Ordering Policy Rules with an Unconditional Welfare Measure

The unconditional expectation of social welfare is often used to assess alternative macroeconomic policy rules in applied quantitative research. It is shown that it is generally possible to derive a linear - quadratic problem that approximates the exact non-linear problem where the unconditional expectation of the objective is maximised and the steady-state is distorted. Thus, the measure of pol icy performance is a linear combinat ion of second moments of economic variables which is relatively easy to compute numerically, and can be used to rank alternative policy rules. The approach is applied to a simple Calvo-type model under various monetary policy rules.

Development of tools to measure and explain changes in health inequalities in Scotland and benchmark performance

This project will develop a modelling framework to explain changes in income-related health inequalities and benchmark the performance of Scotland in tackling income-related health inequalities, both over time and relative to that of England and Wales.

Fast numerical algorithms for the computation of invariant tori in Hamiltonian systems

In this paper, we develop numerical algorithms that use small requirements of storage and operations for the computation of invariant tori in Hamiltonian systems (exact symplectic maps and Hamiltonian vector fields). The algorithms are based on the parameterization method and follow closely the proof of the KAM theorem given in [LGJV05] and [FLS07]. They essentially consist in solving a functional equation satisfied by the invariant tori by using a Newton method. Using some geometric identities, it is possible to perform a Newton step using little storage and few operations. In this paper we focus on the numerical issues of the algorithms (speed, storage and stability) and we refer to the mentioned papers for the rigorous results. We show how to compute efficiently both maximal invariant tori and whiskered tori, together with the associated invariant stable and unstable manifolds of whiskered tori. Moreover, we present fast algorithms for the iteration of the quasi-periodic cocycles and the computation of the invariant bundles, which is a preliminary step for the computation of invariant whiskered tori. Since quasi-periodic cocycles appear in other contexts, this section may be of independent interest. The numerical methods presented here allow to compute in a unified way primary and secondary invariant KAM tori. Secondary tori are invariant tori which can be contracted to a periodic orbit. We present some preliminary results that ensure that the methods are indeed implementable and fast. We postpone to a future paper optimized implementations and results on the breakdown of invariant tori.

A doubling measure on R(d) can charge a rectifiable curve

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Quality of life: a potentially useful measure to indicate subclinical flares in Crohn disease.

Background:  While quality of life (QoL) is a well-recognised outcome measure of Crohn disease (CD) activity, its influence on other outcome measures, including exacerbation of CD is poorly understood. If QoL measures were to be associated with intestinal inflammatory activity, they might be useful for early detection of subclinical flares. Aims:  We hypothesised that low QoL might be associated with subsequent CD flares. Methods:  A cohort of 318 adult CD patients was observed for 1 year after assessment of baseline characteristics. Data were collected in Swiss university hospitals, regional hospitals and private practices. At inclusion, patients completed the Inflammatory Bowel Disease QoL Questionnaire (gastrointestinal QoL; range: 32 to 224 points) and the Short Form-36 Health Survey (general QoL; range: 35 to 145 points). During follow up, flares were recorded. Binary logistic regression was performed to estimate the relation between QoL and the odds of subsequent flares. Results:  A twofold decrease in the odds of flares (99% CI: 1.1; 4.0) per standard deviation of gastrointestinal QoL and a threefold decrease (99% CI: 1.5; 6.2) per standard deviation of general QoL were observed. Conclusions:  The close association between QoL and subsequent flares suggests that QoL measures might be useful in detecting upcoming flares before they become clinically apparent.

Destruction of invariant curves in the restricted circular planar three body problem using comparison of action

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Hausdorff measure of quasicircles

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Generic super-exponential stability of invariant tori in Hamiltonian systems

In this article, we consider solutions starting close to some linearly stable invariant tori in an analytic Hamiltonian system and we prove results of stability for a super-exponentially long interval of time, under generic conditions. The proof combines classical Birkhoff normal forms and a new method to obtain generic Nekhoroshev estimates developed by the author and L. Niederman in another paper. We will mainly focus on the neighbourhood of elliptic fixed points, the other cases being completely similar.

Sobolev mappings: Lipschitz density is not an isometric invariant of the target

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The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

A measure of the intensity of response to alcohol to screen for alcohol use disorders in primary care.

Alcohol-dependent subjects tend to report lower level of response to alcohol (LR) in the years before the disorder developed, compared to control subjects. The Self-Rating of the Effects of alcohol (SRE) score is a quick and valid retrospective estimate of LR. This study examined the associations between alcohol abuse or dependence and early experience of alcohol as measured on retrospective SRE score (relating to the first five times alcohol was imbibed), and the presence of alcohol abuse or dependence, in patients attending primary care. Higher Early SRE score (i.e. greater early tolerance of alcohol) was obtained in patients with an alcohol-related diagnosis than in patients without those diagnoses. Using a cut-off of 2 on the Early SRE score, the Early SRE score could discriminate between patients with and without an alcohol diagnosis with moderate to high sensitivity (84%) and modest specificity (57%).

The eta invariant and equivariant index of transversally elliptic operators

We prove a formula for the multiplicities of the index of an equivariant transversally elliptic operator on a G-manifold. The formula is a sum of integrals over blowups of the strata of the group action and also involves eta invariants of associated elliptic operators. Among the applications, we obtain an index formula for basic Dirac operators on Riemannian foliations, a problem that was open for many years.

Recovering the Elliott invariant from the Cuntz semigroup

Let A be a simple, separable C*-algebra of stable rank one. We prove that the Cuntz semigroup of C (T, A) is determined by its Murray-von Neumann semigroup of projections and a certain semigroup of lower semicontinuous functions (with values in the Cuntz semigroup of A). This result has two consequences. First, specializing to the case that A is simple, finite, separable and Z-stable, this yields a description of the Cuntz semigroup of C (T, A) in terms of the Elliott invariant of A. Second, suitably interpreted, it shows that the Elliott functor and the functor defined by the Cuntz semigroup of the tensor product with the algebra of continuous functions on the circle are naturally equivalent.

Neither dashboard nor 'mashup' indices: an empirical wealth approach as a pathway to a comprehensive measure of development

The article is composed of two sections. The first one is a critical review of the three main alternative indices to GDP which were proposed in the last decades – the Human Development Index (HDI), the Genuine Progress Indicator (GPI), and the Happy Planet Index (HPI) – which is made on the basis of conceptual foundations, rather than looking at issues of statistical consistency or mathematical refinement as most of the literature does. The pars construens aims to propose an alternative measure, the composite wealth index, consistent with an approach to development based on the notion of composite wealth, which is in turn derived from an empirical common sense criterion. Arguably, this approach is suitable to be conveyed into an easily understandable and coherent indicator, and thus appropriate to track development in its various dimensions: simple in its formulation, the wealth approach can incorporate social and ecological goals without significant alterations in conceptual foundations, while reducing to a minimum arbitrary weighting.

Human invariant V alpha 24-J alpha Q TCR supports the development of CD1d-dependent NK1.1+ and NK1.1- T cells in transgenic mice.

A sizable fraction of T cells expressing the NK cell marker NK1.1 (NKT cells) bear a very conserved TCR, characterized by homologous invariant (inv.) TCR V alpha 24-J alpha Q and V alpha 14-J alpha 18 rearrangements in humans and mice, respectively, and are thus defined as inv. NKT cells. Because human inv. NKT cells recognize mouse CD1d in vitro, we wondered whether a human inv. V alpha 24 TCR could be selected in vivo by mouse ligands presented by CD1d, thereby supporting the development of inv. NKT cells in mice. Therefore, we generated transgenic (Tg) mice expressing the human inv. V alpha 24-J alpha Q TCR chain in all T cells. The expression of the human inv. V alpha 24 TCR in TCR C alpha(-/-) mice indeed rescues the development of inv. NKT cells, which home preferentially to the liver and respond to the CD1d-restricted ligand alpha-galactosylceramide (alpha-GalCer). However, unlike inv. NKT cells from non-Tg mice, the majority of NKT cells in V alpha 24 Tg mice display a double-negative phenotype, as well as a significant increase in TCR V beta 7 and a corresponding decrease in TCR V beta 8.2 use. Despite the forced expression of the human CD1d-restricted TCR in C alpha(-/-) mice, staining with mCD1d-alpha-GalCer tetramers reveals that the absolute numbers of peripheral CD1d-dependent T lymphocytes increase at most by 2-fold. This increase is accounted for mainly by an increased fraction of NK1.1(-) T cells that bind CD1d-alpha-GalCer tetramers. These findings indicate that human inv. V alpha 24 TCR supports the development of CD1d-dependent lymphocytes in mice, and argue for a tight homeostatic control on the total number of inv. NKT cells. Thus, human inv. V alpha 24 TCR-expressing mice are a valuable model to study different aspects of the inv. NKT cell subset.