We are at that moment of network evolution when we have realised that our telecommunication systems should mimic features of human kind, e.g., the ability to understand the medium and take advantage of its changes. Looking towards the future, the mobile industry envisions the use of fully automatised cells able to self-organise all their parameters and procedures. A fully self-organised network is the one that is able to avoid human involvement and react to the fluctuations of network, traffic and channel through the automatic/autonomous nature of its functioning. Nowadays, the mobile community is far from this fully self-organised kind of network, but they are taken the first steps to achieve this target in the near future. This thesis hopes to contribute to the automatisation of cellular networks, providing models and tools to understand the behaviour of these networks, and algorithms and optimisation approaches to enhance their performance. This work focuses on the next generation of cellular networks, in more detail, in the DownLink (DL) of Orthogonal Frequency Division Multiple Access (OFDMA) based networks. Within this type of cellular system, attention is paid to interference mitigation in self-organising macrocell scenarios and femtocell deployments. Moreover, this thesis investigates the interference issues that arise when these two cell types are jointly deployed, complementing each other in what is currently known as a two-tier network. This thesis also provides new practical approaches to the inter-cell interference problem in both macro cell and femtocell OFDMA systems as well as in two-tier networks by means of the design of a novel framework and the use of mathematical optimisation. Special attention is paid to the formulation of optimisation problems and the development of well-performing solving methods (accurate and fast).

This thesis proposes four novel techniques to solve the problem of growing energy consumption requirements in cellular communication networks. The first and second part of this work propose a novel energy efficient scheduling mechanism and two new bandwidth management techniques, while the third part provides an algorithm to actively manage the power state of base stations (BSs) so that energy consumption is minimized throughout the day while users suffer a minimal loss in achieved data rate performance within the system. The proposed energy efficient score based scheduler (EESBS) is based on the already existing principle of score based resource allocation. Resource blocks (RBs) are given scores based on their energy efficiency for every user and then their allocation is decided based on a comparison between the scores of the different users on each RB. Two additional techniques are introduced that allow the scheduler to manage the user’s bandwidth footprint or in other words the number of RBs allocated. The first one, bandwidth expansion mode (BEM), allows users to expand their bandwidth footprint while retaining their overall transmission data rate. This allows the system to save energy due to the fact that data rate scales linearly with bandwidth and only logarithmically with transmission power. The second technique, time compression mode (TCoM), is targeted at users whose energy consumption is dominated by signalling overhead transmissions. If the assumption is made that the overhead is proportional to the number of RBs allocated, then users who find themselves having low data rate demands can release some of their allocated RBs by using a higher order modulation on the remaining ones and thus reduce their overall energy expenditure. Moreover, a system that combines all of the aforementioned scheduling techniques is also discussed. Both theoretical and simulation results on the performance of the described systems are provided. The energy efficient hardware state control (EESC) algorithm works by first collecting statistical information about the loading of each BS during the day that is due to the particular mobility patterns of users. It then uses that information to allow the BSs to turn off for parts of the day when the expected load is low and they can offload their current users to nearby cell sites. Simplified theoretical, along with complete system computer simulation, results are included. All the algorithms presented are very straightforward to implement and are not computationally intensive. They provide significant energy consumption reductions at none to minimal cost in terms of experienced user data rate.

In wireless networks, there is an ever-increasing demand for higher system throughputs, along with growing expectation for all users to be available to multimedia and Internet services. This is especially difficult to maintain at the cell-edge. Therefore, a key challenge for future orthogonal frequency division multiple access (OFDMA)-based networks is inter-cell interference coordination (ICIC). With full frequency reuse, small inter-site distances (ISDs), and heterogeneous architectures, coping with co-channel interference (CCI) in such networks has become paramount. Further, the needs for more energy efficient, or “green,” technologies is growing. In this light, Uplink Interference Protection (ULIP), a technique to combat CCI via power reduction, is investigated. By reducing the transmit power on a subset of resource blocks (RBs), the uplink interference to neighbouring cells can be controlled. Utilisation of existing reference signals limits additional signalling. Furthermore, cell-edge performance can be significantly improved through a priority class scheduler, enhancing the throughput fairness of the system. Finally, analytic derivations reveal ULIP guarantees enhanced energy efficiency for all mobile stations (MSs), with the added benefit that overall system throughput gains are also achievable. Following this, a novel scheduler that enhances both network spectral and energy efficiency is proposed. In order to facilitate the application of Pareto optimal power control (POPC) in cellular networks, a simple feasibility condition based on path gains and signal-to-noise-plus- interference ratio (SINR) targets is derived. Power Control Scheduling (PCS) maximises the number of concurrently transmitting MSs and minimises their transmit powers. In addition, cell/link removal is extended to OFDMA operation. Subsequently, an SINR variation technique, Power SINR Scheduling (PSS), is employed in femto-cell networks where full bandwidth users prohibit orthogonal resource allocation. Extensive simulation results show substantial gains in system throughput and energy efficiency over conventional power control schemes. Finally, the evolution of future systems to heterogeneous networks (HetNets), and the consequently enhanced network management difficulties necessitate the need for a distributed and autonomous ICIC approach. Using a fuzzy logic system, locally available information is utilised to allocate time-frequency resources and transmit powers such that requested rates are satisfied. An empirical investigation indicates close-to-optimal system performance at significantly reduced complexity (and signalling). Additionally, base station (BS) reference signals are appropriated to provide autonomous cell association amongst multiple co-located BSs. Detailed analytical signal modelling of the femto-cell and macro/pico-cell layouts reveal high correlation to experimentally gathered statistics. Further, superior performance to benchmarks in terms of system throughput, energy efficiency, availability and fairness indicate enormous potential for future wireless networks.

La méthode de factorisation est appliquée sur les données initiales d'un problème de mécanique quantique déja résolu. Les solutions (états propres et fonctions propres) sont presque tous retrouvés. / The factorization methode is applied to the initial data of an already solved quantum mechanics problem. The solutions (eigenfunctions and eigenvalues) are almost all rederived.

Almost one-half of the annual precipitation in the southwestern United States occurs during the North American monsoon (NAM). Given favorable synoptic-scale conditions, organized monsoon thunderstorms may affect relatively large geographic areas. Through an objective analysis of atmospheric reanalysis and observational data, the dominant synoptic patterns associated with NAM extreme events are determined for the period from 1993 to 2010. Thermodynamically favorable extreme-weather-event days are selected on the basis of atmospheric instability and precipitable water vapor from Tucson, Arizona, rawinsonde data. The atmospheric circulation patterns at 500 hPa associated with the extreme events are objectively characterized using principal component analysis. The first two dominant modes of 500-hPa geopotential-height anomalies of the severe-weather-event days correspond to type-I and type-II severe-weather-event patterns previously subjectively identified by Maddox et al. These patterns reflect a positioning of the monsoon ridge to the north and east or north and west, respectively, from its position in the "Four Corners" region during the period of the climatological maximum of monsoon precipitation from mid-July to mid-August. An hourly radar gauge precipitation product shows evidence of organized, westward-propagating convection in Arizona during the type-I and type-II severe weather events. This new methodological approach for objectively identifying severe weather events may be easily adapted to inform operational forecasting or analysis of gridded climate data.

過去針對動態相關係數的模擬多是固定條件相關(Constant Conditional Correlation; CCC)模型或動態條件相關(Dynamic Conditional Correlation; DCC)模型，且大多只針對權益風險相關係數。 本研究參照台灣RBC之C1風險與EIOPA (2014)對Solvency II的規範「The underlying assumptions in the standard formula for the Solvency Capital Requirement calculation」，針對市場風險：權益風險、利率風險、外匯風險，探討各類別間的相關係數是否顯著具動態性質。首先以Orthogonal-GARCH(O-GARCH)模型，對各個風險因子配適單變量的時間序列模型，此方法除了可縮減資料維度，也可改善多變量時間模型估計較不精準的問題。最後，以蒙地卡羅模擬出的動態相關係數情境，與原始非條件相關係數做比較。結果顯示許多相關係數顯著為動態序列，因此推斷保險公司的市場風險衡量，採用動態相關係數較為準確，更能符合保險監理本質。

In this thesis, we investigate the pathwise regularity of partial sum process of general orthogonal series, and prove that the partial sum process is a geometric 2-rough process under the same condition as in Menshov-Rademacher Theorem. For Fourier series, the condition can be improved, and an equivalent condition on the limit function is identified.

Chapter One introduces molecular irnaging and the modalities available for oncological irnaging. The radioisotopes and imaging agents for Positron Emission Tomography (PET) and Single Photon Emission Computed Tomography (SPECT) are discussed together with the bifunctional chelator approach for radio labelling of biomolecules. Finally, the chemistry and radioisotopes of copper are described, and copper bis(thiosemicarbazonato) complexes introduced in the context of PET irnaging. Chapter Two describes the synthesis and characterisation of novel carboxylate- and maleirnide- functionalised bis(thiosemicarbazonates) and their conjugation to biologically active molecules. Radiolabelling of a chelator-bombesin conjugate demonstrated site-specific labelling at room temperature and preliminary in vitro and in vivo studies confirmed its potential as an imaging agent. Bioconjugation to a model protein and subsequent radiolabelling was also investigated. Chapter Three introduces molecular irnaging of hypoxia with a focus on CuATSM. An overview of the currently accepted mechanism of hypoxia selectivity is presented. The emphasis is placed on the relationship between oxygenation status, uptake and retention which display cell- and tumour- line dependency. Chapter Four presents the synthesis of copper bis(thiosemicarbazonates), radiolabelled either at the metal (64CU) or at the ligand e8F or 123n for mechanistic studies. The physicochemical characteristics of the copper complexes were measured and the complexes evaluated for their in vitro hypoxia selectivity. Chapter Five describes in vitro and in vivo studies of the orthogonally radiolabelled complexes, inclusive of control experiments with [64Cu]CuATS~, the radiolabelled proligand and [64CU]CU2+ salts. In vitro cellular assays, as well as in vivo biodistribution studies including dynamic PET and SPECT were performed. Stability studies contrasting the in vitro and in vivo behaviour were carried out. The collective data suggest that the currently proposed redox trapping mechanism might not provide a full understanding of the factors governing biodistribution and tumour uptake. Chapter Six contains full experimental details for the work described in this thesis.

In this paper, there are three chapters. The first chapter discusses interpolation. Here a theorem about the uniqueness of the solution to the general interpolation problem is proven. Then the problem of how to represent this unique solution is discussed. Finally, the error involved in the interpolation and the convergence of the interpolation process is developed. In the second chapter a theorem about the uniform approximation to continuous functions is proven. Then the best approximation and the least squares approximation (a special case of best approximation) is discussed. In the third chapter orthogonal polynomials as discussed as well as bounded linear functionals in Hilbert spaces, interpolation and approximation and approximation in Hilbert space.

A multifunctional strain sensor based on Surface Acoustic Wave (SAW) Orthogonal Frequency Coding (OFC) technology on a Langasite substrate has been investigated. Second order transmission matrix models have been developed and verified. A new parameterizable library of SAW components was created to automate the layout process. Using these new tools, a SAW strain sensor with OFC reflectors was designed, fabricated and tested. The Langasite coefficients of velocity for strain (γS = 1.699) and Temperature (γT = 2.562) were experimentally determined. The strain and temperature characterization of this strain sensor, along with the coefficients of velocity, have been used to demonstrate both the ability to sense strain and the capability for temperature compensation. The temperature-compensated SAW OFC strain sensor has been used to detect anomalous strain conditions that are indicators of fastener failures during structural health monitoring of aircraft panels with and without noise on a NASA fastener failure test stand. The changes in strain that are associated with single fastener failures were measured up to a distance of 80 cm between the sensor and the removed fastener. The SAW OFC strain sensor was demonstrated to act as an impact sensor with and without noise on the fastener failure test stand. The average measured signal to noise ratio (SNR) of 50, is comparable to the 29.1 SNR of an acoustic emission sensor. The simultaneous use of a high pass filter for impact detection, while a low pass filter is used for strain or fastener failure, demonstrates the multifunctional capabilities of the SAW OFC sensor to act as both as a fastener failure detector and as an impact detector.