Elimination For Systems Of Algebraic Differential Equations, 2017 The Graduate Center, City University of New York

#### Elimination For Systems Of Algebraic Differential Equations, Richard Gustavson

*All Graduate Works by Year: Dissertations, Theses, and Capstone Projects*

We develop new upper bounds for several effective differential elimination techniques for systems of algebraic ordinary and partial differential equations. Differential elimination, also known as decoupling, is the process of eliminating a fixed subset of unknown functions from a system of differential equations in order to obtain differential algebraic consequences of the original system that do not depend on that fixed subset of unknowns. A special case of differential elimination, which we study extensively, is the question of consistency, that is, if the given system of differential equations has a solution. We first look solely at the ``algebraic data" of ...

Testing The Consistency Of Nested Logit Models With Utility Maximization, 2017 Iowa State University

#### Testing The Consistency Of Nested Logit Models With Utility Maximization, Joseph A. Herriges, Catherine L. Kling

*Catherine Kling*

The Nested Multinomial Logit (NMNL) model is used extensively in modeling consumer choices among discrete alternatives when the number of alternatives is large. Unfortunately, applied researchers often find that estimated NMNL models fail to meet the Daly-ZacharyMcFadden (DZM) sufficient conditions for consistency with stochastic utility maximization. Borsch-Supan (1990) provides a relaxed set of conditions to test for consistency. While these conditions are increasingly cited, they are seldom tested. This paper corrects and extends BorschSupan's Theorem 2, providing simple necessary conditions on first, second, and third derivatives of choice probabilities and a graph oft he bounds they place on dissimilarity ...

Motion Planning For Educational Robots, 2017 Loyola University Chicago

#### Motion Planning For Educational Robots, Ronald I. Greenberg, Jeffery M. Karp

*Computer Science: Faculty Publications and Other Works*

This paper considers various simple ways of navigating in a 2-dimensional territory with a two-wheeled robot of a type typical in educational robotics. We determine shortest paths under various modes of operation and compare.

P26. Global Exponential Stabilization On So(3), 2017 sberkane@uwo.ca

#### P26. Global Exponential Stabilization On So(3), Soulaimane Berkane

*Western Research Forum*

Global Exponential Stabilization on SO(3)

Application Of Inverse Problems In Imaging, 2017 Linfield College

#### Application Of Inverse Problems In Imaging, Xiaoyue Luo

*Post-Grant Reports*

In this project, we studied how to enhance image quality by denoising and deblurring a given image mathematically. We compared some existing state-of-the-art methods for image denoising and deblurring. We implemented the algorithms numerically using Matlab.

We studied the possibility of combining statistical analysis with the traditional image restoration methods including using wavelets and framelets and we derived some encouraging preliminary results.

My research student Alleta Maier gave a sequence of talks on the project including the Pacific Northwest Mathematical Association of America conference at Oregon State University in April, 2016; Linfield College Taylor Series in March, 2016, and Linfield ...

When Cp(X) Is Domain Representable, 2017 University of Kansas

#### When Cp(X) Is Domain Representable, William Fleissner, Lynne Yengulalp

*Lynne Yengulalp*

Let M be a metrizable group. Let G be a dense subgroup of M^{X} . If G is domain representable, then G = MX . The following corollaries answer open questions. If X is completely regular and C_{p}(X) is domain representable, then X is discrete. If X is zero-dimensional, T_{2} , and C_{p}(X;D) is subcompact, then X is discrete.

Sphere Representations, Stacked Polytopes, And The Colin De Verdière Number Of A Graph, 2017 American Mathematical Society

#### Sphere Representations, Stacked Polytopes, And The Colin De Verdière Number Of A Graph, Lon Mitchell, Lynne Yengulalp

*Lynne Yengulalp*

We prove that a k-tree can be viewed as a subgraph of a special type of (k + 1)- tree that corresponds to a stacked polytope and that these “stacked” (k + 1)-trees admit representations by orthogonal spheres in R k+1. As a result, we derive lower bounds for Colin de Verdi`ere’s µ of complements of partial k-trees and prove that µ(G) + µ(G) > |G| − 2 for all chordal G.

Coarser Connected Topologies And Non-Normality Points, 2017 University of Dayton

#### Coarser Connected Topologies And Non-Normality Points, Lynne Yengulalp

*Lynne Yengulalp*

We investigate two topics, coarser connected topologies and non-normality points. The motivating question in the first topic is:

Question 0.0.1. When does a space have a coarser connected topology with a nice topological property? We will discuss some results when the property is Hausdorff and prove that if X is a non-compact metric space that has weight at least c, then it has a coarser connected metrizable topology. The second topic is concerned with the following question:

Question 0.0.2. When is a point *y* ∈ β X\X a non-normality point of β X\X? We will ...

Non-Normality Points Of Β X\X, 2017 University of Kansas

#### Non-Normality Points Of Β X\X, William Fleissner, Lynne Yengulalp

*Lynne Yengulalp*

We seek conditions implying that (β X\X) \ {y} is not normal. Our main theorem: Assume GCH and all uniform ultrafilters are regular. If X is a locally compact metrizable space without isolated points, then (β X\X) \ {y} is not normal for all y ∈ β X\X. In preparing to prove this theorem, we generalize the notions “uniform”, “regular”, and “good” from set ultrafilters to z-ultrafilters. We discuss non-normality points of the product of a discrete space and the real line. We topologically embed a nonstandard real line into the remainder of this product space.

A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, 2017 West Chester University of Pennsylvania

#### A Discontinuous Galerkin Method For Unsteady Two-Dimensional Convective Flows, Andreas C. Aristotelous, N. C. Papanicolaou

*Andreas Aristotelous*

We develop a High-Order Symmetric Interior Penalty (SIP) Discontinuous Galerkin (DG) Finite Element Method (FEM) to investigate two-dimensional in space natural convective flows in a vertical cavity. The physical problem is modeled by a coupled nonlinear system of partial differential equations and admits various solutions including stable and unstable modes in the form of traveling and/or standing waves, depending on the governing parameters. These flows are characterized by steep boundary and internal layers which evolve with time and can be well-resolved by high-order methods that also are adept to adaptive meshing. The standard no-slip boundary conditions which apply on ...

An Improved Convergence Analysis Of Cyclic Block Coordinate Descent-Type Methods For Strongly Convex Minimization, 2017 University of Minnesota - Twin Cities

#### An Improved Convergence Analysis Of Cyclic Block Coordinate Descent-Type Methods For Strongly Convex Minimization, Xingguo Li, Tuo Zhao, Raman Arora, Han Liu, Mingyi Hong

*Mingyi Hong*

The cyclic block coordinate descent-type (CBCD-type) methods have shown remarkable computational performance for solving strongly convex minimization problems. Typical applications include many popular statistical machine learning methods such as elastic-net regression, ridge penalized logistic regression, and sparse additive regression. Existing optimization literature has shown that the CBCD-type methods attain iteration complexity of O(p · log(1/e)), where e is a pre-specified accuracy of the objective value, and p is the number of blocks. However, such iteration complexity explicitly depends on p, and therefore is at least p times worse than those of gradient descent methods. To bridge this theoretical ...

Convergence Analysis Of Alternating Direction Method Of Multipliers For A Family Of Nonconvex Problems, 2017 Iowa State University

#### Convergence Analysis Of Alternating Direction Method Of Multipliers For A Family Of Nonconvex Problems, Mingyi Hong, Zhi-Quan Luo, Mesiam Razaviyayn

*Mingyi Hong*

The alternating direction method of multipliers (ADMM) is widely used to solve large-scale linearly constrained optimization problems, convex or nonconvex, in many engineering fields. However there is a general lack of theoretical understanding of the algorithm when the objective function is nonconvex. In this paper we analyze the convergence of the ADMM for solving certain nonconvex consensus and sharing problems. We show that the classical ADMM converges to the set of stationary solutions, provided that the penalty parameter in the augmented Lagrangian is chosen to be sufficiently large. For the sharing problems, we show that the ADMM is convergent regardless ...

Nestt: A Nonconvex Primal-Dual Splitting Method For Distributed And Stochastic Optimization, 2017 Iowa State University

#### Nestt: A Nonconvex Primal-Dual Splitting Method For Distributed And Stochastic Optimization, Davood Hajinezhad, Mingyi Hong, Tuo Zhao, Zhaoran Wang

*Mingyi Hong*

We study a stochastic and distributed algorithm for nonconvex problems whose objective consists a sum *N/* nonconvex *Li/N/ *smooth functions, plus a nonsmooth regularizer. The proposed NonconvEx primal-dual SpliTTing (NESTT) algorithm splits the problem into *N/ * subproblems, and utilizes an augmented Lagrangian based primal-dual scheme to solve it in a distributed and stochastic manner. With a special non-uniform sampling, a version of NESTT achieves *e-1* stationary solution using...gradient evaluations, which can be up to *O(N)/ * times better than the (proximal) gradient descent methods. It also achieves Q-linear convergence rate for nonconvex l1 penalized quadratic problems with polyhedral ...

The Subject Librarian Newsletter, Mathematics, Spring 2017, 2017 University of California, Irvine School of Law

#### The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

*Libraries' Newsletters*

No abstract provided.

Utilizing Social Network Analysis To Study Communities Of Women In Conflict Zones, 2017 United States Military Academy

#### Utilizing Social Network Analysis To Study Communities Of Women In Conflict Zones, James R. Gatewood, Candice R. Price

*Journal of Humanistic Mathematics*

This article proposes to study the plight of women in conflict zones through the lens of social network analysis. We endorse the novel idea of building a social network within troubled regions to assist in understanding the structure of women's communities and identifying key individuals and groups that will help rebuild and empower the lives of women. Our main argument is that we can better understand the complexity of a society with quantitative measures using a network analysis approach. Given the foundation of this paper, one can develop a model that will represent the connections between women in these ...

Data Predictive Control For Building Energy Management, 2017 University of Pennsylvania

#### Data Predictive Control For Building Energy Management, Achin Jain, Madhur Behl, Rahul Mangharam

*Real-Time and Embedded Systems Lab (mLAB)*

Decisions on how to best optimize energy systems operations are becoming ever so complex and conflicting, that model-based predictive control (MPC) algorithms must play an important role. However, a key factor prohibiting the widespread adoption of MPC in buildings, is the cost, time, and effort associated with learning first-principles based dynamical models of the underlying physical system. This paper introduces an alternative approach for implementing finite-time receding horizon control using control-oriented data-driven models. We call this approach Data Predictive Control (DPC). Specifically, by utilizing separation of variables, two novel algorithms for implementing DPC using a single regression tree and with ...

Extracting Geography From Datasets In Social Sciences, 2017 Yale University

#### Extracting Geography From Datasets In Social Sciences, Yuke Li, Tianhao Wu, Nicholas Marshall, Stefan Steinerberger

*Yale Day of Data*

No abstract provided.

Steady State Probabilities In Relation To Eigenvalues, 2017 Liberty University

#### Steady State Probabilities In Relation To Eigenvalues, Pellegrino Christopher

*The Kabod*

By using the methods of Hamdy Taha, eigenvectors can be used in solving problems to compute steady state probabilities, and they work every time.

Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, 2017 Dublin Institute of Technology

#### Hamiltonian Model For Coupled Surface And Internal Waves In The Presence Of Currents, Rossen Ivanov

*Articles*

We examine a two dimensional fluid system consisting of a lower medium bounded underneath by a flatbed and an upper medium with a free surface. The two media are separated by a free common interface. The gravity driven surface and internal water waves (at the common interface between the media) in the presence of a depth-dependent current are studied under certain physical assumptions. Both media are considered incompressible and with prescribed vorticities. Using the Hamiltonian approach the Hamiltonian of the system is constructed in terms of ’wave’ variables and the equations of motion are calculated. The resultant equations of motion ...

A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, 2017 University of Kentucky

#### A Physics-Based Approach To Modeling Wildland Fire Spread Through Porous Fuel Beds, Tingting Tang

*Theses and Dissertations--Mechanical Engineering*

Wildfires are becoming increasingly erratic nowadays at least in part because of climate change. CFD (computational fluid dynamics)-based models with the potential of simulating extreme behaviors are gaining increasing attention as a means to predict such behavior in order to aid firefighting efforts. This dissertation describes a wildfire model based on the current understanding of wildfire physics. The model includes physics of turbulence, inhomogeneous porous fuel beds, heat release, ignition, and firebrands. A discrete dynamical system for flow in porous media is derived and incorporated into the subgrid-scale model for synthetic-velocity large-eddy simulation (LES), and a general porosity-permeability model ...