The first essay provides an introduction into the literature of spatial competition models and studies their predictions on the degree of horizontal product differentiation. For this purpose a selection of articles, mainly from the game theoretical strand of the literature, is re-examined in which each model extends and modifies basic parameters of the original model of Hotelling (1929). The literature survey emphasizes that markets consisting of intersecting roads represent a particular fruitful subject of future research. The nature of competition in this market setting is different compared to the linear city exemplified by the importance of asymmetrical location patterns. Consequently, the strategic interaction, firms' profit-maximizing behavior and potential equilibrium outcomes under sequential entry in a market with intersecting roads remain to be an interesting field to study. The second essay addresses this research gap and based on the work of Anderson (1987) studies a two-stage market entry game in a spatially extended Hotelling's duopoly. Particularly, the effect of a demand dependent centrality bonus Z distributed in the middle of the linear city is examined on the reaction functions of an incumbent firm and the strategic entry decision of an entrant firm. A solution is provided for an entry accommodating scenario where both players optimize profits over their strategic variables and the center Z is taken by the incumbent firm. The results further suggest that the entrant is not capable of capturing Z. In addition, the model implies a lower degree of product differentiation as Z increases. A comparison with the literature shows that these results are well in line with Anderson's model for Z = 0. In a business strategy view the outcome supports the thesis of Gelman & Salop (1983), coined by the term 'judo economics', since the entrant earns highest profits by committing himself to a distant location and charging a comparatively lower price than the incumbent. The third essay analyzes the price distribution of diesel in the Austrian retail gasoline market and tests predictions of the impact of the fraction of informed and uninformed consumers on the mean price and price variance. Further, introducing two measures of spatial competition, the relation of local competition between stations and the mean and variance are examined. In a pooled cross-section analysis a two step approach is followed. Initially, price levels are estimated with respect to the influence of competition, search costs, stations' location and further station-specific characteristics. Controlling for these observable price characteristics, the residuals are used in the second step to investigate the behavior of the price variance. In addition to OLS, to account for spatial spillover effects a Spatial Error Model (SEM) is applied to estimate the price function. Additionally, tests on model specification and robustness checks using different weighting matrices, search cost proxies and dispersion measures are carried out. The results reveal a negative (positive) correlation between the fraction of informed (uninformed) consumers and the mean price. Further, price variance shows an inverse U-shape with the fraction of informed consumers. Thus, the variance initially increases as the proportion of informed consumers increases and starts to decline after the share of informed exceeds a threshold of roughly 43%. These findings are in line with predictions of classical search models, most notably Stahl (1989), and empirically support the meaning of consumer search in the context of oligopolistic pricing. Further, the mean price decreases as competition intensifies whereas the Price variance increases under increased entry competition (Janssen & Moraga-Gonzalez (2004), Carlson & McAfee (1983)). This suggests stations' tendency to focus more strongly on the lower price segment as competition increases.

abstract: The primary focus of this dissertation lies in extremal combinatorics, in particular intersection theorems in finite set theory. A seminal result in the area is the theorem of Erdos, Ko and Rado which finds the upper bound on the size of an intersecting family of subsets of an n-element set and characterizes the structure of families which attain this upper bound. A major portion of this dissertation focuses on a recent generalization of the Erdos--Ko--Rado theorem which considers intersecting families of independent sets in graphs. An intersection theorem is proved for a large class of graphs, namely chordal graphs which satisfy an additional condition and similar problems are considered for trees, bipartite graphs and other special classes. A similar extension is also formulated for cross-intersecting families and results are proved for chordal graphs and cycles. A well-known generalization of the EKR theorem for k-wise intersecting families due to Frankl is also considered. A stability version of Frankl's theorem is proved, which provides additional structural information about k-wise intersecting families which have size close to the maximum upper bound. A graph-theoretic generalization of Frankl's theorem is also formulated and proved for perfect matching graphs. Finally, a long-standing conjecture of Chvatal regarding structure of maximum intersecting families in hereditary systems is considered. An intersection theorem is proved for hereditary families which have rank 3 using a powerful tool of Erdos and Rado which is called the Sunflower Lemma. / Dissertation/Thesis / Ph.D. Mathematics 2011

Something Like Wilderness: A Journey into the Heart of the Tundra is a work of creative non-fiction that chronicles Jennifer Kingsley’s 54-day canoe expedition down Nunavut’s Back River in the summer of 2005. This manuscript explores the themes of wilderness and belonging, and it investigates the notion of intersecting journeys. Something Like Wilderness seeks to engage readers with a compelling story while articulating some of the ideas we have about wild places. / Graduate / 10000-01-01

The problems we study in this thesis are all related to covering arrays. Covering arrays are combinatorial designs, widely used as templates for efficient interaction-testing suites. They have connections to many areas including extremal set theory, design theory, and graph theory. We define and study several generalizations of covering arrays, and we develop a method which produces an infinite family of LYM inequalities for graph-intersecting collections. A common theme throughout is the dependence of these problems on graphs. Our main contribution is an extremal method yielding LYM inequalities for $H$-intersecting collections, for every undirected graph $H$. Briefly, an $H$-intersecting collection is a collection of packings (or partitions) of an $n$-set in which the classes of every two distinct packings in the collection intersect according to the edges of $H$. We define ``$F$-following" collections which, by definition, satisfy a LYM-like inequality that depends on the arcs of a ``follow" digraph $F$ and a permutation-counting technique. We fully characterize the correspondence between ``$F$-following" and ``$H$-intersecting" collections. This enables us to apply our inequalities to $H$-intersecting collections. For each graph $H$, the corresponding inequality inherently bounds the maximum number of columns in a covering array with alphabet graph $H$. We use this feature to derive bounds for covering arrays with the alphabet graphs $S_3$ (the star on three vertices) and $\kvloop{3}$ ($K_3$ with loops). The latter improves a known bound for classical covering arrays of strength two. We define covering arrays on column graphs and alphabet graphs which generalize covering arrays on graphs. The column graph encodes which pairs of columns must be $H$-intersecting, where $H$ is a given alphabet graph. Optimizing covering arrays on column graphs and alphabet graphs is equivalent to a graph-homomorphism problem to a suitable family of targets which generalize qualitative independence graphs. When $H$ is the two-vertex tournament, we give constructions and bounds for covering arrays on directed column graphs. FOR arrays are the broadest generalization of covering arrays that we consider. We define FOR arrays to encompass testing applications where constraints must be considered, leading to forbidden, optional, and required interactions of any strength. We model these testing problems using a hypergraph. We investigate the existence of FOR arrays, the compatibility of their required interactions, critical systems, and binary relational systems that model the problem using homomorphisms.

This theses presents an image processing approach to estimating the length of cynobacteria strands in digitally acquired images. An algorithm utilizing the Hough transform to determine strand continuity at strand intersections is presented. The algorithm is demonstrated on selected images, the examined strands are separated and their lengths are estimated. A Delphi implementation of the algorithm is included.

An intersectionality-based content analysis was done; an eclectic and abductive approach was needed to understand the entanglement of comorbidity and intersectionalities impacting self-identified women transnationally.  The research project is presented in three parts detailing its specific features. For example: Part 1 contains the aim and research questions. The scope is nine transcripts/extracts from the narratives collected from sources of public domain (such as web-based channels and platforms where speakers, either orally or in writing, expressed their experience with types of autoimmune disease. Theoretical framework takes place in this section and it is formed by foundations from theories, social transformation-based arguments and contributions from the authors whose expertise in their fields have made a permanent difference in diverse societal, educational and scientific contexts. Authors such as Butler, Ahmed, Crenshaw, Joyce et al., Olkin, Celinski and Gow, Brinkman et al., and many more are valuable citations included in each of their respective sections. Part 2 describes the methods of analysis, coded collected data material and research design; Part 3 describes the analysis on content material and findings to answer the research questions previously created, to address and understand the studied phenomena. The work-in-progress related to our non-profit association (NPA) is also briefly mentioned as the emancipatory technology I have designed from scratch, where I am the main member and first founder. Based in Linköping, Sweden, it is a space to empower one another to face our unique complexities while sharing a place to strengthen each other through education within transnational environments.

As an architectural language, what elements and systems constitute a work of architecture? They are the structural system, enclosure system, circulation system, functional requirements, context, light, views, proportion, scale, forms, cultural characteristics, color and many others. In this thesis, I focus on the structural system, the spatial organization and quality of light with a view to how they contribute to the identity of spaces. the vehicle of my study is an Environmental Learning Center, for Franklin County, Virginia. The building design enploys two different structural systems in two parts of the building, arranging dissimilar spatial organizations in building sections. Various enclosure materials are used to exhibit distinct light qualities. Design is not only to satisfy functional needs, but to architecturally determine spatial differentiation,which accordingly generates the identity of spaces. / Master of Architecture

Seismic hazard assessment of intersecting fault systems, such as the strike-slip and reverse faults of the Los Angeles basin, is hindered by complex patterns of rupture that are currently difficult to predict. To improve this understanding, constraints on the previous rupture patterns of such systems are needed. The junction between the Transverse Ranges and the Eastern California shear zone in southern California provides a natural analog to the seismic setting of the Los Angeles basin. Along the northern flank of the San Bernardino Mountains, the east-west trending North Frontal thrust system is intersected by several northwest trending dextral faults of known Holocene and historical rupture activity. This structural setting, along with an apparent decay in uplift rate along the thrust (from a 3-Myr average of 0.5 mm/yr to a late Pleistocene rate estimated as slow as 0.05 mm/yr), suggests the thrust system may have been rendered inactive by the shear zone that dissects it. However, a clear cross-cutting relationship does not exist, raising the possibility that the two systems are coactive. To test this, we have constrained the recent rupture history of one thrust fault segment with paleoseismic investigations. We have excavated an apparently young thrust fault scarp along the central portion of the thrust system, chosen as the most likely to have ruptured in the recent past. At this location, just west of the intersection of the Helendale fault, a 7-m-high thrust scarp in older fanglomerate is dissected and replaced by younger alluvium with a 1.5-m-high scarp. An excavation across the smaller scarp revealed a 3-m-thick sequence of coarse alluvium cut by a shallow, south-dipping thrust fault with 1.65 m of throw. The simple, smooth trace of the fault plane and the lack of evidence for repeated deformation suggest the offset was produced by one event. A maximum age for this event is provided by disagregated detrital charcoal sampled from a sand lens in the lowermost gravel of the hangingwall, which yielded a calibrated radiocarbon age of 9220 BC (11220 yr BP). Subsequent to this inferred depositional age, an additional 2-m of gravel was deposited prior to fault rupture. Although a minimum age is not constrained, the event may thus have been as young as mid- to late-Holocene, consistent with the poor degree of soil development in several buried soil horizons in the alluvium. This indicates that at least part of the thrust system is coactive with the strike-slip strands that intersect it and implies that such intersections do not require either fault system to be extinct. However, it is crucial to obtain a minimum age in order to constrain the recent rupture history. This is inherently difficult because where the required onlapping relationships are present, scarps associated with the most recent event have been buried or eroded. A second site does occur several km from our original site, yet without knowing the exact location or depth of the fault an excavation would be risky. To increase the likelihood of finding the fault with an excavation, we employed geophysical exploration techniques to image the fault at depth. Ground Penetrating Radar (GPR) is a technique that can be used for shallow high-resolution imaging by recording the propagation of radio waves. To calibrate this technique to locating a shallow fault in the conditions of the study area, we returned to the site of our original excavation. We observed reflections from subhorizontal strata and the fault plane extending to a depth ~10 meters. This was identical to our initial trench observations. Using the same technique at our candidate minimum-age site, we resolved the exact location of a dipping fault plane covered by several meters of young alluvium. Now that the fault has been located, excavation of the site can be undertaken with a good chance of success. This result shows the value of GPR being used as an innovative predictive tool in paleoseismology. / Master of Science

With the publication of the famous Erdős-Ko-Rado Theorem in 1961, intersection problems became a popular area of combinatorics. A family of combinatorial objects is t-intersecting if any two of its elements mutually t-intersect, where the latter concept needs to be specified separately in each instance. This thesis is split into two parts; the first is concerned with intersecting injections while the second investigates intersecting posets. We classify maximum 1-intersecting families of injections from {1, ..., k} to {1, ..., n}, a generalisation of the corresponding result on permutations from the early 2000s. Moreover, we obtain classifications in the general t>1 case for different parameter limits: if n is large in terms of k and t, then the so-called fix-families, consisting of all injections which map some fixed set of t points to the same image points, are the only t-intersecting injection families of maximal size. By way of contrast, fixing the differences k-t and n-k while increasing k leads to optimal families which are equivalent to one of the so-called saturation families, consisting of all injections fixing at least r+t of the first 2r+t points, where r=|_ (k-t)/2 _|. Furthermore we demonstrate that, among injection families with t-intersecting and left-compressed fixed point sets, for some value of r the saturation family has maximal size . The concept that two posets intersect if they share a comparison is new. We begin by classifying maximum intersecting families in several isomorphism classes of posets which are linear, or almost linear. Then we study the union of the almost linear classes, and derive a bound for an intersecting family by adapting Katona's elegant cycle method to posets. The thesis ends with an investigation of the intersection structure of poset classes whose elements are close to the antichain. The overarching theme of this thesis is fixing versus saturation: we compare the sizes and structures of intersecting families obtained from these two distinct principles in the context of various classes of combinatorial objects.

nÃo hà / Modelos baseados em splats tÃm ganhado crescente atenÃÃo devido a seu potencial para renderizaÃÃes de modelos geomÃtricos complexos de forma eficiente e com alta qualidade. A ausÃncia de informaÃÃes de conectividade desses modelos permite operaÃÃes de modelagem complexas, como operaÃÃes booleanas, e fraturas em simulaÃÃes fÃsicas. Entretanto, essas operaÃÃes geralmente geram modelos com arestas e cantos que nÃo podem ser representados corretamente com um nÃmero finito de splats sem que um tratamento seja feito. Neste trabalho, um grafo de vizinhanÃa utiliza uma estimativa que garante a conexÃo de todos os splats presentes em lados opostos de uma descontinuidade e que precisam ser recortados uns contra os outros. ApÃs utilizar um mÃtodo de detecÃÃo de descontinuidades no grafo gerado, os vizinhos que participam do recorte de um splat, os clip partners, sÃo determinados e classificados para que recortem o splat de forma a adaptÃ-lo à curva da descontinuidade. Outro problema encontrado na renderizaÃÃo de modelos baseados em splats à reconstruÃÃo de superfÃcies intersectantes. Nas proximidades de interseÃÃes de superfÃcies, as superfÃcies sÃo misturadas, resultando em artefatos. Para tratar esses casos, um algoritmo de segmentaÃÃo realiza a separaÃÃo das diversas superfÃcies presentes no modelo, identificando os splats que as formam e impedindo que eles sejam combinados em Ãreas prÃximas de interseÃÃes de superfÃcies na etapa de reconstruÃÃo da superfÃcie em espaÃo de imagem / Splats based models have gained increasing attention due to its potential for rendering complex geometric models efficiently and with high quality. The absence connectivity information of these models allows complex modeling operations, as Boolean operations, and fractures in physics simulations. However, these operations often generate models with edges and corners that can not be represented correctly with a finite number of splats without a treatment to be done. In this work, a neighborhood graph uses an estimate which ensures the connection of all these splats on opposite sides a discontinuity and that need to be clipped against each other. After using a method for detecting discontinuities in the generated graph, the neighbors participating in the a splat clipping, clip partners are determined to cut out and sorted splat so as to adapt it to the curve of discontinuity. Another problem encountered in rendering models based on reconstruction of splats is intersecting surfaces. Close intersections of surfaces, the surfaces are mixed, resulting in artifacts. to treat these cases, a segmentation algorithm performs separation of the various surfaces present in the model, identifying the splats that form and hold them to be combined into areas near the intersections of surfaces in the surface reconstruction phase space image