本研究利用台灣2001年資料以Ramsey與OLG假設分別建立區分四部門別與八部門別之動態可計算一般均衡模型，進行「提高間接稅（消費稅、環境稅）、降低直接稅（資本、勞動所得稅）」之稅制改革模擬分析。結果發現若以單一時點比較靜態方式分析可能迥異於動態長期分析結果；其次以Ramsey分析所欠缺的代際分配影響結果在OLG分析中可以察見，特別是進行以消費稅或環境稅替代資本所得稅模擬時；再者OLG因代際傳遞效果可能較Ramsey假設下反應緩慢，故也可觀察到Ramsey模型面對衝擊後若干變數增減幅度會較OLG模型陡峭。最後特別在環境稅替代所得稅模擬中經由替代稅率變化發現，活在初期世代雖可享受所得稅下降好處但卻也面臨排放稅課徵，因此福利水準增減變化不大，惟屆至排放稅課徵瀕至臨界點需使用原所得稅來平衡稅收時，此為另一波必須為減量政策付出代價的時點與世代。 / Based on a thorough comparison of the basic assumptions and economic underpinning of the Ramsey and Overlapping generation (OLG) model, this study builds both static and dynamic computable general equilibrium tax policy models to analyze the effect of tax reform on Taiwan’s economy. The new tax structure considers mainly a replacement of some parts of direct tax - labor and capital income taxes by indirect tax- consumption tax or environment tax. The benchmark year of the model is 2001, and the economy is divided into four and eight sectors. The modeling framework is implemented on top of MPSGE, which is a special module within the General Algebraic Modeling System (GAMS).Our simulation results show differential outcomes for static and dynamic models. The slower speed of transition inherent in OLG model has caused variables such as welfare, capital stock, and replacement consumption tax rate change less than that in the Ramsey model when the tax reform policy is imposed. And the intergeneration effects of different tax burden between young and old generations can be found in the OLG model but not in the Ramsey model. Finally, we find as the income tax rate coming lower and the environment tax going up when simulation of tax replacement, causing the welfare does not change much at the beginning of shock, and generations especially born in the near future when environment tax does not grow and revenue neutrality needs to be meet are another cost payers of abatement policy.

Bibliography: pages 192-195 / The avoidability, or unavoidability of patterns in words over finite alphabets has been studied extensively. The word α over a finite set A is said to be unavoidable for an infinite set B+ of nonempty words over a finite set B if, for all but finitely many elements w of B+, there exists a semigroup morphism φ ∶ A+ → B+ such that φ(α) is a factor of w. In this treatise, we start by presenting a historical background of results that are related to unavoidability. We present and discuss the most important theorems surrounding unavoidability in detail. We present various complexity-related properties of unavoidable words. For words that are unavoidable, we provide a constructive upper bound to the lengths of words that avoid them. In particular, for a pattern α of length n over an alphabet of size r, we give a concrete function N(n, r) such that no word of length N(n, r) over the alphabet of size r avoids α. A natural subsequent question is how many unavoidable words there are. We show that the fraction of words that are unavoidable drops exponentially fast in the length of the word. This allows us to calculate an upper bound on the number of unavoidable patterns for any given finite alphabet. Subsequently, we investigate computational aspects of unavoidable words. In particular, we exhibit concrete algorithms for determining whether a word is unavoidable. We also prove results on the computational complexity of the problem of determining whether a given word is unavoidable. Specifically, the NP-completeness of the aforementioned problem is established. / Decision Sciences / D. Phil. (Operations Research)

Die Regularitätsmethode für Graphen wurde vor über 30 Jahren von Szemerédi, für den Beweis seines Dichteresultates über Teilmengen der natürlichen Zahlen, welche keine arithmetischen Progressionen enthalten, entwickelt. Grob gesprochen besagt das Regularitätslemma, dass die Knotenmenge eines beliebigen Graphen in konstant viele Klassen so zerlegt werden kann, dass fast alle induzierten bipartiten Graphen quasi-zufällig sind, d.h. sie verhalten sich wie zufällige bipartite Graphen mit derselben Dichte. Das Regularitätslemma hatte viele weitere Anwendungen, vor allem in der extremalen Graphentheorie, aber auch in der theoretischen Informatik und der kombinatorischen Zahlentheorie, und gilt mittlerweile als eines der zentralen Hilfsmittel in der modernen Graphentheorie. Vor wenigen Jahren wurden Regularitätslemmata für andere diskrete Strukturen entwickelt. Insbesondere wurde die Regularitätsmethode für uniforme Hypergraphen und dünne Graphen verallgemeinert. Ziel der vorliegenden Arbeit ist die Weiterentwicklung der Regularitätsmethode und deren Anwendung auf Probleme der theoretischen Informatik. Im Besonderen wird gezeigt, dass vererbbare (entscheidbare) Hypergrapheneigenschaften, das sind Familien von Hypergraphen, welche unter Isomorphie und induzierten Untergraphen abgeschlossen sind, testbar sind. D.h. es existiert ein randomisierter Algorithmus, der in konstanter Laufzeit mit hoher Wahrscheinlichkeit zwischen Hypergraphen, welche solche Eigenschaften haben und solchen die „weit“ davon entfernt sind, unterscheidet. / About 30 years ago Szemerédi developed the regularity method for graphs, which was a key ingredient in the proof of his famous density result concerning the upper density of subsets of the integers which contain no arithmetic progression of fixed length. Roughly speaking, the regularity lemma asserts, that the vertex set of every graph can be partitioned into a constant number of classes such that almost all of the induced bipartite graphs are quasi-random, i.e., they mimic the behavior of random bipartite graphs of the same density. The regularity lemma had have many applications mainly in extremal graph theory, but also in theoretical computer science and additive number theory, and it is considered one of the central tools in modern graph theory. A few years ago the regularity method was extended to other discrete structures. In particular extensions for uniform hypergraphs and sparse graphs were obtained. The main goal of this thesis is the further development of the regularity method and its application to problems in theoretical computer science. In particular, we will show that hereditary, decidable properties of hypergraphs, that are properties closed under isomorphism and vertex removal, are testable. I.e., there exists a randomised algorithm with constant running time, which distinguishes between Hypergraphs displaying the property and those which are “far” from it.

Student Number : 7909638 - MCom dissertation - School of Economics and Business Sciences - Faculty of Commerce, Law and Management / Healthcare, it can be argued, is a commodity that has a social constitution. The reason may be because healthcare is seen to have its foundation in socio-economic principles but has evolved through scientific study and business application into a profitable business. The delivery of healthcare in South Africa and in many parts of the world has come under immense scrutiny from policy-makers, high-volume purchasers, patient-consumers and the healthcare community. Arguments criticizing the high cost of healthcare delivery range from levelling the blame on one component (pharmaceuticals, medical fees, inadequate medical scheme cover to name a few examples) to a condemnation of the entire healthcare delivery system. The healthcare cost deliberation has also shifted to the centre stage in many public-policy debates and certainly caught the imagination of the public and journalists alike. It is an emotional debate. A review of related literature of the past fifty years (such as the Sainsbury Report (1967), the Kefauver Hearings (1963) and the Snyman Report (1962)), reveals that healthcare and the cost of healthcare delivery are some of the most frequently debated areas amongst the citizens and policy makers of both the developed and developing world. Pharmaceutical prices, more often than not, have been cast as the primary reason that the delivery cost of healthcare is so high. The methods used by pharmaceutical companies to promote their products – elaborate conventions, colourful brochures and generous amounts of free samples (certainly in previous years) to physicians may have contributed to this perception. Furthermore, the fact that the absolute cost of manufacturing a single capsule or tablet (including drugs that are no longer under patent) is a small fraction of the actual selling price also tends to raise the public ire. A greater understanding of pricing structures is necessary to appreciate this sector. The writer’s own experience in the area of healthcare that involves insurance for medical risks (medical schemes - the private healthcare funding system) suggests that it is crucial that pharmaceutical pricing structures be understood against this backdrop. Therefore the main reasons for undertaking this study are: i. to appreciate the pricing structures of pharmaceuticals to inform policy debates; ii. the current empirical evidence1 in the South African market has indicated that pharmaceuticals are unfairly priced and has prompted the Department of Health to introduce price regulations2. One goal of the research is to ascertain whether this is accurate; and iii. to obtain a broader knowledge base of the issue of pharmaceutical pricing practices in the South African healthcare market. It was with this approach that the area of pharmaceutical pricing and the topic was decided upon.

Let P = (p1, p2, . . . , pN ) be a sequence of points in the plane, where pi = (xi, yi) and x1 < x2 < · · · < xN . A famous 1935 Erdős-Szekeres theorem asserts that every such P contains a monotone subsequence S of √ N points. Another, equally famous theorem from the same paper implies that every such P contains a convex or concave subsequence of Ω(log N) points. First we define a (k + 1)-tuple K ⊆ P to be positive if it lies on the graph of a function whose kth derivative is everywhere nonnegative, and similarly for a negative (k + 1)-tuple. Then we say that S ⊆ P is kth-order monotone if its (k + 1)- tuples are all positive or all negative. In this thesis we investigate quantitative bound for the corresponding Ramsey-type result. We obtain an Ω(log(k−1) N) lower bound ((k − 1)-times iterated logarithm). We also improve bounds for related problems: Order types and One-sided sets of hyperplanes. 1

Le thème central de cette thèse est l'étude des problèmes d'optimisation multicritère avec ou sans dynamique ainsi que le problème général de Bolza et ses applications. Après avoir rappelé quelques concepts d'analyse non lisse, on étudie dans la première partie de cette thèse l'existence des multiplicateurs de Lagrange pour des problèmes d'optimisation multicritère en dimension infinie en termes d'une préférence générale. En introduisant la notion de la régularité d'une préférence et en utilisant la condition de qualification calme, on établit l'existence des multiplicateurs de Karush-Kuhn-Tucker. Ceci nous permet d'exhiber des multiplicateurs de Fritz-John en termes du sous-différentiel approché au sens de Ioffe. En conséquence on obtient des résultats similaires pour le cas d'une préférence définie par un cône convexe ou bien par une fonction d'utilité. On établit dans la deuxième partie des conditions nécessaires d'optimalité pour le problème général de Bolza en termes du sous différentiel Fréchet limite sans aucune hypothèse de convexité. Ce résultat nous permet de retrouver les résultats de Vinter-Zheng, Ioffe-Rockafellar et d'établir le principe du maximum avec une nouvelle inclusion d'Euler-Lagrange. On applique ce dernier aux problèmes isopérimetriques, au modèle général de croissance économique de Ramsey et à un problème de génie chimique. En utilisant la notion de préférence de la première partie et les résultats de la deuxième, on établit dans la troisième partie des conditions nécessaires d'optimalité et des conditions Hamiltoniennes d'un problème d'optimisation multicritère dynamique. Enfin on donne des résultats similaires pour le cas d'une préférence définie par un cône convexe ou une fonction d'utilité.

L'objectif de la thèse était d'utiliser les développements de la manipulation d'atomes par lasers pour réaliser un appareil capable de mesurer les vitesses de rotation avec une sensibilité équivalente à celle des meilleurs gyromètres optiques. Les gyromètres atomiques, comme les gyromètres optiques sont fondés sur l'effet Sagnac. Cet effet est l'apparition d'un déphasage à la sortie d'un interféromètre d'aire non nulle, lorsque le dispositif est en rotation. On montre que l'effet Sagnac appliqué aux ondes de matière associées à des atomes de césium par exemple, est 1011 fois plus sensible que lorsqu'il est appliqué aux ondes lumineuses. La principale difficulté du dispositif est de séparer et de recombiner de façon cohérente les ondes atomiques. Dans notre dispositif, ceci est réalisé dans la zone d'interaction, grâce à des transitions à deux photons appelées transitions Raman stimulées. C'est l'impulsion des deux photons qui, une fois transférée à l'atome au cours de la transition, va provoquer la séparation angulaire des deux paquets d'ondes atomiques. La réalisation du dispositif s'appuie sur un grand nombre de nouvelles solutions techniques qui ont été validées au cours de la thèse. L'un des soucis principal a été de réaliser un appareil compact et suffisamment insensible aux paramètres extérieurs (champ magnétique, température, ?) pour qu'il puisse être transportable. Notre source atomique est une source à atomes refroidis par lasers, permettant ainsi d'avoir une zone d'interaction réduite tout en conservant un très bon niveau de performance. L'appareil est également sensible aux accélérations ; une technique de double jets atomiques contra-propageant a donc été mise en ?uvre pour discriminer les déphasages liés à la rotation et à l'accélération.

This study aims to provide an empirical investigation of Postal Services pricing in Turkey by way of computing Ramsey prices and examining the sensitivity of Ramsey prices to changes in demand and cost parameters. In this study, the Ramsey pricing problem is stated as maximizing a welfare function subject to the Post Office attaining a certain degree of profitability. The conditions necessary for the Post Office to be able to price efficiently have implications for Ramsey pricing. We estimate demand functions and cost structure of letters and express mail using data from Turkish Postal Services. The robustness of the Ramsey rule is assessed under alternative estimates of demand and similarly, in the absence of reliable data, under alternative intervals of marginal cost. Ramsey prices for two letter categories and welfare gains of moving from the existing pricing structure to Ramsey are determined and examined. Sensitivity analysis indicates that the existing policy is not Ramsey optimal and that this is a fairly robust result.

We investigate two combinatorial properties of classes of finite structures, as well as related applications to topological dynamics. Using the Hrushovski property of classes of finite structures -- a finite extension property of homomorphisms -- we can show the existence of ample generics. For example, Solecki proved the existence of ample generics in the context of finite metric spaces that do indeed possess this extension property. Furthermore, Kechris, Pestov and Todorcevic have shown that the Ramsey property of Fraisse classes of finite structures implies that the automorphism group of the corresponding Fraisse limit is extremely amenable, i.e., it possesses a very strong fixed point property. Gromov and Milman had shown that the unitary group of the infinite-dimensional separable Hilbert space is extremely amenable using non-combinatorial methods. This result encourages a deeper look into structural Euclidean Ramsey theory, i.e., Euclidean Ramsey theory in which we colour more than just points. In particular, we look at complete finite labeled graphs whose vertex sets are subsets of the Hilbert space and whose labels correspond to the inner products. We prove "Ramsey-type" and "Hrushovski-type" theorems for linearly ordered metric subspaces of "sufficiently" orthogonal sets. In particular, the latter is used to show a "Hrushovski version" of the Ramsey-type Matousek-Rodl theorem for simplices. It is known that the square root of the metric induced by the distance between vertices in graphs produces a metric space embeddable in a Euclidean space if and only if the graph is a metric subgraph of the Cartesian product of three types of graphs. These three are the half-cube graphs, the so-called cocktail party graphs, and the Gosset graph. We show that the class of metric spaces related to half-cube graphs -- metric spaces on sets with the symmetric difference metric -- satisfies the Hrushovski property up to 3 points, but not more. Moreover, the amalgamation in this class can be too restrictive to permit the Ramsey Property. Finally, following the work of Fouche, we compute the Ramsey degrees of structures induced by the leaf sets of boron trees. Also, we briefly show that this class does not satisfy the full Hrushovski property. Fouche's trees are in fact related to ultrametric spaces, as was observed by Lionel Nguyen van The. We augment Fouche's concept of orientation so that it applies to these boron tree structures. The upper bound computation of the Ramsey degree in this case, turns out to be an "asymmetric" version of the Graham-Rothschild theorem. Finally, we extend these structures to "oriented" ones, yielding a Ramsey class and a corresponding Fraisse limit whose automorphism group is extremely amenable.

We investigate two combinatorial properties of classes of finite structures, as well as related applications to topological dynamics. Using the Hrushovski property of classes of finite structures -- a finite extension property of homomorphisms -- we can show the existence of ample generics. For example, Solecki proved the existence of ample generics in the context of finite metric spaces that do indeed possess this extension property. Furthermore, Kechris, Pestov and Todorcevic have shown that the Ramsey property of Fraisse classes of finite structures implies that the automorphism group of the corresponding Fraisse limit is extremely amenable, i.e., it possesses a very strong fixed point property. Gromov and Milman had shown that the unitary group of the infinite-dimensional separable Hilbert space is extremely amenable using non-combinatorial methods. This result encourages a deeper look into structural Euclidean Ramsey theory, i.e., Euclidean Ramsey theory in which we colour more than just points. In particular, we look at complete finite labeled graphs whose vertex sets are subsets of the Hilbert space and whose labels correspond to the inner products. We prove "Ramsey-type" and "Hrushovski-type" theorems for linearly ordered metric subspaces of "sufficiently" orthogonal sets. In particular, the latter is used to show a "Hrushovski version" of the Ramsey-type Matousek-Rodl theorem for simplices. It is known that the square root of the metric induced by the distance between vertices in graphs produces a metric space embeddable in a Euclidean space if and only if the graph is a metric subgraph of the Cartesian product of three types of graphs. These three are the half-cube graphs, the so-called cocktail party graphs, and the Gosset graph. We show that the class of metric spaces related to half-cube graphs -- metric spaces on sets with the symmetric difference metric -- satisfies the Hrushovski property up to 3 points, but not more. Moreover, the amalgamation in this class can be too restrictive to permit the Ramsey Property. Finally, following the work of Fouche, we compute the Ramsey degrees of structures induced by the leaf sets of boron trees. Also, we briefly show that this class does not satisfy the full Hrushovski property. Fouche's trees are in fact related to ultrametric spaces, as was observed by Lionel Nguyen van The. We augment Fouche's concept of orientation so that it applies to these boron tree structures. The upper bound computation of the Ramsey degree in this case, turns out to be an "asymmetric" version of the Graham-Rothschild theorem. Finally, we extend these structures to "oriented" ones, yielding a Ramsey class and a corresponding Fraisse limit whose automorphism group is extremely amenable.