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Articles 1 - 15 of 15
Full-Text Articles in Algebra
A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin
A Graphical User Interface Using Spatiotemporal Interpolation To Determine Fine Particulate Matter Values In The United States, Kelly M. Entrekin
Honors College Theses
Fine particulate matter or PM2.5 can be described as a pollution particle that has a diameter of 2.5 micrometers or smaller. These pollution particle values are measured by monitoring sites installed across the United States throughout the year. While these values are helpful, a lot of areas are not accounted for as scientists are not able to measure all of the United States. Some of these unmeasured regions could be reaching high PM2.5 values over time without being aware of it. These high values can be dangerous by causing or worsening health conditions, such as cardiovascular and lung diseases. Within …
Lecture 09: Hierarchically Low Rank And Kronecker Methods, Rio Yokota
Lecture 09: Hierarchically Low Rank And Kronecker Methods, Rio Yokota
Mathematical Sciences Spring Lecture Series
Exploiting structures of matrices goes beyond identifying their non-zero patterns. In many cases, dense full-rank matrices have low-rank submatrices that can be exploited to construct fast approximate algorithms. In other cases, dense matrices can be decomposed into Kronecker factors that are much smaller than the original matrix. Sparsity is a consequence of the connectivity of the underlying geometry (mesh, graph, interaction list, etc.), whereas the rank-deficiency of submatrices is closely related to the distance within this underlying geometry. For high dimensional geometry encountered in data science applications, the curse of dimensionality poses a challenge for rank-structured approaches. On the other …
Lecture 14: Randomized Algorithms For Least Squares Problems, Ilse C.F. Ipsen
Lecture 14: Randomized Algorithms For Least Squares Problems, Ilse C.F. Ipsen
Mathematical Sciences Spring Lecture Series
The emergence of massive data sets, over the past twenty or so years, has lead to the development of Randomized Numerical Linear Algebra. Randomized matrix algorithms perform random sketching and sampling of rows or columns, in order to reduce the problem dimension or compute low-rank approximations. We review randomized algorithms for the solution of least squares/regression problems, based on row sketching from the left, or column sketching from the right. These algorithms tend to be efficient and accurate on matrices that have many more rows than columns. We present probabilistic bounds for the amount of sampling required to achieve a …
Lecture 13: A Low-Rank Factorization Framework For Building Scalable Algebraic Solvers And Preconditioners, X. Sherry Li
Lecture 13: A Low-Rank Factorization Framework For Building Scalable Algebraic Solvers And Preconditioners, X. Sherry Li
Mathematical Sciences Spring Lecture Series
Factorization based preconditioning algorithms, most notably incomplete LU (ILU) factorization, have been shown to be robust and applicable to wide ranges of problems. However, traditional ILU algorithms are not amenable to scalable implementation. In recent years, we have seen a lot of investigations using low-rank compression techniques to build approximate factorizations.
A key to achieving lower complexity is the use of hierarchical matrix algebra, stemming from the H-matrix research. In addition, the multilevel algorithm paradigm provides a good vehicle for a scalable implementation. The goal of this lecture is to give an overview of the various hierarchical matrix formats, such …
Lecture 03: Hierarchically Low Rank Methods And Applications, David Keyes
Lecture 03: Hierarchically Low Rank Methods And Applications, David Keyes
Mathematical Sciences Spring Lecture Series
As simulation and analytics enter the exascale era, numerical algorithms, particularly implicit solvers that couple vast numbers of degrees of freedom, must span a widening gap between ambitious applications and austere architectures to support them. We present fifteen universals for researchers in scalable solvers: imperatives from computer architecture that scalable solvers must respect, strategies towards achieving them that are currently well established, and additional strategies currently being developed for an effective and efficient exascale software ecosystem. We consider recent generalizations of what it means to “solve” a computational problem, which suggest that we have often been “oversolving” them at the …
Lecture 11: The Road To Exascale And Legacy Software For Dense Linear Algebra, Jack Dongarra
Lecture 11: The Road To Exascale And Legacy Software For Dense Linear Algebra, Jack Dongarra
Mathematical Sciences Spring Lecture Series
In this talk, we will look at the current state of high performance computing and look at the next stage of extreme computing. With extreme computing, there will be fundamental changes in the character of floating point arithmetic and data movement. In this talk, we will look at how extreme-scale computing has caused algorithm and software developers to change their way of thinking on implementing and program-specific applications.
Lecture 00: Opening Remarks: 46th Spring Lecture Series, Tulin Kaman
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.
Lecture 06: The Impact Of Computer Architectures On The Design Of Algebraic Multigrid Methods, Ulrike Yang
Lecture 06: The Impact Of Computer Architectures On The Design Of Algebraic Multigrid Methods, Ulrike Yang
Mathematical Sciences Spring Lecture Series
Algebraic multigrid (AMG) is a popular iterative solver and preconditioner for large sparse linear systems. When designed well, it is algorithmically scalable, enabling it to solve increasingly larger systems efficiently. While it consists of various highly parallel building blocks, the original method also consisted of various highly sequential components. A large amount of research has been performed over several decades to design new components that perform well on high performance computers. As a matter of fact, AMG has shown to scale well to more than a million processes. However, with single-core speeds plateauing, future increases in computing performance need to …
Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, Sasha Verona Malone
Some Generalizations Of Classical Integer Sequences Arising In Combinatorial Representation Theory, Sasha Verona Malone
Masters Theses & Specialist Projects
There exists a natural correspondence between the bases for a given finite-dimensional representation of a complex semisimple Lie algebra and a certain collection of finite edge-colored ranked posets, laid out by Donnelly, et al. in, for instance, [Don03]. In this correspondence, the Serre relations on the Chevalley generators of the given Lie algebra are realized as conditions on coefficients assigned to poset edges. These conditions are the so-called diamond, crossing, and structure relations (hereinafter DCS relations.) New representation constructions of Lie algebras may thus be obtained by utilizing edge-colored ranked posets. Of particular combinatorial interest are those representations whose corresponding …
Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg
Mathematics And Programming Exercises For Educational Robot Navigation, Ronald I. Greenberg
Computer Science: Faculty Publications and Other Works
This paper points students towards ideas they can use towards developing a convenient library for robot navigation, with examples based on Botball primitives, and points educators towards mathematics and programming exercises they can suggest to students, especially advanced high school students.
High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt
High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt
Electronic Thesis and Dissertation Repository
Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit …
An Implementation Of The Solution To The Conjugacy Problem On Thompson's Group V, Rachel K. Nalecz
An Implementation Of The Solution To The Conjugacy Problem On Thompson's Group V, Rachel K. Nalecz
Senior Projects Spring 2018
We describe an implementation of the solution to the conjugacy problem in Thompson's group V as presented by James Belk and Francesco Matucci in 2013. Thompson's group V is an infinite finitely presented group whose elements are complete binary prefix replacement maps. From these we can construct closed abstract strand diagrams, which are certain directed graphs with a rotation system and an associated cohomology class. The algorithm checks for conjugacy by constructing and comparing these graphs together with their cohomology classes. We provide a complete outline of our solution algorithm, as well as a description of the data structures which …
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo
Distributed Evolution Of Spiking Neuron Models On Apache Mahout For Time Series Analysis, Andrew Palumbo
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin
Predicting Locations Of Pollution Sources Using Convolutional Neural Networks, Yiheng Chi, Nickolas D. Winovich, Guang Lin
The Summer Undergraduate Research Fellowship (SURF) Symposium
Pollution is a severe problem today, and the main challenge in water and air pollution controls and eliminations is detecting and locating pollution sources. This research project aims to predict the locations of pollution sources given diffusion information of pollution in the form of array or image data. These predictions are done using machine learning. The relations between time, location, and pollution concentration are first formulated as pollution diffusion equations, which are partial differential equations (PDEs), and then deep convolutional neural networks are built and trained to solve these PDEs. The convolutional neural networks consist of convolutional layers, reLU layers …
Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta
Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta
STAR Program Research Presentations
With advances in technology in brighter sources and larger and faster detectors, the amount of data generated at national user facilities such as SLAC is increasing exponentially. Humans have a superb ability to recognize patterns in complex and noisy data and therefore, data is still curated and analyzed by humans. However, a human brain is unable to keep up with the accelerated pace of data generation, and as a consequence, the rate of new discoveries hasn't kept pace with the rate of data creation. Therefore, new procedures to quickly assess and analyze the data are needed. Machine learning approaches are …