Browsing by Duke Department "Mathematics"

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  • Hultgren, Nils (2011-05-20)
    The purpose of this paper is to investigate methods for analyzing networks from an algebraic perspective. The main focus will be on the dominant eigenpair of the adjacency matrix representing a graph, as many different ...
  • Chongchitmate, Wutichai (2010-05-04)
    We write a program in Java to generate all grid diagrams of up to size 10. Using equivalence between grid diagrams modulo a set of Cromwell moves and classification of Legendrian links up to Legendrian isotopy, together ...
  • Haftel, Jared (2009-05-04)
    In the past thirty years, academia and the marketplace have devoted signi cant e ort and resources toward gaining a better understanding of how volatility changes over time in the nancial markets and how changes in one ...
  • Lan, Kathleen (2014-01-11)
    Fix a discrete-time Markov chain $(V,P)$ with finite state space $V$ and transition matrix $P$. Let $(V_n,P_n)$ be the Markov chain on n-blocks induced by $(V,P)$, which we call the n-block process associated with the base ...
  • Gratton, Michael B. (2008-04-15)
    Observed in many physical systems, coarsening is an orderly decrease in the number of localized structures, such as particles, drops, shear bands, solitons, or point defects. Coarsening is a type of pattern formation in ...
  • Narkawicz, Anthony Joseph (2007-12-12)
    Two standard invariants used to study the fundamental group of the complement X of a hyperplane arrangement are the Malcev completion of its fundamental group G and the cohomology groups of X with coefficients in rank one ...
  • Thielman, Daniel Wilson (2012-04-25)
    This work pertains to chemical reaction networks and their equilibria, called steady-states. Our main result states that for a cyclic chemical reaction net- work, there is a straightforward characterization for when a ...
  • Wertheim, Alexander (2014-12-24)
    We describe the theory of complex multiplication on elliptic curves as it pertains to constructing abelian extensions of imaginary quadratic fields. We also briefly explore how one may construct abelian extensions of real ...
  • Schulhof, James; Moore, Matthew (2009)
    During periods of market dislocation, which can be characterized by high asset volatility, correlations between assets generally tend to increase. However, there has been little research on the behavior of correlations ...
  • Miller, Ryan Theodore (2009)
    The purpose of this paper is to discover the determinants of Congressional voting in the House on the two different versions the Emergency Economic Stabilization Act of 2008, and to determine what caused Congressmen to ...
  • Wang, Kangkang (2015)
    <p>We apply the definition of determinant in the compactified moduli space as a generalization of the discriminant. We study the relationship between the wall monodromy and the determinant in the GIT wall crossing. The ...
  • Balachandran, Prakash (2011)
    <p>Machine learning is a powerful branch of mathematics and statistics that allows the automation of tasks that would otherwise require humans a long time to perform. Two particular fields of machine learning that have ...
  • Tormey, Griffin T. (2009)
    Over the last decade, the number of underclassmen selected in the first round of the NBA Draft has dramatically increased. Even when controlling for performance in college, underclassmen are paid significantly more than ...
  • Smith, Allison (2009)
    The effect of public transportation on commuters’ sensitivity to gas prices is examined using a proxy for the quality of public transportation. This proxy is measured as the difference in the individual’s predicted commute ...
  • Johnson, Matt (2009-04-15)
    The impact of medical malpractice reforms on the cost and quality of health care is of great interest to policy makers. This study examines national data on malpractice reforms implemented and health care provided to ...
  • McKenzie, Scott (2009-04)
    People like to think of themselves as more honest than the person sitting next to them. In practice, this cannot always be the case. Through two experiments, we investigated behavior in golf—a sport of self-governance, ...
  • Sgouralis, Ioannis (2014)
    <p>The main functions of the kidney take place in the nephrons. For their proper operation, nephrons need to be supplied with a stable blood flow that remains constant despite fluctuations of arterial pressure. Such stability ...
  • Jenista, Michael Joseph (2010)
    <p>Switching networks are a common model for biological systems, especially</p><p>for genetic transcription networks. Stuart Kaufman originally proposed</p><p>the usefulness of the Boolean framework, but much of the ...
  • Jiang, Xiaoyu (2015-04-22)
    Human Papilloma Virus (HPV) is a widespread sexually transmitted disease which can lead to cervical cancer. Understanding the factors influencing HPV transmission has been a challenge for scientists and policy makers. We ...
  • Nisonoff, Hunter (2015-05-07)
    By computational protein design we mean the use of computer algorithms to design new proteins or redesign existing ones. A significant challenge in this field involves computing the partition function of the ensemble of ...