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.

Predicting smear negative pulmonary tuberculosis with classification trees and logistic regression: a cross-sectional study

Abstract Background Smear negative pulmonary tuberculosis (SNPT) accounts for 30% of pulmonary tuberculosis cases reported yearly in Brazil. This study aimed to develop a prediction model for SNPT for outpatients in areas with scarce resources. Methods The study enrolled 551 patients with clinical-radiological suspicion of SNPT, in Rio de Janeiro, Brazil. The original data was divided into two equivalent samples for generation and validation of the prediction models. Symptoms, physical signs and chest X-rays were used for constructing logistic regression and classification and regression tree models. From the logistic regression, we generated a clinical and radiological prediction score. The area under the receiver operator characteristic curve, sensitivity, and specificity were used to evaluate the model's performance in both generation and validation samples. Results It was possible to generate predictive models for SNPT with sensitivity ranging from 64% to 71% and specificity ranging from 58% to 76%. Conclusion The results suggest that those models might be useful as screening tools for estimating the risk of SNPT, optimizing the utilization of more expensive tests, and avoiding costs of unnecessary anti-tuberculosis treatment. Those models might be cost-effective tools in a health care network with hierarchical distribution of scarce resources.

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.

Perceptual maps analysis for organic food consumers in China: a study on Shanghai consumers

Although in Europe and in the USA many studies focus on organic, little is known on the topic in China. This research provides an insight on Shanghai consumers’ perception of organic, aiming at understanding and representing in graphic form the network of mental associations that stems from the organic concept. To acquire, process and aggregate the individual networks it was used the “Brand concept mapping” methodology (Roedder et al., 2006), while the data analysis was carried out also using analytic procedures. The results achieved suggest that organic food is perceived as healthy, safe and costly. Although these attributes are pretty much consistent with the European perception, some relevant differences emerged. First, organic is not necessarily synonymous with natural product in China, also due to a poor translation of the term in the Chinese language that conveys the idea of a manufactured product. Secondly, the organic label has to deal with the competition with the green food label in terms of image and positioning on the market, since they are easily associated and often confused. “Environmental protection” also emerged as relevant association, while the ethical and social values were not mentioned. In conclusion, health care and security concerns are the factors that influence most the food consumption in China (many people are so concerned about food safety that they found it difficult to shop), and the associations “Safe”, “Pure and natural”, “without chemicals” and “healthy” have been identified as the best candidates for leveraging a sound image of organic food .

Entwicklung von computergestützten Hangstabilitätsmodellen zur Erstellung einer Gefahrenhinweiskarte für die Region Rheinhessen

Das Ziel der Arbeit war die Entwicklung computergestützter Methoden zur Erstellung einer Gefahrenhinweiskarte für die Region Rheinhessen, zur Minimierung der Hangrutschungsgefährdung. Dazu wurde mit Hilfe zweier statistischer Verfahren (Diskriminanzanalyse, Lo­gistische Regression) und einer Methode aus dem Bereich der Künstlichen Intelligenz (Fuzzy Logik) versucht, die potentielle Gefährdung auch solcher Hänge zu klassifizieren, die bis heute noch nicht durch Massenbewegungen aufgefallen sind. Da ingenieurgeologische und geotechnische Hanguntersuchungen aus Zeit und Kostengründen im regionalen Maßstab nicht möglich sind, wurde auf punktuell vorhandene Datenbestände zu einzelnen Rut­schungen des Winters 1981/82, die in einer Rutschungsdatenbank zu­sammengefaßt sind, zurückgegriffen, wobei die daraus gewonnenen Erkenntnisse über Prozeßmechanismen und auslösende Faktoren genutzt und in das jeweilige Modell integriert wurden. Flächenhafte Daten (Lithologie, Hangneigung, Landnutzung, etc.), die für die Berechnung der Hangstabilität notwendig sind, wurden durch Fernerkundungsmethoden, dem Digitalisieren von Karten und der Auswertung von Digitalen Geländemodellen (Reliefanalyse) gewonnen. Für eine weiterführende Untersuchung von einzelnen, als rutschgefährdet klassifi­zierten Bereichen der Gefahrenhinweiskarte, wurde am Beispiel eines Testgebietes, eine auf dem infinite-slope-stability Modell aufbauende Me­thode untersucht, die im Maßstabsbereich von Grundkarten (1:5000) auch geotechnische und hydrogeologische Parameter berücksichtigt und damit eine genauere, der jeweiligen klimatischen Situation angepaßte, Gefahrenabschätzung ermöglicht.

Diffusion maps in the Subriemannian motion group and perceptual grouping

Il presente lavoro è motivato dal problema della constituzione di unità percettive a livello della corteccia visiva primaria V1. Si studia dettagliatamente il modello geometrico di Citti-Sarti con particolare attenzione alla modellazione di fenomeni di associazione visiva. Viene studiato nel dettaglio un modello di connettività. Il contributo originale risiede nell'adattamento del metodo delle diffusion maps, recentemente introdotto da Coifman e Lafon, alla geometria subriemanniana della corteccia visiva. Vengono utilizzati strumenti di teoria del potenziale, teoria spettrale, analisi armonica in gruppi di Lie per l'approssimazione delle autofunzioni dell'operatore del calore sul gruppo dei moti rigidi del piano. Le autofunzioni sono utilizzate per l'estrazione di unità percettive nello stimolo visivo. Sono presentate prove sperimentali e originali delle capacità performanti del metodo.