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Articles 31 - 60 of 92
Full-Text Articles in Applied Mathematics
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Mathematical Sciences Technical Reports (MSTR)
From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Spontaneous Synchrony On Graphs And The Emergence Of Order From Disorder, Dylan Linville, Daniel Trugillo Martins Fontes
Rose-Hulman Undergraduate Research Publications
From pulsars to pedestrians and bacteria to brain cells, objects that exhibit cyclical behavior, called oscillators, are found in a variety of different settings. When oscillators adjust their behavior in response to nearby oscillators, they often achieve a state of synchrony, in which they all have the same phase and frequency. Here, we explore the Kuramoto model, a simple and general model which describes oscillators as dynamical systems on a graph and has been used to study synchronization in systems ranging from firefly swarms to the power grid. We discuss analytical and numerical methods used to investigate the governing system …
Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader
Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader
Mathematical Sciences Technical Reports (MSTR)
A circulant tridiagonal system is a special type of Toeplitz system that appears in a variety of problems in scientific computation. In this paper we give a formula for the inverse of a symmetric circulant tridiagonal matrix as a product of a circulant matrix and its transpose, and discuss the utility of this approach for solving the associated system.
Discovering Exoplanets Through Hidden Markov Model Analysis, Jon Drobny
Discovering Exoplanets Through Hidden Markov Model Analysis, Jon Drobny
Rose-Hulman Undergraduate Research Publications
The goal for the project is to develop a Hidden Markov Model for the detection and characterization of extrasolar planets through the analysis of light curves.
Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik
Thermal Detection Of Inaccessible Corrosion, Matthew Charnley, Andrew Rzeznik
Mathematical Sciences Technical Reports (MSTR)
In this paper, we explore the mathematical inverse problem of detecting corroded material on the reverse side of a partially accessible metal plate. We will show how a linearization can be used to simplify the initial problem and explain a regularization method used to obtain acceptable results for the corrosion profile. We will also state and perform some calculations for the full three-dimensional problem for possible future work.
Determining Properties Of Metal By Analyzing Changes In Impedance, Chase Mathison, Laura Booton
Determining Properties Of Metal By Analyzing Changes In Impedance, Chase Mathison, Laura Booton
Mathematical Sciences Technical Reports (MSTR)
In certain situations it is useful to identify an unknown sample of metal without contact or visual inspection. We wish to do this by inducing a current in a coil and placing the sample in the resulting magnetic field. For the special case in which the sample is an infinite slab, we have a model that gives the change in impedance of the coil based on the properties of the sample. In this paper we analyze the inverse problem of finding the metal properties from impedance measurements over a wide range of frequencies.
Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer
Robust Analysis Of Metabolic Pathways, Emily Gruber, Amy Ko, Michael Macgillvray, Miranda Sawyer
Mathematical Sciences Technical Reports (MSTR)
Flux Balance Analysis (FBA) is a widely used computational model for studying the metabolic pathways of cells and the role individual metabolites and reactions play in maintaining cell function. However, the successes of FBA have been limited by faulty biological assumptions and computational imperfections. We introduce Robust Analysis of Metabolic Pathways (RAMP) to provide a more theoretically sound and computationally accurate model of cellular metabolism. RAMP overcomes the faulty assumptions of traditional FBA by allowing deviation from steady-state and accounting for variability across a cellular culture. Computationally, RAMP more successfully predicts the lethality of gene knockouts and reduces degeneracy in …
Nondestructive Electrothermal Detection Of Corrosion, Brittany Ambeau, Harris Enniss, Stefan Schnake
Nondestructive Electrothermal Detection Of Corrosion, Brittany Ambeau, Harris Enniss, Stefan Schnake
Mathematical Sciences Technical Reports (MSTR)
Nondestructive testing and imaging plays an important role in many industries, e.g., the monitoring and maintenance of corrosion in aircraft. The general technique is to input energy in some form into an object, observe the object’s response, and from this input-output information determine the internal structure. New techniques are always being explored, and recently there has been much interest in methods that use multiple forms of energy. In this vein, we examine a new technique for imaging corrosion or material loss in an object by combining electrical and thermal measurements on some accessible portion of the object’s outer boundary. The …
Cloaking Against Thermal Imaging, Maple So
Cloaking Against Thermal Imaging, Maple So
Mathematical Sciences Technical Reports (MSTR)
There has been a lot of recent interest in cloaking and invisibility in the mathematics and science communities, and in fact physically plausible mechanisms have been proposed (some built) for cloaking an object against detection using a variety of electromagnetic methods. The ideas are very general, however, and should allow one to design cloaks that work against other forms of imaging. We examine the possibility of cloaking an object to make it invisible to an observer using thermal energy (heat) as the imaging tool. Specifically, we desire to cloak an object inside a two-dimensional disk by cutting a small hole …
Computational Biology, Harvey Greenberg, Allen Holder
Computational Biology, Harvey Greenberg, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Computational biology is an interdisciplinary field that applies the techniques of computer science, applied mathematics, and statistics to address biological questions. OR is also interdisciplinary and applies the same mathematical and computational sciences, but to decision-making problems. Both focus on developing mathematical models and designing algorithms to solve them. Models in computational biology vary in their biological domain and can range from the interactions of genes and proteins to the relationships among organisms and species.
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
G-Lattices For An Unrooted Perfect Phylogeny, Monica Grigg
Mathematical Sciences Technical Reports (MSTR)
We look at the Pure Parsimony problem and the Perfect Phylogeny Haplotyping problem. From the Pure Parsimony problem we consider structures of genotypes called g-lattices. These structures either provide solutions or give bounds to the pure parsimony problem. In particular, we investigate which of these structures supports an unrooted perfect phylogeny, a condition that adds biological interpretation. By understanding which g-lattices support an unrooted perfect phylogeny, we connect two of the standard biological inference rules used to recreate how genetic diversity propagates across generations.
A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder
A Spectral Approach To Protein Structure Alignment, Yosi Shibberu, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
We present two algorithms that use spectral methods to align protein folds. One of the algorithms is suitable for database searches, the other for difficult alignments. We present computational results for 780 pairwise alignments used to classify 40 proteins as well as results for a separate set of 36 protein alignments used for comparison to four other alignment algorithms. We also provide a mathematically rigorous development of the intrinsic geometry underlying our spectral approach.
Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine
Bilinear Programming And Protein Structure Alignment, J. Cain, D. Kamenetsky, N. Lavine
Mathematical Sciences Technical Reports (MSTR)
Proteins are a primary functional component of organic life, and understanding their function is integral to many areas of research in biochemistry. The three-dimensional structure of a protein largely determines this function. Protein structure alignment compares the structure of a protein with known function to that of a protein with unknown function. A protein’s three-dimensional structure can be transformed through a smooth piecewise-linear sigmoid function to a real symmetric contact matrix that represents the functional significance of certain parts of the protein. We address the protein alignment problem as a minimization of the 2-norm difference of two proteins’ contact matrices. …
Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper
Intrinsic Contact Geometry Of Protein Dynamics, Yosi Shibberu, Allen Holder, David Cooper
Mathematical Sciences Technical Reports (MSTR)
We introduce a new measure for comparing protein structures that is especially applicable to analysis of molecular dynamics simulation results. The new measure generalizes the widely used root-mean-squared-deviation (RMSD) measure from three dimensional to n-dimensional Euclidean space, where n equals the number of atoms in the protein molecule. The new measure shows that despite significant fluctuations in the three dimensional geometry of the estrogen receptor protein, the protein's intrinsic contact geometry is remarkably stable over nanosecond time scales. The new measure also identifies significant structural changes missed by RMSD for a residue that plays a key biological role in …
Parametric Lp Analysis, Allen Holder
Parametric Lp Analysis, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
Parametric linear programming is the study of how optimal properties depend on data parametrizations. The study is nearly as old as the field of linear programming itself, and it is important since it highlights how a problem changes as what is often estimated data varies. We present what is a modern perspective on the classical analysis of the objective value's response to parametrizations in the right-hand side and cost vector. We also mention a few applications and provide citations for further study
Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz
Fast Protein Structure Alignment, Yosi Shibberu, Allen Holder, Kyla Lutz
Mathematical Sciences Technical Reports (MSTR)
We address the problem of aligning the 3D structures of two proteins. Our pairwise comparisons are based on a new optimization model that is succinctly expressed in terms of linear transformations and highlights the problem’s intrinsic geometry. The optimization problem is approximately solved with a new polynomial time algorithm. The worst case analysis of the algorithm shows that the solution is bounded by a constant depending only on the data of the problem.
Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach
Electrical Impedance Imaging Of Corrosion On A Partially Accessible 2-Dimensional Region, Court Hoang, Katherine Osenbach
Mathematical Sciences Technical Reports (MSTR)
In this paper we examine the inverse problem of determining the amount of corrosion on an inaccessible surface of a two-dimensional region. Using numerical methods, we develop an algorithm for approximating corrosion profile using measurements of electrical potential along the accessible portion of the region. We also evaluate the effect of error on the problem, address the issue of ill-posedness, and develop a method of regularization to correct for this error. An examination of solution uniqueness is also presented.
Anti-Cloaking: The Mathematics Of Disguise, Theresa C. Anderson, Brooke E. Phillips
Anti-Cloaking: The Mathematics Of Disguise, Theresa C. Anderson, Brooke E. Phillips
Mathematical Sciences Technical Reports (MSTR)
Recent developments in cloaking, the ability to selectively bend electromagnetic waves so as to render an object invisible, have been abundant. Based on cloaking principles, we will describe several ways to mathematically disguise objects in the context of electrical impedance imaging. Through the use of a change-of-variables scheme we show how one can make an object appear enlarged, translated, or rotated by surrounding it with a suitable "metamaterial," a man-made material that selectively redirects current. Analysis of eigenvectors and eigenvalues, which describe how current flows, follow. We prove that in order to disguise an object, a metamaterial must encompass both …
Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling
Electrothermal Imaging In One And Two Dimensions, Michael Janus, David Kibbling
Mathematical Sciences Technical Reports (MSTR)
Developing methods for the nondestructive testing of materials is an important area of research for industry. Situations often arise in which the integrity of an object is questioned, but testing it is very difficult. For example, a support bar may be embedded in a larger structure so that testing the bar’s integrity directly would require the impractical task of breaking down the larger structure. Instead, the ends of the bar might be accessible without dismantling the enclosing structure. The goal of nondestructive testing is to use methods that require taking measurements at the ends of the bar alone to give …
Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones
Determining The Shape Of A Resistor Grid, Esther Chiew, Vincent Selhorst-Jones
Mathematical Sciences Technical Reports (MSTR)
Impedance imaging has received a lot of attention in the past two decades, as a means for non-destructively imaging the interior of a conductive object. One injects a known electrical current pattern into an object at the exterior boundary, then measures the induced potential (voltage) on some portion of the boundary. The goal is to recover information about the interior conductivity of the object, which (we hope) influences the voltages we measure. Of course one can also use multiple input currents and measured voltages. A variation on this problem is that of "boundary identification," in which some portion of the …
Optimization In The Undergraduate Curriculum, Allen Holder
Optimization In The Undergraduate Curriculum, Allen Holder
Mathematical Sciences Technical Reports (MSTR)
A discussion of how an optimization course fits into the undergraduate mathematics curriculum
Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G Mcquillen, D Nevin, P Uhlig, B Salter
Radiotherapy Optimal Design: An Academic Radiotherapy Treatment Design System, R Acosta, W Brick, A Hanna, Allen Holder, D Lara, G Mcquillen, D Nevin, P Uhlig, B Salter
Mathematical Sciences Technical Reports (MSTR)
Optimally designing radiotherapy and radiosurgery treatments to increase the likelihood of a successful recovery from cancer is an important application of operations research. Researchers have been hindered by the lack of academic software that supports head-to-head comparisons of different techniques, and this article addresses the inherent difficulties of designing and implementing an academic treatment planning system. In particular, this article details the algorithms and the software design of Radiotherapy optimAl Design (RAD).
The Barycenter Of The Numerical Range Of A Matrix, Sean A. Broughton, Roger G. Lautzenheiser, Thomas Werne
The Barycenter Of The Numerical Range Of A Matrix, Sean A. Broughton, Roger G. Lautzenheiser, Thomas Werne
Mathematical Sciences Technical Reports (MSTR)
The numerical range W(A) of an nxn matrix A is the totality of the scalar products <Ax,x> as x varies over all unit vectors in Cn The barycenter (center of mass) of the numerical range is defined geometrically as the center of mass of W(A) considered as a planar lamina with variable density and also as a limit of sample averages (<Ax1,x1>+...+<AxN,xN>)/N. Under a wide range the sampling schemes it is shown that the barycenter is the average of the spectrum …
Utilizing Thermal Testing For Recovering, James Preciado, Thomas Werne
Utilizing Thermal Testing For Recovering, James Preciado, Thomas Werne
Mathematical Sciences Technical Reports (MSTR)
Given a two-dimensional region that contains one or more circular voids, we develop mathematical methods to locate the center and radius of the voids based on thermal boundary data. These methods can be readily applied in the field of non-destructive evaluation.
Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker
Thermal Imaging To Recover A Defect In Three Dimensional Objects, Breanne Baker
Mathematical Sciences Technical Reports (MSTR)
This paper focuses on the inverse problem of identifying an internal void in a bounded two- or three-dimensional region. Information, in form of a heat flux and temperature, is assumed to be obtainable only on the external boundary of the region. The reciprocity gap approach with a suitable test functions is used in both the two- and three-dimensional cases.
Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi
Non-Destructive Recovery Of Voids Within A Three Dimensional Domain Using Thermal Imaging, Victor B. Oyeyemi
Mathematical Sciences Technical Reports (MSTR)
We develop an algorithm capable of detecting the presence of spherical voids in a thermally conducting object. In addition, the process recovers both the radii and locations of each void. Our method involves the application of a known steady state heat flux to the object's boundary and measurement of the induced steady state temperature on the boundary.
Foundations Of Generalized Cwatsets, Jesse Beder
Foundations Of Generalized Cwatsets, Jesse Beder
Mathematical Sciences Technical Reports (MSTR)
We present a new, abstract definition for a generalized cwatset that produces notions of subcwatset and quotient cwatset that behave naturally. We use small cancellation theory to prove a result analogous to the statement that every group is isomorphic to some permutation group.
Thermal Imaging Of Circular Inclusions Within A Two-Dimensional Region, Shannon Talbott, Hilary Spring
Thermal Imaging Of Circular Inclusions Within A Two-Dimensional Region, Shannon Talbott, Hilary Spring
Mathematical Sciences Technical Reports (MSTR)
The ability to study the interior of an object without destroying it is an important industrial tool. One method of recent interest is steady-state thermal or impedance imaging. In this paper we will use the steady-state heat equation to locate one or more circular inclusions within a two-dimensional region, where the boundaries of the inclusions have partially disbonded from the surrounding material; this disbond is modelled as between the heat flux and jump discontinuity at the disbonded interface.
Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal
Time-Dependent Thermal Imaging Of Circular Inclusions, Donald L. Brouwn, Mark Hubenthal
Mathematical Sciences Technical Reports (MSTR)
This paper considers the inverse problem of locating one or more circular inclusions in a two-dimensional domain using thermal boundary data, specifically, the input heat flux and measured boundary temperature. The forward problem is governed by the heat equation. We show how the position and size of such defects can be recovered using the boundary data and various approximations of the solution to the forward problem. We also consider the stability of the algorithm involved to recover the defects.
Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh
Reconstruction Of Partially Conductive Cracks Using Boundary Data, David Mccune, Janine Haugh
Mathematical Sciences Technical Reports (MSTR)
This paper develops an algorithm for finding one or more non-insulated, pair-wise disjoint, linear cracks in a two dimensional region using boundary measurements.