Mathematics Commons^™

Understanding The Effect Of Adaptive Mutations On The Three-Dimensional Structure Of Rna, Justin Cook

Undergraduate Research and Scholarship Symposium

Single-nucleotide polymorphisms (SNPs) are variations in the genome where one base pair can differ between individuals.¹ SNPs occur throughout the genome and can correlate to a disease-state if they occur in a functional region of DNA.¹According to the central dogma of molecular biology, any variation in the DNA sequence will have a direct effect on the RNA sequence and will potentially alter the identity or conformation of a protein product. A single RNA molecule, due to intramolecular base pairing, can acquire a plethora of 3-D conformations that are described by its structural ensemble. One SNP, rs12477830, which …

Translation Of: Isoparametrische Hyperflächen In Sphären, Math. Ann. 251, 57–71 (1980) By Hans Friedrich Münzner., Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an English translation of the article "Isoparametrische Hyperflächen in Sphären" by Hans Friedrich Münzner, which was originally published in Math. Ann. 251, 57–71 (1980).

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in German. All references should be made to the original paper. I want to thank Cristina Ballantine for her help with the translation.

Translation Of: Isoparametrische Hyperflächen In Sphären Ii. Über Die Zerlegung Der Sphäre In Ballbündel, Math. Ann. 256, 215–232 (1981) By Hans Friedrich Münzner., Thomas E. Cecil

Mathematics and Computer Science Department Faculty Scholarship

This is an English translation of the article "Isoparametrische Hyperflächen in Sphären II. Über die Zerlegung der Sphäre in Ballbündel" by Hans Friedrich Münzner, which was originally published in Math. Ann. 256, 215–232 (1981).

A note from Thomas E. Cecil, translator: This is an unofficial translation of the original paper which was written in German. All references should be made to the original paper. I want to thank Cristina Ballantine for her help with the translation.

Reviving The Media Station: A Study In Reverse Engineering, Nathanael Gentry, Melesa Poole

Liberty University Research Week

Undergraduate

Applied

Emerald Ash Borer And The Application Of Biological Control In Virginia, Shuheng Chen, Yihui Wu, Shengjie Liu

Arts & Sciences Student Symposium

The emerald ash borer (Agrilus planipennis; EAB) is an invasive wood-boring beetle whose larvae feed on ash phloem. After only 1-5 years of infestation, the larvae create extensive tunnels under the bark that disrupt the tree’s ability to transport water and nutrients, which eventually girdles and kills the tree. Since 2008, EAB has spread to all but the eastern-most counties in Virginia. Bological control is one strategy to limit EAB populations. In this project we study control by native agents (woodpeckers) and imported agents (parasitoid wasps).

Mathematical models of host-parasitoid interactions and simulations based on both models and field studies …

Reducing The Maximum Degree Of A Graph: Comparisons Of Bounds, Peter Borg

Theory & Applications of Graphs

Let λ(G) be the smallest number of vertices that can be removed from a non-empty graph G so that the resulting graph has a smaller maximum degree. Let λ_e(G) be the smallest number of edges that can be removed from G for the same purpose. Let k be the maximum degree of G, let t be the number of vertices of degree k, let M(G) be the set of vertices of degree k, let n be the number of vertices in the closed neighbourhood of M(G), and let m be the …

Road Network Detection Based On Improved Flicm-Mrf Method Using High Resolution Sar Images, Lamei Zhang, Chenwei Jiang, Bin Zou, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The automatic detection of road network from satellite and aerial images is highly significant in many actual applications, for instance, urban traffic measurement, military emergency response, and vehicle target tracking. Compared with other high-resolution satellite remote sensing images, high-resolution synthetic aperture radar (SAR) has become a popular research perspective for road detection owing to its insensitivity to the atmosphere and sun-illumination. However, the method of road network detection is still lagging due to the strong multiplicative speckle noise and complex background interference, causing the loss and break in the road segment extraction results. Aiming to solve this problem, a three-step …

A High-Precision Sar Echo Simulation Method Based On Fdtd, Bin Zou, Yanqiu Jia, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

Synthetic aperture radar (SAR) echo simulation offers a low-cost and convenient way to obtain high-resolution images of targets, and plays an important role in system design and algorithm validation. Although high frequency approximation simulation is widely used, it is considered to be imprecise when calculating scattering field of fine structures, such as exhaust pipes and groove structures, especially in low frequency band. In this paper, a finite-difference time-domain (FDTD) based method is proposed for high-precision SAR echo simulation. In this method, scattering process of electromagnetic wave is accurately simulated to obtain equivalent electric and magnetic current on the surface of …

On The Third Moment Of L(½​, ΧD​) {Ii}: The Number Field Case, A. Diaconu, Ian Whitehead

Mathematics & Statistics Faculty Works

We establish a smoothed asymptotic formula for the third moment of quadratic Dirichlet L-functions at the central value. In addition to the main term, which is known, we prove the existence of a secondary term of size x^¾. The error term in the asymptotic formula is on the order of O(x^⅔+δ) for every δ > 0.

Teacher Educators Learning With Prospective Teachers: Finding Relevant Mathematics In Our (Their) Lives, Lindsay M. Keazer, Eryn Stehr Maher

Mathematical Sciences: Faculty Publications

Two mathematics teacher educators (MTEs) discuss the mathematical contexts generated by prospective teachers (PTs) when pushed to look for relevant mathematics in their lives and communities. Through collaborative teacher action research focused on iterations of collecting, categorizing, and discussing PTs’ mathematical contexts, and posing selected examples for PTs’ own examination, layers of learning occurred for both PTs and MTEs. PTs began to craft more personalized, story-like contexts, seemingly noticing more mathematics in their lives. MTEs were unexpectedly pushed to clarify their thinking about what it means to develop contexts that are authentic and relevant, and to contemplate how their actions …

Lecture 08: Partial Eigen Decomposition Of Large Symmetric Matrices Via Thick-Restart Lanczos With Explicit External Deflation And Its Communication-Avoiding Variant, Zhaojun Bai

Mathematical Sciences Spring Lecture Series

There are continual and compelling needs for computing many eigenpairs of very large Hermitian matrix in physical simulations and data analysis. Though the Lanczos method is effective for computing a few eigenvalues, it can be expensive for computing a large number of eigenvalues. To improve the performance of the Lanczos method, in this talk, we will present a combination of explicit external deflation (EED) with an s-step variant of thick-restart Lanczos (s-step TRLan). The s-step Lanczos method can achieve an order of s reduction in data movement while the EED enables to compute eigenpairs in batches along with a number …

Getting Over It, Thomas Kade, Kevorc Ibrahimian, Max Simpson

Arts & Sciences Student Symposium

The research extended a 2D motion planning system to three dimensional environments. The updated system is now able to plan the motion for robots over 3D terrains modeled by polyhedrons.

The School Mathematics Study Group: Lessons In Mathematics Education, Madeline Polhill

Arts & Sciences Student Symposium

This work argues that the "new math" project called the School Mathematics Study Group offers a valuable case study for mathematics educators seeking to venture into the future better informed about both the successes and failures of previous projects. Understanding this project requires recognizing that the School Mathematics Study Group was wholly a product of the forces—personal, educational, mathematical, and political—that shaped it. Admittedly, some of the SMSG's shortcomings resulted from its members' lack of understanding of the changes needed in mathematics education. Still, the majority of the SMSG's public vilification resulted through no fault of its own, but rather …

Curve Reconstruction From The Apparent Contour Graph, Nkosi Alexander-Williams

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Project of Merit Winner

This project concerns the two-dimensional Scenery Reconstruction Problem (2D-AC), a simplified version of the Scenery Reconstruction Problem (3D-AC) studied by Bellettini, Beorchia, Paolini, and Pasquarelli. In our research, we take a picture of a 2D object, take information from the picture, specifically the edges of the object as seen in the picture, and from this information, we determine if we can reconstruct the original 2D object. Utilizing knowledge of the concepts regarding contour generators and apparent contours, we determine the labelings for these points and call the labelings the Apparent Contour Graph. This project answers the …

Opioid Epidemic On The First Coast​, Jeremiah Baclig, Noah Dedeo, Rukhaiya Husain, Iliya Kulbaka, Michelle Dedeo

Showcase of Osprey Advancements in Research and Scholarship (SOARS)

Project of Merit Winner

The nation has been focusing on the opioid epidemic for many years. Aggregate quarterly data on opioid distribution at a general level has been available through the Drug Enforcement Administration (DEA) but cannot be used to do analyses on the effects of opioids in local areas. Quantifying impacts of the opioid epidemic at the local level has never been easy: what little data was provided by the DEA was not user-friendly, overly broad and did not follow the desired timeline of data collection. This project focuses on database exploration and uses statistical methods and Decision Tree …

Determination Of The Traits In Leguminous Crops Under Saline Condition, Tojiddin Kuliev, Karomat Ismailova

Karakalpak Scientific Journal

In this study, the variability and determination of genetic traits for winter legume crop varieties the Vostok-55 (Pisum arvense L) and Mirzachul-1 (Vicia villoza Roth L) were investigated under moderate saline soil condition. Results show that the weight of the bean was marked as variable and highly deterministic, and the height of the plants was the most stable. The selection of plants based on these traits is the most effective way of salinity. Both variety the forage pea Vostok-55 and vetch Mirzachul-1 is highly recommended as a sideration and forage crop in saline lands.

The Agnostic Structure Of Data Science Methods, Domenico Napoletani, Marco Panza, Daniele Struppa

MPP Published Research

In this paper we argue that data science is a coherent and novel approach to empirical problems that, in its most general form, does not build understanding about phenomena. Within the new type of mathematization at work in data science, mathematical methods are not selected because of any relevance for a problem at hand; mathematical methods are applied to a specific problem only by `forcing’, i.e. on the basis of their ability to reorganize the data for further analysis and the intrinsic richness of their mathematical structure. In particular, we argue that deep learning neural networks are best understood within …

Lecture 10: Preconditioned Iterative Methods For Linear Systems, Edmond Chow

Mathematical Sciences Spring Lecture Series

Iterative methods for the solution of linear systems of equations – such as stationary, semi-iterative, and Krylov subspace methods – are classical methods taught in numerical analysis courses, but adapting these methods to run efficiently at large-scale on high-performance computers is challenging and a constantly evolving topic. Preconditioners – necessary to aid the convergence of iterative methods – come in many forms, from algebraic to physics-based, are regularly being developed for linear systems from different classes of problems, and similarly are evolving with high-performance computers. This lecture will cover the background and some recent developments on iterative methods and preconditioning …

Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman

Mathematical Sciences Spring Lecture Series

Opening remarks for the 46th Annual Mathematical Sciences Spring Lecture Series at the University of Arkansas, Fayetteville.

Long-Time Asymptotics For Mkdv Type Reduced Equations Of The Akns Hierarchy In Weighted L2 Sobolev Spaces, Fudong Wang

USF Tampa Graduate Theses and Dissertations

The long-time asymptotics of nonlinear integrable partial differential equations is one of the important research areas in the field of integrable systems. The main tool to analyze the long-time behaviors is the so-called nonlinear steepest descent method, or Deift-Zhou's method, which was born in 1993. To apply Deift-Zhou's method, one first uses the inverse scattering transform to formulate the nonlinear PDEs in terms of an oscillatory 2 by 2 matrix Riemann-Hilbert problem (RHP). After about 15 years of development, a generalized version of Deift-Zhou's method, the ∂—steepest method, came out. The ∂—steepest descent method is a useful method for analyzing …