L'objectif principal de ce mémoire est de généraliser du cas discret au cas continu plusieurs quantités, inégalités et preuves qui surviennent en théorie de l'information. Dans plusieurs cas, à la place de transposer la preuve ou les quantités d'intérêts au continu, le cas discret est étendu à l'extrême en prenant un très grand nombre de probabilités discrètes. Nous espérons que ce mémoire puisse servir de ressource pour faciliter la transition du discret au continu et que les différentes quantités trouvées puissent servir de fondation à toute autre preuve concernant les variables continues en théorie de l'information. Les premières sections présenteront un survol des fondements de la théorie de l'information, une introduction aux probabilités ainsi que des fondements mathématiques requis pour la compréhension du reste du document. Les sections subséquentes introduiront les analogues continus à la théorie de l'information classique, en plus de différentes inégalités et preuves en rapport avec ces quantités. / This document's main goal is to generalize multiple quantities, inequalities, and proofs that arise in information theory. Many of these proofs use discrete variables. We seek here to generalize these proofs to the continuous case. In many instances, instead of transposing the proofs to the continuous case, the discrete case is taken to the extreme by taking very large pools of discrete possibilities. We hope that this thesis can serve as a tool to ease the transition from the discrete case to the continuous case and that the various quantities and bounds found herein will help in establishing a framework to prove statements regarding continuous variables in information theory. The first few sections will present a review of elementary information theory, as well as a primer on probabilities and fundamental mathematical concepts required for the rest of the document. The later sections will introduce the continuous counterparts of classical information theory, as well as various inequalities and proofs with respect to these new quantities.

Doctor of Philosophy / Department of Physics / Jingyu Lin / Time-resolved deep ultraviolet (DUV) Photoluminescence (PL) spectroscopy system has been employed to systematically monitor crystalline quality, identify the defects and impurities, and investigate the light emission mechanism in III-nitride semiconducting materials and photonic structures. A time correlated single photon counting system and streak camera with corresponding time resolutions of 20 and 2 ps, respectively, were utilized to study the carrier excitation and recombination dynamics. A closed cycle He-flow cryogenic system was employed for temperature dependent measurements. This system is able to handle sample temperatures in a wide range (from 10 to 900 K). Structural, electrical, and morphological properties of the material were monitored by x-ray diffraction (XRD), Hall-effect measurement, and atomic force microscopy (AFM), respectively. Most of the samples studied here were synthesized in our laboratory by metal organic chemical vapor deposition (MOCVD). Some samples were bulk AlN synthesized by our collaborators, which were also employed as substrates for homoepilayer growth. High quality AlN epilayers with (0002) XRD linewidth as narrow as 50 arcsec and screw type dislocation density as low as 5x10[superscript]6 cm[superscript]-2 were grown on sapphire substrates. Free exciton transitions related to all valence bands (A, B, and C) were observed in AlN directly by PL, which allowed the evaluation of crystal field (Δ[subscript]CF) and spin-orbit (Δ[subscript]SO) splitting parameters exerimentally. Large negative Δ[subscript]CF and, consequently, the difficulties of light extraction from AlN and Al-rich AlGaN based emitters due to their unique optical polarization properties have been further confirmed with these new experimental data. Due to the ionic nature of III-nitrides, exciton-LO phonon Frohlich interaction is strong in these materials, which is manifested by the appearance of phonon replicas accompanying the excitonic emission lines in their PL spectra. The strength of the exciton-phonon interactions in AlN has been investigated by measuring the Huang-Rhys factor. It compares the intensity of the zero phonon (exciton emission) line relative to its phonon replica. AlN bulk single crystals, being promising native substrate for growing nitride based high quality device structures with much lower dislocation densities (<10[superscript]4 cm[superscript]-2), are also expected to be transparent in visible to UV region. However, available bulk AlN crystals always appear with an undesirable yellow or dark color. The mechanism of such undesired coloration has been investigated. MOCVD was utilized to deposit ~0.5 μm thick AlN layer on top of bulk crystal. The band gap of strain free AlN homoepilayers was 6.100 eV, which is ~30 meV lower compared to hetero-epitaxial layers on sapphire possessing compressive strain. Impurity incorporation was much lower in non-polar m-plane growth mode and the detected PL signal at 10 K was about an order of magnitude higher from a-plane homo-epilayers compared to that from polar c-plane epilayers. The feasibility of using Be as an alternate p-type dopant in AlN has been studied. Preliminary studies indicate that the Be acceptor level in AlN is ~330 meV, which is about 200 meV shallower than the Mg level in AlN. Understanding the optical and electronic properties of native point defects is the key to achieving good quality material and improving overall device performance. A more complete picture of optical transitions in AlN and GaN has been reported, which supplements the understanding of impurity transitions in AlGaN alloys described in previous reports.

Master of Science / Department of Physics / Robert Szoszkiewicz / Proteins are involved in many of the essential cellular processes, such as cell adhesion, muscle function, enzymatic activity or signaling. It has been observed that the biological function of many proteins is critically connected to their folded conformation. Thus, the studies of the process of protein folding have become one of the central questions at the intersection of biophysics and biochemistry. We propose to use the changes of the nanomechanical properties of these biomolecules as a proxy to study how the single proteins fold. In the first steps towards this goal, the work presented in this thesis is concentrated on studies of unfolding forces and pathways of one particular multidomain protein, as well as on development of the novel method to study elastic spring constant and mechanical energy dissipation factors of simple proteins and peptides. In the first part of this thesis we present the results of the mean unfolding forces of the NRR region of the Notch1 protein. Those results are obtained using force spectroscopy techniques with the atomic force microscope (AFM) on a single molecule level. We study force-induced protein unfolding patterns and relate those to the conformational transitions within the protein using available crystal structure of the Notch protein and molecular dynamics simulations. Notch is an important protein, involved in triggering leukemia and breast cancers in metazoans, i.e., animals and humans. In the second part of this thesis we develop a model to obtain quantitative measurements of the molecular stiffness and mechanical energy dissipation factors for selected simple proteins and polypeptides from the AFM force spectroscopy measurements. We have developed this model by measuring the shifts of several thermally excited resonance frequencies of atomic force microscopy cantilevers in contact with the biomolecules. Next, we provided partial experimental validation of this model using peptide films. Ultimately, our results are expected to contribute in the future to the developments of medical sciences, which are advancing at a level, where human health and disease can be traced down to molecular scale.

The objective of this work is to develop an on-line planning and delivery technique for palliative radiotherapy of spinal metastases using a linear accelerator capable of cone-beam CT (CBCT) imaging. This technique integrates all preparation and delivery steps into a single session equivalent to an initial treatment session. The key technical challenges pertaining to the development and implementation of this novel treatment technique are related to CBCT image performance, efficient system integration, development of on-line planning tools and design of novel quality assurance (QA) phantoms and processes. Hardware and software image corrections were first implemented to make CBCT images suitable for target definition and planning. These corrections reduced CBCT non-uniformity and improved CBCT-number accuracy. The on-line treatment technique workflow and the integration of all the subsystems involved in the process were assessed on a customized spine phantom constructed for the study. The challenges related to the routine QA of the highly integrated on-line treatment technique were addressed with the construction and validation of an integral test phantom. This phantom, which contains point detectors (diodes) allows for real-time QA of the entire image guidance, planning and treatment process in terms of dose delivery accuracy. The integral test phantom was also effective for the QA of high-dose, high-precision spinal radiosurgery. Simulation of the on-line treatment technique on patient data showed that the planning step was the one of the most time consuming tasks due predominantly to manual target definition. A semi-automatic method for detection and identification of vertebrae on CBCT images was developed and validated to streamline vertebra segmentation and improve the on-line treatment efficiency. With a single patient setup at the treatment unit, patient motion during the on-line process represents the main source of geometric uncertainty for dose delivery. Spine intra-fraction motion was assessed on CBCT for a group of 49 patients treated with a palliative intent. The use of surface marker tracking as a surrogate for spine motion was also evaluated. Finally, the complete on-line planning and delivery technique was implemented in a research ethics board (REB) approved clinical study at the Princess Margaret Hospital and 7 patients have been successfully treated at the time of this report with this novel treatment approach.

Doctor of Philosophy / Department of Physics / Itzik Ben-Itzhak / One ultimate goal of ultrafast, strong- field laser science is to coherently control chemical reactions. Present laser technology allows for the production of intense (>10[superscript]13 W/cm[superscript]2), ultrashort ( 5 fs), carrier-envelope phase-stabilized pulses. By knowing the electric field waveform, sub-cycle resolution on the order of 100's of attoseconds (1 as=10[superscript]-18 s) can be reached -- the timescale for electron motion. Meanwhile, the laser field strengths are comparable to that which binds electrons to atoms or molecules. In this intense-field ultrashort-pulse regime one can both measure and manipulate dynamics of strong-field, quantum-mechanical processes in atoms and molecules. Despite much progress in the technology, typical durations for which lasers can be reliably locked to a specific carrier-envelope phase ranges from a few minutes to a few hours. Experiments investigating carrier-envelope phase effects that have necessarily long data acquisition times, such as those requiring coincidence between fragments originating from the same atom or molecule, are thus challenging and uncommon. Therefore, we combined the new technology for measuring the carrier-envelope phase of each and every laser shot with other single-shot coincidence three-dimensional momentum imaging techniques to alleviate the need for carrier-envelope phase stabilized laser pulses. Using phase-tagged coincidence techniques, several targets and laser-induced processes were studied. One particular highlight uses this method to study the recollision process of non-sequential double ionization of argon. By measuring the momentum of the two electrons emitted in the process, we could study their energy sharing. Furthermore, by selecting certain carrier-envelope phase values, and therefore laser pulses with a particular waveform, events with single recollision could be isolated and further analyzed. Another highlight is our studies of carrier-envelope phase effects in the dissociation of the benchmark H[subscript]2[superscript[+] ion beam. Aided by near-exact quantum mechanical calculations, we could identify interfering pathways which lead to the observed spatial asymmetry. These and other similar experiments are described in this thesis as significant steps toward their ultimate control.

Doctor of Philosophy / Department of Physics / Chii-Dong Lin / Imaging of molecules has always occupied an essential role in physical, chemical and biological sciences. X-ray and electron diffraction methods routinely achieve sub-angstrom spatial resolutions but are limited to probing dynamical timescales longer than a picosecond. With the advent of femtosecond intense lasers, a new imaging paradigm emerges in last decade based on laser-induced electron diffraction (LIED). It has been placed on a firm foundation by the quantitative rescattering theory, which established that large-angle e-ion elastic differential cross sections (DCS) can be retrieved from the LIED spectrum. We further demonstrate that atomic potentials can be accurately retrieved from those extracted DCSs at energies from a few to several tens of electron volts. Extending to molecules, we show mid-infrared (mid-IR) lasers are crucial to generate high-energy electron wavepackets (> 100 eV) to resolve the atomic positions in a molecule. These laser-driven 100 eV electrons can incur core-penetrating collisions where the momentum transfer is comparable to those attained in conventional keV electron diffraction. Thus a simple independent atom model (IAM), which has been widely used in conventional electron diffractions, may apply for LIED. We theoretically examine and validate the applicability of IAM for electron energies above 100 eV using e-molecule large-angle collision data obtained in conventional experiments, demonstrating its resolving powers for bond lengths about 0.05 angstrom. The Validity of IAM is also checked by an experimental LIED investigation of rare gas atoms in the mid-IR regime. We show that the electron’s high energy promotes core-penetrating collisions at large scattering angles, where the e-atom interaction is dominated by the strong short range atomic-like potential. Finally, we analyze the measured LIED spectrum of N[subscript]2 and O[subscript]2 at three mid-IR wavelengths (1.7, 2.0, and 2.3 μm). As expected, the retrieved bond lengths of N[subscript]2 at three wavelengths are about same as the equilibrium N[subscript]2 bond length. For O[subscript]2, the data is also consistent with a bond length contraction of 0.1 angstrom within 4-6 fs after tunnel ionization. This investigation establishes a foundation for this novel imaging method for spatiotemporal imaging of gas-phase molecules at the atomic scale.

Plane-layer geometry convection models remain useful for modelling planetary mantle dynamics however they yield significantly warmer mean temperatures than spherical shell models. For example, in a uniform property spherical shell with the same radius ratio, f, as the Earth's mantle; a bottom heating Rayleigh number, Ra, of 10^7 and a nondimensional internal heating rate, H, of 23 (arguably Earth-like values) are insufficient to heat the mean temperature, θ, above the mean of the non-dimensional boundary value temperatures (0.5), the temperature in a plane-layer model with no internal heating. This study investigates the impact of this geometrical effect in convection models featuring uniform and stratified viscosity. To address the effect of geometry, heat sinks are implemented to lower the mean temperature in 3D plane-layer isoviscous convection models. Over 100 models are analyzed, and their mean temperatures are used to derive a single equation for predicting θ, as a function of Ra, H and f in spherical and plane-layer systems featuring free-slip surfaces. The inclusion of first-order terrestrial characteristics is introduced to quantitatively assess the influence of system geometry on planetary scale simulations. Again, over 100 models are analyzed featuring a uniform upper mantle viscosity and a lower mantle viscosity that increases by a factor of 30 or 100. An effective Rayleigh number, Raη, is defined based on the average viscosity of the mantle. Equations for the relationship between θ, Raη, and H are derived for convection in a spherical shell with f = 0.547 and plane-layer geometries. These equations can be used to determine the appropriate heating rate for a plane-layer convection model to emulate spherical shell convection mean temperatures for effective Rayleigh numbers comparable to the Earth’s value and greater. Comparing cases with the same H and Raη, the increased lower mantle viscosity amplifies the mismatch in mean temperatures between spherical shell and plane-layer models. These findings emphasize the importance of adjusting heating rates in plane-layer geometry models and have important implications for studying convection with temperature-dependent parameters in plane-layer systems. The findings are particularly relevant to the study of convection in super-Earths where full spherical shell calculations remain intractable.

Plane-layer geometry convection models remain useful for modelling planetary mantle dynamics however they yield significantly warmer mean temperatures than spherical shell models. For example, in a uniform property spherical shell with the same radius ratio, f, as the Earth's mantle; a bottom heating Rayleigh number, Ra, of 10^7 and a nondimensional internal heating rate, H, of 23 (arguably Earth-like values) are insufficient to heat the mean temperature, θ, above the mean of the non-dimensional boundary value temperatures (0.5), the temperature in a plane-layer model with no internal heating. This study investigates the impact of this geometrical effect in convection models featuring uniform and stratified viscosity. To address the effect of geometry, heat sinks are implemented to lower the mean temperature in 3D plane-layer isoviscous convection models. Over 100 models are analyzed, and their mean temperatures are used to derive a single equation for predicting θ, as a function of Ra, H and f in spherical and plane-layer systems featuring free-slip surfaces. The inclusion of first-order terrestrial characteristics is introduced to quantitatively assess the influence of system geometry on planetary scale simulations. Again, over 100 models are analyzed featuring a uniform upper mantle viscosity and a lower mantle viscosity that increases by a factor of 30 or 100. An effective Rayleigh number, Raη, is defined based on the average viscosity of the mantle. Equations for the relationship between θ, Raη, and H are derived for convection in a spherical shell with f = 0.547 and plane-layer geometries. These equations can be used to determine the appropriate heating rate for a plane-layer convection model to emulate spherical shell convection mean temperatures for effective Rayleigh numbers comparable to the Earth’s value and greater. Comparing cases with the same H and Raη, the increased lower mantle viscosity amplifies the mismatch in mean temperatures between spherical shell and plane-layer models. These findings emphasize the importance of adjusting heating rates in plane-layer geometry models and have important implications for studying convection with temperature-dependent parameters in plane-layer systems. The findings are particularly relevant to the study of convection in super-Earths where full spherical shell calculations remain intractable.

The objective of this work is to develop an on-line planning and delivery technique for palliative radiotherapy of spinal metastases using a linear accelerator capable of cone-beam CT (CBCT) imaging. This technique integrates all preparation and delivery steps into a single session equivalent to an initial treatment session. The key technical challenges pertaining to the development and implementation of this novel treatment technique are related to CBCT image performance, efficient system integration, development of on-line planning tools and design of novel quality assurance (QA) phantoms and processes. Hardware and software image corrections were first implemented to make CBCT images suitable for target definition and planning. These corrections reduced CBCT non-uniformity and improved CBCT-number accuracy. The on-line treatment technique workflow and the integration of all the subsystems involved in the process were assessed on a customized spine phantom constructed for the study. The challenges related to the routine QA of the highly integrated on-line treatment technique were addressed with the construction and validation of an integral test phantom. This phantom, which contains point detectors (diodes) allows for real-time QA of the entire image guidance, planning and treatment process in terms of dose delivery accuracy. The integral test phantom was also effective for the QA of high-dose, high-precision spinal radiosurgery. Simulation of the on-line treatment technique on patient data showed that the planning step was the one of the most time consuming tasks due predominantly to manual target definition. A semi-automatic method for detection and identification of vertebrae on CBCT images was developed and validated to streamline vertebra segmentation and improve the on-line treatment efficiency. With a single patient setup at the treatment unit, patient motion during the on-line process represents the main source of geometric uncertainty for dose delivery. Spine intra-fraction motion was assessed on CBCT for a group of 49 patients treated with a palliative intent. The use of surface marker tracking as a surrogate for spine motion was also evaluated. Finally, the complete on-line planning and delivery technique was implemented in a research ethics board (REB) approved clinical study at the Princess Margaret Hospital and 7 patients have been successfully treated at the time of this report with this novel treatment approach.

Les capteurs biologiques basés sur l’électronique nanométrique ont la propriété intéressante d’être à l’échelle des molécules étudiées. Plus spécifiquement, grâce à leurs propriétés électroniques exceptionnelles, les transistors à effet de champ à base de graphène (TECG) permettent des mesures électriques locales à grandes vitesses d’acquisition et sur de longues durées, offrant un cadre idéal pour la biodétection et l’étude de la cinétique moléculaire. Le présent mémoire traite de l’analyse, la mesure et la fonctionnalisation des TECG dans l’optique d’en faire des biocapteurs performants. En introduction, nous décrirons les propriétés électroniques du graphène ainsi que les principaux concepts reliés aux transistors de graphène et à la détection biologique. Puis, nous établirons les trois objectifs qui seront élaborés en autant de chapitres. Dans le premier chapitre, nous présenterons une revue de littérature critique qui cible l’analyse statistique et l’assemblage de l’interface de détection comme facteurs déterminants de la performance à l’aide d’analyses originales et d’une description approfondie de l’état du domaine. Dans le deuxième chapitre, nous présenterons des ajustements concrets aux sysèmes expérimentaux basés sur les recommandations émises dans la revue. D’abord, nous améliorons la productivité de la fabrication des transistors, puis développons une instrumentation permettant de mesurer plusieurs capteurs en parallèle. Dans le troisième chapitre, nous prendrons avantage de ces modifications pour présenter dans le deuxième article une méthode permettant une fonctionnalisation du graphène à la fois contrôlée et solide. En utilisant le voltage de grille, nous initions et suspendons la fonctionnalisation covalente du graphène aux sels de diazonium afin d’obtenir le taux de greffage désiré, tout en observant la réaction en temps-réel. Ainsi, par nos avancées méthodologiques et d’instrumentation, nous résolvons un enjeu critique du développement de la chimie de surface, centrale à la performance de biodétection. / Nanoscale electronics are a promising tool for biosensing as they fit their target’s size and allow for local, fast-paced measurements over long time scales. Because of their exceptional electronic properties, graphene field-effect transistors (GFETs) are excellent candidates for biosensing and studying molecular kinetics. This work discusses the analysis, measurement, and functionalization of GFETs as optimized biosensors. In the introduction, we describe the electronic properties of graphene and the main concepts related to GFETs and biodetection. We also establish the three aims of the project, elaborated in three chapters. The first chapter contains a critical literature review that uses original analyses and a thorough state-of-the-field to target statistical analysis and the biorecognition interface assembly as determining factors in sensing performance. In the second chapter, we present the practical adjustments to the experimental systems based on the review’s recommendations. First, we increase the productivity of device fabrication, then we develop a multiplexed electrical measurement setup. In the third chapter, we take advantage of these modifications to present in the second article a method for stable and controlled functionalization. Using the gate voltage, we start and stop the covalent functionalization of graphene with aryldiazonium salts to get the desired grafting level, while observing the reaction in real-time. Thus, with our advances in methodology and instrumentation, we solve a critical aspect of surface chemistry, central for biodetection performance