Spatiotemporal Interpolation Methods For The Application Of Estimating Population Exposure To Fine Particulate Matter In The Contiguous U.S. And A Real-Time Web Application,
2016
Georgia Southern University
Spatiotemporal Interpolation Methods For The Application Of Estimating Population Exposure To Fine Particulate Matter In The Contiguous U.S. And A Real-Time Web Application, Lixin Li, Xiaolu Zhou, Marc Kalo, Reinhard E. Piltner
Mathematical Sciences: Faculty Publications
Appropriate spatiotemporal interpolation is critical to the assessment of relationships between environmental exposures and health outcomes. A powerful assessment of human exposure to environmental agents would incorporate spatial and temporal dimensions simultaneously. This paper compares shape function (SF)-based and inverse distance weighting (IDW)-based spatiotemporal interpolation methods on a data set of PM2.5 data in the contiguous U.S. Particle pollution, also known as particulate matter (PM), is composed of microscopic solids or liquid droplets that are so small that they can get deep into the lungs and cause serious health problems. PM2.5 refers to particles with a mean aerodynamic …
Partial Differential Equations And Function Spaces,
2016
Georgia Southern University
Partial Differential Equations And Function Spaces, Shijun Zheng, Simone Secchi, Huoxiong Wu, Nguyen Cong Phuc
Mathematical Sciences: Faculty Publications
It is well known that PDEs and the theory of function spaces have played a central role in the mathematical analysis of problems arising from mathematical physics, biology, and other branches of modern applied sciences. This special issue addresses the current advances in these two broad areas; in particular it focuses on the connections and interactions between them. We are happy that this issue has received the attention of active researchers with interesting and valuable contributions in the field. Topics cover areas from existence and nonexistence theorems for degenerate differential operators to multilinear fractional singular integral operators on weighted function …
A Three-Fold Approach To The Heat Equation: Data, Modeling, Numerics,
2016
Gettysburg College
A Three-Fold Approach To The Heat Equation: Data, Modeling, Numerics, Kimberly R. Spayd, James G. Puckett
Math Faculty Publications
This article describes our modeling approach to teaching the one-dimensional heat (diffusion) equation in a one-semester undergraduate partial differential equations course. We constructed the apparatus for a demonstration of heat diffusion through a long, thin metal rod with prescribed temperatures at each end. The students observed the physical phenomenon, collected temperature data along the rod, then referenced the demonstration for purposes in and out of the classroom. Here, we discuss the experimental setup, how the demonstration informed practices in the classroom and a project based on the collected data, including analytical and computational components.
Mutation Selection On The Metabolic Pathway And The Effects On Protein Co-Evolution And The Rate Limiting Steps On The Tree Of Life,
2016
Ursinus College
Mutation Selection On The Metabolic Pathway And The Effects On Protein Co-Evolution And The Rate Limiting Steps On The Tree Of Life, Katherine S. Porter
Mathematics Summer Fellows
Metabolic pathways are made of a series of reactions by enzymes at different speeds. These pathways include the rate limiting step, which is the slowest step that determines the rate of the overall reaction. To date, one study has examined the pathway of glycolysis and found no evidence of evolutionary stability of its rate limiting step. In addition, phylogenetic evidence has shown evolution in the pathway over time including gene duplication and positive selection within the pathway. This evidence suggests that there is coevolutionary selection on glycolysis. The evidence from this previous study is simulation-based. The Michaelis-Menten kinetics that describe …
Ciliate Codon Translator Program Manual,
2016
Ursinus College
Ciliate Codon Translator Program Manual, Quentin D. Altemose
Mathematics Summer Fellows
Understanding the evolutionary history of organisms allows us to better comprehend selective pressures and their effects on larger populations. In our study, we focused on analyzing the DNA of ciliate groups, which are single celled protozoans characterized by the presence of cilia on their outer membrane. We utilized the DNA of the organisms to analyze the changes in population genotype over time. We tested existing evolutionary models (designed to represent natural genetic variation over time in populations) against our data to identify the model with the best fit and likelihood. From the DNA and the evolutionary model with the highest …
Theorems On Boundedness Of Solutions To Stochastic Delay Differential Equations,
2016
University of Dayton
Theorems On Boundedness Of Solutions To Stochastic Delay Differential Equations, Youssef Raffoul, Dan Ren
Mathematics Faculty Publications
In this report, we provide general theorems about boundedness or bounded in probability of solutions to nonlinear delay stochastic differential systems. Our analysis is based on the successful construction of suitable Lyapunov functionals. We offer several examples as application of our theorems.
From Exam To Education: The Math Exam/Education Resources,
2016
The University of Texas Rio Grande Valley
From Exam To Education: The Math Exam/Education Resources, Carmen Bruni, Christina Koch, Bernhard Konrad, Michael R. Lindstrom, Iain Moyles, Will Thompson
School of Mathematical & Statistical Sciences Faculty Publications
The Math Exam/Education Resources (MER) is an open online learning resource hosted at The University of British Columbia (UBC), aimed at providing mathematics education resources for students and instructors at UBC. In this paper, there will be a discussion of the motivation for creating this resource on the MediaWiki platform, key features of the implementation that support student learning (including the evolution of the MER wiki from an exam database to a more-general learning resource), data on student use and response, potential for future development, and a brief description of how the project was implemented. Preliminary correlation data between wiki …
Efficient Algorithms And Applications In Topological Data Analysis,
2016
University of South Florida
Efficient Algorithms And Applications In Topological Data Analysis, Junyi Tu
USF Tampa Graduate Theses and Dissertations
Topological Data Analysis (TDA) is a new and fast growing research field developed over last two decades. TDA finds many applications in computer vision, computer graphics, scientific visualization, molecular biology, and material science, to name a few. In this dissertation, we make algorithmic and application contributions to three data structures in TDA: contour trees, Reeb graphs, and Mapper. From the algorithmic perspective, we design a parallel algorithm for contour tree construction and implement it in OpenCL. We also design and implement critical point pairing algorithms to compute persistence diagrams directly from contour trees, Reeb graphs, and Mapper. In terms of …
Example Of An Order 16 Non Symplectic Action On A K3 Surface,
2016
Georgia Southern University
Example Of An Order 16 Non Symplectic Action On A K3 Surface, Jimmy J. Dillies
Mathematical Sciences: Faculty Publications
We exhibit an example of a K3 surface of Picard rank 14 with a non-symplectic automorphism of order 16 which fixes a rational curve and 10 isolated points. This settles the existence problem for the last case of Al Tabbaa, Sarti and Taki's classification.
Logical Reduction Of Biological Networks To Their Most Determinative Components,
2016
University of Nebraska at Omaha
Logical Reduction Of Biological Networks To Their Most Determinative Components, Mihaela Teodora Matache, Valentin Matache
Mathematics Faculty Publications
Boolean networks have been widely used as models for gene regulatory networks, signal transduction networks, or neural networks, among many others. One of the main difficulties in analyzing the dynamics of a Boolean network and its sensitivity to perturbations or mutations is the fact that it grows exponentially with the number of nodes. Therefore, various approaches for simplifying the computations and reducing the network to a subset of relevant nodes have been proposed in the past few years. We consider a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain. …
Kolmogorov’S Axioms For Probabilities With Values In Hyperbolic Numbers,
2016
Chapman University
Kolmogorov’S Axioms For Probabilities With Values In Hyperbolic Numbers, Daniel Alpay, M. E. Luna-Elizarrarás, Michael Shapiro
Mathematics, Physics, and Computer Science Faculty Articles and Research
We introduce the notion of a probabilistic measure which takes values in hyperbolic numbers and which satisfies the system of axioms generalizing directly Kolmogorov’s system of axioms. We show that this new measure verifies the usual properties of a probability; in particular, we treat the conditional hyperbolic probability and we prove the hyperbolic analogues of the multiplication theorem, of the law of total probability and of Bayes’ theorem. Our probability may take values which are zero–divisors and we discuss carefully this peculiarity.
Optimal Control Analysis Of Ebola Disease With Control Strategies Of Quarantine And Vaccination,
2016
Prince Sultan University
Optimal Control Analysis Of Ebola Disease With Control Strategies Of Quarantine And Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, Mudassar Imran
Mathematics Faculty Publications
The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.
Anomalous Fluctuations In The Orientation And Velocity Of Swarming Bacteria,
2016
Cleveland State University
Anomalous Fluctuations In The Orientation And Velocity Of Swarming Bacteria, Shawn D. Ryan, Gil Ariel, Avraham Be’Er
Mathematics and Statistics Faculty Publications
Simultaneous acquisition of phase-contrast light microscopy and fluorescently labeled bacteria, moving within a dense swarm, reveals the intricate interactions between cells and the collective flow around them. By comparing wild-type and immotile cells embedded in a dense wild-type swarm, the effect of the active thrust generated by the flagella can be singled out. It is shown that while the distribution of angles among cell velocity, cell orientation, and the local flow around it is Gaussian-like for immotile bacteria, wild-type cells exhibit anomalous non-Gaussian deviations and are able to move in trajectories perpendicular to the collective flow. Thus, cells can maneuver …
Eccentricity Sum In Trees,
2016
University of South Carolina
Eccentricity Sum In Trees, Heather Smith, Laszlo A. Szekely, Hua Wang
Mathematical Sciences: Faculty Publications
The eccentricity of a vertex, eccT(v)=maxu∈TdT(v,u), was one of the first, distance-based, tree invariants studied. The total eccentricity of a tree, Ecc(T), is the sum of eccentricities of its vertices. We determine extremal values and characterize extremal tree structures for the ratios Ecc(T)/eccT(u), Ecc(T)/eccT(v), eccT(u)/eccT(v), and eccT(u)/eccT(w) where u,w are leaves of T and v is in the center of T. In addition, we determine the tree structures that minimize and maximize total eccentricity among trees with a given degree sequence.
How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics,
2016
Utah State University
How The Magnitude Of Prey Genetic Variation Alters Predator-Prey Eco-Evolutionary Dynamics, Michael H. Cortez
Mathematics and Statistics Faculty Publications
Evolution can alter the stability and dynamics of ecological communities; for example, prey evolution can drive cyclic dynamics in predator-prey systems that are not possible in the absence of evolution. However, it is unclear how the magnitude of additive genetic variation in the evolving species mediates those effects. In this study, I explore how the magnitude of prey additive genetic variation determines what effects prey evolution has on the dynamics and stability of predator-prey systems. I use linear stability analysis to decompose the stability of a general eco-evolutionary predator-prey model into components representing the stabilities of the ecological and evolutionary …
On A Desert Island With Unit Sticks, Continued Fractions And Lagrange,
2016
University of South Florida
On A Desert Island With Unit Sticks, Continued Fractions And Lagrange, Victor J. Ricchezza, H. L. Vacher
Numeracy
GLY 4866, Computational Geology, provides an opportunity, welcomed by our faculty, to teach quantitative literacy to geology majors at USF. The course continues to evolve although the second author has been teaching it for some 20 years. This paper describes our experiences with a new lab activity that we are developing on the core issue of measurement and units. The activity is inspired by a passage in the 2008 publication of lectures that Joseph Louis Lagrange delivered at the Ecole Normale in 1795. The activity envisions that young scientists are faced with the need to determine the dimensions of a …
Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis,
2016
Colorado State University-Pueblo
Why Be So Critical? Nineteenth Century Mathematics And The Origins Of Analysis, Janet Heine Barnett
Analysis
No abstract provided.
Henri Lebesgue And The Development Of The Integral Concept,
2016
Colorado State University-Pueblo
Henri Lebesgue And The Development Of The Integral Concept, Janet Heine Barnett
Analysis
No abstract provided.
The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry,
2016
New Mexico State University
The Failure Of The Euclidean Parallel Postulate And Distance In Hyperbolic Geometry, Jerry Lodder
Geometry
No abstract provided.
Impartial Avoidance And Achievement Games For Generating Symmetric And Alternating Groups,
2016
College of Saint Benedict/Saint John's University
Impartial Avoidance And Achievement Games For Generating Symmetric And Alternating Groups, Bret J. Benesh, Dana C. Ernst, Nándor Sieben
Mathematics Faculty Publications
Anderson and Harary introduced two impartial games on finite groups. Both games are played by two players who alternately select previously unselected elements of a finite group. The first player who builds a generating set from the jointly-selected elements wins the first game. The first player who cannot select an element without building a generating set loses the second game. We determine the nim-numbers, and therefore the outcomes, of these games for symmetric and alternating groups.
