The analytic torsion of a disc

In this article, we study the Reidemeister torsion and the analytic torsion of the m dimensional disc, with the Ray and Singer homology basis (Adv Math 7:145-210, 1971). We prove that the Reidemeister torsion coincides with a power of the volume of the disc. We study the additional terms arising in the analytic torsion due to the boundary, using generalizations of the Cheeger-Muller theorem. We use a formula proved by Bruning and Ma (GAFA 16:767-873, 2006) that predicts a new anomaly boundary term beside the known term proportional to the Euler characteristic of the boundary (Luck, J Diff Geom 37:263-322, 1993). Some of our results extend to the case of the cone over a sphere, in particular we evaluate directly the analytic torsion for a cone over the circle and over the two sphere. We compare the results obtained in the low dimensional cases. We also consider a different formula for the boundary term given by Dai and Fang (Asian J Math 4:695-714, 2000), and we compare the results. The results of these work were announced in the study of Hartmann et al. (BUMI 2:529-533, 2009).

An analytic method to compute the stress dependence on the dimensions and its influence in the characteristics of triple gate devices

Triple-gate devices are considered a promising solution for sub-20 nm era. Strain engineering has also been recognized as an alternative due to the increase in the carriers mobility it propitiates. The simulation of strained devices has the major drawback of the stress non-uniformity, which cannot be easily considered in a device TCAD simulation without the coupled process simulation that is time consuming and cumbersome task. However, it is mandatory to have accurate device simulation, with good correlation with experimental results of strained devices, allowing for in-depth physical insight as well as prediction on the stress impact on the device electrical characteristics. This work proposes the use of an analytic function, based on the literature, to describe accurately the strain dependence on both channel length and fin width in order to simulate adequately strained triple-gate devices. The maximum transconductance and the threshold voltage are used as the key parameters to compare simulated and experimental data. The results show the agreement of the proposed analytic function with the experimental results. Also, an analysis on the threshold voltage variation is carried out, showing that the stress affects the dependence of the threshold voltage on the temperature. (C) 2011 Elsevier Ltd. All rights reserved.

A quantitative approach to evolution of music and philosophy

The development of new statistical and computational methods is increasingly making it possible to bridge the gap between hard sciences and humanities. In this study, we propose an approach based on a quantitative evaluation of attributes of objects in fields of humanities, from which concepts such as dialectics and opposition are formally defined mathematically. As case studies, we analyzed the temporal evolution of classical music and philosophy by obtaining data for 8 features characterizing the corresponding fields for 7 well-known composers and philosophers, which were treated with multivariate statistics and pattern recognition methods. A bootstrap method was applied to avoid statistical bias caused by the small sample data set, with which hundreds of artificial composers and philosophers were generated, influenced by the 7 names originally chosen. Upon defining indices for opposition, skewness and counter-dialectics, we confirmed the intuitive analysis of historians in that classical music evolved according to a master apprentice tradition, while in philosophy changes were driven by opposition. Though these case studies were meant only to show the possibility of treating phenomena in humanities quantitatively, including a quantitative measure of concepts such as dialectics and opposition, the results are encouraging for further application of the approach presented here to many other areas, since it is entirely generic.

Short communication: Principal components and factor analytic models for test-day milk yield in Brazilian Holstein cattle

A total of 46,089 individual monthly test-day (TD) milk yields (10 test-days), from 7,331 complete first lactations of Holstein cattle were analyzed. A standard multivariate analysis (MV), reduced rank analyses fitting the first 2, 3, and 4 genetic principal components (PC2, PC3, PC4), and analyses that fitted a factor analytic structure considering 2, 3, and 4 factors (FAS2, FAS3, FAS4), were carried out. The models included the random animal genetic effect and fixed effects of the contemporary groups (herd-year-month of test-day), age of cow (linear and quadratic effects), and days in milk (linear effect). The residual covariance matrix was assumed to have full rank. Moreover, 2 random regression models were applied. Variance components were estimated by restricted maximum likelihood method. The heritability estimates ranged from 0.11 to 0.24. The genetic correlation estimates between TD obtained with the PC2 model were higher than those obtained with the MV model, especially on adjacent test-days at the end of lactation close to unity. The results indicate that for the data considered in this study, only 2 principal components are required to summarize the bulk of genetic variation among the 10 traits.

Competitive artistic gymnastics and coaches' philosophy

The current study is a piece from the original project entitled "Diagnosis of the Artistic Gymnastics Development Program in Brazil". Among others issues, the coaching philosophy of coaches who are developing gymnasts that may be representative of the national team was a matter of analysis. We interviewed 46 coaches from 29 sports institutions in Brazil. As data collection we used a semi-structured interview and for data treatment we adopted the content analysis method of Bardin (2010). We have found out that there is an inconsistent philosophical basis, and in many institutions this has been mixed up with the objectives of the training program or just doesn't exist. This fact needs consideration and criticism, but we know that the coaching philosophy is not developed during the coaching education courses.

Die Debatte über die Ziele des Vierten Kreuzzugs : ein Beitrag zur Lösung geschichtswissenschaftlich umstrittener Fragen mit Hilfe sozialwissenschaftlicher Instrumente

Der Rational-Choice-Ansatz (RCA) hat in den letzten Jahrzehnten eine weite Ver-rnbreitung in vielen sozialwissenschaftlichen Disziplinen erfahren. Insbesondere in den letzten zwei Jahrzehnten gab es wiederholte Bemühungen, den RCA auchrnauf geschichtswissenschaftliche Fragestellungen und Themen anzuwenden. Ein interssanter Ansatz dafür ist eine integrative Methodik, die unter der Bezeichnung „Analytic Narrative“ bekannt wurde. Damit wird versucht, die klassische narrative Form der Erklärung historischer Phänomene mit spieltheoretischen Modellierungen zu verbinden. Inspiriert durch diesen Ansatz geht die vorliegende Untersuchung der Frage nach, in welcher Form und unter welchen Umständen der RCA als analytische Grundlage für historische Themenfelder und Fragestellungen geeignet sein mag. Dies wird nicht nur theoretisch, sondern an einem historischen Beispiel untersucht. Konkreter Betrachtungsgegenstand der Arbeit ist der Vierte Kreuzzug. Vor über 800 Jahren endete dieser mit der Eroberung und Plünderung Konstantinopels sowie der Zerschlagung des Byzantinischen Reichs. Seit mehr als 150 Jahren streiten Historiker über die Ursachen für diese Ereignisse. Die theoretischenrnGrundpositionen, die innerhalb dieser Debatte durch einzelne Historiker einge-rnnommen wurden, dienen als Ausgangspunkt für die hier verfolgte Untersuchung.rnEs wird gezeigt, dass die Daten, die uns über den Vierten Kreuzzug vorliegen,rndie Möglichkeit eröffnen, verschiedene auf dem RCA basierende Analyseverfah-rnren zur Anwendung zu bringen. Das zentrale Ziel der Analyse besteht darin, ausrnden vorhandenen Quellen neue Einsichten in die strategischen Handlungsoptionen der für den Verlauf des Kreuzzugs relevanten Akteure zu generieren undrnüberdies ein Höchstmaß an Überprüfbarkeit zu gewährleisten.