On differential operators of Calabi-Yau type

This thesis is devoted to the study of Picard-Fuchs operators associated to one-parameter families of $n$-dimensional Calabi-Yau manifolds whose solutions are integrals of $(n,0)$-forms over locally constant $n$-cycles. Assuming additional conditions on these families, we describe algebraic properties of these operators which leads to the purely algebraic notion of operators of CY-type. rnMoreover, we present an explicit way to construct CY-type operators which have a linearly rigid monodromy tuple. Therefore, we first usernthe translation of the existence algorithm by N. Katz for rigid local systems to the level of tuples of matrices which was established by M. Dettweiler and S. Reiter. An appropriate translation to the level of differential operators yields families which contain operators of CY-type. rnConsidering additional operations, we are also able to construct special CY-type operators of degree four which have a non-linearly rigid monodromy tuple. This provides both previously known and new examples.

Data sanitization in a clearing system for public transport operators

In this work we will discuss about a project started by the Emilia-Romagna Regional Government regarding the manage of the public transport. In particular we will perform a data mining analysis on the data-set of this project. After introducing the Weka software used to make our analysis, we will discover the most useful data mining techniques and algorithms; and we will show how these results can be used to violate the privacy of the same public transport operators. At the end, despite is off topic of this work, we will spend also a few words about how it's possible to prevent this kind of attack.

Spectral theory of differential operators on finite metric graphs and on bounded domains

Die vorliegende Arbeit widmet sich der Spektraltheorie von Differentialoperatoren auf metrischen Graphen und von indefiniten Differentialoperatoren auf beschränkten Gebieten. Sie besteht aus zwei Teilen. Im Ersten werden endliche, nicht notwendigerweise kompakte, metrische Graphen und die Hilberträume von quadratintegrierbaren Funktionen auf diesen betrachtet. Alle quasi-m-akkretiven Laplaceoperatoren auf solchen Graphen werden charakterisiert, und Abschätzungen an die negativen Eigenwerte selbstadjungierter Laplaceoperatoren werden hergeleitet. Weiterhin wird die Wohlgestelltheit eines gemischten Diffusions- und Transportproblems auf kompakten Graphen durch die Anwendung von Halbgruppenmethoden untersucht. Eine Verallgemeinerung des indefiniten Operators $-tfrac{d}{dx}sgn(x)tfrac{d}{dx}$ von Intervallen auf metrische Graphen wird eingeführt. Die Spektral- und Streutheorie der selbstadjungierten Realisierungen wird detailliert besprochen. Im zweiten Teil der Arbeit werden Operatoren untersucht, die mit indefiniten Formen der Art $langlegrad v, A(cdot)grad urangle$ mit $u,vin H_0^1(Omega)subset L^2(Omega)$ und $OmegasubsetR^d$ beschränkt, assoziiert sind. Das Eigenwertverhalten entspricht in Dimension $d=1$ einer verallgemeinerten Weylschen Asymptotik und für $dgeq 2$ werden Abschätzungen an die Eigenwerte bewiesen. Die Frage, wann indefinite Formmethoden für Dimensionen $dgeq 2$ anwendbar sind, bleibt offen und wird diskutiert.

Pervasive Algebras and Maximal Subalgebras.

A uniform algebra A on its Shilov boundary X is maximal if A is not C(X) and no uniform algebra is strictly contained between A and C(X) . It is essentially pervasive if A is dense in C(F) whenever F is a proper closed subset of the essential set of A. If A is maximal, then it is essentially pervasive and proper. We explore the gap between these two concepts. We show: (1) If A is pervasive and proper, and has a nonconstant unimodular element, then A contains an infinite descending chain of pervasive subalgebras on X . (2) It is possible to find a compact Hausdorff space X such that there is an isomorphic copy of the lattice of all subsets of N in the family of pervasive subalgebras of C(X). (3) In the other direction, if A is strongly logmodular, proper and pervasive, then it is maximal. (4) This fails if the word “strongly” is removed. We discuss examples involving Dirichlet algebras, A(U) algebras, Douglas algebras, and subalgebras of H∞(D), and develop new results that relate pervasiveness, maximality, and relative maximality to support sets of representing measures.

Efficient implementation of discrete Pascal transform using difference operators

An alternative way is provided to define the discrete Pascal transform using difference operators to reveal the fundamental concept of the transform, in both one- and two-dimensional cases, which is extended to cover non-square two-dimensional applications. Efficient modularised implementations are proposed.

Angiographic maximal luminal diameter and appropriate deployment of the everolimus-eluting bioresorbable vascular scaffold as assessed by optical coherence tomography: an ABSORB cohort B trial sub-study

Bioresorbable vascular scaffolds (BVS) present different mechanical properties as compared to metallic platform stents. Therefore, the standard procedural technique to achieve appropriate deployment may differ.

Effect of acute hypoxia on maximal oxygen uptake and maximal performance during leg and upper-body exercise in Nordic combined skiers

We examined the effect of normobaric hypoxia (3200 m) on maximal oxygen uptake (VO2max) and maximal power output (Pmax) during leg and upper-body exercise to identify functional and structural correlates of the variability in the decrement of VO2max (DeltaVO2max) and of maximal power output (DeltaPmax). Seven well trained male Nordic combined skiers performed incremental exercise tests to exhaustion on a cycle ergometer (leg exercise) and on a custom built doublepoling ergometer for cross-country skiing (upper-body exercise). Tests were carried out in normoxia (560 m) and normobaric hypoxia (3200 m); biopsies were taken from m. deltoideus. DeltaVO2max was not significantly different between leg (-9.1+/-4.9%) and upper-body exercise (-7.9+/-5.8%). By contrast, Pmax was significantly more reduced during leg exercise (-17.3+/-3.3%) than during upper-body exercise (-9.6+/-6.4%, p<0.05). Correlation analysis did not reveal any significant relationship between leg and upper-body exercise neither for DeltaVO2max nor for DeltaPmax. Furthermore, no relationship was observed between individual DeltaVO2max and DeltaPmax. Analysis of structural data of m. deltoideus revealed a significant correlation between capillary density and DeltaPmax (R=-0.80, p=0.03), as well as between volume density of mitochondria and DeltaPmax (R=-0.75, p=0.05). In conclusion, it seems that VO2max and Pmax are differently affected by hypoxia. The ability to tolerate hypoxia is a characteristic of the individual depending in part on the exercise mode. We present evidence that athletes with a high capillarity and a high muscular oxidative capacity are more sensitive to hypoxia.

Monotone Constrained Tensor-product B-spline with application to screening studies

When different markers are responsive to different aspects of a disease, combination of multiple markers could provide a better screening test for early detection. It is also resonable to assume that the risk of disease changes smoothly as the biomarker values change and the change in risk is monotone with respect to each biomarker. In this paper, we propose a boundary constrained tensor-product B-spline method to estimate the risk of disease by maximizing a penalized likelihood. To choose the optimal amount of smoothing, two scores are proposed which are extensions of the GCV score (O'Sullivan et al. (1986)) and the GACV score (Ziang and Wahba (1996)) to incorporate linear constraints. Simulation studies are carried out to investigate the performance of the proposed estimator and the selection scores. In addidtion, sensitivities and specificities based ona pproximate leave-one-out estimates are proposed to generate more realisitc ROC curves. Data from a pancreatic cancer study is used for illustration.