Meeting the food demands of a growing population is one of the currently most critical issues for the world community. Additionally, negative impacts of climate change on agriculture are expected in some densely populated regions of developing economies. In this thesis, I examine spatial patterns of future impacts of population development and climate change on food security and how these impacts correlate with current patterns of food security and poverty. I aim to assess the global spatial patterns of food insecurity, concerning the current situation and future prognosis, to quantify the impact of population development and climate change on food security, and to examine to what extent poverty can explain spatial patterns. To identify spatial patterns, I performed a multiple correlation analysis. The aggregated impact estimate of population development and climate change was calculated by adding their respective national predictions. The explanatory power of poverty was evaluated using regression models which contained population development  predictions and current food security as functions of poverty rate. Based on the my results and a literature review I discuss the future geographic disparities of food security and the corresponding consequences for combating hunger. My results show that global geographic disparities are likely to increase substantially, mainly because population, and in turn food demand, will increase strongly in sub-Saharan Africa, the region with the highest decline of resources in relation to population. Impacts of climate change show a similar geographic pattern where foodinsecure regions will be affected the most. I found that poverty is a significant explanatory variable for both population growth and food security. The literature review support causality between variables, which places poverty at the core of food security issues. Poverty causes both a barrier to access food markets and population growth,which ultimately decrease food availability. In order to reach zero hunger for the coming generations, there is an urgent need to redistribute resources, change direction in agriculture practices and implement extensive political measures that carefully consider both local and global contexts.

Submitted by Fabio Sobreira Campos da Costa (fabio.sobreira@ufpe.br) on 2017-03-09T12:11:00Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao_LeonardoDallaPorta.pdf: 4244662 bytes, checksum: 214ab17f2ee3583441af553e0a0a7931 (MD5) / Made available in DSpace on 2017-03-09T12:11:00Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) Dissertacao_LeonardoDallaPorta.pdf: 4244662 bytes, checksum: 214ab17f2ee3583441af553e0a0a7931 (MD5) Previous issue date: 2016-08-26 / FACEPE / Avalanches neuronais, assim como oscilações e sincronização, são padrõesde atividade espontânea observados em redes neuronais. O conceito de avalanches neuronais foi concebido na última década.EssepadrãodeatividadetemdistribuiçõesdetamanhosP(s)eduraçõesP(d)invariantes por escala, i.e., obedecem relações do tipo lei de potênciaP(s)∼s−τ, com expoenteτ≃3/2, e P(d)∼d−τt, com expoenteτt ≃2, respectivamente. Essas propriedades são compatíveis com a ideia de que o cérebro opera em um regime crítico. A partir dessas constatações, muitos estudos teóricos e experimentais reportaram os potenciais benefícios de um cérebro operando na criticalidade, como por exemplo a máxima sensibilidade aos estímulos sensoriais, máxima capacidade de informação e transmissão e uma ótima capacidade computacional. Modelos da classe de universalidade de percolação direcionada (DP) têm sido amplamente utilizados para explicar a estatística invariante por escala das avalanches neuronais. Porém estes modelos não levam em consideração a dinâmica dos neurônios inibitórios e, além disso, como apresentam uma transição de fase entre um estado absorvente e uma fase ativa, torna-se difícil conciliar o modelo com correlações temporais de longo alcance que são observadas experimentalmente em diferentes escalas espaciais. Neste contexto, um novo modelo computacional (CROs, do original em inglês Critical Oscillations) surgiu na literatura (Poil et al., J. Neurosci.,32 9817, 2012), incluindo neurônios inibitórios e buscando conciliar correlações temporais com avalanches neuronais. Neste modelo não há uma fase absorvente, e uma suposta transição de fases ocorre entre uma fase ativa e outra com oscilações coletivas. Devido à ausência de uma fase absorvente, avalanchesneuronaissãodefinidascomparando-seaatividadeinstantâneadaredecomumlimiar que depende da mediana da atividade total. Justamente na linha crítica do espaço de parâmetros, quandoháumabalançoentreexcitaçãoeinibiçãoneuronal,avalanchesneuronaisinvariantespor escala são observadas juntamente com correlações temporais de longo alcance (ruído 1/f). No presente trabalho, um estudo mais profundo a respeito dos resultados reportados para o modelo CROs foi realizado. As oscilações neuronais mostraram-se robustas para diferentes tamanhos de rede, e observamos que a dinâmica local reflete a dinâmica oscilatória global da rede. Correlações temporais de longo alcance foram observadas (num intervalo de escalas temporais) através da técnica deDetrendedFluctuationAnalysis, sendo robustas perante modificações no tamanho da rede. O resultado foi confirmado pela análise direta do espectro, que apresentou decaimento do tipo 1/f numa determinada faixa de frequências. O diagrama de fases do modelo mostrou-se robusto em relação ao tamanho da rede, mantendo-se o alcance das interações locais. Entretanto,osresultadosmostraram-sefortementedependentesdolimiarutilizadoparadetecção dasavalanchesneuronais.Porfim,mostramosquedistribuiçõesdeduraçõesdeavalanchessãodo tipo lei de potência, com expoenteτt ≃2. Este resultado é inédito e o valor encontrado coincide com o expoente crítico da classe de universalidade de DP na dimensão crítica superior. Em conjunto, nossos resultados fornecem mais evidências de que o modelo CROs de fato apresenta uma transição de fases. / Neuronal avalanches, as well as waves and synchronization, are types of spontaneous activity experimentally observed in neuronal networks. The concept of neuronal avalanches was conceivedinthepastdecade.ThispatternofactivityhasdistributionsofsizeP(s)anddurationP(d) which are scale invariant, i.e., follow power-law relationsP(s)∼s−τ, with exponentτ≃3/2, and P(d)∼ d−τd, with exponentτt ≃ 2, respectively. These properties are compatible with the idea that the brain operates in a critical regime. From these findings, many theoretical and experimental studies have reported the potential benefits of a brain operating at criticality, such as maximum sensitivity to sensory stimuli, maximum information capacity and transmission and an optimal computational capabilities. Models belonging to the directed percolation universality class (DP) have been widely used to explain the scale invariant statistic of neuronal avalanches. However,these modelsdo not take into account the dynamics ofinhibitory neuronsand, since as they present a phase transition between an absorbing state and an active phase, it is difficult to reconcile the model with long-range temporal correlations that are observed experimentally at different spatial scales. In this context, a new computational model (CROs, Critical Oscillations) appeared in the literature (Poil et al., J. Neurosci.,32 9817, 2012), including inhibitory neurons and seeking to reconcile temporal correlations with neuronal avalanches. In this model there is no absorbing phase, and a supposed phase transition occurs between an active phase and another with collective oscillations. Due to the lack of an absorbing phase, neuronal avalanches are defined comparing by the instant network activity with a threshold that depends of the total activity median. Precisely at the critical line in parameter space, when a balance between neuronal excitation and inhibition occurs, scale invariant neuronal avalanches are observed with long-range temporal correlations (1/f-like noise). In the present work, a deeper study about the resultsreportedfortheCROsmodelwasperformed.Neuronaloscillationshavebeenshowntobe robust to increasing network sizes, and it was observed that local dynamic reflects the oscillatory global dynamic of the network. Long-range temporal correlations were observed (in a range of time scales) via Detrended Fluctuation Analysis, being robust against changes in network size. The result was confirmed by direct analysis of the spectrum, which showed a decay like 1/f in a given frequency band. The phase diagram of the model was robust with respect to the network size, as long as the range of local interactions was kept. However, the results were dependent of the thresholdused to detect neuronal avalanches.Finally,we have shown thatthe distributions of avalanches duration follows a power-law with exponentτt ≃2. This result is unprecedented and the value obtainedcoincides with the criticalexponent of the DP universality class in the upper criticaldimension.Together,ourresultsprovidefurtherevidencethatinfacttheCROsmodel presents aphasetransition.

Dados coletados de experimentos de melhoramento geralmente contêm observações fenotípicas para vários caracteres avaliados em múltiplos ambientes. Especificamente para cana-de-açúcar, medidas repetidas são obtidas para cana-planta e uma ou mais socas. Tal cenário presta-se naturalmente ao uso de modelos mistos para modelagem de variâncias genéticas heterogêneas e correlações entre caracteres, locais e cortes. Essa abordagem também nos permite incluir informações de marcadores moleculares, auxiliando no entendimento da arquitetura genética dos caracteres quantitativos através do mapeamento de QTLs. Este trabalho teve como objetivo detectar QTLs e interação QTL por ambiente pelo método do Mapeamento de Múltiplos Intervalos, o qual também permite a inclusão de epistasia no processo de busca. Nossa população de mapeamento foi composta por 100 indivíduos oriundos de um cruzamento biparental entre os cultivares brasileiros pré-comerciais SP80-180 e SP80-4966, avaliados em duas localidades (Piracicaba e Jaú, SP, Brasil) e três anos (2004 a 2006) para percentual de fibra, conteúdo de sacarose (POL) e toneladas de cana por hectare (TCH). Um mapa genético com 96 grupos de ligação cobrindo 2468,14 cM já estava disponível para esse cruzamento. O modelo fenotípico selecionado conteve matrizes de covariância separadas para caracteres e ambientes, o que resultou em um modelo mais parcimonioso com bom ajuste aos dados. Foram detectados 13 QTLs com efeitos principais e 8 interações epistáticas, cada um deles exibindo interação QTL por local, QTL por corte ou a interação tripla. Assim, nenhum QTL apresentou efeitos estáveis ao longo de todas as combinações de ambientes. No total, 13 dos 21 efeitos apresentaram algum grau de pleiotropia, afetando pelo menos dois dos três caracteres. Além disso, esses QTLs sempre afetaram os caracteres fibra e TCH na mesma direção, enquanto que POL foi afetado no sentido oposto. Não foi observada evidência em favor da hipótese de QTLs ligados em detrimento da hipótese de QTL pleiotrópico para qualquer das posições genômicas detectadas. Esses resultados fornecem valiosas informações sobre a base genética da variação quantitativa em cana-de-açúcar e sobre a relação genética entre caracteres. / Data collected from breeding trials usually comprise phenotypic observations for various traits evaluated at multiple test environments. Specifically for sugarcane, repeated measures are obtained for plant crop and one or more ratoons. Such scenario naturally lends itself to the use of mixed models for modeling heterogeneous genetic variances and correlations between traits, locations and harvests. This modeling approach also enables us to include molecular marker information, aiding in understanding the genetic architecture of quantitative traits through QTL mapping. Our work was aimed at detecting QTL and QTL by environment interaction by the Multiple Interval Mapping method, which also allows the inclusion of epistasis in the search process. Our mapping population was composed of 100 individuals derived from a biparental cross between the Brazilian pre-commercial cultivars SP80-180 and SP80-4966, evaluated at two locations (Piracicaba and Jaú, SP, Brazil) and three harvest years (2004 through 2006) for fiber content, sugar content (POL) and tonnes of cane per hectare (TCH). A genetic linkage map with 96 linkage groups covering 2468.14 cM was already available for this cross. The selected phenotypic model contained separate covariance matrices for traits and environments, which resulted in a more parsimonious model with good fit to the data. We detected 13 QTL with main effects and 8 epistatic interactions, each exhibiting QTL by location, QTL by harvest or the three-way interaction. Thus, no QTL displayed stable effects across all environment combinations. Overall, 13 of the 21 effects presented some degree of pleiotropy, affecting at least two of the three traits. Furthermore, these QTL always affected fiber and TCH in the same direction, while POL was affected in the opposite way. There was no evidence in favor of the linked QTL over the pleiotropic QTL hypothesis for any of the detected genome positions. These results give valuable insights about the genetic basis of quantitative variation in sugarcane and about the genetic relation between traits.

A demanda por óleos vegetais tem sido crescente, principalmente para utilização como fonte de energia renovável na forma de biodiesel. Somando-se a isso, a podridão vermelha das raízes da soja (PVR), ou síndrome da morte súbita, causada pelo fungo Fusarium solani f.sp. glycines, tornou-se uma doença preocupante para os sojicultores, técnicos e pesquisadores, sendo uma estratégia recomendada a adoção de um sistema de controle integrado em que a utilização de cultivares tolerantes é um componente indispensável. Assim, este trabalho teve por objetivo verificar a possibilidade de se reunir em uma mesma planta de soja genes para alta produtividade de óleo e para tolerância a PVR. O sistema genético compreendeu um dialelo parcial 7x7, envolvendo sete genitores com alta produtividade de óleo e sete genitores tolerantes a PVR. A maioria dos genitores compreendeu linhagens experimentais desenvolvidas no Setor de Genética Aplicada às Espécies Autógamas (ESALQ/USP). Os experimentos envolveram as plantas F2, na safra 2008/2009 e progênies F2:3, na safra 2009/2010, para avaliação de caracteres agronômicos, do teor de óleo e produtividade de óleo em campo experimental; já a avaliação da reação a PVR foi realizada em progênies F2:4, em casa de vegetação com inoculação artificial do patógeno, por meio de uma escala de notas para a severidade dos sintomas radiculares. Além disso, por meio de marcadores microssatélites fez-se um estudo de genética de associação entre os marcadores e os caracteres reação a PVR e teor de óleo em três populações. Os resultados evidenciaram a existência de variabilidade nos genitores e nas progênies para todos os caracteres avaliados. O genitor com a maior capacidade geral de combinação e média de teor de óleo foi a cultivar A 7002; por outro lado, os menores valores foram verificados em PI 520733 e IAC 100. Os cruzamentos mais produtivos em óleo foram aqueles que envolveram o genitor A 7002, exceto quando este foi cruzado com IAC 100. Dez cruzamentos (USP 70004 com USP 14-10-38, USP 14-01-20, USP 14-13-16 e M-Soy 8001; USP 14-10-38 com USP 70057 e USP 70080; M-Soy 8001 com USP 70006, USP 70080 e USP 70123; e USP 14-01-20 x USP 70006) destacaram-se por originar a maioria de suas progênies com as melhores características em todos os caracteres, ou seja, apresentaram ciclo precoce ou semi-precoce, altura média, plantas eretas e com valor agronômico bom ou médio, alta produtividade de grãos e de óleo, alto teor de óleo e tolerância a PVR. Nenhum cruzamento originou a maioria de suas progênies com as piores características em todos os caracteres. Teor de óleo apresentou baixa correlação genética com altura da planta na maturidade, acamamento, valor agronômico, produtividade de grãos e reação a PVR. PVR apresentou baixa correlação genética com acamamento, produtividade de grãos, teor de óleo, produtividade de óleo; entretanto, foi possível obter progênies com alta produtividade de grãos e de óleo e tolerantes a PVR. Os marcadores microssatélites mostraram-se polimórficos e, foram associados dois locos SSR ao caráter teor de óleo e outros dois locos ao caráter reação a PVR. / The demand for vegetable oils has increased, mainly because of its use as a renewable energy source like biodiesel. Moreover, the sudden death syndrome (SDS) in soybean, caused by the fungus Fusarium solani f.sp. glycines, has become a worrying disease for soybean producers, technicians and researchers, and the adoption of an integrated control system using tolerant cultivars as an essential component has been a recommended strategy. This work aimed to verify the possibility of gathering genes for high oil yield and tolerance to SDS in the same soybean plant. The genetic system comprised a partial diallel 7x7 involving seven parents with high oil yield and seven parents tolerant to SDS. Most of the parents were experimental lines developed at the Sector of Genetics Applied to Self-Pollinated Species (ESALQ/USP). The 2008/2009 trials involved the F2 plants, and the 2009/2010 trials involved the evaluation of F2:3 progenies traits, such as agronomic characters, oil content and oil yield in the experimental field; whereas the analysis of the SDS reaction was tested in F2:4 progenies, in a greenhouse with artificial inoculation of the pathogen through a rating scale for severity of radicular symptoms. Moreover, a study of genetic association among microsatellite markers and the characters reaction to SDS and oil content in three populations was performed. The results showed the existence of variability in parents and progenies for all characters. The parent who had the highest general combining ability and average oil content was the cultivar A 7002; on the other hand, the lowest values were found in PI 520733 and IAC 100. The crosses that originated the best oil content progenies have involved the parent A 7002, except when it was crossed with IAC 100. Ten crosses (USP 70004 with USP 14-10-38, USP 14-01-20, USP 14-13-16 and M-Soy 8001; USP 14-10-38 with USP 70057 and USP 70080; M-Soy 8001 with USP 70006, USP 70080 and USP 70123; USP 14-01-20 x USP 70006) distinguished from the others by originating the majority of their progenies with the best features in all traits, in other words, showed early and semi-early maturity, medium height, upright plants, good or average agronomic value, high grain and oil yield, high oil content and tolerance to SDS. None of the crosses originated the majority of their progeny with the worst characteristics in all traits. Oil content showed low genetic correlation with plant height at maturity, lodging, agronomic value, yield and reaction to SDS. SDS showed a low genetic correlation with lodging, grain yield, oil content, oil yield. However, it was possible to obtain progenies with high grain and oil yield and tolerance to SDS. The microsatellite markers were polymorphic and, moreover, two SSR loci were associated with the character oil content and other two loci to the character SDS reaction.

Cette thèse porte sur l'étude de la dynamique et de la morphologie de bulles non confinées dans des colonnes à bulles et de bulles confinées dans des microcanaux, ainsi que sur l'étude du transfert de matière entre une bulle sphérique confinée dans un microcanal et le liquide environnant. <p><p>Un dispositif expérimental d'imagerie et une méthode de posttraitement des images brutes ont été développés afin d'analyser la dynamique et la morphologie de bulles non confinées ayant une trajectoire non rectiligne de leur centre de masse en évitant les effets de perspectives et en déterminant un seuil pour la binarisation des images brutes sur base d'un critère bien défini. Ce dispositif expérimental et cette méthode de posttraitement des images brutes ont permis de générer des données relatives à la dynamique et la morphologie de bulles ellipsoïdales isolées et non confinées, pour des nombres d'Eötvös (Eo) et de Morton (Mo) de ces bulles tels que 0.8 < Eo < 8 et 10 <SUP>-11</SUP> < Mo < 10 <SUP>-7</SUP>. L'analyse de ces données a permis de cartographier la nature de la trajectoire d'une bulle et la présence d'une éventuelle oscillation de son interface en fonction de ses nombres d'Eötvös et de Morton. Les bulles ayant une trajectoire hélicoïdale sans oscillation de leur interface ont été sélectionnées afin de proposer des corrélations pour calculer l'amplitude et la fréquence de leur trajectoire en fonction de leurs nombres d'Eötvös et de Morton. Concernant les bulles ayant une trajectoire en zigzag ou hélicoïdale sans oscillation de leur interface, l'analyse des données a permis de montrer l'alignement entre le vecteur vitesse de leur centre de masse et leur petit axe. Les rayons de courbure de l'avant et l'arrière de l'interface de ces bulles ont été évalués. Pour les bulles ayant une trajectoire en zigzag, une corrélation a été établie pour calculer le rapport des rayons de courbure à l'avant et à l'arrière de leur interface en fonction de leurs nombres d'Eötvös et de Morton. Une pulsation dans la composante verticale du mouvement du centre de masse d'une bulle a été observée dans le cas d'une trajectoire en zigzag de la bulle et ce à une fréquence égale au double de celle de sa trajectoire. Une telle pulsation n'a pas pu être identifiée dans le cas d'une trajectoire hélicoïdale d'une bulle. <p><p>Concernant l'analyse de la dynamique de bulles sphériques confinées dans des microcanaux de sections carrée et circulaire, ainsi que du transfert de matière entre ces bulles et le liquide environnant, une méthode numérique a été développée dans laquelle deux conditons aux limites sont considérées sur l'interface liquide-gaz: une condition de contrainte tangentielle nulle et une condition de non glissement. Les résultats obtenus avec cette méthode ont permis de caractériser les champs de vitesse et de concentration autour des bulles considérées, et de montrer leurs interactions. Grâce à ces résultats, des corrélations ont été établies, dans ces microcanaux et pour ces deux conditions aux limites, pour calculer la vitesse des bulles et pour caractériser le transfert de matière entre ces bulles et le liquide en fonction des paramètres définissant le système. Sur base de ces corrélations et de bilans de matière et de quantité de mouvement, un modèle pour la dissolution de bulles le long de microcanaux de sections carrée et circulaire a été proposé, pour le régime bubbly flow, et comparé avec des données expérimentales disponibles dans la littérature. Ce modèle permet de prédire, pour une bulle se mouvant le long d'un microcanal de section carrée ou circulaire, les évolutions des pressions dans le liquide et le gaz, de son diamètre, de sa vitesse, de la concentration du gaz dissous dans le liquide, de la distance de séparation entre cette bulle et la bulle qui la suit et du coefficient de transfert de matière entre cette bulle et le liquide environnant.<p><p> / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

Comovement is ubiquitous in financial markets. The evolution of asset characteristics, such as price, volatility or liquidity, exhibits a high degree of correlation across assets---a phenomenon that in this thesis will generically be denoted with the term comovement. The origins of such comovement are legion. In their investment decisions, economic agents are not only influenced by their idiosyncrasies---a large part of investment motivations are shared over a population. Demographics or the political situation can generate constraints that are similar for a large number of people. A country's geography can greatly influence the sectors in which it is most productive, which implies that many people are sometimes subject to the same risk factors. Moreover, it is well known that mimesis is part of human psychology, and that people mimic their peers even when taking personal decisions. For these reasons, and many more, financial markets have a very systematic character, and studying the nature and intensity of such comovement is important from a risk management point of view. <p>This thesis studies comovement in financial markets under three dimensions. First, I consider comovement in equity liquidity. The liquidity of an asset is the ease with which that asset can be bought or sold. Liquidity can be measured in various ways and the first chapter concludes that market movements of two different liquidity measures have the same origin. Second, I study the impact correlation comovement on the price of stocks. The correlations between stock returns and the market return evolve through time and are correlated themselves. The effect of this correlation comovement on asset prices is however ambiguous and there is not enough evidence to depict a clear image. Finally, I develop a model to investigate contagion dynamics in the secondary market for European sovereign bonds over the past two years. More particularly, I study whether changes in the bond price of one specific country have an impact the next day on the average bond price in Europe. The study concludes of that bonds of France, Ireland, Portugal, Spain and Italy have been most contagious, whereas the much more volatile Greek bonds have had little impact on the other European countries. / Doctorat en Sciences économiques et de gestion / info:eu-repo/semantics/nonPublished

Le sujet principal de cette thèse est l’étude des valeurs moyennes et corrélations de fonctions multiplicatives. Les résultats portant sur ces derniers sont subséquemment appliqués à la résolution de plusieurs problèmes. Dans le premier chapitre, on rappelle certains résultats classiques concernant les valeurs moyennes des fonctions multiplicatives. On y énonce également les théorèmes principaux de la thèse. Le deuxième chapitre consiste de l’article “Mean values of multiplicative functions over the function fields". En se basant sur des résultats classiques de Wirsing, de Hall et de Tenenbaum concernant les fonctions multiplicatives arithmétiques, on énonce et on démontre des théorèmes qui y correspondent pour les fonctions multiplicatives sur les corps des fonctions Fq[x]. Ainsi, on résoud un problème posé dans un travail récent de Granville, Harper et Soundararajan. On décrit dans notre thése certaines caractéristiques du comportement des fonctions multiplicatives sur les corps de fonctions qui ne sont pas présentes dans le contexte des corps de nombres. Entre autres, on introduit pour la première fois une notion de “simulation” pour les fonctions multiplicatives sur les corps de fonctions Fq[x]. Les chapitres 3 et 4 comprennent plusieurs résultats de l’article “Correlations of multiplicative functions and applications". Dans cet article, on détermine une formule asymptotique pour les corrélations X n6x f1(P1(n)) · · · fm(Pm(n)), où f1, . . . ,fm sont des fonctions multiplicatives de module au plus ou égal à 1 ”simulatrices” qui satisfont certaines hypothèses naturelles, et P1, . . . ,Pm sont des polynomes ayant des coefficients positifs. On déduit de cette formule plusieurs conséquences intéressantes. D’abord, on donne une classification des fonctions multiplicatives f : N ! {−1,+1} ayant des sommes partielles uniformément bornées. Ainsi, on résoud un problème d’Erdos datant de 1957 (dans la forme conjecturée par Tao). Ensuite, on démontre que si la valeur moyenne des écarts |f(n + 1) − f(n)| est zéro, alors soit |f| a une valeur moyenne de zéro, soit f(n) = ns avec iii Re(s) < 1. Ce résultat affirme une ancienne conjecture de Kátai. Enfin, notre théorème principal est utilisé pour compter le nombre de représentations d’un entier n en tant que somme a+b, où a et b proviennent de sous-ensembles multiplicatifs fixés de N. Notre démonstration de ce résultat, dû à l’origine à Brüdern, évite l’usage de la “méthode du cercle". Les chapitres 5 et 6 sont basés sur les résultats obtenus dans l’article “Effective asymptotic formulae for multilinear averages and sign patterns of multiplicative functions," un travail conjoint avec Alexander Mangerel. D’après une méthode analytique dans l’esprit du théorème des valeurs moyennes de Halász, on détermine une formule asymptotique pour les moyennes multidimensionelles x−l X n2[x]l Y 16j6k fj(Lj(n)), lorsque x ! 1, où [x] := [1,x] et L1, . . . ,Lk sont des applications linéaires affines qui satisfont certaines hypothèses naturelles. Notre méthode rend ainsi une démonstration neuve d’un résultat de Frantzikinakis et Host avec, également, un terme principal explicite et un terme d’erreur quantitatif. On applique nos formules à la démonstration d’un phénomène local-global pour les normes de Gowers des fonctions multiplicatives. De plus, on découvre et explique certaines irrégularités dans la distribution des suites de signes de fonctions multiplicatives f : N ! {−1,+1}. Visant de tels résultats, on détermine les densités asymptotiques des ensembles d’entiers n tels que la fonction f rend une suite fixée de 3 ou 4 signes dans presque toutes les progressions arithmétiques de 3 ou 4 termes, respectivement, ayant n comme premier terme. Ceci mène à une généralisation et amélioration du travail de Buttkewitz et Elsholtz, et donne un complément à un travail récent de Matomäki, Radziwiłł et Tao sur les suites de signes de la fonction de Liouville. / The main theme of this thesis is to study mean values and correlations of multiplicative functions and apply the corresponding results to tackle some open problems. The first chapter contains discussion of several classical facts about mean values of multiplicative functions and statement of the main results of the thesis. The second chapter consists of the article “Mean values of multiplicative functions over the function fields". The main purpose of this chapter is to formulate and prove analog of several classical results due to Wirsing, Hall and Tenenbaum over the function field Fq[x], thus answering questions raised in the recent work of Granville, Harper and Soundararajan. We explain some features of the behaviour of multiplicative functions that are not present in the number field settings. This is accomplished by, among other things, introducing the notion of “pretentiousness" over the function fields. Chapter 3 and Chapter 4 include results of the article “Correlations of multiplicative functions and applications". Here, we give an asymptotic formula for correlations X n_x f1(P1(n))f2(P2(n)) · · · · · fm(Pm(n)) where f . . . ,fm are bounded “pretentious" multiplicative functions, under certain natural hypotheses. We then deduce several desirable consequences. First, we characterize all multiplicative functions f : N ! {−1,+1} with bounded partial sums. This answers a question of Erdos from 1957 in the form conjectured by Tao. Second, we show that if the average of the first divided difference of multiplicative function is zero, then either f(n) = ns for Re(s) < 1 or |f(n)| is small on average. This settles an old conjecture of Kátai. Third, we apply our theorem to count the number of representations of n = a + b where a,b belong to some multiplicative subsets of N. This gives a new "circle method-free" proof of the result of Brüdern. Chapters 5 and Chapter 6 are based on the results obtained in the article “Effective asymptotic formulae for multilinear averages and sign patterns of multiplicative functions," joint with Alexander Mangerel. Using an analytic approach in the spirit of Halász’ mean v value theorem, we compute multidimensional averages x−l X n2[x]l Y 16j6k fj(Lj(n)) as x ! 1, where [x] := [1,x] and L1, . . . ,Lk are affine linear forms that satisfy some natural conditions. Our approach gives a new proof of a result of Frantzikinakis and Host that is distinct from theirs, with explicit main and error terms. As an application of our formulae, we establish a local-to-global principle for Gowers norms of multiplicative functions. We reveal and explain irregularities in the distribution of the sign patterns of multiplicative functions by computing the asymptotic densities of the sets of integers n such that a given multiplicative function f : N ! {−1, 1} yields a fixed sign pattern of length 3 or 4 on almost all 3- and 4-term arithmetic progressions, respectively, with first term n. The latter generalizes and refines the work of Buttkewitz and Elsholtz and complements the recent work of Matomaki, Radziwiłł and Tao. We conclude this thesis by discussing some work in progress.

La théorie covariance de la fonctionnelle de la densité (CDF), basée sur un petit nombre de paramètres ajustables, a été utilisée avec succès pour décrire l’état fondamental et les états excités des noyaux de la carte nucléaire, pour A>12. Cette approche permet de décrire les systèmes nucléaires finis avec un Lagrangien hadronique universel résolu dans le cadre de l'approche Relativiste-Hartree-Fock-Bologuibov (RHFB). Ce modèle est également utilisé pour l'étude des étoiles compactes, car il peut être étendu à des densités élevées où la relativité restreinte ne peut pas être ignoré. Ce modèle peut également être étendu pour inclure la contribution des hypérons et ainsi que d'autres particules exotiques. Dans ce travail, la description et des prédictions basées sur l'approche RHFB pour les noyaux dans des conditions extrêmes de la masse, d'isospin et de température sont présentés.Dans la première partie de cette thèse, nous explorons l'apparition de nouvelles fermetures de couches sphériques pour des noyaux super-lourds, où les fermetures de couches sont caractérisées en termes de gap à deux nucléons. Les résultats dépendent légèrement des Lagrangians effectifs utilisés, mais les nombres magiques au-delà de ^{208} Pb sont prédit pour un nombre de protons Z=120 et 138, et pour un nombre de neutrons N=172, 184, 228, et 258. Les effets de couche sont sensibles à différents termes de champ de moyen, tels que le couplage spin-orbite, la masse scalaire et la masses effective, ainsi que l'interaction de tensorielle de Lorentz. Ces termes ont des poids différents dans les Lagrangians effectifs employées, expliquant les variations, somme toute petites, dans leurs prédictions. Employant le modèle RHFB le plus avancé, nous avons trouvé que le nucléide ^{304} 120 est favorisée comme étant le prochain noyau sphérique doublement magique au-delà de ^{208} Pb.Dans la deuxième partie de cette thèse, nous étudions l'apparition de nouveaux nombres magiques pour les noyaux de masse intermédiaire riches en neutrons, et nous analysons le rôle des interactions pseudo-vecteur et de tensorielle de Lorentz. Basé sur la transformation de Foldy-Wouthuysen, nous discutons en détail le rôle joué par les différents termes des interactions pseudo-vecteur et de tensorielle de Lorentz. Dans l'apparition des nouveaux nombres magiques N=16 , 32 et 34. Les noyaux ^{24} O ^{48} Si et ^{52,54} Ca sont prédits avec un grand gap au niveau de Fermi et un gap d'appariement zéro (^{24} O,^{54}Ca ) ou quasi-nul (^{48} Si,^{54} Ca), les rendant candidats pour de nouveaux nombres magiques des noyaux riches en neutrons. Nous constatons que les interactions de Lorentz pseudo-vecteur et tensorielle induisent des évolutions très spécifiques des énergies à une particule, ce qui pourrait signer la présence et la nécessité d'approches relativistes avec des interactions d'échanges de mésons.Dans la dernière partie de cette thèse, nous étudions les transitions de phase et excitations thermiques des deux noyaux stables et faiblement liés. Les prédictions de divers Lagrangiens relativistes et des différentes interactions d'appariement sont discutées. La température critique de la transition d'appariement dépend linéairement du gap d'appariement à température nulle, et cette dépendance est similaire pour une interaction de portée nulle ou bien finie. Les calculs présentés montrent des caractéristiques intéressantes des corrélations d'appariement à température finie, comme la persistance d'appariement et les phénomènes de re-entrance superfluide. En outre, nous analysons la réponse thermique de certains noyaux.En conclusion, le travail présenté dans cette thèse montre des résultats très intéressants et nouveaux pour trois des questions les plus importantes en physique nucléaire: la quête d'un nouvel îlot de stabilité dans la région des super-lourds, l'apparition de nouveaux nombres magiques dans les noyaux exotiques, et la réponse d'un système finis aux excitations thermiques. / The covariant density functional (CDF) theory with a few number of parameters has been successfully employed to describe ground-state and excited-states of nuclei over the entire nuclear landscape for A > 12. It describes finite nuclear systems with a universal hadronic Lagrangian, which is solved considering the relativistic-Hartree-Fock-Bologuibov approach (RHFB). This model is also employed for the study of compact stars, since it can be extended to high densities where special relativity cannot be ignore. This model can also be extended to include the contribution of hyperons and as well as other exotic particles. In this work, the description and some predictions based on RHFB approach for nuclei under extreme conditions of mass, isospin and temperature are presented.In the first part, we explore the occurrence of spherical shell closures for superheavy nuclei, where shell closures are characterized in terms of two-nucleon gaps. The results depend slightly on the effective Lagrangians used, but the magic numbers beyond ^{208}Pb are generally predicted to be Z = 120 and 138 for protons, and N = 172, 184, 228, and 258 for neutrons. Shell effects are sensitive to various terms of the mean-field, such as the spin-orbit coupling, the scalar and the effective masses, as well as the Lorentz-tensor interaction. These terms have different weights in the effective Lagrangians employed, explaining the (relatively small) variations in the predictions. Employing the most advanced RHFB model, we founded that the nuclide ^{304}120 is favored as being the next spherical doubly-magic nucleus beyond ^{208}Pb.In the second part, we investigate the formation of new shell gaps in intermediate mass neutron-rich nuclei, and analyze the role of the Lorentz pseudo-vector and tensor interactions. Based on the Foldy-Wouthuysen transformation, we discuss in detail the role played by the different terms of the Lorentz pseudo-vector and tensor interactions in the appearance of the N=16, 32 and 34 shell gaps. The nuclei ^{24}O, ^{48}Si and ^{52,54}Ca are predicted with a large shell gap and zero (^{24}O, ^{52}Ca) or almost zero (^{48}Si, ^{54}Ca) pairing gap, making them candidates for new magic numbers in neutron rich nuclei. We find that the Lorentz pseudo-vector and tensor interactions induce very specific evolutions of single-particle energies, which could clearly sign their presence and reveal the need for relativistic approaches with exchange interactions.In the last part, we study the phase transitions and thermal excitations of both stable and weakly-bound nuclei. The predictions of various relativistic Lagrangians and different pairing interactions are discussed. The critical temperature of the pairing transition is found to depend linearly on the zero-temperature pairing gap, and this dependence is similar for a zero-range or a finite-range pairing interaction. The present calculations show interesting features of the pairing correlations at finite temperature, such as the pairing persistence and pairing re-entrance phenomena. Also, we analyze the thermal response of some nuclei.In conclusion, the work presented in this thesis shown interesting and new results for three of the most important questions in nuclear physics: the quest for a new island of stability in the superheavy region, the appearance of new magic numbers in exotic nuclei, and the response of finite-systems to thermal excitations.

In the last decade, a large number of studies have been devoted to the peculiarities of correlated physics found in the quasi-two-dimensional square lattice iridium oxides. It was shown that this 5d family of transition metal oxides has strong structural and electronic similarities to the famous 3d family of copper oxides. Moreover, a delicate interplay of on-site spin-orbit coupling, Coulomb repulsion and crystalline electric field interactions is expected to drive various exotic quantum states. Many theoretical proposals were made in the last decade including the prediction of possible superconductivity in square-lattice iridates emerging as a sister system to high-Tc cuprates, which however met only limited experimental confirmation. One can, therefore, raise a general question: To what extent is the low-energy physics of the quasi-two-dimensional square-lattice iridium oxides different from other transition metal oxides including cuprates? In this thesis we investigate some of the effects which are usually neglected in studies on iridates, focusing on quasi-two-dimensional square-lattice iridates such as Sr2IrO4 or Ba2IrO4. In particular, we discuss the role of the electron-phonon coupling in the form of Jahn-Teller interaction, electron-hole asymmetry introduced by the strong correlations and some effects of coupling scheme chosen to calculate multiplet structure for materials with strong on-site spin-orbit coupling. Thus, firstly, we study the role of phonons, which is almost always neglected in Sr2IrO4, and discuss the manifestation of Jahn-Teller effect in the recent data obtained on Sr2IrO4 with the help of resonant inelastic x-ray scattering. When strong spin-orbit coupling removes orbital degeneracy, it would at the same time appear to render the Jahn-Teller mechanism ineffective. We show that, while the Jahn-Teller effect does indeed not affect the antiferromagnetically ordered ground state, it leads to distinctive signatures in the spin-orbit exciton. Second, we focus on charge excitations and determine the motion of a charge (hole or electron) added to the Mott insulating, antiferromagnetic ground-state of square-lattice iridates. We show that correlation effects, calculated within the self-consistent Born approximation, render the hole and electron case very different. An added electron forms a spin-polaron, which closely resembles the well-known cuprates, but the situation of a removed electron is far more complex. Many-body configurations form that can be either singlets and triplets, which strongly affects the hole motion. This not only has important ramifications for the interpretation of angle-resolved photoemission spectroscopy and inverse photoemission spectroscopy experiments of square lattice iridates, but also demonstrates that the correlation physics in electron- and hole-doped iridates is fundamentally different. We then discuss the application of this model to the calculation of scanning tunneling spectroscopy data. We show that using scanning tunneling spectroscopy one can directly probe the quasiparticle excitations in Sr2IrO4: ladder spectrum on the positive bias side and multiplet structure of the polaron on the negative bias side. We discuss in detail the ladder spectrum and show its relevance for Sr2IrO4 which is in general described by more complicated extended t-J -like model. Theoretical calculation reveals that on the negative bias side the internal degree of freedom of the charge excitation introduces strong dispersive hopping channels encaving ladder-like features. Finally, we discuss how the choice of the coupling scheme to calculate multiplet structure can affect the theoretical calculation of angle-resolved photoemission spectroscopy and scanning tunnelling spectroscopy spectral functions.

L'informatique quantique, ce surprenant mariage entre informatique et physique, est un domaine riche en nouvelles idées, autant pour la technologie future qu'une meilleure compréhension de notre univers. C'est le phénomène de l'intrication qui est au coeur de cette nouvelle façon de voir l'information. Ce mémoire porte sur l'étude des corrélations quantiques observées dans la nature, mises de l'avant, entre autres, par John Bell. Plus particulièrement, deux jeux non signalants, dans lesquels ces corrélations se manifestent, sont étudiés: le jeu CHSH, probablement l'exemple le plus connu à ce jour, et le jeu de pseudotélépathie du carré magique. Pour ce faire, deux points de vue seront adoptés, soit probabiliste et algorithmique. Le premier est motivé par la prédiction (ce qui aurait pu se passer), tandis que le second s'intéresse à l'information intrinsèque contenue dans un objet (ce qui s'est passé). Les concepts «aléatoire» et «information» seront donc abordés premièrement à la Shannon (approche probabiliste) puis à la Kolmogorov (approche algorithmique). C'est la complexité de Kolmogorov qui sera utilisée pour quantifier l'information de façon factuelle. De plus, le cas particulier où plusieurs répétitions d'un jeu sont jouées en parallèle dans un monde classique sera examiné. Le théorème des répétitions parallèles, résultat important sur le sujet démontré par Ran Raz, sera présenté et utilisé par la suite dans l'étude algorithmique des jeux CHSH et du carré magique. / Quantum information, this intriguing marriage between computer science and physics, is a promising field of research for future technologies as well as a better understanding of our universe. Entanglement is at the very heart of this new way of understanding information. This thesis focuses on quantum correlations that are observed in nature. They have been studied in great detail by, among others, John Bell. More specifically, two non-signaling games, in which these correlations arise, are studied: the CHSH game, which is probably the best-known example of such games, and the magic square pseudotelepathy game. To do so, two points of view will be adopted: probabilistic and algorithmic. The first is motivated by prediction (what could have happened) and the second focuses on the intrinsic information about an object (what happened). Therefore, the concepts of randomness and information are first addressed from Shannon’s point of view (probabilistic approach) and second from Kolmogorov’s point of view (algorithmic approach). Kolmogorov complexity is used to quantify information in a factual way. Furthermore, the particular case in which multiple repetitions of a game are played in parallel in a classical world is considered. The parallel repetition theorem, an important result on the subject proven by Ran Raz, is presented and used in the algorithmic study of the CHSH game and the magic square game.