Browsing Mathematics by Title
Now showing items 89-108 of 188
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Lam-Williams Markov chains on symmetric groups
(2014-02-24)This paper reviews the current state of the Lam-Williams conjectures on a multivariate Markov chain on the symmetric group S_n. We start with Lam's work on random core partitions which led to a remarkable Markov chain on ... -
Local and Global Convergence for Convex-Composite Optimization
Convex-composite optimization seeks to minimize f(x):=h(c(x)) over x in R^n, where h is closed, proper, and convex, and c is smooth. Such problems include nonlinear programming, mini-max optimization, estimation of nonlinear ... -
Local cohomology at generic singularities of Schubert varieties in cominuscule flag varieties
(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 ... -
Local Set Approximation: Infinitesimal to Local Theorems for Sets in Euclidean Space and Applications
In this thesis we develop the theory of Local Set Approximation (LSA), a framework which arises naturally from the study of sets with singularities. That is, we describe the local structure of a set A in Euclidean space ... -
Major Index Statistics: Cyclic Sieving, Branching Rules, and Asymptotics
Major index statistics have been studied for over a century in many guises and appear throughout algebraic combinatorics. We pursue major index statistics from two complementary perspectives: algebraic and asymptotic. We ... -
Markov chain mixting time, card shuffling and spin systems dynamics
(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. ... -
Markov partitions for hyperbolic toral automorphisms
(1992)The study of the dynamical properties of hyperbolic toral automorphisms is simplified when the automorphisms are represented as shifts of finite type. The conventional method used to represent such an automorphism symbolically ... -
Mathematical Aspects of Gerrymandering
(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 ... -
Matrix free methods for large scale optimization
Sequential quadratic optimization (SQP) methods are widely used to solve large-scale nonlinear optimization problems. We build two matrix-free methods for approximately solving exact penalty subproblems that arise when ... -
Minkowski-type Estimates on the Quantitative Strata of the Generalized Critical set of Green's functions for Two-Sided NTA Domains arising from a Free-Boundary Problem for Harmonic Measure
In this work, we prove three things. The main results are two different results on Minkowski-type estimates on the quantitative strata of the generalized critical set of Green's functions of 2-Sided NTA domains arising ... -
Morphisms, Minors, and Minimal Obstructions to Convexity of Neural Codes
We study open and closed convex codes from a geometric and combinatorial point of view. We prove constructive geometric results that establish new upper bounds on the open and closed embedding dimensions of intersection ... -
Non-interior path-following methods for complementarity problems
(1998)Because of its excellent numerical performance, non-interior path following methods (also called smoothing methods) have become an important class of methods for solving complementarity problems. However, no rate of ... -
Non-local operators, jump diffusions and Feynman-Kac tranforms
Non-local operators are analytically defined by integrals over the whole space, hence hard to study certain properties. This thesis studies inverse local times at $0$ of one-dimensional reflected diffusions on $[0, ... -
The nonexistence of certain free pro-p extensions and capitulation in a family of dihedral extensions of Q
(1996)$\doubz\sbsp{p}{d}$-extensions are a natural way to extend Iwasawa's theory of $\doubz\sb{p}$-extensions. A further extension would be to look at free pro-p extensions which though nonabelian, can be studied by looking at ... -
Nonholonomic Euler-Poincaré equations and stability in Chaplygin's sphere
(2000)A method of reducing several classes of nonholonomic mechanical systems that are defined on semidirect products of Lie groups is developed. The method reduces the Lagrange-d'Alembert principle to obtain a reduced constrained ... -
Nonlinear PDEs: regularity, rigidity, and an inverse problem
Based on joint work with Arunima Bhattacharya, we obtain a sharp regularity result for Lagrangian mean curvature type equations with possibly H\"older continuous Lagrangian phases. Along the way, the constant rank theorem ... -
Novel uses of the Mallows model in coloring and matching
A natural model of a highly ordered random ranking is the Mallows model. Disorder is measured by the number of inversions; these are pairs of elements whose order is reversed. The Mallows model assigns to each ranking of ... -
On an inverse problem for fractional connection Laplacians
Classical inverse problems seek to determine the unknown coefficients of a PDE from boundary or local measurements of solutions. In the past few years, there has been a sharp increase in attention paid to inverse problems ... -
On Computing the Tate Shafarevich group order and type of some rational elliptic curves of conductor less than a million.
In this dissertation, I will present the tabulation of the Tate Shafarevich group order and type of around 4.5 million rational elliptic curves of conductor less than a million. These curves were obtained from the database ... -
On Cross Sections to the Horocycle and Geodesic Flows on Quotients by Hecke Triangle Groups
The study of continuous dynamical systems via surfaces of section is one of the standard techniques in nonlinear mathematics. This is done by considering the intersections of trajectories in a phase space with a subspace ...