Since the 19th century the remains of Quaternary mammals were an important source of data for reconstructing past environmental conditions. I tested two basic assumptions that underlie Quaternary vertebrate paleoecology. The first assumption is that fossils mammals can be identified reliably to species. The second assumption is that correlations established between extant mammals and environmental parameters can be used to interpret reliably the paleoenvironment from the latest Pleistocene. Incorrect specimen identifications could lead to errors in paleoecologic interpretations. I explicitly tested an alternative to the traditional approach to identification by identifying fossil shrews based on apomorphies. My results indicated that some traditional characters are useful for identification, but only complete specimens with a combination of characters can be identified to species. This indicates that previous authors who identified shrews to species did not compare them to the full diversity of species. I tested the reliability of cenograms and species-richness models as approaches for the reconstruction of environmental conditions in the past. I used faunal data from Hall’s Cave, Kerr County, Texas to construct cenograms and species-richness models and compared the results to independent paleoclimate proxies. Neither species-richness models nor cenograms agree with paleoenvironmental reconstructions based on proxy data from the Late Pleistocene and Holocene. Cenograms and species-richness models are unreliable and fraught with problems, and both approaches should be abandoned as tools for paleoecological reconstruction. To test for potential geographic bias in the identification of Quaternary fossils I developed a GIS (geographic information systems) database of Quaternary paleontological sites within Texas. I was able to show that the identification of species of fossil soricids, heteromyids, Odocoileus, and Spilogale was influenced by geography. Those fossils should be treated as generic identifications until they are re-evaluated against the full diversity of species. Utilizing GIS I also developed a method of paleoecological analysis. My analysis showed that the environmental conditions found today in Texas might not be limiting the current range of shrews. Based on the known geographic range of shrew fossils, other ecological factors besides environmental conditions are shaping the current distribution of shrews. / text

It is well known that for highly skewed distributions the standard method of using the t statistic for the confidence interval of the mean does not give robust results. This is an important problem for importance sampling (IS) as its final distribution is often skewed due to a heavy tailed weight distribution. In this paper, we first explain Hall's transformation and its variants to correct the confidence interval of the mean and then evaluate the performance of these methods for two numerical examples from finance which have closed-form solutions. Finally, we assess the performance of these methods for credit risk examples. Our numerical results suggest that Hall's transformation or one of its variants can be safely used in correcting the two-sided confidence intervals of financial simulations.(author's abstract) / Series: Research Report Series / Department of Statistics and Mathematics

La géométrie combinatoire est une large et belle branche des mathématiques. Cette thèse doctorale se compose de l'étude de cinq sujets différents dans ce domaine. Même si les problèmes et les techniques utilisés pour y faire face sont divers, ils partagent le mêeme objectif: Étudier l'interaction entre les structures combinatoires et géométriques. Dans le chapitre 1, nous étudions le problème suivant : pour un entier positif k, combien de points en position générale devons-nous prendre dans le plan de sorte que nous pouvons toujours trouver k d'entre eux définissant des triangles avec un rayon du cercle circonscrit distinct ? Cette question a été posée par Paul Erdös en 1975 qui a lui même proposé une solution en 1978. Toutefois, la preuve a omis par inadvertance un cas non trivial. Nous avons repris ce cas et donné une solution à la question en utilisant des outils de base de la géométrie algébrique et nous fournissons une borne polynomiale pour le nombre de points nécessaires.Dans le chapitre 2, nous sommes intéressés par de généralisations géométriques du critère de Hall pour les couplages dans les graphes bipartits (1935). Nous obtenons des théorèmes géométriques type Hall pour des ensembles convexes disjoints et pour points en position générale dans l'espace euclidien. Les outils de ce chapitre sont topologiques, et l'approche est motivés par une méthode remarquable introduite par Aharoni et Haxell en $2000$ ainsi que par ses généralisations.D'autre part, dans le chapitre 3, nous commençons par un théorème de Helly fractionné de 1979 due à A. Liu et M. Katchalski pour motiver un résultat combinatoire. Nous étudions des conditions combinatoires que des familles de graphes doivent avoir pour permettre d'obtenir des versions plus fine du théorème de Turán. Nous trouvons des liens intéressants entre les nombres de Turán, les nombres chromatiques et les nombres de clique dans la famille. Les outils de ce chapitre sont purement combinatoires.Dans le chapitre 4, nous nous concentrons sur l'obtention des résultats pour la bien connue classe des matroïde chemin du réseau introduite par Bonin, de Mier et Noy en 2003. La contribution principale est de prouver pour cette classe la validité d'une conjecture de Merino et Welsh (1999) sur une inégalité de certaines valeurs du polynôme de Tutte. Pour ce faire, nous introduisons et étudions des serpents, une classe spéciale de matroïdes chemin du réseau ``mince''.Enfin, dans le chapitre 5, nous étudions une variante d'un problème des transversales posé par J.L. Arocha, J. Bracho, L. Montejano et J.L. Ramírez-Alfonsín en 2010. Dans leur travaux originaux, ils ont rémarqué que si nous avons peu de points dans l'espace euclidien alors il est possible de trouver une transversale d'une dimension donnée qui travers les enveloppes convexes de tous les k-ensembles de points. De m&eme, ils montrent qu'il est impossible de trouver une telle transversale lorsque nous avons beaucoup de points. Les auteurs donnent des bornes spécifiques et ils laissent aussi quelques problèmes ouverts. Si la définition de transversale est légèrement plus restrictive, alors le problème peut être étudié en utilisant la théorie des matroïdes orientés. Dans la présente thèse, nous fournissons les détails de cette relation et nous donnons des bornes pour la famille de polytopes cycliques. / Combinatorial geometry is a broad and beautiful branch of mathematics. This PhD Thesis consists of the study of five different topics in this area. Even though the problems and the tools used to tackle them are diverse, they share a unifying goal: To explore the interaction between combinatorial and geometric structures.In Chapter 1 we study a problem by Paul Erdös: for a positive integer k, how many points in general position do we need in the plane so that we can always find a k-subset of them defining triangles with distinct circumradii? This question was posed in 1975 and Erdös himself proposed a solution in 1978. However, the proof inadvertently left out a non-trivial case. We deal with the case using basic tools from algebraic geometry and we provide a polynomial bound for the needed number of points.In Chapter 2 we are interested in providing geometric extensions of Hall's criterion for matchings in bipartite graphs (1935). We obtain geometric Hall-type theorems for pairwise disjoint convex sets and for points in general position in euclidean space. The tools of this chapter are topological, and are motivated by a remarkable method introduced by Aharoni and Haxell in 2000 and its generalizations.On the other hand, in Chapter 3 we begin with a fractional Helly theorem from 1979 by A. Liu and M. Katchalski to motivate a combinatorial result. We study combinatorial conditions on families of graphs that allow us to have sharpened variants of Turán's theorem. We find interesting relations between the Turán numbers, the chromatic numbers and the clique numbers of graphs in the family. The tools in this chapter are only combinatorial.In Chapter 4 we focus on obtaining some results for the well studied class of lattice path matroids introduced by Bonin, de Mier and Noy in 2003. The main contribution is proving for this class the validity of a 1999 conjecture of Merino and Welsh concerning an inequality involving certain values of the Tutte polynomial. In order to do this, we introduce and study snakes, a special class of ``thin'' lattice path matroids.Finally, in Chapter 5 we explore a variant of a transversal problem posed by J.L. Arocha, J. Bracho, L. Montejano and J.L. Ramírez-Alfonsín in 2010. In their original work, they realized that if we have few points in euclidean space then it is possible to find a transversal of a given dimension that goes through all the convex hulls of k-subsets of points. Similarly, they show that it is impossible to find such a transversal when we have many points. The authors give some specific bounds and they also leave some open problems. If the definition of transversal is slightly more restrictive, then the problem can be tackled using oriented matroid theory. We provide the details of the relation and we give bounds for the family of cyclic polytopes.

Records of change of [delta]13C values in vertebrate teeth offer an opportunity to gain insight into changes in past vegetation. Increasingly, teeth from small mammals are used for such purposes, but because their teeth grow very rapidly, seasonal changes in vegetation potentially provide a large source of variability in carbon isotope composition, complicating interpretations of small mammal tooth isotope data. To investigate the controls of seasonality on the stable isotope composition of fossil teeth, we constructed a Monte-Carlo-based model to simulate the effects of changes in the seasonal pattern of diet in leporid lagomorphs (rabbits and hares) on the distribution of [delta]¹³C values in random populations of leporid teeth from the Edwards Plateau in central Texas. Changes in mean-state, seasonal vegetation range, and relative season length manifest themselves in predictable ways in the median, standard deviation, and skewness of simulated tooth [delta]¹³C populations, provided sufficient numbers of teeth are analyzed. This Monte Carlo model was applied to the interpretation of a 20,000 year record of leporid tooth [delta]¹³C values from Hall's Cave on the Edwards Plateau in central Texas. Variations in the [delta]¹³C values of teeth deposited at the same time (standard deviation = 1.69%) are larger than changes in the mean vegetation composition reconstructed from bulk organic carbon [delta]¹³C, indicating the influence of short-term variability, making it difficult to assess changes in mean C3/C4 vegetation from the tooth [delta]¹³C data. However, populations of teeth from different climate intervals (e.g., the late Glacial, Younger Dryas, and the Holocene) display changes in the shape of the tooth [delta]¹³C distributions. Interpretation of these changes as shifts in seasonal vegetation patterns that are based upon results from our model are consistent with hypothesized climatic changes. An increase in the standard deviation of the tooth population between the late Glacial and the Younger Dryas -- Holocene is consistent with an increase in seasonality. Furthermore, a shift to more C3-dominated vegetation in the tooth [delta]¹³C distribution during the Younger Dryas is accompanied by a more skewed population -- indicative of not only wetter conditions but an increase in the duration in the C3 growing season. However, late Holocene changes in vegetation are not clear in the tooth data, despite the evidence from bulk organic carbon [delta]¹³C values for an increase in % C3 vegetation of 57%. Small mammal teeth can potentially provide unique insights into climate and vegetation on seasonal and longer timescales that complement other data, but should be interpreted with a careful consideration of local conditions, taxon ecology and physiology, and the dominant timescales of isotope variability. / text

This thesis explores the cultural considerations American technical communicators must address when working with French colleagues and when creating technical documentation for French audiences. A review of the literature on intercultural communication theory was conducted, along with a review of the limited research on technical communication in France and the needs of French audiences. A qualitative online survey of French technical communicators was also conducted. Through this survey, French technical communicators reported on their intercultural beliefs, experiences, and practices, and information, language, and cultural needs. Survey responses were analyzed using inductive thematic analysis. Two main themes were developed as a result of this analysis: the importance of adapting content to French audiences, and the cultural differences between French and American information needs and communication styles. Survey findings are combined with theoretical and practical literature to offer American technical communicators guidance for successful intercultural interactions. This thesis concludes with suggestions for future practice and research in intercultural technical communication.

本文希望藉著K.T Arasu, D.Jungnickel, A.Pott推廣Wilbrink定理的方法去尋找Wilbrink等式的推廣式在p^k∥n,k≧4的推廣式和其應用。 / In this thesis we formulate and provide rigorous proofs of Wilbrink's theorem and it's variations due to Arasu, A.Pott and D.Jungnickel. some questions on further generalizations of Wilbrink's theorem are discussed; known generalization are study in A.Pott's dissertation.