Stable matchings were introduced in 1962 by David Gale and Lloyd Shapley to study the college admissions problem. The seminal work of Gale and Shapley has motivated hundreds of research papers and found applications in many areas of mathematics, computer science, economics, and even medicine. This thesis studies stable matchings in graphs and hypergraphs. We begin by introducing the work of Gale and Shapley. Their main contribution was the proof that every bipartite graph has a stable matching. Our discussion revolves around the Gale-Shapley algorithm and highlights some of the interesting properties of stable matchings in bipartite graphs. We then progress to non-bipartite graphs. Contrary to bipartite graphs, we may not be able to find a stable matching in a non-bipartite graph. Some of the work of Irving will be surveyed, including his extension of the Gale-Shapley algorithm. Irving's algorithm shows that many of the properties of bipartite stable matchings remain when the general case is examined. In 1991, Tan showed how to extend the fundamental theorem of Gale and Shapley to non-bipartite graphs. He proved that every graph contains a set of edges that is very similar to a stable matching. In the process, he found a characterization of graphs with stable matchings based on a modification of Irving's algorithm. Aharoni and Fleiner gave a non-constructive proof of Tan's Theorem in 2003. Their proof relies on a powerful topological result, due to Scarf in 1965. In fact, their result extends beyond graphs and shows that every hypergraph has a fractional stable matching. We show how their work provides new and simpler proofs to several of Tan's results. We then consider fractional stable matchings from a linear programming perspective. Vande Vate obtained the first formulation for complete bipartite graphs in 1989. Further, he showed that the extreme points of the solution set exactly correspond to stable matchings. Roth, Rothblum, and Vande Vate extended Vande Vate's work to arbitrary bipartite graphs. Abeledo and Rothblum further noticed that this new formulation can model fractional stable matchings in non-bipartite graphs in 1994. Remarkably, these formulations yield analogous results to those obtained from Gale-Shapley's and Irving's algorithms. Without the presence of an algorithm, the properties are obtained through clever applications of duality and complementary slackness. We will also discuss stable matchings in hypergraphs. However, the desirable properties that are present in graphs no longer hold. To rectify this problem, we introduce a new ``majority" stable matchings for 3-uniform hypergraphs and show that, under this stronger definition, many properties extend beyond graphs. Once again, the linear programming tools of duality and complementary slackness are invaluable to our analysis. We will conclude with a discussion of two open problems relating to stable matchings in 3-uniform hypergraphs.

As a result of the legacy of industrial contamination over the last century, areas of sediment deposition in the St. Lawrence River at Cornwall, ON, contain high concentrations of mercury (Hg). The popular sport-fish species, yellow perch (Perca flavescens) and walleye (Sander vitreus) have been found to contain mercury concentrations exceeding Ontario Ministry of Environment consumption guidelines. Interestingly, a paradox exists between two contaminated sites – despite elevated sediment Hg concentrations at Zone 2, fish from Zone 1 contain higher Hg concentrations. Further research has indicated that these patterns of Hg were not attributed to growth rate, condition factor, diet composition, or trophic position of yellow perch. Rather, Hg concentrations in yellow perch may be described by the heterogeneity of prey contamination and fish bioenergetics. As a result of the paradox between total Hg (THg) concentrations in sediments and biota between two contaminated sites, it was necessary to examine the benthic invertebrate community and how it may transfer Hg from sediments to yellow perch. This apparent paradox now extends to all prey items, since prey items from the stomach contents of yellow perch caught in Zone 1 were significantly more contaminated than those of Zone 2. Use of δ15N and δ13C, measures of trophic position and energy source, respectively, indicated that prey selection, but not food chain length, may also be an important factor in explaining the variation in Hg burdens in yellow perch. Small-scale patterns of biomagnification, as shown by a comparison of δ15N and logTHg, indicated that the rates of biomagnification were similar among zones, but the amount of THg present at the base of the food web was twice as high at Zone 1 as at other contaminated sites. Overall, the relative importance of vertical and horizontal food web structure changed spatially and temporally, highly influencing THg concentrations of prey items and yellow perch. / Thesis (Master, Biology) -- Queen's University, 2007-08-02 08:02:40.26

Thesis (Ph.D. (Zoology & Entomology)) - Rhodes University, 2008.

There are broad differences in regional oceanography and primary production around the South African coast, which we might expect to give rise to major differences in trophic pathways. δ⁻¹³C and δ⁻¹⁵N isotopic ratios of suspended particulate matter (SPM), mussels, various intertidal consumers and common macroalgae along the South African coastline were explored using stable isotope analysis to investigate biogeographic and temporal variability of isotopic signatures of marine intertidal consumers and their food sources around the coast of South Africa, with a focus on evaluating the dependence of intertidal mussels on phytoplankton and macroalgal-derived organic carbon. Isotopic equilibration rates of four mussel tissues were determined through laboratory feeding experiments, which established that adductor tissue had the slowest isotopic turnover rate, and was subsequently used as an indication of overall mussel diet. Biogeographic, temporal and nearshore/offshore trends of isotopic ratios of SPM were investigated along 10km transects perpendicular to the coast and SPM exhibited overall trends of carbon depletion when moving from west to east along the coastline and from nearshore to offshore water, in both cases suggesting a shift from macrophyte detritus to a phytoplankton signature. δ⁻¹³C signatures of SPM also revealed temporal and biogeographic variation that had strong ties to local oceanography, being closely correlated to regional hydrographic features and tidal influences. Mixing models indicated filter feeders demonstrated over 50% dependence on nearshore SPM for organic carbon and it was possible to categorize them into geographic groups based on their carbon and nitrogen signatures, suggesting biogeographic shifts in resources. Biogeographic shifts in diet were also seen in some grazers. Difficulties in relating macroalgae to mussel diet led to investigations into the isotopic changes associated with macroalgal decomposition. Variation in photosynthetic fractionation, leaching and microbial mineralization are believed to have resulted from species-specific patterns of degradation. Although the strong links between carbon signatures and local oceanography indicate that stable isotope analysis is a powerful tool for the study of water mixing and coastal hydrography in relation to food-web analyses, substantial variation in fractionation of primary consumers, along with different periods of time integration between consumers and their food sources must be considered in future studies, to resolve trophic links in marine food webs successfully.

Soient k un corps algébriquement clos de caractéristique p > 0 et C/k une courbe projective, lisse, intègre de genre g > 1 munie d’un p-groupe d’automorphismes G tel que |G| > 2p/(p-1)g. Le couple (C,G) est appelé grosse action. Si (C,G) est une grosse action, alors |G| <=4p/(p-1)^2g^2 (*). Dans cette thèse, nous étudions les répercussions arithmétiques des propriétés géométriques de grosses actions. Nous étudions d’abord l’arithmétique de l’extension de monodromie sauvage maximale de courbes sur un corps local K d’inégale caractéristique p à corps résiduel algébriquement clos, de genre arbitrairement grand ayant pour potentielle bonne réduction une grosse action satisfaisant le cas d’égalité de (*). On étudie en particulier les conducteurs de Swan attachés à ces courbes. Nous donnons ensuite les premiers exemples, à notre connaissance, de grosses actions (C,G) telles que le groupe dérivé D(G) soit non abélien. Ces courbes sont obtenues comme revêtements de S-corps de classes de rayons de P1(Fq) pour S non vide un sous-ensemble fini de P1(Fq). Enfin, on donne une méthode de calcul des S-corps de classes de Hilbert de revêtements abéliens de la droite projective d’exposant p et supersinguliers que l’on illustre pour des courbes de Deligne-Lusztig. / Let k be an algebraically closed field of characteristic p > 0 and C/k be a projective,smooth, integral curve of genus g > 1 endowed with a p-group of automorphisms G such that |G| > 2p/(p-1)g. The pair (C,G) is called big action. If (C,G) is a big action, then |G|<=4p/(p-1)^2g^2 (*). In this thesis, one studies arithmetical repercussions of geometric properties of big actions. One studies the arithmetic of the maximal wild monodromy extension of curves over a local field K of mixed characteristic p with algebraically closed residue field, with arbitrarily high genus having for potential good reduction a big action achieving equality in (*). One studies the associated Swan conductors. Then, one gives the first examples, to our knowledge, of big actions (C,G) with non abelian derived group D(G). These curves are obtained as coverings of S-ray class fields of P1(Fq) where S is a finite non empty subset of P1(Fq). Finally, one describes a method to compute S-Hilbert class fields of supersingular abelian covers of the projective line having exponent p and one illustrates it for some Deligne-Lusztig curves.

Stable isotope analysis is a powerful tool that can be used to describe a population’s foraging niche by identifying basal resource use, trophic feeding levels, environmental stability, seasonal ecological variation, important shifts in life history, ontogenetic shifts, intraspecific habitat use, and population dynamics. Describing these relationships in endangered marine turtle populations and their critical foraging grounds is essential for determining informed management decisions. This study systematically describes the foraging niche of hawksbills Eretmochelys imbricata, and green turtles, Chelonia mydas in Buck Island Reef National Monument, U.S. Virgin Islands, a critical habitat for nesting and foraging. It assesses the relationships within and between the species in terms of overlap, annual and seasonal variation, and life history and feeding strategies within the community. Most importantly it describes these relationships with metrics that can be used in global comparisons or to measure change in local conditions. / Includes bibliography. / Thesis (M.S.)--Florida Atlantic University, 2020. / FAU Electronic Theses and Dissertations Collection

I höstas undersökte min studiegrupp tätorten Mölnbo som ligger 10 minuter med bil söder om Södertälje stad. Vi utvecklade en strategi som byggde på att flertalet omkring liggande tätorter kunde stärka varandra, i hopp om en starkare, mer sammansvetsad landsbygd. Vi föreslog nya friluftsspår som skulle länka samman dessa orter, med sevärdheter på vägen där målet var att lyfta fram det befintliga, istället för att ersätta det med nytt. Vår ambition var att göra friluftslivet lika och tillgängligt för alla, med hänsyn till de globala målen jämställdhet (5) och minskad ojämlikhet (10). I detta projekt har syftet varit att finna en plats som kan rymma Folkets Hus +. Genom höstens analys har jag funnit behovet av en verksamhet som kan attrahera och inkludera en mångfald av människor. Mölnbo har goda möjligheter att erbjuda denna plats med stor tillgång till öppen mark samt bra kommunikationer, tack vare sin pendeltågsstation. Hästsporten är en på många sätt segregerad sport som i dagsläget inte är tillgänglig för alla. För att ett barn eller ungdom ska involveras krävs ofta resursstarka och kunniga föräldrar. För människor med funktionsvariationer är kontakten med hästar och stallmiljö ofta begränsad. Jag vill i detta projekt skapa en holistisk häst- och djurverksamhet där fler kan vara delaktiga. Verksamheten  kommer även eftersträva ekologisk hållbarhet med ett cirkulärt tänk. I designprocessen har stråket fått en central roll utifrån analysen i höstas där gång-, cykel- och vandringsstigen lyftes fram. I detta projekt dominerar gångstråket och ridstigen, vilket gestaltas genom att de tillåts separera och penetrera byggnadskropparna. På platsen samsas människor och djur om utrymmet och min ambition är att sudda ut hierarkierna däremellan. Jag vill genom min design skapa nya typologier för mötet mellan djur och människa. Därför beter sig inte mitt projekt som en klassisk ridanläggning, som en uppmaning att hitta nya och mer tillgängliga sätt för människa och djur att mötas. / My group in the previous course explored the urban area of ​​Mölnbo, which is located 10 minutes by car southof the city of Södertälje. We developed a strategy that was based on making the small rural villages and urban areas nearby Mölnbo strengthen each other, in the hope of a stronger, more cohesive countryside. We proposed new outdoor trails that would link these places together, with sights along the trail where the goal was to highlight the existing, instead of replacing it with new. Our ambition was to make outdoor life equal and accessible to all, taking into account the global goals of gender equality (5) and reducing inequality (10). In this project, the aim has been to find a place that can accommodate Folkets Hus + which was this years theme for the candidate project. Through this autumn's analysis, I have found the need for a place that can attract and include a diversity of people. Mölnbo has good opportunities to offer this place with great access to open land and good communications, thanks to its commuter train station. Equestrian sport is in many ways a segregated sport in Sweden that is currently not available to everyone. In order for a child or young person to be involved resourceful and knowledgeable parents are often required. For people with different disabilities, contact with horses and stable environment is often limited. In this project, I want to create a Folkets Hus + where more people can participate and find ways to holistically associate with horses and other animals.  In the design process, the path has been given a central role based on the analysis in the autumn, where the walking, cycling and hiking path was highlighted. In this project, the walkway and the riding path dominate, which is shaped by allowing them to separate and penetrate the building bodies. At the site, people and animals share the space and my ambition is to erase the hierarchies between them. Through my design, I want to create new typologies for the meeting between animals and humans. Therefore, my project does not behave like a classic equestrian facility, as a call to find new and more accessible ways for humans and animals to meet.

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No description available.

It is believed that in the long time limit, the limiting behavior of the discrete-time quantum random walk will cross from quantum to classical if we take into account of the decoherence. The computer simulation has already shown that for the discrete-time one-dimensional Hadamard quantum random walk with coin decoherence such that the measurement operators on the coin space are defined by A0 = Ic √1 − p, A1 = |R > < R| √p and A2 = |L > < L > < L| √p is diffusive when 0 < p ≤ 1 and it is ballistic when P = 0. In this thesis, we are going to let p to be dynamical depending on the step t, that is, we consider p = 1/tß, ß ≥ 0 and we found that it has sub-ballistic behavior for 0 < ß < 1. Furthermore, we study not only the coin decoherence, but the total decoherence, that means the measurement operators apply on the Hilbert space H = Hp ⊗ Hc instead of the coin space only. We find that the results are both sub-ballistic for the coin and total decoherence when 0 < ß < 1. Moreover, according to the model given in [T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A 67, 032304 (2003)], we know that if the walker has chance to hop to the second nearest neighbor lattice in one step, the long-time behavior is also sub-ballistic and it is similar to that the walker can hop to the third nearest neighbor lattice in one step. By the way, we also find that if we combine the classical part of the model given in [Jing Zhao and Peiqing Tong. One-dimensional quantum walks subject to next nearest neighbor hopping decoherence, Nanjing Normal University, preprint (2014)] with different step length, then this decoherence will also cross from quantum to classical. Finally, we define the quantum γ-stable walk and obtain the quantum γ-stable law with decoherence. By this decoherence, we can see that the limiting behavior of the quantum stable walk will also cross from quantum to classical and we shows that it spreads out faster than the classical stable walk. / Mathematics