Other Applied Mathematics Commons^™

Modeling Traffic At An Intersection, Kaleigh L. Mulkey, Saniita K. Fasenntao

Symposium of Student Scholars

The main purpose of this project is to build a mathematical model for traffic at a busy intersection. We use elements of Queueing Theory to build our model: the vehicles driving into the intersection are the “arrival process” and the stop light in the intersection is the “server.”

We collected traffic data on the number of vehicles arriving to the intersection, the duration of green and red lights, and the number of vehicles going through the intersection during a green light. We built a SAS macro code to simulate traffic based on parameters derived from the data.

In our program …

Helping A Microfinance Institution Select Its Clients: A Risk Analysis Using Social Networks, Sayantan Mitra, Varunavi Newar

Black & Gold

This paper formulates an objective mathematical model for a Microfinance Institution (MFI) to measure the credit worthiness associated with a potential client. We use concepts from network theory to determine the credit worthiness of an individual in relation to other households in the community. We use the concept of eigenvector centrality to evaluate the relative credit worthiness in the network. The latter part of the model focuses on the absolute measures of credit worthiness such as income, ownership of assets and risk of the proposed investment. This model would help MFIs reduce the risk of borrowing by ensuring that there …

Relationship Between High School Math Course Selection And Retention Rates At Otterbein University, Lauren A. Fisher

Undergraduate Honors Thesis Projects

Binary logistic regression was used to study the relationship between high school math course selection and retention rates at Otterbein University. Graduation rates from postsecondary institutions are low in the United States and, more specifically, at Otterbein. This study is important in helping to determine what can raise retention rates, and ultimately, graduation rates. It directs focus toward high school math course selection and what should be changed before entering a post-secondary institution. Otterbein will have a better idea of what type of students to recruit and which students may be good candidates with some extra help. Recruiting is expensive, …

The Riemann Curvature Tensor, Its Invariants, And Their Use In The Classification Of Spacetimes, Jesse Hicks

Presentations and Publications

The equivalence problem in general relativity is to determine whether two solutions of the Einstein field equations are isometric. Petrov has given a classification of metrics according to their isometry algebras. This talk discusses the use of the Petrov classification scheme, together with the use of scalar curvature invariants, to address the equivalence problem. These are the slides for a presentation at the Mathematics Association of America Spring 2015 conference at Brigham Young University.

Firing Rate Dynamics In Recurrent Spiking Neural Networks With Intrinsic And Network Heterogeneity, Cheng Ly

Statistical Sciences and Operations Research Publications

Heterogeneity of neural attributes has recently gained a lot of attention and is increasing recognized as a crucial feature in neural processing. Despite its importance, this physiological feature has traditionally been neglected in theoretical studies of cortical neural networks. Thus, there is still a lot unknown about the consequences of cellular and circuit heterogeneity in spiking neural networks. In particular, combining network or synaptic heterogeneity and intrinsic heterogeneity has yet to be considered systematically despite the fact that both are known to exist and likely have significant roles in neural network dynamics. In a canonical recurrent spiking neural network model, …

A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach

College of Graduate Studies: Theses & Dissertations

In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model

Solutions Of Inequality Constrained Spline Optimization Problems With The Active Set Method, Joshua A. Holloway

College of Graduate Studies: Theses & Dissertations

We solve the problem of finding a near-interpolant curve, subject to constraints, which minimizes the bending energy of the curve. Using B-splines as our tools, we give a brief overview of spline properties and develop several different cases of inequality constrained optimization problems of this type. In particular, we develop the active set method and use it to solve these problems, emphasizing the fact that this algorithm will converge to a solution in finite iterations. Our solution will solve an open problem regarding near-interpolant spline curves. Furthermore, we supplement this with an iterative technique for better choosing data sites so …

Clique Topology Reveals Intrinsic Geometric Structure In Neural Correlations, Chad Giusti, Eva Pastalkova, Carina Curto, Vladimir Itskov

Department of Mathematics: Faculty Publications

Detecting meaningful structure in neural activity and connectivity data is challenging in the presence of hidden nonlinearities, where traditional eigenvalue-based methods may be misleading. We introduce a novel approach to matrix analysis, called clique topology, that extracts features of the data invariant under nonlinear monotone transformations. These features can be used to detect both random and geometric structure, and depend only on the relative ordering of matrix entries. We then analyzed the activity of pyramidal neurons in rat hippocampus, recorded while the animal was exploring a 2D environment, and confirmed that our method is able to detect geometric organization using …

Analysis And Constructions Of Subspace Codes, Carolyn E. Troha

Theses and Dissertations--Mathematics

Random network coding is the most effcient way to send data across a network, but it is very susceptible to errors and erasures. In 2008, Kotter and Kschischang introduced subspace codes as an algebraic approach to error correcting in random network coding. Since this paper, there has been much work in constructing large subspace codes, as well as exploring the properties of such codes. This dissertation explores properties of one particular construction and introduces a new construction for subspace codes. We begin by exploring properties of irreducible cyclic orbit codes, which were introduced in 2011 by Rosenthal et al. As …

The Relationship Among Math Anxiety, Mathematical Performance, And Math Education In Undergraduate Nursing Students, Joshua D. Beall, Troy Roebuck, Paul Penkalsky

Williams Honors College, Honors Research Projects

Although nurses spend up to 40% of their day calculating and administering medication doses, undergraduate nursing students often perform poorly on nursing math exams. The purpose of this study was (a) to examine the relationship among mathematical education, performance, and anxiety and (b) to compare the mathematical education, performance, and anxiety in sophomore and senior baccalaureate nursing students at a public university in the Midwest. This cross-sectional, descriptive study was guided by Bandura's self-efficacy theory. Math performance was measured with an 11-item math instrument, math education was measured with number of math courses, and math anxiety was measured with Fennema–Sherman …

Evaluating The Long-Term Effects Of Logging Residue Removals In Great Lakes Aspen Forests, Michael I. Premer

Dissertations, Master's Theses and Master's Reports

Commercial aspen (Populus spp.) forests of the Great Lakes region are primarily managed for timber products such as pulp fiber and panel board, but logging residues (topwood and non-merchantable bolewood) are potentially important for utilization in the bioenergy market. In some regions, pulp and paper mills already utilize residues as fuel in combustion for heat and electricity, and progressive energy policies will likely cause an increase in biomass feedstock demand. The effects of removing residues, which have a comparatively high concentration of macronutrients, is poorly understood when evaluating long-term site productivity, future timber yields, plant diversity, stand dynamics, and …

Graphs Of Classroom Networks, Rebecca Holliday

College of Graduate Studies: Theses & Dissertations

In this work, we use the Havel-Hakimi algorithm to visualize data collected from students to investigate classroom networks. The Havel-Hakimi algorithm uses a recursive method to create a simple graph from a graphical degree sequence. In this case, the degree sequence is a representation of the students in a classroom, and we use the number of peers with whom a student studied or collaborated to determine the degree of each. We expand upon the Havel-Hakimi algorithm by coding a program in MATLAB that generates random graphs with the same degree sequence. Then, we run another algorithm to find the isomorphism …

Enumerating Graphs Using Integrals From Quantum Field Theory, William A. Coggins

College of Graduate Studies: Theses & Dissertations

Enumerating graphs is a relatively new subfield of mathematics. In this thesis, we will discuss a enumerative method that derives from Quantum Field Theory. We begin with the basic ideas of Calculus and extend them into a enumerative method that will allow us to classify graphs embedded on surfaces.

A Periodic Matrix Population Model For Monarch Butterflies, Emily Hunt

Senior Honors Projects, 2010-2019

The migration pattern of the monarch butterfly (Danaus plexippus) consists of a sequence of generations of butterflies that originate in Michoacan, Mexico each spring, travel as far north as Southern Canada, and ultimately return to the original location in Mexico the following fall. We use periodic population matrices to model the life cycle of the eastern monarch butterfly and find that, under this model, this migration is not currently at risk. We extend the model to address the three primary obstacles for the long-term survival of this migratory pattern: deforestation in Mexico, increased extreme weather patterns, and milkweed degradation.

On A Nonlinear Hyperbolic Partial Differential Equation With Irregular Data, Victor D´Evou´E

Applications and Applied Mathematics: An International Journal (AAM)

The main purpose of this paper is to study the existence and properties of solutions of a certain nonlinear non-Lipschitz hyperbolic partial differential equation in two independent variables with irregular data. Using regularization techniques, we give a meaning to this problem by replacing it by a tow parameters family of Lipschitz regular problems. We prove existence and uniqueness of the solution in an appropriate algebra of generalized functions and we precise how it depends on the choices made. We study the relationship with the classical solution.

A Semiparametric Estimation For Regression Functions In The Partially Linear Autoregressive Time Series Model, R. Farnoosh, M. Hajebi, S. J. Mortazavi

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, a semiparametric method is proposed for estimating regression function in the partially linear autoregressive time series model . Here, we consider a combination of parametric forms and nonlinear functions, in which the errors are independent. Semiparametric and nonparametric curve estimation provides a useful tool for exploring and understanding the structure of a nonlinear time series data set to make for a more efficient study in the partially linear autoregressive model. The unknown parameters are estimated using the conditional nonlinear least squares method, and the nonparametric adjustment is also estimated by defining and minimizing the local L2 -fitting …

Modelling The Dynamics Of A Renewable Resource Under Harvesting With Taxation As A Control Variable, B. Dubey, Atasi Patra, S. K. Sahani

Applications and Applied Mathematics: An International Journal (AAM)

The present paper describes a model of resource biomass and population with a non-linear catch rate function on resource biomass. The harvesting effort is assumed to be a dynamical variable. Tax on per unit harvested resource biomass is used as a tool to control exploitation of the resource. Pontryagin’s Maximum Principle is used to find the optimal control to maintain the resource biomass and population at an optimal level. A numerical simulation is also carried out to support the analytical results.

Approximation Of The Scattering Amplitude Using Nonsymmetric Saddle Point Matrices, Amber Sumner Robertson

Master's Theses

In this thesis we look at iterative methods for solving the primal (Ax = b) and dual (A^T y = g) systems of linear equations to approximate the scattering amplitude defined by g^Tx =y^Tb. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from "matrices, moments, and quadrature" to compute the scattering amplitude …

Partitioning Bipartite Graphs: A Modified Louvain, Emily Diana

Yale Day of Data

Abstract

How do we find communities in a graph? How does this change if the graph is bipartite? The Louvain method maximizes links within communities and minimizes those between in order to determine an optimal grouping. Yet, because it may fail when bipartite restrictions are introduced, we have adjusted the null model so as to improve performance in these conditions.

Conclusion

Our Bipartite Louvain is more robust with respect to permutations of vertices than the standard Louvain. For our synthetic examples, Bipartite Louvain typically yields a higher modularity and uncovers the ground truth communities with a higher probability. In the …

The Neural Ring: Using Algebraic Geometry To Analyze Neural Codes, Nora Youngs

Department of Mathematics: Dissertations, Theses, and Student Research

Neurons in the brain represent external stimuli via neural codes. These codes often arise from stimulus-response maps, associating to each neuron a convex receptive field. An important problem confronted by the brain is to infer properties of a represented stimulus space without knowledge of the receptive fields, using only the intrinsic structure of the neural code. How does the brain do this? To address this question, it is important to determine what stimulus space features can - in principle - be extracted from neural codes. This motivates us to define the neural ring and a related neural ideal, algebraic objects …