A Metric for genus-zero surfaces

We present a new method to compare the shapes of genus-zero surfaces. We introduce a measure of mutual stretching, the symmetric distortion energy, and establish the existence of a conformal diffeomorphism between any two genus-zero surfaces that minimizes this energy. We then prove that the energies of the minimizing diffeomorphisms give a metric on the space of genus-zero Riemannian surfaces. This metric and the corresponding optimal diffeomorphisms are shown to have properties that are highly desirable for applications.Comment: 33 pages, 8 figure

How round is a protein? Exploring protein structures for globularity using conformal mapping.

We present a new algorithm that automatically computes a measure of the geometric difference between the surface of a protein and a round sphere. The algorithm takes as input two triangulated genus zero surfaces representing the protein and the round sphere, respectively, and constructs a discrete conformal map f between these surfaces. The conformal map is chosen to minimize a symmetric elastic energy E S (f) that measures the distance of f from an isometry. We illustrate our approach on a set of basic sample problems and then on a dataset of diverse protein structures. We show first that E S (f) is able to quantify the roundness of the Platonic solids and that for these surfaces it replicates well traditional measures of roundness such as the sphericity. We then demonstrate that the symmetric elastic energy E S (f) captures both global and local differences between two surfaces, showing that our method identifies the presence of protruding regions in protein structures and quantifies how these regions make the shape of a protein deviate from globularity. Based on these results, we show that E S (f) serves as a probe of the limits of the application of conformal mapping to parametrize protein shapes. We identify limitations of the method and discuss its extension to achieving automatic registration of protein structures based on their surface geometry

Pricing of Non-redundant Derivatives in a Complete Market

We consider a complete financial market with primitive assets and derivatives on these primitive assets. Nevertheless, the derivative assets are non-redundant in the market, in the sense that the market is complete, only with their existence. In such a framawork, we derive an equilibrium restriction on the admissible prices of derivatives assets. The equilibrium condition imposes a well-ordering principle equivalent martingale measures. This restriction is preference free and applies whenever the utility functions belong to the general class of Von-Neumann Morgenstern functions. We provide numerical examples that show the applicability of restriction for the computation of option pricespricing

Redrawing Winnipeg's municipal boundaries 1991 : an inner city focus

iv, 13, [32] p. : maps

Estimating Ancestry and Genetic Diversity in Admixed Populations.

Admixture is a form of gene flow that occurs when long separated populations come into contact and exchange mates. Admixture has been a primary mechanism in the formation of many modern human populations. The genetic characteristics of an admixed population are intermediate to, yet distinct from, those of its ancestors. In this dissertation, I investigate biological and statistical factors that enter into the analysis of admixed populations using genetic marker data. In chapters one and two, I use genotype data from published sources that contain 618 microsatellite loci. In chapter three, I simulate genotypes of 500 microsatellite loci. In chapter two, I present an analysis of genetic diversity within and among 17 populations in the Americas that were formed by admixture among continental Indigenous Americans, Africans and Europeans. This is the first application of a new method to partition the genetic distance between pairs of populations into components related to ancestry and genetic drift. I show that the genetic relationships among the continental sources and genetic drift occurring after population formation strongly influence the genetic structure of these populations. In chapter three, I investigate a new strategy to find modern populations to serve as models for ancestors in admixture events that occurred in the past. This is a long-standing challenge to admixture studies. This chapter focuses on the Cape Coloured people of South Africa, a population that formed by mixture of indigenous Africans, Europeans, and Asians. I propose a series of models for their ancestry and use the Akaike Information Criterion to choose the best model. This method from information theory identifies a simple model that proposes only African and Asian ancestors. I interpret this result in terms of both the principle of parsimony and the evolutionary recent common ancestor of the human species. In chapter four, I use computer simulations to assess bias in ancestry fractions estimated by using maximum likelihood. These novel simulations were designed to produce data sets that mimic actual patterns of variation in human populations. I have found sampling strategies that produce reasonably unbiased results, despite the potential for maximum likelihood to produce biased estimates

Telehealth Assessment in the Elderly Using the 4Ms

The current 2019 novel coronavirus, or COVID-19, has presented new threats and challenges in healthcare, especially when attempting to conduct wellness exams amongst the most vulnerable. Older adults with underlying medical conditions are at great risk for exposure and infection of COVID-19. The Geriatric Workforce Enhancement Program (GWEP) grant was given to the University of North Dakota (UND) to create a geriatric telehealth team and implement a telehealth project, promoting the use of telehealth technologies amongst older adults utilizing the 4Ms (mentation, medication, mobility, and what matters). A modified wellness assessment tool was created and administered through telehealth technology to five older participants. A pre-survey questionnaire was given asking about previous telehealth use and comfort level with technology use. A post-survey questionnaire was given to evaluate the participant’s telehealth experience. Forty percent of the participants felt they received the same level-of-care using telehealth as if they had physically gone to their provider’s office. Overall, 80% of the five participants felt telehealth would be beneficial to them in the future and 80% would also use it again. The project was successful in promoting telehealth while keeping vulnerable participants safely in their homes, reducing their risk of exposure to COVID-19