In this paper, we will review two fundamental counting methods: inclusionexclusion and pigeonhole principles. The inclusion-exclusion principle considers the elements of the sets satisfied some conditions, and avoids repeat counting by disjoint sets. We also use the inclusion-exclusion principle to solve the problems of Euler phi function and the number of onto functions in number theory, and derangement and the number of nonnegative integer solutions of equations in combinatorics. We derive the closed-form formula to those problems. For the forbidden positions problems, we use the rook polynomials to simplify the counting process. We also show the form of the inclusion-exclusion principle in probability, and use it to solve some probability problems. The pigeonhole principle is an easy concept. We can establish some sets and use the pigeonhole principle to discuss the extreme value about the number of elements. Choose the pigeons and pigeonholes, properly, and solve problems by the concept of the pigeonhole principle. We also introduce the Ramsey theorem which is an important application of the pigeonhole principle. This theorem provides a method to solve problems by complete graph. Finally, we give some contest problems about the inclusion-exclusion and pigeonhole principles to show how those principles are used.

Ramsey-type results for ordered hypergraphs Martin Balko Abstract We introduce ordered Ramsey numbers, which are an analogue of Ramsey numbers for graphs with a linear ordering on their vertices. We study the growth rate of ordered Ramsey numbers of ordered graphs with respect to the number of vertices. We find ordered match- ings whose ordered Ramsey numbers grow superpolynomially. We show that ordered Ramsey numbers of ordered graphs with bounded degeneracy and interval chromatic number are at most polynomial. We prove that ordered Ramsey numbers are at most polynomial for ordered graphs with bounded bandwidth. We find 3-regular graphs that have superlinear ordered Ramsey numbers, regardless of the ordering. The last two results solve problems of Conlon, Fox, Lee, and Sudakov. We derive the exact formula for ordered Ramsey numbers of mono- tone cycles and use it to obtain the exact formula for geometric Ramsey numbers of cycles that were introduced by Károlyi et al. We refute a conjecture of Peters and Szekeres about a strengthening of the fa- mous Erd˝os-Szekeres conjecture to ordered hypergraphs. We obtain the exact formula for the minimum number of crossings in simple x-monotone drawings of complete graphs and provide a combinatorial characterization of these drawings in terms of colorings of ordered...

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The tidal stream industry has seen large growth in recent years, and the number of pre-commercial scale devices currently being tested reflects this development. However, commercialising this technology whilst showing that their environmental impacts is minimal remains a challenge. The impact on benthic communities is not considered to be a key strategic consenting issue, yet it is anticipated that the benthic habitat will change as a result of the presence of tidal turbines. To date, only single tidal turbine devices have been installed to demonstrate the application of tidal stream technology but despite successful tests there are still uncertainties surrounding the quantitative impacts these turbines have on local benthic communities. Unlike the wind industry, where physical effects of wind turbines have been catalogued through deployment of thousands of turbines, the tidal stream industry lacks these array scale quantitative data. Local impacts are known, but understanding the scale of the impacts and their relative significance of large arrays remains unknown. Tidal turbines (both single and arrays) interact with the hydrodynamics by decreasing the near field current flow directly in its wake through energy extraction and the drag caused by the physical structure. However, turbines may also affect the far field hydrodynamics, altering bed characteristics, sediment transport regimes and suspended sediment concentrations. As benthic habitats are closely linked to the physical seabed composition and the hydrodynamic conditions, the benthic environment is affected by to changes in the current flow. This thesis presents a series of studies investigating the interaction between tidal turbines and the benthic environment. Based on the hydrodynamic modelling software, TELEMAC2D, a numerical model has been developed to investigate the hydrodynamic impact of a single tidal array at Ramsey Sound, Pembrokeshire as well as the cumulative impact of multiple tidal developments in the Irish Sea. Based on the results of the models, the hydrodynamic outputs were used as inputs to drive a species distribution model, based on the software MaxEnt, to investigate how the distribution of benthic species altered in the presence of a 10MW tidal array at Ramsey Sound. Results of the study showed the development would have a minimal negative impact on the benthic environment.

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Economic uncertainty may affect significantly people’s behavior and hence macroeconomic variables. It is thus important to understand how people behave in presence of different kinds of economic risk. The present dissertation focuses therefore on the impact of the uncertainty in capital and labor income on the individual saving behavior. The underlying uncertain variables are here modeled as stochastic processes that each obey a specific stochastic differential equation, where uncertainty stems either from Poisson or Lévy processes. The results on the optimal behavior are derived by maximizing the individual expected lifetime utility. The first chapter is concerned with the necessary mathematical tools, the change-of-variables formula and the Hamilton-Jacobi-Bellman equation under Poisson uncertainty. We extend their possible field of application in order make them appropriate for the analysis of the dynamic stochastic optimization problems occurring in the following chapters and elsewhere. The second chapter considers an optimum-saving problem with labor income, where capital risk stems from asset prices that follow geometric L´evy processes. Chapter 3, finally, studies the optimal saving behavior if agents face not only risk but also uncertain spells of unemployment. To this end, we turn back to Poisson processes, which here are used to model properly the separation and matching process.

Economic uncertainty may affect significantly people’s behavior and hence macroeconomic variables. It is thus important to understand how people behave in presence of different kinds of economic risk. The present dissertation focuses therefore on the impact of the uncertainty in capital and labor income on the individual saving behavior. The underlying uncertain variables are here modeled as stochastic processes that each obey a specific stochastic differential equation, where uncertainty stems either from Poisson or Lévy processes. The results on the optimal behavior are derived by maximizing the individual expected lifetime utility. The first chapter is concerned with the necessary mathematical tools, the change-of-variables formula and the Hamilton-Jacobi-Bellman equation under Poisson uncertainty. We extend their possible field of application in order make them appropriate for the analysis of the dynamic stochastic optimization problems occurring in the following chapters and elsewhere. The second chapter considers an optimum-saving problem with labor income, where capital risk stems from asset prices that follow geometric L´evy processes. Chapter 3, finally, studies the optimal saving behavior if agents face not only risk but also uncertain spells of unemployment. To this end, we turn back to Poisson processes, which here are used to model properly the separation and matching process.

This thesis is essentially a portfolio of four disjoint yet thematically related articles that deal with some semantic aspect or another of natural language conditionals. The thesis opens with a brief introductory chapter that offers a short yet opinionated historical overview and a theoretical background of several important semantic issues of conditionals. The second chapter then deals with the issue of truth values and conditions of indicative conditionals. So-called Gibbard Phenomenon cases have been used to argue that indicative conditionals construed in terms of the Ramsey Test cannot have truth values. Since that conclusion is somewhat incredible, several alternative options are explored. Finally, a contextualised revision of the Ramsey Test is offered which successfully avoids the threats of the Gibbard Phenomenon. The third chapter deals with the question of where to draw the so-called indicative/ subjunctive line. Natural language conditionals are commonly believed to be of two semantically distinct types: indicative and subjunctive. Although this distinction is central to many semantic analyses of natural conditionals, there seems to be no consensus on the details of its nature. While trying to uncover the grounds for the distinction, we will argue our way through several plausible proposals found in the literature. Upon discovering that none of these proposals seem entirely suited, we will reconsider our position and make several helpful observations into the nature of conditional sentences. And finally, in light of our observations, we shall propose and argue for plausible grounds for the indicative/subjunctive distinction.distinction. The fourth chapter offers semantics for modal and amodal natural language conditionals based on the distinction proposed in the previous chapter. First, the nature of modal and amodal suppositions will be explored. Armed with an analysis of modal and amodal suppositions, the corresponding conditionals will be examined further. Consequently, the syntax of conditionals in English will be uncovered for the purpose of providing input for our semantics. And finally, compositional semantics in generative grammar will be offered for modal and amodal conditionals. The fifth and final chapter defends Modus Ponens from alleged counterexamples. In particular, the chapter offers a solution to McGee’s infamous counterexamples. First, several solutions offered to the counterexamples hitherto are all argued to be inadequate. After a couple of observations on the counterexamples’ nature, a solution is offered and demonstrated. the solution suggests that the semantics of embedded natural language conditionals is more sophisticated than their surface syntax indicates. The heart of the solution is a translation function from the surface form of natural language conditionals to their logical form. Finally, the thesis ends with a conclusion that briefly summarises the main conclusions drawn in its preceding chapters.

L’objectif de la thèse est d’identifier la pertinence des modèles en équilibre général calculable (MEGC) pour analyser la problématique posée par les Accords de Partenariat Économique (APE) entre l’Union européenne et les pays ACP. Une revue de la littérature est d’abord réalisée, puis un modèle en équilibre général calculable (MEGC) à dynamique intertemporelle est construit pour analyser l’impact de l’APE sur un pays spécifique : le Ghana. À partir du constat portant sur la diversité des résultats de simulations, qui dépendent essentiellement de la structure du modèle et des modes de fermeture choisis par le modélisateur, ce travail cherche à mettre en évidence la largeur du faisceau de résultats possibles et l’impossibilité de mettre en avant les bénéfices potentiels qui peuvent être attendus d’un tel accord en s’appuyant simplement sur des MEGC néoclassiques standards. / This work aims to analyze to what extent the use of an applied general equilibrium model (AGE) allows to correctly assess the potential economic impact of EPAs between ACP countries and the European Union. First, a review of the literature is conducted and then an intertemporal dynamic AGE model is built in order to assess the potential impact of EPA on a specific country: Ghana. From the variety of results resulting from the models simulations and depending on hypothesis made on the model structure and the type of closure chosen by the modeler, our work aims to stress the risk of using standard neoclassical Walrasian models to assess the potential benefits of an EPA on ACP countries economy.

Le principe de complémentarité est un concept fondamental de la<br />mécanique quantique. Il prédit que, dans une expérience d'interférométrie, toute<br />tentative pour déterminer quel chemin la particule choisit entre les deux lames<br />séparatrices brouille inévitablement les franges d'interférence. Dans ce mémoire,<br />nous présentons une expérience qui illustre ce principe dans un interféromètre de<br />Ramsey. Des atomes de Rydberg circulaires sont soumis à deux impulsions micro-onde<br />résonantes sur une transition atomique, qui jouent le rôle de lames séparatrices en<br />énergie. On observe alors des franges d'interférence dans la probabilité de détecter<br />l'atome dans un état donné. Dans notre expérience, l'une des deux impulsions est<br />effectuée dans le mode d'une cavité supraconductrice. Grâce au couplage fort entre<br />l'atome et la cavité, nous avons pu effectuer l'impulsion même lorsque le champ dans<br />la cavité contient très peu de photons en moyenne (N<1, impulsion quantique). Les<br />franges ont alors un contraste réduit car l'état de la cavité mesure celui de<br />l'atome au sein de l'interféromètre. Cette mesure est de moins en moins efficace<br />lorsque N augmente. Le contraste des franges augmente donc, jusqu'à atteindre le<br />contraste intrinsèque d'un interféromètre de Ramsey classique lorsque N>>1. Un<br />modèle simple, qui ne tient compte que de l'intrication entre l'atome et la cavité,<br />reproduit quantitativement les observations. Un des intérêts majeurs du dispositif<br />d'électrodynamique quantique en cavité est de permettre la génération d'états<br />non-classiques du champ. Il est alors particulièrement intéressant de les<br />caractériser complètement. Nous présentons en dernière partie de ce mémoire une<br />méthode directe pour mesurer la fonction de Wigner d'un état quelconque de la<br />cavité, et son application à un état de Fock à un photon.