Factorization method and irregular inclusions in electrical impedance tomography

In electrical impedance tomography, one tries to recover the conductivity inside a physical body from boundary measurements of current and voltage. In many practically important situations, the investigated object has known background conductivity but it is contaminated by inhomogeneities. The factorization method of Andreas Kirsch provides a tool for locating such inclusions. Earlier, it has been shown that under suitable regularity conditions positive (or negative) inhomogeneities can be characterized by the factorization technique if the conductivity or one of its higher normal derivatives jumps on the boundaries of the inclusions. In this work, we use a monotonicity argument to generalize these results: We show that the factorization method provides a characterization of an open inclusion (modulo its boundary) if each point inside the inhomogeneity has an open neighbourhood where the perturbation of the conductivity is strictly positive (or negative) definite. In particular, we do not assume any regularity of the inclusion boundary or set any conditions on the behaviour of the perturbed conductivity at the inclusion boundary. Our theoretical findings are verified by two-dimensional numerical experiments.

Costruzioni modulari in linguaggi con tipi dipendenti.

In questa tesi si indaga come è possibile strutturare in modo modulare programmi e prove in linguaggi con tipi dipendenti. Il lavoro è sviluppato nel linguaggio di programmazione con tipi dipendenti Agda. Il fine è quello di tradurre l'approccio Datatypes à la carte, originariamente formulato per Haskell, in Type Theory: puntiamo ad ottenere un simile embedding di una nozione di sottotipaggio per tipi ricorsivi, che permetta sia la definizione di programmi con side-effect dove i diversi effetti sono definiti modularmente, che la modularizzazione di sintassi, semantica e ragionamento relativi a descrizioni di linguaggi.

Novel algorithms for electronic structure based molecular dynamics with linear system-size scaling

Die vorliegende Arbeit behandelt die Entwicklung und Verbesserung von linear skalierenden Algorithmen für Elektronenstruktur basierte Molekulardynamik. Molekulardynamik ist eine Methode zur Computersimulation des komplexen Zusammenspiels zwischen Atomen und Molekülen bei endlicher Temperatur. Ein entscheidender Vorteil dieser Methode ist ihre hohe Genauigkeit und Vorhersagekraft. Allerdings verhindert der Rechenaufwand, welcher grundsätzlich kubisch mit der Anzahl der Atome skaliert, die Anwendung auf große Systeme und lange Zeitskalen. Ausgehend von einem neuen Formalismus, basierend auf dem großkanonischen Potential und einer Faktorisierung der Dichtematrix, wird die Diagonalisierung der entsprechenden Hamiltonmatrix vermieden. Dieser nutzt aus, dass die Hamilton- und die Dichtematrix aufgrund von Lokalisierung dünn besetzt sind. Das reduziert den Rechenaufwand so, dass er linear mit der Systemgröße skaliert. Um seine Effizienz zu demonstrieren, wird der daraus entstehende Algorithmus auf ein System mit flüssigem Methan angewandt, das extremem Druck (etwa 100 GPa) und extremer Temperatur (2000 - 8000 K) ausgesetzt ist. In der Simulation dissoziiert Methan bei Temperaturen oberhalb von 4000 K. Die Bildung von sp²-gebundenem polymerischen Kohlenstoff wird beobachtet. Die Simulationen liefern keinen Hinweis auf die Entstehung von Diamant und wirken sich daher auf die bisherigen Planetenmodelle von Neptun und Uranus aus. Da das Umgehen der Diagonalisierung der Hamiltonmatrix die Inversion von Matrizen mit sich bringt, wird zusätzlich das Problem behandelt, eine (inverse) p-te Wurzel einer gegebenen Matrix zu berechnen. Dies resultiert in einer neuen Formel für symmetrisch positiv definite Matrizen. Sie verallgemeinert die Newton-Schulz Iteration, Altmans Formel für beschränkte und nicht singuläre Operatoren und Newtons Methode zur Berechnung von Nullstellen von Funktionen. Der Nachweis wird erbracht, dass die Konvergenzordnung immer mindestens quadratisch ist und adaptives Anpassen eines Parameters q in allen Fällen zu besseren Ergebnissen führt.

Quadratically Hyponormal Weighted Shifts with Recursive Tail

We characterize positive quadratic hyponormality of the weighted shift W-alpha(x) associated to the weight sequence alpha(x) : 1, 1, root x, (root u, root v, root w)(Lambda) with Stampfli recursive tail, and produce an interval in x with non-empty interior in the positive real line for quadratic hyponormality but not positive quadratic hyponormality for such a shift. (C) 2013 Elsevier Inc. All rights reserved.

Large deviations for heavy-tailed random elements in convex cones

We prove large deviation results for sums of heavy-tailed random elements in rather general convex cones being semigroups equipped with a rescaling operation by positive real numbers. In difference to previous results for the cone of convex sets, our technique does not use the embedding of cones in linear spaces. Examples include the cone of convex sets with the Minkowski addition, positive half-line with maximum operation and the family of square integrable functions with arithmetic addition and argument rescaling.

The Distribution of the Irreducibles in an Algebraic Number Field

The objective of this thesis is to study the distribution of the number of principal ideals generated by an irreducible element in an algebraic number field, namely in the non-unique factorization ring of integers of such a field. In particular we are investigating the size of M(x), defined as M ( x ) =∑ (α) α irred.|N (α)|≤≠ 1, where x is any positive real number and N (α) is the norm of α. We finally obtain asymptotic results for hl(x).

Systematic derivation of partition functions for ligand binding to two-dimensional lattices

The Ising problem consists in finding the analytical solution of the partition function of a lattice once the interaction geometry among its elements is specified. No general analytical solution is available for this problem, except for the one-dimensional case. Using site-specific thermodynamics, it is shown that the partition function for ligand binding to a two-dimensional lattice can be obtained from those of one-dimensional lattices with known solution. The complexity of the lattice is reduced recursively by application of a contact transformation that involves a relatively small number of steps. The transformation implemented in a computer code solves the partition function of the lattice by operating on the connectivity matrix of the graph associated with it. This provides a powerful new approach to the Ising problem, and enables a systematic analysis of two-dimensional lattices that model many biologically relevant phenomena. Application of this approach to finite two-dimensional lattices with positive cooperativity indicates that the binding capacity per site diverges as Na (N = number of sites in the lattice) and experiences a phase-transition-like discontinuity in the thermodynamic limit N → ∞. The zeroes of the partition function tend to distribute on a slightly distorted unit circle in complex plane and approach the positive real axis already for a 5×5 square lattice. When the lattice has negative cooperativity, its properties mimic those of a system composed of two classes of independent sites with the apparent population of low-affinity binding sites increasing with the size of the lattice, thereby accounting for a phenomenon encountered in many ligand-receptor interactions.

Competition for procurement shares

We propose a new procurement procedure that allocates shares of the total amount to be procured depending on the bids of suppliers. Among the properties of the mechanism are the following: (i) Bidders have an incentive to participate in the procurement procedure, as equilibrium payoffs are strictly positive. (ii) The mechanism allows variations in the extent to which affirmative action objectives, like promoting local industries, are pursued. (iii) Surprisingly, even while accomplishing affirmative action goals, procurement expenditures might be lower than under a standard auction format.

Some properties of g- and P-spaces

A γ-space with a strictly positive measure is separable. An example of a non-separable γ−space with c.c.c. is given. A P−space with c.c.c. is countable and discrete.

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

L’objectif de modifier ou de contrôler son poids chez les adolescents : vecteur de promotion des saines habitudes de vie ou facteur de risque à la santé ?

L’objectif de modifier son poids est associé à certains comportements potentiellement dangereux, mais ses retombées sur les saines habitudes de vie des adolescents sont peu connues. L’objectif du mémoire est de quantifier les associations entre l’objectif relatif au contrôle du poids et la consommation de fruits et légumes, de boissons sucrées et d’aliments de restauration rapide, la prise du déjeuner et la pratique d’activité physique. Des régressions logistiques ont été effectuées sur les données de l’Enquête québécoise sur la santé des jeunes du secondaire 2010-2011. Respectivement, 25 %, 34 %, 12 % et 29 % des adolescents essayaient de perdre, maintenir, gagner du poids et ne rien faire à propos de leur poids. Chez les garçons et les filles, essayer de perdre du poids était associé à une probabilité plus faible de déjeuner quotidiennement (RC garçons = 0,72 ; 95%IC = 0,61 - 0,84, RC filles = 0,61 ; 95%IC = 0,56 -0,70) et chez les filles, cela était aussi associé à une probabilité plus élevée de consommer au moins cinq portions de fruits et légumes par jour (RC = 1,20 ; 95%IC = 1,04 - 1,37) et une probabilité plus faible de consommer des boissons sucrées quotidiennement (RC = 0,77 ; 95%IC = 0,66 - 0,90). Essayer de maintenir son poids et de gagner du poids étaient minimalement associés à une habitude plus délétère. L’objectif de contrôler son poids n’est donc pas strictement positif ou négatif. Il semble plus prudent de promouvoir directement les saines habitudes de vie plutôt que d’encourager l’adoption d’un objectif de contrôle du poids.

L’objectif de modifier ou de contrôler son poids chez les adolescents : vecteur de promotion des saines habitudes de vie ou facteur de risque à la santé ?

L’objectif de modifier son poids est associé à certains comportements potentiellement dangereux, mais ses retombées sur les saines habitudes de vie des adolescents sont peu connues. L’objectif du mémoire est de quantifier les associations entre l’objectif relatif au contrôle du poids et la consommation de fruits et légumes, de boissons sucrées et d’aliments de restauration rapide, la prise du déjeuner et la pratique d’activité physique. Des régressions logistiques ont été effectuées sur les données de l’Enquête québécoise sur la santé des jeunes du secondaire 2010-2011. Respectivement, 25 %, 34 %, 12 % et 29 % des adolescents essayaient de perdre, maintenir, gagner du poids et ne rien faire à propos de leur poids. Chez les garçons et les filles, essayer de perdre du poids était associé à une probabilité plus faible de déjeuner quotidiennement (RC garçons = 0,72 ; 95%IC = 0,61 - 0,84, RC filles = 0,61 ; 95%IC = 0,56 -0,70) et chez les filles, cela était aussi associé à une probabilité plus élevée de consommer au moins cinq portions de fruits et légumes par jour (RC = 1,20 ; 95%IC = 1,04 - 1,37) et une probabilité plus faible de consommer des boissons sucrées quotidiennement (RC = 0,77 ; 95%IC = 0,66 - 0,90). Essayer de maintenir son poids et de gagner du poids étaient minimalement associés à une habitude plus délétère. L’objectif de contrôler son poids n’est donc pas strictement positif ou négatif. Il semble plus prudent de promouvoir directement les saines habitudes de vie plutôt que d’encourager l’adoption d’un objectif de contrôle du poids.

Positive results in a real-time PCR for type A influenza associated with the use of an inactivated vaccine.

A real-time reverse transcription polymerase chain reaction (qRT-PCR) test for the matrix gene of type A influenza viruses was used during the 2007 Australian equine influenza (EI) outbreak in order to confirm diagnosis and, later, eradication of the virus. During the EI outbreak, horses being exported required vaccination and individual proof of freedom from EI. At the end of the outbreak, positive results were obtained from four horses destined for export, because of contamination of the samples with the vaccine. This report highlights the need for EI testing and vaccination to occur on separate days and with the collection of swabs for testing to precede vaccination.

A complete characterization of pre-Mueller and Mueller matrices in polarization optics

The Mueller-Stokes formalism that governs conventional polarization optics is formulated for plane waves, and thus the only qualification one could require of a 4 x 4 real matrix M in order that it qualify to be the Mueller matrix of some physical system would be that M map Omega((pol)), the positive solid light cone of Stokes vectors, into itself. In view of growing current interest in the characterization of partially coherent partially polarized electromagnetic beams, there is a need to extend this formalism to such beams wherein the polarization and spatial dependence are generically inseparably intertwined. This inseparability brings in additional constraints that a pre-Mueller matrix M mapping Omega((pol)) into itself needs to meet in order to be an acceptable physical Mueller matrix. These additional constraints are motivated and fully characterized. (C) 2010 Optical Society of America

Efficient Methods for Robust Classification Under Uncertainty in Kernel Matrices

In this paper we study the problem of designing SVM classifiers when the kernel matrix, K, is affected by uncertainty. Specifically K is modeled as a positive affine combination of given positive semi definite kernels, with the coefficients ranging in a norm-bounded uncertainty set. We treat the problem using the Robust Optimization methodology. This reduces the uncertain SVM problem into a deterministic conic quadratic problem which can be solved in principle by a polynomial time Interior Point (IP) algorithm. However, for large-scale classification problems, IP methods become intractable and one has to resort to first-order gradient type methods. The strategy we use here is to reformulate the robust counterpart of the uncertain SVM problem as a saddle point problem and employ a special gradient scheme which works directly on the convex-concave saddle function. The algorithm is a simplified version of a general scheme due to Juditski and Nemirovski (2011). It achieves an O(1/T-2) reduction of the initial error after T iterations. A comprehensive empirical study on both synthetic data and real-world protein structure data sets show that the proposed formulations achieve the desired robustness, and the saddle point based algorithm outperforms the IP method significantly.