Shrinkage Function And Its Applications In Matrix Approximation, 2017 University of Florida, Gainesville

#### Shrinkage Function And Its Applications In Matrix Approximation, Toby Boas, Aritra Dutta, Xin Li, Katie Mercier, Eric Niderman

*Electronic Journal of Linear Algebra*

The shrinkage function is widely used in matrix low-rank approximation, compressive sensing, and statistical estimation. In this article, an elementary derivation of the shrinkage function is given. In addition, applications of the shrinkage function are demonstrated in solving several well-known problems, together with a new result in matrix approximation.

Rainbow Copies Of C4 In Edge-Colored Hypercubes, 2017 University of Illinois at Urbana-Champaign

#### Rainbow Copies Of C4 In Edge-Colored Hypercubes, József Balogh, Michelle Delcourt, Bernard Lidický, Cory Palmer

*Bernard Lidický*

For positive integers k and d such that 4≤k4in a k-edge-coloring of the d-dimensional hypercube Qd. Interestingly, the k-edge-colorings of Qd yielding the maximum number of rainbow copies of C4 also have the property that every copy of C4 which is not rainbow is monochromatic.

Uncovering Functional Relationships In Leukemia, 2017 Mathematical Biosciences Institute

#### Uncovering Functional Relationships In Leukemia, Reginald Mcgee

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, 2017 University of Leeds

#### On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

A Single Shape From Multiple Cues: How Local And Global Information Organizes Shape Inference, 2017 Brown University

#### A Single Shape From Multiple Cues: How Local And Global Information Organizes Shape Inference, Benjamin Kunsberg, Steven W. Zucker

*MODVIS Workshop*

No abstract provided.

Evolution Of Influenza H3n2: A Random Walk In High Dimensions, 2017 Emory University

#### Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Dynamics Of Fluorescent Imaging In Glob-Driven Breakup, 2017 University of Delaware

#### Dynamics Of Fluorescent Imaging In Glob-Driven Breakup, Lan Zhong, Christiaan Ketelaar, Richard J. Braun, Carolyn G. Begley, Peter Ewen King-Smith

*Biology and Medicine Through Mathematics Conference*

No abstract provided.

Role Of The Cost Of Plasticity In Determining The Features Of Fast Vision In Humans., 2017 Department NEUROFARBA ,University of Florence

#### Role Of The Cost Of Plasticity In Determining The Features Of Fast Vision In Humans., Maria M. Del Viva Phd, Renato Budinich M. Sc, Laura Palmieri M. Sc, Vladimir S Georgiev Phd, Giovanni Punzi Phd

*MODVIS Workshop*

No abstract provided.

Inventory Optimization Using A Simpy Simulation Model, 2017 East Tennessee State University

#### Inventory Optimization Using A Simpy Simulation Model, Lauren Holden

*Electronic Theses and Dissertations*

Existing multi-echelon inventory optimization models and formulas were studied to get an understanding of how safety stock levels are determined. Because of the restrictive distribution assumptions of the existing safety stock formula, which are not necessarily realistic in practice, a method to analyze the performance of this formula in a more realistic setting was desired. A SimPy simulation model was designed and implemented for a simple two-stage supply chain as a way to test the performance of the safety stock formula. This implementation produced results which led to the conclusion that the safety stock formula tends to underestimate the level ...

Quantifying The Structure Of Misfolded Proteins Using Graph Theory, 2017 East Tennessee State University

#### Quantifying The Structure Of Misfolded Proteins Using Graph Theory, Walter G. Witt

*Electronic Theses and Dissertations*

The structure of a protein molecule is highly correlated to its function. Some diseases such as cystic fibrosis are the result of a change in the structure of a protein so that this change interferes or inhibits its function. Often these changes in structure are caused by a misfolding of the protein molecule. To assist computational biologists, there is a database of proteins together with their misfolded versions, called decoys, that can be used to test the accuracy of protein structure prediction algorithms. In our work we use a nested graph model to quantify a selected set of proteins that ...

Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, 2017 East Tennessee State University

#### Differentiating Between A Protein And Its Decoy Using Nested Graph Models And Weighted Graph Theoretical Invariants, Hannah E. Green

*Electronic Theses and Dissertations*

To determine the function of a protein, we must know its 3-dimensional structure, which can be difficult to ascertain. Currently, predictive models are used to determine the structure of a protein from its sequence, but these models do not always predict the correct structure. To this end we use a nested graph model along with weighted invariants to minimize the errors and improve the accuracy of a predictive model to determine if we have the correct structure for a protein.

3-Manifold Perspective On Surface Homeomorphisms For Surfaces With Very Negative Euler Characteristic, 2017 University of Arkansas, Fayetteville

#### 3-Manifold Perspective On Surface Homeomorphisms For Surfaces With Very Negative Euler Characteristic, Michael Harris

*Theses and Dissertations*

The goal of this paper is to show for a compact triangulated 3-manifold M with boundary which fibers over the circle that whenever F is a fiber with sufficiently negative Euler characteristic the monodromymaps an essential simple closed curve or an essential simple arc in F to be disjoint from its image (possibly after isotopy). This is shown by applying the theorem of Ichihara, Kobayashi, and Rieck in [10] to the double of M to get a pair of pants. We then find an equivariant pair of pants and use it to find an essential simple closed curve or an ...

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.

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 ...

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 ...

Mri-Based Susceptibility Mapping For In-Vivo Iron And Blood Oximetry Measurements, 2017 University of Colorado, Boulder

#### Mri-Based Susceptibility Mapping For In-Vivo Iron And Blood Oximetry Measurements, Hannah Erdevig

*Undergraduate Honors Theses*

MRI is increasingly used in mapping tissue susceptibility to identify cerebral microbleeds associated with traumatic brain injury and pathological iron deposits associated with neurodegenerative diseases such as Parkinson's and Alzheimer's disease [1,2]. Accurate measurement is important for determining oxygen and iron content in blood vessels and tissue in the brain, which are in turn used for noninvasive clinical diagnosis and treatment assessments. Magnetic field distortions with a resolution of a few parts per billion can be measured using MRI phase maps. The field distortion map can then be inverted to obtain a quantitative susceptibility map. The primary ...

Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, 2017 Claremont McKenna College

#### Triple Non-Negative Matrix Factorization Technique For Sentiment Analysis And Topic Modeling, Alexander A. Waggoner

*CMC Senior Theses*

Topic modeling refers to the process of algorithmically sorting documents into categories based on some common relationship between the documents. This common relationship between the documents is considered the “topic” of the documents. Sentiment analysis refers to the process of algorithmically sorting a document into a positive or negative category depending whether this document expresses a positive or negative opinion on its respective topic. In this paper, I consider the open problem of document classification into a topic category, as well as a sentiment category. This has a direct application to the retail industry where companies may want to scour ...

Cyclic Codes And Cyclic Lattices, 2017 Claremont McKenna College

#### Cyclic Codes And Cyclic Lattices, Scott Maislin

*CMC Senior Theses*

In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two ...

Pattern Recognition In Stock Data, 2017 Harvey Mudd College

#### Pattern Recognition In Stock Data, Kathryn Dover

*HMC Senior Theses*

Finding patterns in high dimensional data can be difficult because it cannot be easily visualized. There are many different machine learning methods to fit data in order to predict and classify future data but there is typically a large expense on having the machine learn the fit for a certain part of a dataset. We propose a geometric way of defining different patterns in data that is invariant under size and rotation. Using a Gaussian Process, we find that pattern within stock datasets and make predictions from it.

Incorporating The Centers For Disease Control And Prevention Into Vaccine Pricing Models, 2017 Harvey Mudd College

#### Incorporating The Centers For Disease Control And Prevention Into Vaccine Pricing Models, Dina Sinclair

*HMC Senior Theses*

The American vaccine pricing market has many actors, making it a complex system to model. Because of this, previous papers have chosen to model only vaccine manufacturers while leaving out the government. However, the government is also an important actor in the market, since it buys over half of vaccines produced. In this work, we aim to introduce the government into vaccine pricing models to better recommend pricing strategies to the Centers for Disease Control and Prevention.