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Articles 1 - 29 of 29
Full-Text Articles in Mathematics
Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa
Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski
On The Application Of Principal Component Analysis To Classification Problems, Jianwei Zheng, Cyril Rakovski
Mathematics, Physics, and Computer Science Faculty Articles and Research
Principal Component Analysis (PCA) is a commonly used technique that uses the correlation structure of the original variables to reduce the dimensionality of the data. This reduction is achieved by considering only the first few principal components for a subsequent analysis. The usual inclusion criterion is defined by the proportion of the total variance of the principal components exceeding a predetermined threshold. We show that in certain classification problems, even extremely high inclusion threshold can negatively impact the classification accuracy. The omission of small variance principal components can severely diminish the performance of the models. We noticed this phenomenon in …
Multilateration Index., Chip Lynch
Multilateration Index., Chip Lynch
Electronic Theses and Dissertations
We present an alternative method for pre-processing and storing point data, particularly for Geospatial points, by storing multilateration distances to fixed points rather than coordinates such as Latitude and Longitude. We explore the use of this data to improve query performance for some distance related queries such as nearest neighbor and query-within-radius (i.e. “find all points in a set P within distance d of query point q”). Further, we discuss the problem of “Network Adequacy” common to medical and communications businesses, to analyze questions such as “are at least 90% of patients living within 50 miles of a covered emergency …
Preconditioned Nesterov’S Accelerated Gradient Descent Method And Its Applications To Nonlinear Pde, Jea Hyun Park
Preconditioned Nesterov’S Accelerated Gradient Descent Method And Its Applications To Nonlinear Pde, Jea Hyun Park
Doctoral Dissertations
We develop a theoretical foundation for the application of Nesterov’s accelerated gradient descent method (AGD) to the approximation of solutions of a wide class of partial differential equations (PDEs). This is achieved by proving the existence of an invariant set and exponential convergence rates when its preconditioned version (PAGD) is applied to minimize locally Lipschitz smooth, strongly convex objective functionals. We introduce a second-order ordinary differential equation (ODE) with a preconditioner built-in and show that PAGD is an explicit time-discretization of this ODE, which requires a natural time step restriction for energy stability. At the continuous time level, we show …
Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Contributions To The Teaching And Learning Of Fluid Mechanics, Ashwin Vaidya
Department of Mathematics Facuty Scholarship and Creative Works
This issue showcases a compilation of papers on fluid mechanics (FM) education, covering different sub topics of the subject. The success of the first volume [1] prompted us to consider another follow-up special issue on the topic, which has also been very successful in garnering an impressive variety of submissions. As a classical branch of science, the beauty and complexity of fluid dynamics cannot be overemphasized. This is an extremely well-studied subject which has now become a significant component of several major scientific disciplines ranging from aerospace engineering, astrophysics, atmospheric science (including climate modeling), biological and biomedical science …
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Dynamic Parameter Estimation From Partial Observations Of The Lorenz System, Eunice Ng
Theses and Dissertations
Recent numerical work of Carlson-Hudson-Larios leverages a nudging-based algorithm for data assimilation to asymptotically recover viscosity in the 2D Navier-Stokes equations as partial observations on the velocity are received continuously-in-time. This "on-the-fly" algorithm is studied both analytically and numerically for the Lorenz equations in this thesis.
Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev
Negative Representability Degree Structures Of Linear Orders With Endomorphisms, Nadimulla Kasymov, Sarvar Javliyev
Bulletin of National University of Uzbekistan: Mathematics and Natural Sciences
The structure of partially ordered sets of degrees of negative representability of linear orders with endomorphisms is studied. For these structures, the existence of incomparable, maximum and minimum degrees, infinite chains and antichains is established,and also considered connections with the concepts of reducibility of enumerations, splittable degrees and positive representetions.
Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal
Two Temperature Dual-Phase-Lag Fractional Thermal Investigation Of Heat Flow Inside A Uniform Rod, Vinayak Kulkarni, Gaurav Mittal
Applications and Applied Mathematics: An International Journal (AAM)
A non-classical, coupled, fractionally ordered, dual-phase-lag (DPL) heat conduction model has been presented in the framework of the two-temperature theory in the bounded Cartesian domain. Due to the application of two-temperature theory, the governing heat conduction equation is well-posed and satisfying the required stability criterion prescribed for a DPL model. The mathematical formulation has been applied to a uniform rod of finite length with traction free ends considered in a perfectly thermoelastic homogeneous isotropic medium. The initial end of the rod has been exposed to the convective heat flux and energy dissipated by convection into the surrounding medium through the …
Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh
Application Of Randomness In Finance, Jose Sanchez, Daanial Ahmad, Satyanand Singh
Publications and Research
Brownian Motion which is also considered to be a Wiener process and can be thought of as a random walk. In our project we had briefly discussed the fluctuations of financial indices and related it to Brownian Motion and the modeling of Stock prices.
A Component-Wise Approach To Smooth Extension Embedding Methods, Vivian Montiforte
A Component-Wise Approach To Smooth Extension Embedding Methods, Vivian Montiforte
Dissertations
Krylov Subspace Spectral (KSS) Methods have demonstrated to be highly scalable methods for PDEs. However, a current limitation of these methods is the requirement of a rectangular or box-shaped domain. Smooth Extension Embedding Methods (SEEM) use fictitious domain methods to extend a general domain to a simple, rectangular or box-shaped domain. This dissertation describes how these methods can be combined to extend the applicability of KSS methods, while also providing a component-wise approach for solving the systems of equations produced with SEEM.
Lecture 05: The Convergence Of Big Data And Extreme Computing, David Keyes
Lecture 05: The Convergence Of Big Data And Extreme Computing, 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 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 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 …
Lecture 04: Spatial Statistics Applications Of Hrl, Trl, And Mixed Precision, David Keyes
Lecture 04: Spatial Statistics Applications Of Hrl, Trl, And Mixed Precision, 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 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 02: Tile Low-Rank Methods And Applications (W/Review), David Keyes
Lecture 02: Tile Low-Rank Methods And Applications (W/Review), 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 …
Lecture 01: Scalable Solvers: Universals And Innovations, David Keyes
Lecture 01: Scalable Solvers: Universals And Innovations, 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 10: Preconditioned Iterative Methods For Linear Systems, Edmond Chow
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 …
Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Emergent Hierarchy Through Conductance-Based Degree Constraints, Christopher Tyler Diggans, Jeremie Fish, Erik M. Bollt
Northeast Journal of Complex Systems (NEJCS)
The presence of hierarchy in many real-world networks is not yet fully understood. We observe that complex interaction networks are often coarse-grain models of vast modular networks, where tightly connected subgraphs are agglomerated into nodes for simplicity of representation and computational feasibility. The emergence of hierarchy in such growing complex networks may stem from one particular property of these ignored subgraphs: their graph conductance. Being a quantification of the main bottleneck of flow through the coarse-grain node, this scalar quantity implies a structural limitation and supports the consideration of heterogeneous degree constraints. The internal conductance values of the subgraphs are …
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Numerical Integration Through Concavity Analysis, Daniel J. Pietz
Rose-Hulman Undergraduate Mathematics Journal
We introduce a relationship between the concavity of a C2 func- tion and the area bounded by its graph and secant line. We utilize this relationship to develop a method of numerical integration. We then bound the error of the approximation, and compare to known methods, finding an improvement in error bound over methods of comparable computational complexity.
Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes
Fractals, Fractional Derivatives, And Newton-Like Methods, Eleanor Byrnes
HMC Senior Theses
Inspired by the fractals generated by the discretizations of the Continuous Newton Method and the notion of a fractional derivative, we ask what it would mean if such a fractional derivative were to replace the derivatives in Newton's Method. This work, largely experimental in nature, examines these new iterative methods by generating their Julia sets, computing their fractal dimension, and in certain tractable cases examining the behaviors using tools from dynamical systems.
Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante
Five-Wave Resonances In Deep Water Gravity Waves: Integrability, Numerical Simulations And Experiments, Dan Lucas, Marc Perlin, Dian-Yong Liu, Shane Walsh, Rossen Ivanov, Miguel D. Bustamante
Articles
In this work we consider the problem of finding the simplest arrangement of resonant deep water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wave vectors K1 + K2 = K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wave packets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction …
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman
Pitzer Senior Theses
This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …
A Mathematical Analysis Of The Wind Triangle Problem And An Inquiry Of True Airspeed Calculations In Supersonic Flight, Leonard T. Huang, Lisa I. Cummings
A Mathematical Analysis Of The Wind Triangle Problem And An Inquiry Of True Airspeed Calculations In Supersonic Flight, Leonard T. Huang, Lisa I. Cummings
International Journal of Aviation, Aeronautics, and Aerospace
In the first half of this paper, we present a fresh perspective toward the Wind Triangle Problem in aerial navigation by deriving necessary and sufficient conditions, which we call "go/no-go conditions", for the existence/non-existence of a solution of the problem. Although our derivation is based on simple trigonometry and basic properties of quadratic functions, it is mathematically rigorous. We also offer examples to demonstrate how easy it is to check these conditions graphically. In the second half of this paper, we use function theory to re-examine another problem in aerial navigation, namely, that of computing true airspeed — even in …