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<p>Isotropy representations provide powerful tools for understanding the classification of equivariant principal bundles over the $2$-sphere. We consider a $\Gamma$-equivariant principal $G$-bundle over $S^2$ with structural group $G$ a compact connected Lie group, and $\Gamma \subset SO(3)$ a finite group acting linearly on $S^2.$ Let $X$ be a topological space and $\Gamma$ be a group acting on $X.$ An isotropy subgroup is defined by $\Gamma_x = \{\gamma \in \Gamma \lvert \gamma x=x\}.$ Assume $X$ is a $\Gamma$-space and $A$ is the orbit space of $X$. Let $\varphi: A\rightarrow X$ be a continuous map with $\pi \circ \varphi = 1_A$. An isotropy groupoid is defined by $\mathfrak{I} = \{(\gamma,a) \in \Gamma\times A \lvert \ \gamma \in \Gamma_{\varphi(a)}\}.$ An isotropy representation of $\mathfrak{I}$ is a continuous map $\iota : \mathfrak{I} \rightarrow G$ such that the restriction map $\mathfrak{I}_a \rightarrow G$ is a group homomorphism. $\Gamma$- equivariant principal $G$-bundles are studied in two steps; \begin{enumerate} [1)] \item the restriction of an equivariant bundle to the $\Gamma$ equivariant 1-skeleton $X \subset S^2$ where $\mathfrak{I}$ is isotropy representation of $X$ over singular set of the $\Gamma$-sets in $S^2$ \item the underlying $G$-bundle $\xi$ over $S^2$ determined by $c(\xi)\in \pi_2(BG).$ \end{enumerate}</p> / Master of Science (MSc)

Yes / Recent developments in optical coherence tomography (OCT) technology enable direct enface visualisation of retinal nerve fibre bundle (RNFB) loss in glaucoma. However, the optimum depth at which to visualise RNFBs across the retina is unknown. We aimed to evaluate the range of depths and optimum depth at which RNFBs can be visualised across the retina in healthy eyes. The central ± 25° retina of 10 healthy eyes from 10 people aged 57–75 years (median 68.5 years) were imaged with spectral domain OCT. Slab images of maximum axial resolution (4 μm) containing depth‐resolved attenuation coefficients were extracted from 0 to 193.5 μm below the inner limiting membrane (ILM). Bundle visibility within 10 regions of a superimposed grid was assessed subjectively by trained optometrists (n = 8), according to written instructions. Anterior and posterior limits of RNFB visibility and depth of best visibility were identified for each grid sector. Effects of retinal location and individual eye on RNFB visibility were explored using linear mixed modelling with likelihood ratio tests. Intraclass correlation coefficient (ICC) was used to measure overall agreement and repeatability of grading. Spearman’s correlation was used to measure correlation between depth range of visible RNFBs and retinal nerve fibre layer thickness (RNFLT). Retinal location and individual eye affected anterior limit of visibility (χ2(9) = 58.6 and 60.5, both p < 0.0001), but none of the differences exceeded instrument resolution, making anterior limit consistent across the retina and different eyes. Greater differences were observed in the posterior limit of visibility across retinal areas (χ2(9) = 1671.1, p < 0.0001) and different eyes (χ2(9) = 88.7, p < 0.0001). Optimal depth for visualisation of RNFBs was around 20 µm below the ILM in most regions. It varied slightly with retinal location (χ2(9) = 58.8, p < 0.0001), but it was not affected by individual eye (χ2(9) = 10.7, p = 0.29). RNFB visibility showed good agreement between graders (ICC 0.89, 95%CI 0.87–0.91), and excellent repeatability (ICC 0.96–0.99). Depth range of visible RNFBs was highly correlated with RNFLT (ρ = 0.9, 95%CI: 0.86–0.95). The range of depths with visible RNFBs varies markedly across the healthy retina, consistently with RNFLT. To extract all RNFB information consistently across the retina, slab properties should account for differences across retinal locations and between individual eyes. / This work was supported by a College of Optometrists Research Fellowship (JD).

The background of the thesis is the ongoing struggle for better understanding of driving forces for economic growth. Some important and rewarding new steps have been taken the last decades in the research of economic growth theory. For example, the theory includes not only the use of technology but also the creation and implementation of new technology entwined with management and learning practices at work. However, the development of knowledge on the matter can be described as slow. The explanation is argued to be the lack of data, which complicates and prevents the development of theory. The lack of data and the intertwined dependence with the development of theory in the matter constitutes the starting point for the research in the thesis. The purpose of this thesis is to contribute to the development of measures of management of work and learning practices at work that can be used in productivity models. The analyses are based on the micro-level data from the Swedish MEADOW Survey 2009/2010, at Statistics Sweden. Factor and regression analysis are performed, other analytical techniques are also used. Some key findings of how management and learning practices at work can be described and measured show that the business firms use the different practices in bundles. The findings indicate synergy effects on performance when more than one management and learning practice is applied. Two different management approaches are tested, both models predict productivity. However, there is a difference in the productivity model a such when it includes the two management approaches; the measure of the contemporary use has a better fitness then the theoretical model. Focus and delimitations of research questions in the forthcoming doctoral dissertation are discussed, see Future Research – the Logic Next Step, in Chapter 6. Final Reflections. / Bakgrunden till avhandlingen är den ständigt pågående kampen för bättre förståelse om drivkrafter för ekonomisk tillväxt. Några väsentliga steg har tagits de senaste decennierna inom forskningen om ekonomisk tillväxtteori. Exempelvis, idag innefattar teorin inte bara användningen av teknik utan också skapandet och genomförandet av ny teknik samt hur tekniken är förbunden med ledning och lärande i arbete. Kunskapsutvecklingen kan dock beskrivas som långsam. En förklaring och ett argument är bristen på data, vilket komplicerar och förhindrar utvecklingen av teorin. Bristen på data i den aktuella frågan och det sammanflätade beroendet med teoriutvecklingen är utgångspunkten för forskningen i avhandlingen. Syftet med avhandlingen är att bidra till utveckling av indikatorer om ledning av arbete och lärande i arbete som kan inkluderas i produktivitetsmodeller och som kan användas för att förstå ekonomisk tillväxt bättre. Uppgifterna som används i avhandlingen är mikronivådata (micro-level data) från Statistiska centralbyråns Swedish MEADOW Survey 2009/2010. Faktor- och regressionsanalys används, vissa andra analytiska tekniker används också. Några nyckelresultat om hur ledning och lärande i arbetet kan beskrivas och mätas visar att företagen använder de olika sätten i grupper av praxis ”bundles”. Resultaten visar synergieffekter på företagets prestationsförmåga när mer än en lednings- och inlärningspraxis tillämpas. Två olika sätt för hur att mäta ledning och lärande i arbete används, båda förutsäger produktivitet. Dock finns det en skillnad i produktivitetsmodellen mellan de två olika sättet att mäta: när faktisk användning mäts ger det högre förklaringsgrad än den teoretiska modellen. Inriktning och avgränsning av forskningsfrågor i den kommande planerade doktorsavhandlingen diskuteras, se Future Research – the Logic Next Step, i Chapter 6. Final Reflections. / <p>QC 20171128</p> / Statistics Sweden project: Organisation, growth and work environment (finished 2016)

Master of Science / Department of Mathematics / David Auckly / This report introduces the fiber bundles. It includes the definitions of fiber bundles such as vector bundles and principal bundles, with some interesting examples. Reduction of the structure groups, and covering homotopy theorem and some specific computation using obstruction classes, Cech cohomology, Stiefel-Whitney classes, and first Chern classes are included.

UNICEF and WWF are leading nonprofit organizations in their field. They work globally with different projects and programs, trying to make a change for the better. This study examines and discusses the communication strategies used by nonprofit organizations in their Facebook posts by answering following questions: What communication strategies can be identified in UNICEF and WWF's Facebook posts in their aim to attract followers? Are there any linguistic patterns associated with those strategies? Are there any differences/similarities between the two organizations? The method used is based on corpus linguistics and discourse analysis, categorizing messages into the categories Information, Community and Action. The results show that both organizations mainly produce messages that are information based. They use less of the Community building and Action strategies. Some linguistic patterns were found to be associated with these strategies. These patterns were mostly connected to the communication strategy of Information.

On sait que le nombre de racines réelles d’un polynôme à une variable de degré d et à coefficients réels est compris entre 0 et d. Au début des années 90, E. Kostlan prouve que le nombre moyen de racines vaut racine carrée de d, lorsque ces polynômes sont équipées d’une mesure de probabilité adéquate. Ce résultat possède une interprétation géométrique, où les polynômes apparaissent comme sections au-dessus de la sphère de Riemann, et ils peuvent s’étendre au cadre plus général de sections de fibrés en droites amples sur une surface de Riemann. Il s’agit ici du calcul de l’espérance mathématique du nombre de racines réelles de ces polynômes ou sections. Dans cette thèse, on calcule tous les moments centrés de ces variable aléatoires. Comme application de ce calcul, on prouve que la mesure de l’ensemble des polynômes ou sections dont le nombre de racines s’ écartent de la moyenne est majoré de façon effective en fonction de cet écart, un résultat de type concentration de la mesure en probabilité. Dans une deuxième partie, on présente des résultats analogue dans la théorie de Hurwitz réelle, où plutôt que du nombre de racines réelles d’un polynôme aléatoire, on considère le nombre de points critiques réels d’un revêtement ramifié aléatoire de la sphère de Riemann. On calcul la moyenne et tous les moments centrés du nombre de points critiques réels d'un revêtement aléatoire.Les techniques employées dans la preuve de ces résultats sont de nature analytique (noyau de Bergman, estimées L^2) et géométriques (multi-espaces d'Olver, formule de la coaire) / It is well known that the number of real roots of a real degree d polynomial is at most d. In the 90s, E. Kostlan proved that the average number of real roots equals the square root of d, once we equip the space of polynomials with some natural Gaussian measure. This result has a geometric interpretation, in which the real polynomials are sections of a line bundle over the Riemann sphere. We can extend this study in a more general case of a real Riemann surface equipped with ample line bundle and study the expected value of the number of real zeros of a random section. In this thesis, we compute all the central moments of these random variables. As an application, we prove that the measure of the space of real sections whose number of real zeros deviates from the expected one goes to zeros, as the degree of the line bundle goes to infinity.In a second part, we present analogues results in real Hurwitz theory, in which we study the real critical points of a random branched covering of the Riemann sphere. We compute the expected value of this number and also all the central moments.The techniques we use are of analytique nature (Bergman kernel, L^2 estimates) and gometric one (Olver multispaces, coarea formula)

In der vorliegenden Arbeit verallgemeinern wir im Wesentlichen zwei Theoreme von Mackaay-Picken und Picken (2002, 2004). Im ihrem Artikel zeigen Mackaay und Picken,dass es eine bijektive Korrespodenz zwischen Deligne 2-Klassen $xi in check{H}^2(M, mathcal{D}^2)$ und Holonomie Abbildungen von der zweiten dünnen Homotopiegruppe $pi_2^2(M)$ in die abelsche Gruppe $U(1)$ gibt. Im zweiten Artikel wird eine Verallgemeinerung dieses Theorems bewiesen: Picken zeigt, dass es eine Bijektion gibt zwischen Deligne 2-Kozykeln und gewissen 2-dimensionalen topologischen Quantenfeldtheorien. In dieser Arbeit zeigen wir, dass diese beiden Theoreme in allen Dimensionen gelten.Wir betrachten zunächst den Holonomie Fall und können mittels simplizialen Methoden nachweisen, dass die Gruppe der glatten Deligne $d$-Klassen isomorph ist zu der Gruppe der glatten Holonomie Abbildungen von der $d$-ten dünnen Homotopiegruppe $pi_d^d(M)$ nach $U(1)$, sofern $M$ eine $(d-1)$-zusammenhängende Mannigfaltigkeit ist. Wir vergleichen dieses Resultat mit einem Satz von Gajer (1999). Gajer zeigte, dass jede Deligne $d$-Klasse durch eine andere Klasse von Holonomie-Abbildungen rekonstruiert werden kann, die aber nicht nur Holonomien entlang von Sphären, sondern auch entlang von allgemeinen $d$-Mannigfaltigkeiten in $M$ enthält. Dieser Zugang benötigt dann aber nicht, dass $M$ hoch-zusammenhängend ist. Wir zeigen, dass im Falle von flachen Deligne $d$-Klassen unser Rekonstruktionstheorem sich von Gajers unterscheidet, sofern $M$ nicht als $(d-1)$, sondern nur als $(d-2)$-zusammenhängend angenommen wird. Stiefel Mannigfaltigkeiten besitzen genau diese Eigenschaft, und wendet man unser Theorem auf diese an und vergleicht das Resultat mit dem von Gajer, so zeigt sich, dass es zuviele Deligne Klassen rekonstruiert. Dies bedeutet, dass unser Rekonstruktionsthreorem ohne die Zusatzbedingungen an die Mannigfaltigkeit M nicht auskommt, d.h. unsere Rekonstruktion benötigt zwar weniger Informationen über die Holonomie entlang von d-dimensionalen Mannigfaltigkeiten, aber dafür muss M auch $(d-1)$-zusammenhängend angenommen werden. Wir zeigen dann, dass auch das zweite Theorem verallgemeinert werden kann: Indem wir das Konzept einer Picken topologischen Quantenfeldtheorie in beliebigen Dimensionen einführen, können wir nachweisen, dass jeder Deligne $d$-Kozykel eine solche $d$-dimensionale Feldtheorie mit zwei besonderen Eigenschaften, der dünnen Invarianz und der Glattheit, induziert. Wir beweisen, dass jede $d$-dimensionale topologische Quantenfeldtheorie nach Picken mit diesen zwei Eigenschaften auch eine Deligne $d$-Klasse definiert und prüfen nach, dass diese Konstruktion sowohl surjektiv als auch injektiv ist. Demzufolge sind beide Gruppen isomorph. / In this thesis we mainly generalize two theorems from Mackaay-Picken and Picken (2002, 2004). In the first paper, Mackaay and Picken show that there is a bijective correspondence between Deligne 2-classes $xi in check{H}^2(M,mathcal{D}^2)$ and holonomy maps from the second thin-homotopy group $pi_2^2(M)$ to $U(1)$. In the second one, a generalization of this theorem to manifolds with boundaries is given: Picken shows that there is a bijection between Deligne 2-cocycles and a certain variant of 2-dimensional topological quantum field theories. In this thesis we show that these two theorems hold in every dimension. We consider first the holonomy case, and by using simplicial methods we can prove that the group of smooth Deligne $d$-classes is isomorphic to the group of smooth holonomy maps from the $d^{th}$ thin-homotopy group $pi_d^d(M)$ to $U(1)$, if $M$ is $(d-1)$-connected. We contrast this with a result of Gajer (1999). Gajer showed that Deligne $d$-classes can be reconstructed by a different class of holonomy maps, which not only include holonomies along spheres, but also along general $d$-manifolds in $M$. This approach does not require the manifold $M$ to be $(d-1)$-connected. We show that in the case of flat Deligne $d$-classes, our result differs from Gajers, if $M$ is not $(d-1)$-connected, but only $(d-2)$-connected. Stiefel manifolds do have this property, and if one applies our theorem to these and compare the result with that of Gajers theorem, it is revealed that our theorem reconstructs too many Deligne classes. This means, that our reconstruction theorem cannot live without the extra assumption on the manifold $M$, that is our reconstruction needs less informations about the holonomy of $d$-manifolds in $M$ at the price of assuming $M$ to be $(d-1)$-connected. We continue to show, that also the second theorem can be generalized: By introducing the concept of Picken-type topological quantum field theory in arbitrary dimensions, we can show that every Deligne $d$-cocycle induces such a $d$-dimensional field theory with two special properties, namely thin-invariance and smoothness. We show that any $d$-dimensional topological quantum field theory with these two properties gives rise to a Deligne $d$-cocycle and verify that this construction is surjective and injective, that is both groups are isomorphic.

Experimental data on SuperCritical-Water (SCW) cooled bundles are very limited. Major problems with performing such experiments are: 1) small number of operating SCW experimental setups and 2) difficulties in testing and experimental costs at very high pressures, temperatures and heat fluxes. However, SuperCritical Water-cooled nuclear Reactor (SCWRs) designs cannot be finalized without such data. Therefore, as a preliminary approach experiments in SCW-cooled bare tubes and in bundles cooled with SC modeling fluids can be used. One of the SC modeling fluids typically used is Freon-12 (R-12) where the critical pressure is 4.136 MPa and the critical temperature is 111.97ºC. These conditions correspond to a critical pressure of 22.064 MPa and critical temperature of 373.95ºC in water. A set of experimental data obtained in a Freon-12 cooled vertical bare bundle at the Institute of Physics and Power Engineering (IPPE, Obninsk, Russia) was analyzed. This set consisted of 20 cases of a vertically oriented 7-element bundle installed in a hexagonal flow channel. To secure the bundle in the flow channel 3 thin spacers were used. The dataset was obtained at equivalent parameters of the proposed SCWR concepts. Data was collected at pressures of about 4.65 MPa for several different combinations of wall and bulk-fluid temperatures that were below, at, or above the pseudocritical temperature. Heat fluxes ranged from 9 kW/m2 to 120 kW/m2 and mass fluxes ranged from 440 kg/m2s to 1320 kg/m2s. Also inlet temperatures ranged from 70ºC – 120ºC. The test section consisted of fuel elements that were 9.5 mm in diameter with the total heated length of 1 m. Bulk-fluid and wall temperature profiles were recorded using a combination of 8 different thermocouples.The data was analyzed with respect to its temperature profile and heat transfer coefficient along the heated length of the test section. In a previous study it was confirmed that there is the existence of three distinct regimes for forced convention with supercritical fluids. (1) Normal heat transfer; (2) Deteriorated heat transfer, characterized by higher than expected temperatures; and (3) Improved heat transfer, characterized by lower than expected temperatures. All three regions were observed for the 7 rod bundle experiments. This work compares the experimental data to predictions based upon current 1-D correlations for heat transfer in supercritical fluids. Results show that no current 1-D correlation was able to accurately predict heat transfer coefficients within ±50%. A parametric analysis of the data was also completed to determine if continuity in the experiment was present. Results of this study show that two distinct regions are present in the data. For cases with a mass flux below 1200 kg/m2s wall temperature profiles appear to be normal while in cases with mass flux above 1200 kg/m2s temperature given by the wall thermocouples were higher than normal. This phenomenon occurred regardless of heat flux-to-mass flux ratios. / UOIT