The maximum subarray problem is to find the array portion that maximizes the sum of array elements in it. This problem was first introduced by Grenander and brought to computer science by Bentley in 1984. This problem has been branched out into other problems based on their characteristics. k-overlapping maximum subarray problem where the overlapping solutions are allowed, and k-disjoint maximum subarray problem where all the solutions are disjoint from each other are those. For k-overlapping maximum subarray problems, significant improvement have been made since the problem was first introduced. For k-disjoint maximum subarrsy, Ruzzo and Tompa gave an O(n) time solution for one-dimension. This solution is, however, difficult to extend to two-dimensions. While a trivial solution of O(kn^3) time is easily obtainable for two-dimensions, little study has been undertaken to better this. This paper introduces a faster algorithm for the k-disjoint maximum sub-array problem under the conventional RAM model, based on distance matrix multiplication. Also, DMM reuse technique is introduced for the maximum subarray problem based on recursion for space optimization.

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Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Diese empirische Arbeit untersucht Determinanten des Renteneintritts. Sie basiert auf einem Optionswertmodell, um die Bedeutung finanzieller Überlegungen für ein Aufschieben des Renteneintritts zu analysieren. Zusätzlich wird der Einfluss institutioneller Rahmenbedingungen betrachtet. Ein neu verfügbarer Datensatz des Verbands Deutscher Rentenversicherungsträger wird dazu verwendet. Die Ergebnisse zeigen, dass Arbeitslosigkeit und Krankheit zu einem großen Teil einen frühen Renteneintritt erklären. Zusätzlich hat der Optionswert einen großen Erklärungsgehalt. / This paper empirically investigates determinants of retirement decisions. It is based on the option value approach to assess the importance of financial considerations for delaying immediate retirement. In addition, the impact of institutional conditions is considered. Newly available data from the data base of the statutory pension organization providing exact information about income, pension claims, and unemployment spells is used. The results indicate that unemployment and illness explain a great portion of early retirements. Additionally, the option value has explanatory power.

We consider the problem of maximum likelihood estimation of logistic sinusoidal regression models and develop some asymptotic theory including the consistency and joint rates of convergence for the maximum likelihood estimators. The key techniques build upon a synthesis of the results of Walker and Song and Li for the widely studied sinusoidal regression model and on making a connection to a result of Radchenko. Monte Carlo simulations are also presented to demonstrate the finite-sample performance of the estimators

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Philosophiae Doctor - PhD / Malaria is a common infection in tropical areas, transmitted between humans through female anopheles mosquito bites as it seeks blood meal to carry out egg production. The infection forms a direct threat to the lives of many people in South Sudan. Reports show that malaria caused a large proportion of morbidity and mortality in the fledgling nation, accounting for 20% to 40% morbidity and 20% to 25% mortality, with the majority of the affected people being children and pregnant mothers. In this thesis, we construct and analyze mathematical models for malaria transmission in South Sudan context incorporating national malaria control strategic plan. In addition, we investigate important factors such as climatic conditions and population mobility that may drive malaria in South Sudan. Furthermore, we study a stochastic version of the deterministic model by introducing a white noise.

Développer une méthode de caractérisation théorique complète d'un spray sur base de la connaissance du mécanisme de formation des gouttes et pouvant être appliquée de façon similaire quel que soit le type de spray, constitue l'axe central de la présente recherche. La difficulté principale étant la connaissance de la physique de rupture de la nappe liquide en gouttelettes, l'étude entreprise s'est attachée à la description du spray ultrasonique, qui a l'avantage d'impliquer un mécanisme de formation d'ondes de surface (ondes de Faraday) largement étudié. Les moyens mis en oeuvre pour trouver la loi de distribution théorique qui décrit au mieux la pulvérisation ultrasonique sont, d'un côté, l'analyse de l'instabilité des ondes de surface, qui permet de déterminer les caractéristiques moyennes du spray, et de l'autre, une méthode stochastique, le formalisme de l'entropie maximale, qui fournit la distribution la plus probable basée sur les caractéristiques moyennes et sur les lois de conservation élémentaires applicables à tout type de pulvérisation (conservation de la masse et de l'énergie). La validation expérimentale de cette nouvelle approche théorique a permis en outre de développer de nouveaux designs de pulvérisateurs performants.// To develop a method of complete theoretical characterization of a spray based on the knowledge of the of droplet formation mechanism and being able to be applied in a similar way whatever the type of spray, constitute the central axis of this research. The main difficulty being the knowledge of the physics of liquid film break-up into droplets, the study undertaken was concerned with the description of the ultrasonic spray, which has the advantage of implying a mechanism of formation of surface waves (Faraday waves) largely studied. The means implemented to find the theoretical droplet size distribution which describes ultrasonic atomization as well as possible are, first, analysis of surface waves instability, which allows to determine the average characteristics of the spray, and then, a stochastic method, the maximum entropy formalism, which provides the most probable distribution based on the average characteristics and the elementary laws of conservation applicable to any type of atomization (mass and energy conservation). The experimental validation of this new theoretical approach made it possible moreover to develop new designs of powerful ultrasonic atomizers.

Novel Turbo Equalization Methods for the Magnetic Recording Channel Elizabeth Chesnutt 95 Pages Directed by Dr. John R. Barry The topic of this dissertation is the derivation, development, and evaluation of novel turbo equalization techniques that address the colored noise problem on the magnetic recording channel. One new algorithm presented is the noise-predictive BCJR, which is a soft-output detection strategy that mitigates colored noise in partial-response equalized magnetic recording channels. This algorithm can be viewed as a combination of the traditional BCJR algorithm with the notion of survivors and noise prediction. Additionally, an alternative equalization architecture for magnetic recording is presented that addresses the shortcomings of the PRML approach, which dominates magnetic recording. Specifically, trellis-based equalizers are abandoned in favor of simple equalization strategies based on nonlinear filters whose complexity grows only linearly with their length. This research focuses on the linear-complexity SFE algorithm and on investigating the possibility of lowering the SFE filter calculation complexity. The results indicate that with using the proposed novel SFE method, it is possible to increase the information density on magnetic media without raising the complexity. The most important result presented is that partial-response equalization needs to be reconsidered because of the amount of noise enhancement problems that it adds to the overall system. These results are important for the magnetic recording industry, which is trying to attain a 1 Tb/cm2 information storage goal.

The traditional mobile radio channel has always suffered from the detrimental effects of multipath fading. The use of multiple antennae at both ends of the wireless channel has proven to be very effective in combatting fading and enhancing the channel's spectral efficiency. To exploit the benefits offered by Multi-Input Multi-Output (MIMO) systems, both the transmitter and the receiver have to be optimally designed. In this thesis, we are concerned with the problem of receiver design for MIMO systems in a spatial multiplexing scheme. The MIMO detection problem is an NP-hard combinatorial optimization problem. Solving this problem to optimality requires an exponential search over the space of all possible transmitted symbols in order to find the closest point in a Euclidean sense to the received symbols; a procedure that is infeasible for large systems. We introduce a new heuristic algorithm for the detection of a MIMO wireless system based on the Ant Colony Optimization (ACO) metaheuristic. The new algorithm, AntMIMO, has a simple architecture and achieves near maximum likelihood performance in polynomial time.