Italy and Poland. In all these countries, both personal continuity and specialisation exist in routine care. Eligible patients were admitted for psychiatric in-patient treatment (18 years of age), and clinically diagnosed with a psychotic, mood or anxiety/somatisation disorder.Outcomes were assessed 1 year after the index admission. The primary outcome was re-hospitalisation and analysed for the full sample and subgroups defined by country, and different socio-demographic and clinical criteria. Secondary outcomes were total number of inpatient days, involuntary re-admissions, adverse events and patients' social situation. Outcomes were compared through mixed regression models in intention-to-treat analyses. The study is registered (ISRCTN40256812). RESULTS: We consecutively recruited 7302 patients; 6369 (87.2%) were followed-up. No statistically significant differences were found in re-hospitalisation, neither overall (adjusted percentages: 38.9% in personal continuity, 37.1% in specialisation; odds ratio = 1.08; confidence interval 0.94-1.25; p = 0.28) nor for any of the considered subgroups. There were no significant differences in any of the secondary outcomes. CONCLUSIONS: Whether the same or different psychiatrists provide in- and out-patient treatment appears to have no substantial impact on patient outcomes over a 1-year period. Initiatives to improve long-term outcomes of psychiatric patients may focus on aspects other than the organisation of personal continuity v. specialisation.European Commission Seventh Framework Programme. Grant agreement 60264