Dans la première partie de cette thèse, on présente des bornes supérieures fines pour le nombre de sous-variétés irréductibles de torsion maximales dans une sous-variété du tore complexe algébrique $(\mathbb{C}^{\times})^n$ et d'une variété abélienne. Dans les deux cas, on donne une borne explicite en termes du degré des polynômes définissants et la variété ambiante. De plus, la dépendance en le degré des polynômes est optimale. Dans le cas du tore complexe, on donne aussi une borne explicite en termes du degré torique de la sous-variété. En conséquence de ce dernier résultat, on démontre les conjectures de Ruppert, et Aliev et Smyth pour le nombre de points de torsion isolés dans une hypersurface. Ces conjectures bornent ce nombre en terme, respectivement, du multi-degré et du volume du polytope de Newton d'un polynôme définissant l'hypersurface.Dans la deuxième partie de cette thèse, on présente une borne supérieure pour la hauteur des zéros isolés, dans le tore, d'un système de polynômes de Laurent sur un corps adélique qui satisfait la formule du produit. Cette borne s'exprime en termes des intégrales mixtes des fonctions toit locales associées à la hauteur choisie et le système des polynômes de Laurent. On montre aussi que cette borne est presque optimale dans quelques familles d'exemples. Ce résultat est un analogue arithmétique du théorème de Bern\v{s}tein-Ku\v{s}nirenko. / In the first part of this thesis we present sharp bounds on the number of maximal torsion cosets in a subvariety of a complex algebraic torus $(\mathbb{C}^{\times})^n$ and of an Abelian variety. In both cases, we give an explicit bound in terms of the degree of the defining polynomials and the ambient variety. Moreover, the dependence on the degree of the polynomials is sharp. In the case of the complex torus, we also give an effective bound in terms of the toric degree of the subvariety. As a consequence of the latter result, we prove the conjectures of Ruppert, and Aliev and Smyth on the number of isolated torsion points of a hypersurface. These conjectures bound this number in terms of the multidegree and the volume of the Newton polytope of a polynomial defining the hypersurface, respectively.In the second part of the thesis, we present an upper bound for the height of isolated zeros, in the torus, of a system of Laurent polynomials over an adelic field satisfying the product formula. This upper bound is expressed in terms of the mixed integrals of the local roof functions associated to the chosen height function and to the system of Laurent polynomials. We also show that this bound is close to optimal in some families of examples. This result is an arithmetic analogue of the classical Bern\v{s}tein-Ku\v{s}nirenko theorem.

Prompted by the success of heterotic line bundle model building on Complete Intersection Calabi Yau (CICY) manifolds and the new developments regarding a generalization thereof, I analyze the possibility of model building on generalized CICY (gCICY) manifolds.  Ultimately this is realized on two examples of gCICYs, one of which topologically equivalent to a CICY and one inequivalent to any previously studied examples.  The first chapter is dedicated to reporting background information on CICYs and gCICYs.  The mathematical machinery of CICYs and their generalizations are introduced alongside explicit constructions of two examples.  The second chapter introduces the reader to heterotic line bundle model building on CICYs and gCICYs.  In the setting of gCICYs, similar to regular CICYs, model building is accomplished in two steps: first the larger $E_{8}$ gauge group is broken to an $SU( 5 )$ grand unified theory  through a line bundle model.  Then the GUT is broken using Wilson line symmetry breaking, for which the presence of a freely acting discrete symmetry must be established.  To that end, I proceed to show that the two previous examples benefit from a $\mathbb{Z}_{2}$ freely acting discrete symmetry.  Utilizing this symmetry I construct 20 and 11 explicit models for the two gCICY examples respectively, by scanning over a finite range of line bundle charges. / Ett av de största problemen i modern teoretisk fysik är att hitta en teori för kvantgravitation.För en konsekvent kvantteori gravitation skulle vara en väsentlig del i fysikens pussel, och koppla samman gravitationsfysiken för planeter och galaxer, som beskrivs av allmänna relativitetsteorin, till fysiken för partiklar, beskrivet av kvantfältteori.Bland de mest lovande teorierna finns strängteorin som föreslår att ersätta partiklar med strängar som materiens grundläggande beståndsdel.Förutom att lösa kvantgravitationproblemet hoppas teoretiska fysiker genom strängteorin att förenkla beskrivningen av partikelfysik.Detta skulle ske genom att ersätta hela partikelzoo med ett enda objekt: strängen.Olika vibrationer i strängen skulle motsvara olika partiklar och interaktioner mellan strängar skulle motsvara interaktioner mellan partiklar.För att vara motsägelsefri kräver dock strängteori att det finns minst sex fler dimensioner än de vi kan uppleva.En av strategierna som för närvarande studeras för att förlika extra dimensioner med och moderna experiment kallas ``kompaktifiering'' eller ``compactification'' på engelska.Strategin föreslår att dessa extra dimensioner ska vara kompakta och så små att de är osynliga för observationer.Interesant nog påverkar geometrin i det sexdimensionella kompakta rummet i stor utsträckning fysiken som strängteorin producerar: olika rum skulle producera olika partiklar och olika grundläggande naturkrafter.I den här uppsatsen studerar jag två exempel på sådana sexdimensionella rum som kommer från en uppsättning av rum som kallas `` generaliserade CICYs'' som nyligen har upptäckts.Med hjälp av de tekniker som liknar de som har utvecklats för andra liknade rum, visar jag att vissa aspekter av en strängteori kompaktifierad på generaliserade CICY återspeglar de som mäts genom moderna partikelfysikexperiment.

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Advance warning signals installed upstream of a high-speed signalized intersection (HSSI) warn motorists of impending signal changes in an effort to reduce the frequency of red-light running (RLR) and crashes. A new advance warning signal design was tested on an approach to an HSSI in Utah to study the effects of the modified design on motorist behavior. The new design utilized an overhead dynamic blank-out sign and flashers. A state-of-the-art digital wave radar evaluation system was installed at the study site to collect continuous data of vehicle speeds and RLR events by a non-intrusive method. Crash data were collected from the jurisdiction responsible for the study site and for an additional control intersection. Data were collected prior to, immediately after, and eight months after installation The blank-out overhead dynamic advance warning signal (BODAWS) system reduced RLR at the site during the time period immediately after installation. Eight months later, the number of RLR violations was slightly higher on one approach than before BODAWS system installation. Crash results showed that six months after BODAWS installation, the number of crashes declined at the study site. The number of crashes proportionately declined at the control intersection as well indicating a need to continue to evaluate and monitor changes. Mean vehicle speeds recorded before the onset of the yellow signal increased on the approaches to the study site immediately after BODAWS installation, and remained higher eight months later. Mean vehicle speeds recorded during the yellow signal, increased eight months after BODAWS installation to speeds higher than before the system was installed. Higher speeds during the yellow signal, combined with an increase in the number of RLR violations eight months after BODAWS installation, suggest that motorists may have begun to use the advance warning to speed up in an attempt to enter the intersection before the signal turned red. It is recommended that the lead flash time between activation of the BODAWS signs and flashers and the onset of the yellow signal should be adjusted so that motorists are not provided with more time than is necessary to safely clear the intersection.

Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: The availability of laser systems capable of generating ultrashort optical pulses in the visible spectral range have made it possible to study molecular species with a temporal resolution in the order of intra-molecular dynamics which previously were not accessible. Henceforth, in this study a popular pump-probe technique called ultrafast transient absorption spectroscopy (UTAS) is employed to study the initial photochromic reaction of metal complex, dithizonatophenylmercury (II) (DPM) under various conditions. These conditions include the use of different solvents and electronically altering DPM by the addition of substituents with specific electron affinity properties. For this study the photochromic behaviour of DPM dissolved in methanol is used as standard. Using this standard, the initial photochromic reaction after ultrafast excitation within less than 100 fs caused a radiationless photoreaction with a time constant of about 2 ps, which is interpreted as C=N isomerization along the twist coordinate. It is found that during this isomerization reaction an orthogonally twisted intermediate state was formed and observed through its excited-state absorption, which funnels through a conical intersection onto the ground state potential. Once here, bifurcation along pathways towards the ground states of the reactant and product configurations occurs. This was the first observation of photochromism for DPM in a strong polar solvent such as methanol. From the results of the test compound in methanol, comparisons to the photo-behaviour of DPM dissolved in deuterated methanol and dichloromethane are made. What is established is that changing the solvent resulted in slightly different decay times as well as spectral shifts in the absorption profile which suggested that the potential energy surface of the excited state is modified. This is similar to the results found from the electronically altered DPM species. Here the entire photoreaction is found to either be sped up (1 ps) or slowed down (4 ps) depending on the sample investigated. Previous studies on the photochromicity of DPM like systems concluded that apart from the photo-activated forward reaction, a back reaction occurs in the absence of light. Therefore a detailed look at the back reaction of DPM and its derivatives are also studied. This is done by temporally monitoring the absorption change of the photo-product as it converts back to the reactant. In doing so the lifetime of the photo-product is determined and found to differ greatly depending on the solvent and substituent used. Lastly, in assuming that the back reaction follows first order kinetics, an Arrhenius type measurement on the photo-product of DPM is conducted. The result of this measurement is that a potential energy barrier of 64.8 kJ/mol is overcome in the back reaction. The measurements performed and the results obtained from the photochromicity of DPM contribute to the understanding of photo-induced cis-trans isomerization reactions about a C=N double bond. / AFRIKAANSE OPSOMMING: Die beskikbaarheid van laser sisteme in staat om ultrakort optiese pulse te genereer in die sigbare spektrale gebied, het die studie van molekulˆere spesies met ’n tydresolusie in die orde van intra-molekulˆere dinamika wat voorheen nie toeganklik was nie. Voortaan, in hierdie studie word ’n populˆere aktiveer-interogeer tegniek genaamd ultravinnige tydafhanklike absorpsie spektroskopie (UTAS) aangewend om die aanvanklike fotochromiese reaksie van die metaal kompleks, ditisoonfenielkwik (II) (DFK) onder verskillende kondisies te bestudeer. Hierdie kondisies sluit in die gebruik van verskillende oplosmiddels en die elektroniese verstelling van DFK deur die toevoeging van substituente met spesifieke elektron affiniteit eienskappe. Vir hierdie studie word die fotochromiese gedrag van DFK, opgelos in metanol, as standaard gebruik. Met hierdie standaard, word gevind dat die aanvanklike fotochroom reaksie na ultravinnige opwekking binne minder as 100 fs, ’n stralingslose fotoreaksie met ’n tydkonstante van 2 ps veroorsaak. Hierdie fotoreaksie word verklaar as die C=N isomerisasie met betrekking tot die draai ko¨ordinaat. Daar is ook gevind dat gedurende hierdie isomerisasie reaksie, ’n ortogonaal verdraaide oorgangstoestand gevorm word wat waargeneem is deur sy absorpsie in die opgewekte toestand wat tregter deur ’n koniese kruispunt na die potensiaal van die grondtoestand. By hierdie punt vurk die proses na die grondtoestande van die reaktant en die produk vorme. Di´e was die eerste waarneming van fotochromisme van DFK opgelos in ’n sterk polˆere oplosmiddel soos metanol. Vanuit die resultate vir die toets mengsel in metanol word vergelykings getrek tot die fotogedrag van DFK opgelos in gedeureriese metanol en dichlorometaan. Wat hieruit vasgestel is, is dat die verandering in oplosmiddel wel die fotoreaksie be¨ınvloed deurdat verskillende vervaltye en spekrale verskuiwings in die apsorpsie profiel waargeneem word. Hierdie verskille dui aan dat die potensie¨ele energie oppervlakte van die opgewekte toestand wel gemodifiseer word. Dit is ook soortgelyk aan die resultate vir die elektronies verstelde BFK spesies. Hier is gevind dat die tempo van die totale fotoreaksie `of toeneem (1 ps) `of afneem (4 ps) afhanklik van die spesifieke spesie wat bestudeer word. Vorige studies van die fotochromiese gedrag van sisteme soortgelyk aan DFK het gevind dat behalwe vir die fotogeaktiveerde voorwaartse reaksie, daar ook ’n keersy reaksie plaasvind in die afwesigheid van lig. Dus word die keersy reaksie vir DFK en sy derivate ook in detial bestudeer. In hierdie studie word die absorpsie verskille van die fotoproduk tydelik waargeneem soos dit terugkeer na die reaktant. Op hierdie manier word die leeftyd van die fotoproduk bepaal en gevind dat dit grootliks afhang van die tipe oplosmiddel en tipe substituent wat gebruik word. Ten slote, wanneer daar aanvaar word dat di´e keersy reaksie eerste orde kinetika volg, word ’n Arrhenius tipe meting op die fotoproduk uitgevoer. Die resultaat van hierdie meting is dat ’n potensie¨ele enrgie versperring van 64.8 kJ/mol oorkom word in die keersy reaksie. Die metings wat uitgevoer is en die resultate wat verkry is van die fotochromiese gedrag van DFK dra by tot die verstandhouding van lig-ge¨ınduseerde cis-trans isomerisasie reaksies rondom ’n C=N dubbelbinding.

In Alabama, the Paleozoic Appalachian thrust belt plunges southwest beneath the Mesozoic-Cenozoic Gulf Coastal Plain. In Arkansas, the Paleozoic Ouachita thrust belt plunges southeast beneath the Coastal Plain. The strikes of the exposed thrust belts suggest an intersection beneath the Coastal Plain. Well data and seismic reflection profiles confirm the strike and intersection of the thrust belts, and provide information to determine the structure and general stratigraphy of each thrust belt. In east-central Mississippi, the Appalachian thrust belt curves from the regional northeast trace to westward at the intersection with the southeastern terminus of the Ouachita thrust belt, to northwest where Ouachita thrust sheets are in the Appalachian footwall, and farther west, to a west-southwest orientation. At the intersection, the frontal Appalachian fault truncates the Appalachian thrust sheets. The Appalachian thrust sheets are detached in Lower Cambrian strata and contain a distinctive Cambrian-Ordovician passive-margin carbonate succession. The Ouachita thrust sheets are detached above the carbonate succession and contain a thick Carboniferous clastic succession. The Appalachian thrust sheets east of the intersection rest on an autochthonous footwall with a thin Lower Cambrian sedimentary cover above Precambrian crystalline basement. To the west, the Appalachian thrust sheets rest on an allochthonous footwall of thick Ouachita thrust sheets. The top of Precambrian crystalline basement rocks dips southwestward beneath the Ouachita thrust belt; large-magnitude down-to-southwest basement faults enhance the deepening. Appalachian thrust sheets on the northeast are detached above relatively shallow basement, but to the west, are detached above thick Ouachita thrust sheets, which overlie deeper basement. The structure of the basement reflects the Iapetan rifted margin, where the northwest-striking Alabama-Oklahoma transform bounds the southwest side of the Alabama promontory. The trends of basement structures and subsidence toward the Ouachita thrust belt parallel the Alabama-Oklahoma transform. Shallower basement and synrift basement grabens underlie the northeast-striking Appalachian thrust belt. The curves in strike and along-strike change in footwall structure of the Appalachian thrust belt reflect controls by basement structure and by the structure of the Ouachita thrust belt.

This work is focused on thermodynamic modelling of isobaric vapour-liquid-liquid equilibrium (VLLE) (homogeneous) and (heterogeneous) for binary, ternary and quaternary systems. This work uses data for organic/aqueous systems; historically these mixtures were used in the production of penicillin and were required to be separated by continuous fractional distillation. Modelling of the separation required phase equilibrium data to be available so that predictions could be made for equilibrium stage temperatures, vapour compositions, liquid compositions and any phase splitting occurring in the liquid phase. Relevant data became available in the literature and work has been carried out to use relevant theories in correlating and predicting as was originally required in the distillation equilibrium stage modelling. All the modelling carried out was at atmospheric pressure. The modelling has been done using an Equation of State, specifically Peng Robinson Styrjek Vera (PRSV), combined with the activity coefficient model UNIversal QUAsi Chemical (UNIQUAC) through Wong Sandler mixing rules (WSMR). The success of all correlations and predictions was justified by minimizing the value of the Absolute Average Deviation (AAD) as defined within the thesis. Initially the integral Area Method and a method called Tangent Plane Intersection (TPI) were used in the prediction of liquid-liquid equilibrium (LLE) binary systems. This work used a modified 2-point search, suggested a 3-point search and has successfully applied both of these methods to predict VLLE for binary systems. It was discovered through the application of the TPI on ternary VLLE systems that the method was strongly sensitive to initial values. This work suggested and tested a Systematic Initial Generator (SIG) to provide the TPI method with realistic initial values close to the real solution and has demonstrated the viability of the SIG on improving the accuracy of the TPI results for the ternary systems investigated. In parallel with the TPI another method the Tangent Plane Distance Function (TPDF) was also investigated. This method is based on the minimisation of Gibbs free energy function related to the Gibbs energy surface. This method consistently showed it was capable of predicting VLLE for both ternary and quaternary systems as demonstrated throughout this work. The TPDF method was found to be computationally faster and less sensitive to the initial values. Some of the methods investigated in this work were also found to be applicable as phase predictors and it was discovered that the TPDF and the SIG methods were successful in predicting the phase regions; however the TPI method failed in identifying the 2 phase region. Applying the techniques described to newly available quaternary data has identified the strengths and weaknesses of the methods. This work has expanded the existing knowledge and developed a reliable model for design, operation and optimisation of the phase equilibria required for prediction in many separation processes. Currently available modelling simulation packages are variable in their predictions and sometimes yield unsatisfactory predictions. Many of the current uses of VLLE models are particularly focused on Hydrocarbon/Water systems at high pressure. The work described in this thesis has demonstrated that an EOS with suitable mixing rules can model and predict data for polar organic liquids at atmospheric and below atmospheric pressure and offers the advantage of using the same modelling equations for both phases.

Higher-order recursion schemes are a powerful model of functional computation that grew out of traditional recursive program schemes and generalisations of grammars. It is common to view recursion schemes as generators of possibly-infinite trees, which Ong showed to have a decidable monadic second order theory and opened the door to applications in verification. Kobayashi later presented an intersection type characterisation of the model checking problem, on which most subsequent applied work is based. In recent work, recursion schemes have been considered to play a role similar to Boolean programs in verification of first-order imperative programs: a natural target for abstraction of programs with very large or infinite data domains. In this thesis we focus on the development of model checking algorithms for variants of recursion schemes. We start our contributions with a model checking algorithm inspired by the fully abstract game semantics of recursion schemes, but specified as a goal-directed approach to intersection type inference, that offers a unification of the views of Ong and Kobayashi. We build on this largely theoretical contribution with two orthogonal extensions and practical implementations. First, we develop a new extension of recursion schemes: higher-order recursion schemes with cases, which add non-determinism and a case construct operating over a finite data domain. These additions provide us with a more natural and succinct target for abstraction from functional programs: encoding data using functions inevitably results in an increase in the order and arity of the scheme, which have a direct impact on the worst-case complexity of the problem. We characterise the model checking problem using a novel intersection and union type system and give a practical algorithm for type inference in this system. We have carried out an empirical evaluation of the implementation --- the tool T_RAVMC --- using a variety of problem instances from the literature and a new suite of problem instances derived via an abstraction-refinement procedure from functional programs. Second, we extend our approach from safety properties to all properties expressible in monadic second order logic using alternating parity tree automata as our specification language. We again provide an implementation and an empirical evaluation, which shows that despite the challenges accompanying liveness properties our tool scales beyond the current state of the art.

In this thesis, we address the action retrieval and the object category segmentation problems by directly optimizing application specific performance measures using deep learning. Most deep learning methods are designed to optimize simple loss functions (e.g., cross-entropy or hamming loss). These loss functions are suitable for applications where the performance of the application is measured by overall accuracy. But for many applications, the overall accuracy is not an appropriate performance measure. For example, applications like action retrieval often use the area under the Receiver Operating Characteristic curve (ROC curve) to measure the performance of a retrieval algorithm. Likewise, in object category segmentation from images, the intersection-over-union (IoU) is the standard performance measure. In this thesis, we propose approaches to directly optimize these complex performance measures in deep learning framework. / October 2016

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