Secondary nontwist phenomena in area-preserving maps

Phenomena as reconnection scenarios, periodic-orbit collisions, and primary shearless tori have been recognized as features of nontwist maps. Recently, these phenomena and secondary shearless tori were analytically predicted for generic maps in the neighborhood of the tripling bifurcation of an elliptic fixed point. In this paper, we apply a numerical procedure to find internal rotation number profiles that highlight the creation of periodic orbits within islands of stability by a saddle-center bifurcation that emerges out a secondary shearless torus. In addition to the analytical predictions, our numerical procedure applied to the twist and nontwist standard maps reveals that the atypical secondary shearless torus occurs not only near a tripling bifurcation of the fixed point but also near a quadrupling bifurcation. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4750040]

Nontwist symplectic maps in tokamaks

We review symplectic nontwist maps that we have introduced to describe Lagrangian transport properties in magnetically confined plasmas in tokamaks. These nontwist maps are suitable to describe the formation and destruction of transport barriers in the shearless region (i.e., near the curve where the twist condition does not hold). The maps can be used to investigate two kinds of problems in plasmas with non-monotonic field profiles: the first is the chaotic magnetic field line transport in plasmas with external resonant perturbations. The second problem is the chaotic particle drift motion caused by electrostatic drift waves. The presented analytical maps, derived from plasma models with equilibrium field profiles and control parameters that are commonly measured in plasma discharges, can be used to investigate long-term transport properties. (C) 2011 Elsevier B.V. All rights reserved.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

COMPARISON MEASURES OF MAPS GENERATED BY GEOSTATISTICAL METHODS

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Axioms for the coincidence index of maps between manifolds of the same dimension

We study the coincidence theory of maps between two manifolds of the same dimension from an axiomatic viewpoint. First we look at coincidences of maps between manifolds where one of the maps is orientation true, and give a set of axioms such that characterizes the local index (which is an integer valued function). Then we consider coincidence theory for arbitrary pairs of maps between two manifolds. Similarly we provide a set of axioms which characterize the local index, which in this case is a function with values in Z circle plus Z(2). We also show in each setting that the group of values for the index (either Z or Z circle plus Z(2)) is determined by the axioms. Finally, for the general case of coincidence theory for arbitrary pairs of maps between two manifolds we provide a set of axioms which characterize the local Reidemeister trace which is an element of an abelian group which depends on the pair of functions. These results extend known results for coincidences between orientable differentiable manifolds. (C) 2012 Elsevier B.V. All rights reserved.

Polar foliations and isoparametric maps

A singular Riemannian foliation F on a complete Riemannian manifold M is called a polar foliation if, for each regular point p, there is an immersed submanifold Sigma, called section, that passes through p and that meets all the leaves and always perpendicularly. A typical example of a polar foliation is the partition of M into the orbits of a polar action, i.e., an isometric action with sections. In this article we prove that the leaves of H : M -> Sigma, coincide with the level sets of a smooth map H: M -> Sigma, if M is simply connected. In particular, the orbits of a polar action on a simply connected space are level sets of an isoparametric map. This result extends previous results due to the author and Gorodski, Heintze, Liu and Olmos, Carter and West, and Terng.

Chains of Infinite Order, Chains with Memory of Variable Length, and Maps of the Interval

We show how to construct a topological Markov map of the interval whose invariant probability measure is the stationary law of a given stochastic chain of infinite order. In particular we characterize the maps corresponding to stochastic chains with memory of variable length. The problem treated here is the converse of the classical construction of the Gibbs formalism for Markov expanding maps of the interval.

Wecken type problems for self-maps of the Klein bottle

We consider various problems regarding roots and coincidence points for maps into the Klein bottle . The root problem where the target is and the domain is a compact surface with non-positive Euler characteristic is studied. Results similar to those when the target is the torus are obtained. The Wecken property for coincidences from to is established, and we also obtain the following 1-parameter result. Families which are coincidence free but any homotopy between and , , creates a coincidence with . This is done for any pair of maps such that the Nielsen coincidence number is zero. Finally, we exhibit one such family where is the constant map and if we allow for homotopies of , then we can find a coincidence free pair of homotopies.

Comparison measures of maps generated by geostatistical methods

This study uses several measures derived from the error matrix for comparing two thematic maps generated with the same sample set. The reference map was generated with all the sample elements and the map set as the model was generated without the two points detected as influential by the analysis of local influence diagnostics. The data analyzed refer to the wheat productivity in an agricultural area of 13.55 ha considering a sampling grid of 50 x 50 m comprising 50 georeferenced sample elements. The comparison measures derived from the error matrix indicated that despite some similarity on the maps, they are different. The difference between the estimated production by the reference map and the actual production was of 350 kilograms. The same difference calculated with the mode map was of 50 kilograms, indicating that the study of influential points is of fundamental importance to obtain a more reliable estimative and use of measures obtained from the error matrix is a good option to make comparisons between thematic maps.

Liver transplantation for transthyretin amyloidosis: experience of a single center in Italy

Liver transplantation is the only definitive treatment for transthyretin amyloidosis, with an excellent 5-year survival in endemic countries where the Met30 mutation is predominant. We report our experience of liver transplantation for transthyretin amyloidosis. We reviewed the clinical records of 17 transplanted patients (11 males, 6 females; age at liver transplant: 45.7±11.7 years). We had a wide spectrum of non-Met30 mutations (52.9%), with a predominance of Gln89 (23.5%). Five-year survival after transplantation was 43.8%; at multivariate analysis, both non-Met30 mutations (HR 17.3, 95% CI 1.03-291.7) and modified BMI (HR 0.50, 95% CI 0.29-0.87) showed significant and independent prognostic roles (P=0.048 and P=0.015, respectively). Five out of the 9 non-Met30 carriers received combined heart transplantation because of severe cardiomyopathy; they showed a trend towards a better prognosis vs. the 4 patients who did not receive combined heart transplantation (although not statistically significant; P=0.095). At follow-up, no significant improvement of transthyretin amyloidosis manifestations was observed. The results of liver transplantation for transthyretin amyloidosis in our population are poorer than those reported in the literature probably because of the high prevalence of non-Met30 mutations.

Essays in Applied Health Economics: Evidence on Health and Health Care in Italy and UK

This thesis is the result of my experience as a PhD student taking part in the Joint Doctoral Programme at the University of York and the University of Bologna. In my thesis I deal with topics that are of particular interest in Italy and in Great Britain. Chapter 2 focuses on the empirical test of the existence of the relationship between technological profiles and market structure claimed by Sutton’s theory (1991, 1998) in the specific economic framework of hospital care services provided by the Italian National Health Service (NHS). In order to test the empirical predictions by Sutton, we identify the relevant markets for hospital care services in Italy in terms of both product and geographic dimensions. In particular, the Elzinga and Hogarty (1978) approach has been applied to data on patients’ flows across Italian Provinces in order to derive the geographic dimension of each market. Our results provide evidence in favour of the empirical predictions of Sutton. Chapter 3 deals with the patient mobility in the Italian NHS. To analyse the determinants of patient mobility across Local Health Authorities, we estimate gravity equations in multiplicative form using a Poisson pseudo maximum likelihood method, as proposed by Santos-Silva and Tenreyro (2006). In particular, we focus on the scale effect played by the size of the pool of enrolees. In most of the cases our results are consistent with the predictions of the gravity model. Chapter 4 considers the effects of contractual and working conditions on selfassessed health and psychological well-being (derived from the General Health Questionnaire) using the British Household Panel Survey (BHPS). We consider two branches of the literature. One suggests that “atypical” contractual conditions have a significant impact on health while the other suggests that health is damaged by adverse working conditions. The main objective of our paper is to combine the two branches of the literature to assess the distinct effects of contractual and working conditions on health. The results suggest that both sets of conditions have some influence on health and psychological well-being of employees.