More than half a century ago, Piaget concluded from an investigation of children’s representational thinking about the nature of space that the development of children’s representational thought is topological before it is Euclidean. This conclusion, commonly referred to as the “topological primacy thesis,” has essentially been rejected. By giving emphasis to the ideas that develop rather than the order in which they develop, this work set out to develop a new form of non-metric geometry from young children’s early and intuitive topological, or at least non-metric, ideas. I conducted an eighteen-week teaching experiment with two children, ages six and seven. I developed a new dynamic geometry environment called Configure that I used in tandem with clinical interviews in each of the episodes of the experiment to elicit these children’s non-metric conceptions and subsequently support their development. I found that these children developed significant and authentic forms of geometric reasoning. It is these findings, which I refer to as qualitative geometry, that have implications for the teaching of geometry and for research into students’ mathematical reasoning. / text

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The Richtmyer-Meshkov instability is studied in vertical shock tube experiment. The instability is initiated by the passage of an incident shock wave over an interface between two dissimilar gases. The interface is formed by opposed gas flows in which air and SF₆ enter the shock tube from the top and from the bottom of the shock tube driven section. The gases exit the test section through a series of small holes in the test section side walls, leaving behind a flat, diffuse membrane-free interface at that location. Random three-dimensional perturbations are imposed on the interface by oscillating the column of gases in the vertical direction, using two loud speakers mounted in the shock tube wall. The development of the turbulent mixing is observed as a result of the shock-interface interaction. The flow is visualized using planar Mie scattering in which the light from a laser sheet is scattered by smoke particles seeded in one of the experimental gases and image sequences are captured using high-speed CMOS cameras. The primary interest of the study is the determination of the growth rate of the turbulent mixing layer that develops after an impulsive acceleration of the perturbed interface between the two gases (air/SF₆) by a weak M=1.2 incident shock wave. Measurements of the mixing layer width following the initial shock interaction show a power law growth h ~ tᶿ similar to those observed in previous experiments and simulations with θ ~ 0.40. The experiments reveal that the growth rate of the mixing width significantly varies from one experiment to another. This is attributed to the influence of initial perturbations imposed on the interface. However, better consistency for the mixing layer growth rate is obtained from the mixing generated by the reflected shock wave. A novel approach that is based on mass and linear momentum conservation laws in the moving reference frame leads to a new definition of the spike and bubble mixing layer widths, which does not depend on the initial conditions.

Six primiparous Holstein cows were assigned to a half udder design (n=6) 40 days prior to parturition. Beginning at parturition, one udder half was milked once daily (24hr interval) and the other four times daily (6hr interval). Udder halves were biopsied at days 15, 60, 120, and 230 of lactation for mammary tissue to perform mitochondrial staining and apoptosis studies. Increasing the milking frequency from 1x to 4x elevated the 4x udder half milk yield at early (d1-45) (P<0.0001), mid (d46-150) (P<0.0001) and late (d151-230) (P<0.0001) lactation. Milk protein percent (P= 0.013), lactose percent (P=0.004) and SNF percent (P=0.006), were elevated in milk from 4x udder halves over milk from 1x udder halves. We did not detect an effect of increased milking frequency on milk fat percent (P=0.25); however, yield of all components was increased. Increased milking frequency also increased mitochondrial numbers in mammary cells from 4x udder half (P=0.002) compared to 1x. We did not detect an effect of increased milking frequency on mammary apoptosis percentage. We also did not detect a difference in the abundance of gene transcripts for SOCS1, SOCS2, SOCS3 and CIS in milk; but could find an increase in alpha-lactalbumin (P=0.04) and beta-casein (P=0.001) 4x udder half gene transcripts.

This dissertation consists of three essays in experimental economics. The essays investigate different aspects of reputation in fairness games in a controlled laboratory environment. It has been established in the literature of economics, sociology, and psychology that social norms together with other-regarding preferences often govern subjects' decisions in addition to strategic considerations. The dissertation examines the incentives connected with the existence of social norms that could cause deviations from standard economic model predictions. I use experiments so that I can tightly control the environment and provide rigorous tests of existing theories, stylized facts, and anecdotal evidence on the importance of reputation in economic interactions. The first essay presents findings that reputation triggers indirectly reciprocal behavior of subjects. However, reputation might only be signaling what is considered as socially appropriate behavior. This hypothesis and the results of the first essay led me to develop a set of experiments in the second essay to contrast pure reputation effects with the social influence of reputation. The third part of the dissertation, co-authored with Ninghua Du, examines reputation and efficiency wages in a labor market setting by analyzing the effects of negative technological shocks on long run relationships between firms and workers.

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To manage underused urban grassy spaces like transmission lines as tall-grass prairie habitats or other endangered ecosystems, ecologists need to know how mowing, spraying and surrounding urban lands affect species richness and numbers of plants and animals along transmission lines. I conducted surveys along 48 transmission lines in Winnipeg, Manitoba in 2007-2009 to answer these questions, and I concluded that mowing and spraying should be reduced, but not eliminated, to increase butterflies and other arthropods, resources for butterflies and other arthropods, and arthropod prey for birds. However, the amount of nearby urban land reduced plant species richness and grassland bird abundance along lines more strongly than mowing or spraying, suggesting that lines with less nearby urban land should be selected for management as grassland bird habitats. Mowing and spraying can then be reduced along these lines to benefit other species, enabling urban lands like transmission lines to contribute to conservation.

Passive dynamic walking is a manner of walking developed, partially or in whole, by the energy provided by gravity. Studying passive dynamic walking provides insight into human walking and is an invaluable tool for designing energy efficient biped robots. The objective of this research was to develop a new mathematical model of passive dynamic walking that modeled the ground reaction forces. A physical passive walker was built to validate the proposed mathematical model. The stability of the gait was analyzed using the proposed model. A novel method was created to determine the stability region of the model. Using the insights gained from the stability analysis, the relation between the angular momentum and the stability of the gait was examined. The proposed model matched the gait of the physical passive walker exceptionally well, both in trend and magnitude. The angular momentum of the passive walker was not found to correlate to the stability of the gait.

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When light energy input exceeds the capacity for photosynthesis the plant need to dissipate the excess energy and this is done through non-photo-chemical quenching (NPQ). Photochemical quenching (photosynthesis), NPQ and fluorescence are three alternative faiths of excited chlorophylls. PsbS associates to photosystem II and is involved in NPQ. The results presented in this thesis were generated on Arabidopsis plants and mainly based on wildtype Col-0 together with a mutant deficient in PsbS (npq4) and a transgene overexpressing PsbS (oePsbS). We connect light and herbivore stress and show that the level of PsbS influences the food preference of both a specialist (Plutella) and a generalist (Spodoptera) herbivore as well as oviposition of Plutella. Level of PsbS also affects both metabolomics and transcriptomics of the plant; up-regulation of genes in the jasmonic acid (JA) -pathway and amount of JA has been found in the npq4 plants after herbivory. Since many experiments were performed in field we have also characterized the field plant and how it differs from the commonly used lab plant. We have also studied the natural variation of NPQ in Arabidopsis plants both in the field and the lab. The results show surprisingly no correlation. / Överskottsenergi kan vara skadligt för en växts membran och fotosynteskomplex. Vid överskott av solenergi blir fotosystemen mättade och växten behöver därför ett sätt för att göra sig av med all överskottsenergi, detta kallas för ”icke-fotokemisk quenching” (NPQ). Fotokemisk quenching (fotosyntes), NPQ och fluoresens är tre alternativa vägar för exalterade klorofyller. PsbS är involverad i NPQ och associerar med fotosystem II. De resultat som presenteras i denna avhandling kommer från studier av modellväxten Arabidopsis thaliana (Backtrav), i huvudsak gjorda på vildtypen i jämförelse med en mutant som saknar PsbS (npq4) och en transgen som överuttrycker PsbS (oePsbS). Vi har försökt att undersöka kopplingen mellan ljus- och herbivoristress och visar här att mängden PsbS påverkar både en specialist (Plutella) och en generalist (Spodoptera) insekt vid val av föda, samt Plutella även vid äggläggning. Växternas nivå av PsbS visade sig även påverka metabolomet och transkriptomet, och vi fann en uppreglering av gener i biosyntesen för jasmonat samt mer av själva hormonet jasmonat i npq4 växter efter herbivori. Eftersom vi har gjort många av experimenten ute i fält har vi även karakteriserat en typisk Arabidopsis växt i fält samt hur denna skiljer sig från den vanligt använda lab-växten. Dessutom har vi även undersökt naturlig variation av NPQ av Arabidopsis både i fält och på lab och resultaten visar, till vår förvåning, att det inte går att finna någon korrelation mellan dessa.