Introduzimos a extensão natural da definição de medida DLR para medidas sigma-finitas em shift de Markov com alfabeto enumerável. Provamos que o conjunto de medidas DLR contém o conjunto de medidas conformes associadas aos potenciais satisfazendo a condição de Walters. No caso BIP ou quando o potencial normaliza o operador de Ruelle, provamos que as noções de DLR e conformes coincidem. No shift de renewal obtemos uma caracterização de quando as medidas conformes são infinitas, estudamos o problema para descrever os casos em que o conjunto de medidas conformes pula de medidas finitas para infinitas quando consideramos altas e baixas temperaturas, respectivamente. / We introduce the natural extension of the definition of DLR measure for sigma-finite measures on countable Markov shifts. We prove that the set of DLR measures contains the set of conformal measures associated to Walters potentials. In the BIP case or when the potential normalizes the Ruelle\'s operator we prove that the notions of DLR and conformal coincide. On renewal type shifts we obtained a characterization when the conformal measures are infinite, we study the problem to describe the cases when the set of conformal measures jumps from finite to infinite measures when we consider high and low temperatures, respectively.

Es wird die Twistorgleichung auf Lorentz-Spin-Mannigfaltigkeiten untersucht. Bekanntermaßen existieren Lösungen der Twistorgleichung auf den pp-Mannigfaltigkeiten, den Lorentz-Einstein-Sasaki Mannigfaltigkeiten und den Fefferman-Räumen. Es wird gezeigt, dass in den kleinen Dimensionen 3,4 und 5 Twistor-Spinoren ohne 'Singularitäten' nur für diese genannten Lorentz-Geometrien vorkommen. Von besonderem Interesse sind Lösungen der Twistorgleichung mit Nullstellen. Es wird die Gestalt der Nullstellenmenge von konformen Vektorfeldern und Twistor-Spinoren beschrieben. Weiterhin wird die Twistorgleichung im Kontext der konformen Cartan-Geometrie formuliert. Als Anwendung werden konform-flache semi-Riemannsche Spin-Mannigfaltigkeiten mit Twistor-Spinoren unter Zuhilfenahme der Holonomiedarstellung der ersten Fundamentalgruppe charakterisiert. Abschließend wird eine Anwendung des Twistorraumes einer Lorentz-4-Mannigfaltigkeit in der Flächentheorie diskutiert. Dabei zeigen wir eine Korrespondenz zwischen holomorphen Kurven im Twistorraum und raumartig immergierten Flächen mit lichtartigem mittlerem Krümmungsvektor. Beispielhaft werden solche Flächen in den Lorentzschen Raumformen der Dimension 4 konstruiert. / The twistor equation on Lorentzian spin manifolds is investigated. Known solutions of the twistor equation exist on the pp-manifolds, the Lorentz-Einstein-Sasaki manifolds and the Fefferman spaces. It is shown that in the low dimensions 3,4 and 5 twistor spinors without 'singularities' appear only for these mentioned Lorentzian spin geometries. Solutions of the twistor equation with zeros are of particular interest. The shape of the zero set of conformal vector fields and twistor spinors is described. Moreover, the twistor equation is formulated in the context of conformal Cartan geometry. As an application the conformally flat semi-Riemannian spin spaces with twistor spinors are characterized by the holonomy representation of the first fundamental group. Finally, we discuss an application of the twistor space of a Lorentzian 4-manifold in surface theory. Thereby, we prove a correspondence between holomorphic curves in the twistor space and spacelike immersed surfaces with lightlike mean curvature vector. Exemplary, such surfaces are constructed in the Lorentzian space forms of dimension 4.

In recent years intensity modulated radiation therapy with photons (xIMRT) has gained attention due to its ability to reduce the dose in the tissues close to the tumour volume. However, this technique also results in a large low dose volume. Electron IMRT (eIMRT) has the potential to reduce the integral dose to the patient due to the dose fall off in the electron depth dose curves. This dose fall off makes it possible to modulate the dose distribution in the direction of the beam by selecting appropriate electron energies. The use of a computer based energy selection method was examined in combination with the IMRT technique to optimise the electron dose distribution. It is clearly illustrated that the energy optimisation procedure reduces the dose to lung and heart in a breast cancer treatment. To shape the multiple electron subfields (beamlets) that are used in eIMRT, an electron multi leaf collimator (eMLC) is needed. However, photons produced in a conventional electron treatment head could penetrate such an added eMLC, thus producing an undesirable dose contribution. The leakage levels normally achieved are acceptable for standard single electron field treatments but could become unacceptably high in eIMRT treatments where a lot of small subfields are combined. To limit this photon contribution, the photon MLC (xMLC) was used to shield off large parts of the photon leakage. The effect of this xMLC shielding on the reduction of photon leakage, the electron beam penumbras, and electron output (dose level), was studied using Monte Carlo methods for different electron treatment head designs. The use of helium as a mean to reduce the electron scatter in the treatment head, and thus the perturbating effect of the xMLC on electron beam penumbra and output, was also investigated. This thesis shows that the effect of the xMLC shielding on the electron beam penumbra and output can be made negligible while still obtaining a significantly reduced x-ray leakage dose contribution. The result is a large gain in radiation protection of the patient and a better dynamic range for the eIMRT dose optimisation. For this optimisation a computer based electron energy selection method was developed and tested on two clinical cases.

The quantum Hall (QH) system---cold electrons in two dimensions in a perpendicular magnetic field---is a striking example of a system where unexpected phenomena emerge at low energies. The low-energy physics of this system is effectively one-dimensional due to the magnetic field. We identify an exactly solvable limit of this interacting many-body problem, and provide strong evidence that its solutions are adiabatically connected to the observed QH states in a similar manner as the free electron gas is related to real interacting fermions in a metal according to Landau's Fermi liquid theory. The solvable limit corresponds to the electron gas on a thin torus. Here the ground states are gapped periodic crystals and the fractionally charged excitations appear as domain walls between degenerate ground states. The fractal structure of the abelian Haldane-Halperin hierarchy is manifest for generic two-body interactions. By minimizing a local k+1-body interaction we obtain a representation of the non-abelian Read-Rezayi states, where the domain wall patterns encode the fusion rules of the underlying conformal field theory. We provide extensive analytical and numerical evidence that the Laughlin/Jain states are continuously connected to the exact solutions. For more general hierarchical states we exploit the intriguing connection to conformal field theory and construct wave functions that coincide with the exact ones in the solvable limit. If correct, this construction implies the adiabatic continuation of the pertinent states. We provide some numerical support for this scenario at the recently observed fraction 4/11. Non-QH phases are separated from the thin torus by a phase transition. At half-filling, this leads to a Luttinger liquid of neutral dipoles which provides an explicit microscopic example of how weakly interacting quasiparticles in a reduced (zero) magnetic field emerge at low energies. We argue that this is also smoothly connected to the bulk state.

Conformal airborne antennas have several advantages compared to externally mounted antennas, and they will play an important role in future aircrafts. However, they are subjected to vibration induced deformations which degrade their electromagnetic performances. With the motivation of suppressing such vibrations, use of active vibration control techniques with piezoelectric actuators is investigated in this study. At first, it is aimed to control the first three bending modes of a cantilever beam. In this scope, four different modal controllers / positive position feedback (PPF), resonant control (RC), integral resonant control (IRC) and positive position feedback with feed-through (PPFFT) are designed based on both reduced order finite element model and the system identification model. PPFFT, is a modified version of PPF which is proposed as a new controller in this study. Results of real- time control experiments show that PPFFT presents superior performance compared to its predecessor, PPF, and other two methods. In the second part of the study, it is focused on controlling the first three modes of a rectangular plate with four clamped edges. Best location alternatives for three piezoelectric actuators are determined with modal strain energy method. Based on the reduced order finite element model, three PPFFT controllers are designed for three collocated transfer functions. Disturbance rejection performances show the convenience of PPFFT in multi-input multi-output control systems. Performance of the control system is also verified by discrete-time simulations for a random disturbance representing the in-flight aircraft vibration characteristics.

This thesis is aimed to introduce a newly developed machine learning method, conformal predictors, for air pollution assessment. For the given area of study, the Barcelona Metropolitan Region (BMR), several conformal prediction models have been developed. These models use the specification which is called ridge regression confidence machine (RRCM). The conformal predictors that have been developed for the purposes of the present study are ridge regression models, and they always provide valid predictions. Instead of a point prediction, a conformal predictor outputs a prediction set, which is usually an interval. It is desired that these sets would be as small as possible. The underlying algorithm for the conformal predictors derived in this thesis is ordinary kriging. A kriging-based conformal predictor can capture spatial distribution of the data with the use of so-called "kernel trick" / Aquest treball està destinat a introduir el nou mètode de les màquines d'aprenentatge, els predictors de conformació, per l'avaluació de la contaminació de l'aire a la Regió Metropolitana de Barcelona (RMB). Es fa servir l'especificació anomenada màquina de confiança de la regressió cresta (RRCM). Els predictors de conformació que s'han desenvolupat per les finalitats d'aquest estudi són uns models de regressió cresta, que sempre ofereixen prediccions vàlides. Un predictor de conformació genera un conjunt de predicció, que és gairebé sempre un interval, i la intenció és que sigui el més petit possible. L'algorisme subjacent dels predictors de conformació derivats i discutits al llarg d'aquesta tesi és el kriging. El predictor de conformació basat en el kriging ordinari pot capturar la distribució espacial mitjançant una tècnica que es diu "el truc del nucli" ("kernel trick")

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

Using the AdS/CFT correspondence, we study the anisotropic transport properties of both supersymmetric and non-supersymmetric matter fields on (2+1)-dimensional defects coupled to a (3+1)-dimensional N=4 SYM "heat bath". We address on the one hand the purely conformal defect where the only non-vanishing background field that we turn on is a "topological", parameter parametrizing the impact on the bulk. On the other hand we also address the case of a finite external background magnetic field, finite net charge density and finite mass. We find in the purely conformal limit that the system possesses a conduction threshold given by the wave number of the perturbation and that the charge transport arises from a quasiparticle spectrum which is consistent with an intuitive picture where the defect acquires a finite width in the direction of the SYM bulk. We also examine finite-coupling modifications arising from higher derivative interactions in the probe brane action. In the case of finite density, mass and magnetic field, our results generalize the conformal case. We discover at high frequencies a spectrum of quasiparticle resonances due to the magnetic field and finite density and at small frequencies a Drude-like expansion around the DC limit. Both of these regimes display many generic features and some features that we attribute to strong coupling, such as a minimum DC conductivity and an unusual behavior of the "cyclotron" and plasmon frequencies, which become correlated to the resonances found in the conformal case. We further study the hydrodynamic regime and the relaxation properties, in which the system displays a set of different possible transitions to the collisionless regime. The mass dependence can be cast in two regimes: a generic relativistic behavior dominated by the UV and a non-linear hydrodynamic behavior dominated by the IR. In the massless case, we also extend earlier results to find an interesting duality under the transformation of the conductivity and the exchange of density and magnetic field. Furthermore, we look at the thermodynamics and the phase diagram, which reproduces general features found earlier in 3+1 dimensional systems and demonstrates stability in the relevant phase.

The declining cost of photovoltaic (PV) modules has enabled the vision of ubiquitous photovoltaic (PV) power to become feasible. Emerging PV technologies are facilitating the creation of intentionally non-flat PV modules, which create new applications for this sustainable energy generation currently not possible with the traditional rigid, flat silicon-glass modules. However, since the photovoltaic cells are no longer coplanar, there are significant new requirements for the power electronics necessary to convert the native form of electricity into a usable form and ensure maximum energy harvest. Non-uniform insolation from cell-to-cell gives rise to non-uniform current density in the PV material, which limits the ability to create series-connected cells without bypass diode or other ways to shunt current, which is well known in the maximum power tracking literature. This thesis presents a modeling approach to determine and quantify the variations in generation of energy due to intentionally non-flat PV geometries. This will enable the power electronics circuitry to be optimized to harvest maximum energy from PV pixel elements – clusters of PV cells with similar operating characteristics. This thesis systematically compares different geometries with identical two-dimensional projection "footprints" for energy harvest throughout the day. The results show that for the same footprint, a semi-cylindrical surface harvests more energy over a typical day than a flat plate. The modeling approach is then extended to demonstrate that by using non flat geometries for PV panel, the availability of a remotely located stand-alone power system can be increased when compared to a flat panel of same footprint. These results have broad application to a variety of energy scavenging scenarios in which either total energy harvested needs to be maximized or unusual geometries for the PV active surfaces are required, including building-integrated PV. This thesis develops the analysis of the potential energy harvest gain for advanced non-planar PV collectors as a necessary first step towards the design of the power electronics circuits and control algorithms to take advantage of the new opportunities of conformal and non-flat PV collectors.

Islet transplantation has emerged as a promising cell-based therapy for the treatment of diabetes, but its clinical efficacy remains limited by deleterious host responses that underlie islet destruction. In this dissertation, we describe the assembly of cell surface-supported thin films that confer molecular-level control over the composition and biophysicochemical properties of the islet surface with implications for improving islet engraftment. Specifically, the process of layer-by-layer (LbL) polymer self assembly was employed to generate nanothin films of diverse architecture with tunable properties directly on the extracellular surface of individual islets. Importantly, these studies are the first to report in vivo survival and function of nanoencapsulated cells, and have helped establish a conceptual framework for translating the diverse applications of LbL films to cellular interfaces. Additionally, through proper design of film constituents, coatings displaying ligands and bioorthogonally reactive handles may be generated, providing a modular strategy for incorporating exogenously derived regulators of host responses alongside native constituents of the islet surface. Towards this end, a strategy was developed to tether thrombomodulin to the islet surface in a site-specific manner, thereby facilitating local generation of the powerful anti-inflammatory agent, activated protein C. Collectively, this work offers novel biomolecular strategies for cell surface engineering with broad biomedical and biotechnological applications in cell-based therapeutics and beyond.