Spectrum scarcity is one of the most important challenges in wireless communications networks due to the sky-rocketing growth of multimedia applications. As the latest member of the multiple access family, non-orthogonal multiple access (NOMA) has been recently proposed for 3GPP Long Term Evolution (LTE) and envisioned to be a key component of the 5th generation (5G) mobile networks for its potential ability on spectrum enhancement. The feature of NOMA is to serve multiple users at the same time/frequency/code, but with di erent power levels, which yields a signi cant spectral e ciency gain over conventional orthogonal multiple access (OMA). This thesis provides a systematic treatment of this newly emerging technology, from the basic principles of NOMA, to its combination with simultaneously information and wireless power transfer (SWIPT) technology, to apply in cognitive radio (CR) networks and Heterogeneous networks (HetNets), as well as enhancing the physical layer security and addressing the fairness issue. First, this thesis examines the application of SWIPT to NOMA networks with spatially randomly located users. A new cooperative SWIPT NOMA protocol is proposed, in which near NOMA users that are close to the source act as energy harvesting relays in the aid of far NOMA users. Three user selection schemes are proposed to investigate the e ect of locations on the performance. Besides the closed-form expressions in terms of outage probability and throughput, the diversity gain of the considered networks is determined. Second, when considering NOMA in CR networks, stochastic geometry tools are used to evaluate the outage performance of the considered network. New closed-form expressions are derived for the outage probability. Diversity order of NOMA users has been analyzed based on the derived outage probability, which reveals important design insights regarding the interplay between two power constraints scenarios. Third, a new promising transmission framework is proposed, in which massive multipleinput multiple-output (MIMO) is employed in macro cells and NOMA is adopted in small cells. For maximizing the biased average received power at mobile users, a massive MIMO and NOMA based user association scheme is developed. Analytical expressions for the spectrum e ciency of each tier are derived using stochastic geometry. It is con rmed that NOMA is capable of enhancing the spectrum e ciency of the network compared to the OMA based HetNets. Fourth, this thesis investigates the physical layer security of NOMA in large-scale networks with invoking stochastic geometry. Both single-antenna and multiple-antenna aided transmission scenarios are considered, where the base station (BS) communicates with randomly distributed NOMA users. In addition to the derived exact analytical expressions for each scenario, some important insights such as secrecy diversity order and large antenna array property are obtained by carrying the asymptotic analysis. Fifth and last, the fundamental issues of fairness surrounding the joint power allocation and dynamic user clustering are addressed in MIMO-NOMA systems in this thesis. A two-step optimization approach is proposed to solve the formulated problem. Three e cient suboptimal algorithms are proposed to reduce the computational complexity. To further improve the performance of the worst user in each cluster, power allocation coe cients are optimized by using bi-section search. Important insights are concluded from the generated simulate results.

As startups vêm provocando uma mudança profunda no mundo dos negócios, e a cada ano mais startups são fundadas no Brasil. O sucesso destas empresas não depende exclusivamente do desenvolvimento de um produto/serviço inovador e um modelo de negócio escalável, mas também da aplicação de ferramentas de incentivo de longo prazo que permitam a formação de times de alto desempenho altamente engajados, e o controle do caixa, que nos primeiros anos é tipicamente escasso dadas as características de risco destes novos negócios. No entanto, o desconhecimento de ferramentas de incentivo de longo prazo por parte dos empreendedores e a limitada discussão na literatura do seu efeito conjunto nas dimensões de pessoas e financeira faz com que muitas startups não implementem tais planos nos seus primeiros anos de existência, o que pode afetar diretamente o sucesso do negócio. Mecanismos inovativos de incentivo, como as opções fantasmas (phantom stock options), são particularmente desconhecidos e pouco aplicados no contexto brasileiro de startups. O objetivo deste trabalho é desenvolver um plano de incentivo de longo prazo baseado em opções fantasmas em uma startup, bem como gerar conhecimento para apoiar futuras pesquisas acadêmicas no campo. Este objetivo foi atingido por meio de uma pesquisa-ação e os resultados confirmaram a importância desta ferramenta para a atração de talentos, engajamento do time, redução de exposição de caixa e redução de assimetria da informação na empresa, já que o profissional passa a entender e mensurar o valor de sua contribuição individual para a equipe e, consequentemente, para o atingimento do seu bônus. / Startups have been bringing about a profound change in the business world, and each year more startups are founded in Brazil. The success of these companies does not depend exclusively on the development of an innovative product / service and a scalable business model, but also on the application of long-term incentive tools that allow the formation of highly engaged high performance teams and cash control, which in the early years is typically scarce given the risk characteristics of these new businesses. However, the lack of knowledge of long-term incentive tools on the part of entrepreneurs and the limited discussion in the literature of their combined effect on the human and financial dimensions means that many startups do not implement such plans in their early years of existence. Can directly affect the success of the business. Innovative incentive mechanisms, such as phantom stock options, are particularly unknown and little applied in the Brazilian context of startups. The purpose of this paper is to illustrate the creation and implementation of a long-term incentive plan based on phantom options in a startup, as well as generate knowledge to support future academic research in the field. This objective was reached through an action research and the results confirmed the importance of this tool for the attraction of talents, team engagement, reduction of cash exposure and reduction of asymmetry of information in the company, since the professional comes to understand and measure the value of your individual contribution to the team and, consequently, to the attainment of your bonus.

Objetivos: o objetivo do presente estudo é avaliar a resposta molares e não molares a dois protocolos de atenção periodontal na fase de manutenção periódica preventiva (MPP). Métodos: Sessenta e dois pacientes com periodontite moderada ou avançada (idade média 50.97 ± 9.26 anos, 40 mulheres, 24 fumantes) foram tratados de acordo com um protocolo não-cirúrgico. Finalizada a fase terapêutica, os pacientes iniciaram a fase de MPP e foram randomicamente alocados para receber controle supragengival isolado (SPG) ou combinado ao subgengival (SPG+SBG). Exames periodontais, instruções de higiene bucal e as respectivas intervenções experimentais foram realizados em consultas trimestrais. Resultados: não foram observadas diferenças significativas nas variáveis demográficas, número médio de dentes e distribuição média de dentes não-molares/molares e de sítios livres/proximais entre os dois grupos experimentais. Quando do baseline, os dentes molares apresentaram um maior número de sítios positivos para IPV, ISG, SS e maiores valores médios de PS e PI quando comparados aos não-molares (p<0.001). Ao longo da fase de MPP, foi demonstrado que independente da terapia aplicada, tanto para molares e não molares, a resposta para ambos os grupos dentários não foi diferente. Da mesma forma, a perda dentária entre molares e não molares não diferiu ao longo de 24 meses. Conclusões: Molares apresentam semelhante resposta durante a fase de MPP quando comparados a dentes não molares, independente do protocolo de intervenção clínica aportado. / Aim: The objective of the present study was to evaluate the response of molar teeth and non-molar teeth to two periodontal care protocols in the periodic preventive maintenance phase (PMP). METHODS: Sixty-two patients with moderate or advanced periodontitis (mean age 50.97 ± 9.26 years, 40 women, 24 smokers) were treated according to a non-surgical protocol. After the therapeutic phase, the patients started the PMP and were randomly assigned to receive supragingival (SPG) or combined subgengival (SPG + SBG) control. Periodontal examinations, oral hygiene instructions and the respective experimental interventions were performed in quarterly consultations. Results: There were no significant differences in demographic variables, mean number of teeth and mean distribution of non-molar / molar teeth and free / proximal sites between the two experimental groups. At the baseline, molar teeth had a higher number of positive sites for VPI, GBI, BOP and higher mean values of PPD and CAL when compared to non-molars (p <0.001). Throughout the MPP phase, it was demonstrated that regardless of the applied therapy, for both molars and non-molars, the response for both dental groups was not different. Likewise, tooth loss between molars and non-molars did not differ over 24 months. Conclusions: Molars presented a similar response during the PMP when compared to non-molar teeth, independent of the protocol of clinical intervention provided.

Contrairement à la majorité des maladies chroniques qui s’aggravent progressivement, l’expression de l’asthme est variable au cours du temps. L’asthme peut apparaître, disparaître, s’aggraver ou s’améliorer au cours de plusieurs années, voire une décennie, à tout âge de la vie. Cette variabilité à long terme est particulièrement mal décrite chez l’adulte car les données sont rares. Par une approche épidémiologique, la thèse a pour objectif de mieux comprendre la variabilité de l’expression de l’asthme au long cours chez l’adulte dans deux cohortes françaises : E3N, l’Étude Épidémiologique auprès des femmes de la Mutuelle Générale de l’Éducation Nationale et EGEA, l’étude Épidémiologique des facteurs Génétiques et Environnementaux de l’Asthme. Le premier axe, méthodologique, porte sur la mesure de la variabilité de l’expression de l’asthme au long cours. Le second axe, environnemental, porte sur le rôle de la pollution atmosphérique sur cette variabilité. Concernant l’axe méthodologique, l’étude des réponses à une unique question sur l’asthme répétée 7 fois sur 13 ans dans le cadre de la cohorte E3N a montré qu’une succession incohérente de réponses (positives et négatives) reflétait une partie de la variabilité de l’activité de l’asthme à moyen terme, suggérant l’intérêt de cette approche pour affiner la caractérisation de l’expression de la maladie au cours du temps. Dans le contexte d’un intérêt croissant pour la santé perçue, l’étude d’une question portant sur l’auto-évaluation rétrospective du changement dans la santé respiratoire au cours des 10 dernières années a montré que l’information ainsi obtenue était complémentaire de celle d’outils épidémiologiques et cliniques existants pour décrire la trajectoire à long terme de l’asthme, et permettait de prédire en partie l’évolution de l’asthme.À la suite d’une récente méta-analyse regroupant 6 cohortes européennes (avec 23 000 participants) dont les résultats suggèrent le rôle d’une exposition chronique à la pollution atmosphérique dans l’incidence de l’asthme chez l’adulte, une analyse a porté sur l’évolution des traitements de fond et de secours de l’asthme sur une période de 4 ans en lien avec la pollution atmosphérique. Chez les femmes asthmatiques de la cohorte E3N, plus l’exposition chronique au dioxyde d’azote et aux particules était élevée, plus la consommation de corticoïdes inhalés augmentait au cours du temps, suggérant le rôle à long terme du dioxyde d’azote dans la progression de l’asthme. En conclusion, les résultats de la thèse montrent que des outils simples, tels que l’utilisation de réponses successives à une unique question sur l’asthme et l’auto-évaluation du changement dans la santé respiratoire sur 10 ans, peuvent être utilisés pour mieux caractériser la variabilité de l’expression de l’asthme au long cours, de façon complémentaire aux outils déjà existants. Associés à ceux de la littérature, les résultats de la thèse soutiennent le rôle délétère d’une exposition chronique à la pollution de l’air extérieur sur l’évolution de l’asthme au long cours et renforcent l’intérêt d’interventions de santé publique visant à diminuer la concentration des polluants atmosphériques. / Unlike most chronic diseases, which tend to get progressively worse over time, the expression of asthma is variable over time. Asthma may onset at any age and is known to clinically persist, possibly resolve, or present any combination of remissions and relapses over several years, even decades. Such long-term variability has been difficult to describe in adults as data are scarce. Through an epidemiological approach, the aim of the thesis is to gain a better understanding of the variability of asthma expression over the long term in adults, in two French cohorts: the E3N study (l’Étude Épidémiologique auprès des femmes de la Mutuelle Générale de l’Éducation Nationale) and the EGEA study (the Epidemiological study on the Genetics and Environment of Asthma). The first axis is methodological and relates to the characterization of asthma expression variability over the long term. The second axis is environmental and related to the effect of air pollution on such long-term variability. Regarding the methodological axis, the in-depth analysis of answers to a single question on ever asthma repeated 7 times over 13 years in the E3N study has shown that apparently inconsistent succession of answers (positive and negative) could capture part of the medium-term variability of asthma activity, suggesting the usefulness of such approach to improve the characterization of asthma expression over time. In a context of growing interest for perceived health, a simple retrospective self-assessment of 10-year change in respiratory health has been shown to provide complementary insights to classical epidemiological and clinical tools to describe the long-term trajectory of asthma, and could predict part of the asthma evolution. Following a recent meta-analysis including 6 European cohorts (23000 participants), in which results suggest a deleterious effect of chronic ambient air pollution on asthma incidence in adults, an analysis investigated the evolution of asthma medication dispensations over 4 consecutive years, in relation with air pollution. Among the women with asthma in the E3N study, an increased estimated exposure to outdoor nitrogen dioxide and particles was associated with increased rate of controller dispensations over time, suggesting the long-term effect of air pollution on asthma progression. In conclusion, results of the thesis showed that simple tools such as several repeated answers to a single question on asthma and the self-assessment of long-term change in respiratory health may be useful in order to better characterize the variability of asthma expression over the long term, as a complementary approach alongside with classical tools. Combined with the literature, results of the thesis support the deleterious impact of chronic air pollution on progression of asthma and strengthen the need of public health interventions to reduce air pollutants concentration.

Orientador: Cassiana Mendes Bertoncello Fontes / Resumo: Introdução: As Instituições de longa permanência para idosos (ILPIs) podem ser instituições governamentais; ou não; de caráter residencial, destinadas ao domicilio coletivo de pessoas com idade igual ou superior a 60 anos com ou sem suporte familiar; e em condição de liberdade, dignidade e cidadania. Em ILPI o enfermeiro coordena a equipe de enfermagem, composta por auxiliares e técnicos de enfermagem e é responsável pelo gerenciamento e planejamento individual do cuidado aos idosos, educação e treinamento da equipe assim como a execução dos cuidados de maior complexidade.O planejamento da assistência de enfermagem individualizada ao idoso é exigido pela legislação do COFEN 358/2009 e está representado pelo Processo de Enfermagem (PE).A operacionalização do PE se estabelece pelas etapas da Sistematização da Assistência de Enfermagem (SAE) e nesse contexto corrobora para promover a qualidade e segurança do paciente, de forma a conduzir o processo de cuidar na ILPI; Objetivo: O objetivo do estudo foi compreender a experiência dos enfermeiros, que atuam em ILPIs, com o planejamento da assistência representado pela SAE. Tratou-se de um estudo qualitativo, aprovado pelo Comitê de Ética local, Plataforma Brasil, CAAE 65473317.7.0000.5411, Parecer nº 2.154.867. métodos: Utilizou-se como referencial teórico-metodológico a Teoria de Wanda de Aguiar Horta e como referencial metodológico a Análise de Conteúdo de Bardin. A coleta de dados foi realizada pela pesquisadora por meio de entre... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: Introduction: Long-term Institutions for the Elderly (ILPIs) can be governmental institutions; or not; of residential character, destined to the collective address of people aged 60 or over with or without family support; and in the condition of freedom, dignity and citizenship. In ILPI, the nurse coordinates the nursing team, composed of nursing auxiliaries and technicians and is responsible for the management and individual planning of care for the elderly, education and training of the team as well as the execution of the more complex care. nursing is required by the COFEN 358/2009 legislation and is represented by the Nursing Process (PE). The operationalization of the EP is established through the Nursing Care Systematization (SAE) stages and, in this context, corroborates the patient safety in order to conduct the caring process in the ILPI. Objective: The objective of the study was to understand the experience of nurses, who work in ILPIs, with the planning of care represented by SAE. This was a qualitative study, approved by the Local Ethics Committee,Brazil Platform, CAAE 65473317.7.0000.5411, Opinion no. 2,154,867. Methods: The Wanda Theory of Aguiar Horta was used as theoretical-methodological reference and as a methodological reference to the Bardin Content Analysis. Data collection was performed by the researcher through semi-structured and recorded audio interviews, with ten ILPI nurses from three municipalities in the interior of São Paulo. The guiding question... (Complete abstract click electronic access below) / Mestre

A presente pesquisa trata do estudo de cenários regionais de drenagem urbana das principais sub-bacias pertencentes à área urbana de São Carlos/SP e da aplicação de incentivos ambientais em escala de lote. As projeções temporais realizadas dizem respeito às mudanças do uso e ocupação do solo para os anos de 2025, 2050, 2075 e 2100. Os cenários de uso e ocupação do solo têm como base os estudos referentes ao Millennium Ecosystem Assessment (Global Orchestration, Order from Strength, Adapting Mosaic e TechnoGarden) e sua adequação na escala local, para macrodrenagem urbana, proposta por Mendiondo (2005). Os eventos pluviométricos utilizados nas simulações dos cenários, por sua vez, foram selecionados em função das condições de umidade antecedente. Para os cenários propostos, foram avaliadas variações dos regimes hidrológico e hidráulico através de curvas de permanência em alguns pontos ao longo da parte de montante da sub-bacia do Monjolinho. Ainda, em escala de lote, é proposta uma metodologia de incentivos ambientais com base no armazenamento potencial de água no lote e na vazão máxima instantânea, para cada cenário estudado. A metodologia proposta de incentivo ambiental revela-se de simples aplicação por parte de órgãos públicos e de rápida obtenção dos resultados. Embora os cenários propostos sejam fictícios, os custos estimados (R$/\'M POT.2\') são aplicáveis para condições atuais. / This research discussed the study of regional scenarios of urban drainage of the main sub-basins belonging to the urban area of San Carlos/SP and the application of environmental incentives in lot scale. The projections of time made are related to changes of use and occupation of land for the years of 2025, 2050, 2075 and 2100. The scenarios of use and occupation of land are based on the studies concerning the Millennium Ecosystem Assessment (Global Orchestration, Order from Strength, Adapting Mosaic and TechnoGarden) and its appropriateness in the local scale, to urban macrodrainage, proposed by Mendiondo (2005). The rainfall events used in the simulations of scenarios were selected for the conditions of background humidity. For the proposed scenarios have been evaluated changes in the hydrological and hydraulic systems through remain curves in some points along the top part of sub-basin of Monjolinho. Still, in scale of lot, is proposed a methodology for environmental incentives based on the potential for water storage in the lot and the maximum instantaneous flow for each scenario studied. The proposed methodology of environmental incentive appears to be the simple application by public agencies and quickly get the results. Although the proposed scenarios are fictitious, the estimated costs (R$/\'M POT.2\') are applicable to current conditions.

The Third Chapter: The aim of this research is to study individual choices of precau- tionary saving and long-term care spending when an individual faces the uncertainty of after-retirement health shocks. To do this, an improved two-period life-cycle model is employed. This paper also explores how individual choice affects economic development and capital accumulation in an overlapping generation economy. The study shows that the rise in the possibility of getting after-retirement health shocks will result to an increase in long-term care expenditure and the level of precautionary saving. The steady state will also increase in this case. The Fourth Chapter: The increasing and intensifying long-term care (LTC) demand brings great financial pressures for both governments and individuals. From the public perspective, the underlying economic question is how adequate real resources can be re- distributed to support long-term care need and how efficient the policies targeting is. As many LTC policies are accessed through means tests, individuals saving behaviour can be affected. This paper examines and compares the welfare effects that different means- tested policies have on individuals. We did this by embedding life-cycle models with after-retirement health shocks. Means-tested policies of long-term care, one with a top- up choice, and one without, were then simulated. The results show that the means test regime with a top-up option can bring a higher social welfare. Under this scheme, a higher means test threshold can decrease societys dependency on a social benefit system and increase social welfare. The Fifth Chapter: Attendance Allowance and Disability Living Allowance are the dis- ability cash benefits provided for people who are over 65 in the U.K. As the government plans to divert more public resource from these benefits to means-tested local care ser- vices, it is important to understand the effects and targeting of these cash benefits first. Using the survey data from English Longitudinal Study of Ageing, this study examines the relationship between the receipt of disability cash benefits and recipients’ character- istics among those who are over 65 in England. Although income is not a key factor to decide on the receipt of the benefits in the criteria, the results show that it still has a self- selection process where the benefits are given to those who are both most in need and on low incomes.

A short wakeful rest immediately after new learning boosts verbal memory retention over several minutes. This memory boost is observed both in healthy people and in patients with amnesia, including patients with amnestic mild cognitive impairment (aMCI) and mild Alzheimer’s Disease (AD). Wakeful resting is hypothesized to boost memory by protecting the memory consolidation (strengthening) process from interfering sensory stimulation. The effect of a short wakeful rest immediately after new learning has, to this stage, been tested only over standard retention intervals (≤1 hour). The objectives of this PhD project were to: 1.) examine whether a short wakeful rest immediately after learning boosts memory over a longer retention interval (7 days) in healthy older adults (Experiment 1, Experiment 2) and aMCI/mild AD patients (Experiment 3) 2.) investigate whether intentional rehearsal is necessary and sufficient to boost memory during wakeful rest, over both short-term (15-minute) and long-term (7-day) delays (Experiment 4, 5 and 6) 3.) compare the effect of a short post-learning rest on retention as assessed via cued recall, free recall and recognition, both over short delays (15 minutes) and long delays (7 days and 4 weeks) (Experiments 4,5 and 7) 4.) examine whether a short wakeful rest immediately after learning boosts retention of real-life-like stimuli (face/name paired associates) in healthy older adults and aMCI/mild AD patients (Experiment 8, Experiment 9) In order to accomplish these aims, several samples of healthy adults and amnesic patients were tested, utilising a range of experimental designs. In all experiments, the learning of new material was followed immediately (i) by a brief wakeful rest, or (ii) by a cognitively demanding task. A delayed memory test took place after a range of intervals. The results demonstrate a pronounced memory enhancement over 15-30 minutes and 7 days in aMCI/mild AD patients via a short post-learning wakeful rest. A similar, albeit less pronounced 7-day memory benefit via post-learning wakeful rest was found in healthy older adults. Moreover, it was found that post-learning wakeful resting boosted 7-day recognition memory in healthy older adults, even when the learned material could not be rehearsed intentionally. Although intentional rehearsal did provide a 7-day memory improvement in healthy older adults, the present results indicate that it is not necessary in order to enhance long-term recognition memory via wakeful resting. The long-lived memory benefit gained via post-learning wakeful rest was shown to last at least 4 weeks in healthy adults, and free recall tests were more sensitive to the post-learning delay manipulation than cued recall tests. Finally, healthy controls and aMCI/mild AD patients who were able to learn face/name pairs showed enhanced 30-minute retention of these stimuli following wakeful rest conditions. The present findings demonstrate that both clinical and non-clinical populations are able to retain more new information over long periods, if the time interval immediately after new learning is devoid of further sensory stimulation. These results contribute to a growing body of literature stipulating that minimizing sensory stimulation frees early memory consolidation resources, allowing for superior offline consolidation of verbal material over a standard (≤1 hour) interval. The findings of this thesis extend this hypothesis over (i) a longer interval and (ii) to real-life-like stimuli, and these results are examined in light of memory consolidation theory. Implications of the premise of retroactive interference as a mechanism of longer-term forgetting are discussed.

Patients with temporal lobe epilepsy (TLE) often complain of a fading of new memories over days to weeks. This is particularly the case for patients with transient epileptic amnesia (TEA), a subtype of TLE. Objective memory testing sometimes corroborates this complaint, demonstrating normal or near-normal recall after standard delays (10-30 minutes), followed by a rapid decline in recall over longer delays (i.e. 1 week). This ‘nonstandard’ form of memory impairment has been termed accelerated long-term forgetting (ALF). It may reflect impairment of memory encoding, consolidation or retrieval. The aim of this thesis was to characterise the cognitive basis of ALF in TEA/TLE. The objectives were to: (a) determine the time scale of ALF of words (Chapter 3), (b) establish whether ALF affects picture recognition (Chapter 4), (c) establish whether ALF is affected by repeated retrieval (Chapter 2), number of learning trials (Chapter 5) and post-learning sensory stimulation (interference) (Chapter 5), (d) investigate ALF under incidental encoding conditions (Chapter 6), and (e) examine ALF associated with baclofen, a GABAB – receptor agonist (Chapter 7). A range of experimental paradigms and materials were applied to test memory function in several samples of TEA/TLE patients complaining of ALF and in healthy controls. The experiments revealed the following: ALF for word lists became apparent after 3–8 hours of daytime wakefulness, suggesting that disturbance of sleep related consolidation processes is not necessary for ALF to emerge in TEA. ALF for verbal information occurred both under incidental and intentional encoding conditions, and this rapid forgetting was not prevented by cued or recognition tests or by the matching of encoding conditions for patients and controls. This suggests that ALF is not associated primarily with an encoding or retrieval deficit. Although multiple learning trials and reduced sensory stimulation after learning reduced early forgetting (over 15-30 minutes) in TEA/TLE, neither factor reduced long-term forgetting. Moreover, in contrast to verbal recall, picture recognition was impoverished after minutes, but declined normally thereafter, demonstrating a subtle ‘early’ memory deficit in TEA, which might or might not be related to ALF. Overall, the present research suggests that ALF reflects a consolidation deficit, which results in accelerating forgetting the first few hours to days after memory acquisition, without a requirement for intervening sleep.

This doctoral thesis outlines several methodological advances in network science aimed towards uncovering rapid, complex interdependencies of electromagnetic brain activity recorded from the Electroencephalogram (EEG). This entails both new analyses and modelling of EEG brain network topologies and a novel approach to analyse rapid dynamics of connectivity. Importantly, we implement these advances to provide novel insights into pathological brain function in Alzheimer's disease. We introduce the concept of hierarchical complexity of network topology, providing both an index to measure it and a model to simulate it. We then show that the topology of functional connectivity estimated from EEG recordings is hierarchically complex, existing in a scale between random and star-like topologies, this is a paradigm shift from the established understanding that complexity arises between random and regular topologies. We go on to consider the density appropriate for binarisation of EEG functional connectivity, a methodological step recommended to produce compact and unbiased networks, in light of its new-found hierarchical complexity. Through simulations and real EEG data, we show the benefit of going beyond often recommended sparse representations to account for a broader range of hierarchy level interactions. After this, we turn our attention to assessing dynamic changes in connectivity. By constructing a unified framework for multivariate signals and graphs, inspired by network science and graph signal processing, we introduce graph-variate signal analysis which allows us to capture rapid fluctuations in connectivity robust to spurious short-term correlations. We define this for three pertinent brain connectivity estimates - Pearson's correlation coefficient, coherence and phase-lag index - and show its benefit over standard dynamic connectivity measures in a range of simulations and real data. Applying these novel methods to EEG datasets of the performance of visual short-term memory binding tasks by familial and sporadic Alzheimer's disease patients, we uncover disorganisation of the topological hierarchy of EEG brain function and abnormalities of transient phase-based activity which paves the way for new interpretations of the disease's affect on brain function. Hierarchical complexity and graph-variate dynamic connectivity are entirely new methods for analysing EEG brain networks. The former provides new interpretations of complexity in static connectivity patterns while the latter enables robust analysis of transient temporal connectivity patterns, both at the frontiers of analysis. Although designed with EEG functional connectivity in mind, we hope these techniques will be picked up in the broader field, having consequences for research into complex networks in general.