Now showing items 21-40 of 135

    • Stationary distribution for spinning reflecting diffusions 

      Duarte Espinoza, Mauricio Andres (2012-09-13)
      This dissertation studies two different types of interaction of diffusion processes with the boundary of a domain $DsubRR^n$, which is assumed to be bounded, and of class $C^2(RR^n)$. The first process that is studied is ...
    • Local cohomology at generic singularities of Schubert varieties in cominuscule flag varieties 

      Suryanarayan, Sweta (2012-09-13)
      We study the local cohomology of a Schubert variety in a co-minuscule flag variety at a generic singularity. Let $G$ be a reductive complex algebraic group with a Borel subgroup $B$, let $W$ be the Weyl group of $G$ with ...
    • An Inverse Source Problem in Radiative Transfer 

      Hubenthal, John Mark (2013-02-25)
      We consider the inverse source problem for the radiative transfer equation, under various assumptions on the scattering and absorption parameters, as well as on the accessible data. In such a setup, we measure the outgoing ...
    • Isolated Curves for Hyperelliptic Curve Cryptography 

      Wang, Wenhan (2013-02-25)
      We introduce the notion of isolated genus two curves. There is no known efficient algorithm to explicitly construct isogenies between two genus two curves with large conductor gap. Thus there is no known way of transporting ...
    • Smoothness of Loewner Slits 

      Wong, Chun Wai Carto (2013-02-25)
      In this dissertation, we show that the chordal Loewner differential equation with C^{beta} driving function generates a C^{beta + 1/2} slit for 1/2 < beta <= 2, except when beta = 3/2 the slit is only proved to be weakly C^{1,1}.
    • The Ornstein-Uhlenbeck Process In Neural Decision-Making: Mathematical Foundations And Simulations Suggesting The Adaptiveness Of Robustly Integrating Stochastic Neural Evidence 

      Wojnowicz, Michael Thomas (2013-02-25)
      This master's thesis reviews the concepts behind a stochastic process known as the Ornstein-Uhlenbeck Process, and then uses that process as a way to investigate neural decision making. In particular, MATLAB simulations ...
    • Finite-Difference Methods for the Wave Equation with Reduced Dispersion Errors 

      An, Yajun (2013-04-17)
      A new methodology was proposed in Finkelstein and Kastner (2007,2008) to derive finite-difference (FD) schemes in the joint time-space domain to reduce dispersion error. The key idea is that the true dispersion relation ...
    • A Geometric Perspective on First-Passage Competition 

      Blair-Stahn, Nathaniel Deveroux (2013-04-17)
      We study the macroscopic geometry of first-passage competition on the integer lattice <bold>Z</bold><super>d</super>, with a particular interest in describing the behavior when one species initially occupies the exterior ...
    • Polynomials in Multiview Geometry 

      Aholt, Christopher (2013-04-17)
      We study multiview geometry and some of its applications through the use of polynomials. A three-dimensional world point gives rise to n ≥ 2 two-dimensional projections in n given cameras. The object of focus in this ...
    • Deformations of Categories of Coherent Sheaves and Fourier-Mukai Transforms 

      Grigg, Nathan (2013-07-25)
      In modern algebraic geometry, an algebraic variety is often studied by way of its category of coherent sheaves or derived category. Recent work by Toda has shown that infinitesimal deformations of the category of coherent ...
    • The Radiative Transfer Equation in Photoacoustic Imaging 

      Patrolia, Lee (2013-07-25)
      Photoacoustic tomography is a rapidly developing medical imaging technique that combines optical and ultrasound imaging to exploit the high contrast and high resolution of the respective individual modalities. Mathematically, ...
    • Markov chain mixting time, card shuffling and spin systems dynamics 

      Ning, Weiyang (2013-07-25)
      The mixing time of a Markov chain describes how fast the Markov chain converges to its stationary distribution. In this thesis, we survey some of the knowledge and main tools available in this field by looking at examples. ...
    • Mathematical Aspects of Gerrymandering 

      Solbrig, Mary Katherine (2013-11-14)
      Every 10 years the United States performs a census, and this census determines how many members of congress will represent each state. Then begins an unfortunate battle, as cartographers manipulate the boundaries for ...
    • Thermoacoustic Tomography in Elastic Media 

      Tittelfitz, Justin Jeffrey (2013-11-14)
      We investigate the problem of recovering the initial displacement f for a solution u of a linear, isotropic, non-homogeneous elastic wave equation, given measurements of u on [0, T ] × boundary of Omega, where Omega in R3 ...
    • Estimating Norms of Matrix Functions using Numerical Ranges 

      Choi, Daeshik (2013-11-14)
      We study Crouzeix's conjecture: for any polynomial p and any square matrix A, the spectral norm of the matrix p(A) is at most double of the supremum norm of the polynomial p on the numerical range of the matrix A.
    • Hybrid Inverse Problems Arising from Acousto-Electric Coupling 

      Kocyigit, Ilker (2013-11-14)
      We study hybrid imaging techniques that aim to overcome the ill-posedness of the Electric Impedance Tomography using the acousto-electric coupling. For the isotropic case, we consider the problem of reconstructing the ...
    • Eigenvalue Fluctuations of Random Matrices beyond the Gaussian Universality Class 

      Paquette, Elliot (2013-11-14)
      The goal of this thesis is to develop one of the threads of what is known in random matrix theory as universality, which essentially is that a large class of matrices generalizing the Gaussian matrices (certain Wigner ...
    • Hybrid inverse problems 

      Chen, Jie (2013-11-14)
      Inverse problems arise in different disciplines including exploration geophysics, medical imaging and nondestructive evaluation. In some settings, a single modality displays either high contrast or high resolution but not ...
    • Hopf algebras of finite Gelfand-Kirillov dimension 

      Zhuang, Guangbin (2013-11-14)
      We study Hopf algebras of finite Gelfand-Kirillov dimension. By analyzing the free pointed Hopf algebra F(t), we show the existence of certain Hopf subalgebras of pointed Hopf domains H whose GK-dimension are finite and ...
    • Four Problems in Probability and Optimization 

      Pfeiffer, James (2014-02-24)
      This thesis studies bootstrap percolation, a problem in probability, as well as several topics in the application of sums of squares to combinatorial optimization. In the chapter on percolation, we bound the critical ...