Mathematics Commons^™

Using Mathematics To Gain Insights Into Biology: An Application In Respiratory Mechanics, William Matern

Inquiry Journal 2012

No abstract provided.

Computer-Monitored Problem-Solving Dialogues, Christine Warner, Melissa Butts, Dan Leighty

Symposium on Research and Creative Expression (SORCE)

This project shadows the work of student groups in Math 110, a qualitative literacy class, engaged in exploratory learning exercises. An instructor monitors these groups by both walking around the room and observing group conversation at another computer. Our goal is to put this exercise online, and as a result leave the entire monitoring process up to the computer, assuming the role that the instructor traditionally assumes. Using labeling techniques to decipher meaning in dialogue of students working in groups for Math 110, we try to see how students collaborate to solve problems together. Bits of realization, conversation, and problem-solving …

Teaching Computers To Think: Analysis Of Artificial Intelligence And Connect Four, Kirk Baly, Andrew Freeman, Andrew Jarratt, Kyle Kling, Owen Prough

Symposium on Research and Creative Expression (SORCE)

Connect Four is a classic two person, zero-sum game in which players utilize their wits and gravity to connect four of their own pieces in a horizontal, vertical, or diagonal row while blocking their opponent’s attempt to do the same. We have constructed a simulation of this game which we have used as a base for the implementation and testing of varying Artificial Intelligence (AI) systems. Early strategies worked according to simple strategic methods, while more advanced heuristics employed a Min-Max Tree in tandem with methods to determine how advantageous a certain board would be. This Min-Max Tree goes beyond …

Equitable Labelings Of Caterpillar Graphs, Mark Burek, William Olson, Brock Taulbee

Symposium on Research and Creative Expression (SORCE)

The Graceful Tree Conjecture in graph theory has been open for almost half a century. The conjecture states that the vertices of any tree can be labeled with distinct integers between 0 and the number of edges of the tree in a way that the edges can be uniquely identified by the absolute value of the difference between their vertex labels. One possible approach to prove the conjecture is to prove the more general k-equitable tree conjecture. In a k-equitable labeling we assign integers from the set {0,1,2,…,k-1} to the vertices. Each edge will receive a label that is the …

Section Abstracts: Astronomy, Mathematics And Physics With Materials Science

Virginia Journal of Science

Abstracts of the Astronomy, Mathematics, and Physics with Material Science Section for the 90th Annual Meeting of the Virginia Academy of Science, May 23-25, 2012, Norfolk State University, Norfolk, Virginia

Mathematical Dispositions And Student Learning: A Metaphorical Analysis, Jinfa Cai, Victoria Robison, John Moyer, Ning Wang, Bikai Nie

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Mean-Field Boolean Network Model Of A Signal Transduction Network, Naomi Kochi, Mihaela Teodora Matache

Mathematics Faculty Publications

In this paper we provide a mean-field Boolean network model for a signal transduction network of a generic fibroblast cell. The network consists of several main signaling pathways, including the receptor tyrosine kinase, the G-protein coupled receptor, and the Integrin signaling pathway. The network consists of 130 nodes, each representing a signaling molecule (mainly proteins). Nodes are governed by Boolean dynamics including canalizing functions as well as totalistic Boolean functions that depend only on the overall fraction of active nodes. We categorize the Boolean functions into several different classes. Using a mean-field approach we generate a mathematical formula for the …

2012 (Spring), University Of Dayton. Department Of Mathematics

Colloquia

Abstracts of the talks given at the 2012 Spring Colloquium.

Autologous Stem Cell Transplant Is Feasible In Very Elderly Patients With Lymphoma And Limited Comorbidity, Rebecca L. Elstrom, Peter Martin, Sandra M. Hurtado Rua, Tsiporah B. Shore, Richard R. Furman, Jia Ruan, Roger N. Pearse, Morton Coleman, Tomer Mark, John P. Leonard, Usama Gergis

Mathematics and Statistics Faculty Publications

In patients with recurrent Hodgkin or non-Hodgkin's lymphoma, autologous stem cell transplantation (ASCT) can offer potential for cure or long-term remission. Because of potential toxicity, elderly patients are usually not considered candidates, but data regarding tolerability and efficacy in this group are lacking. The transplant database at Weill Cornell Medical College was reviewed to identify patients with lymphoma undergoing ASCT at age 69 or greater. Clinical data and comorbidities were correlated with outcome. Twenty-one patients were identified. Sixteen of 19 evaluable patients (76%) achieved complete remission following ASCT, while 2 patients died before response assessment. Median progression-free survival following ASCT …

Linear Combinations Of Heuristics For Examination Timetabling, Jay Yellen, Edmund K. Burke, Nam Pham

Faculty Publications

Although they are simple techniques from the early days of timetabling research, graph colouring heuristics are still attracting significant research interest in the timetabling research community. These heuristics involve simple ordering strategies to first select and colour those vertices that are most likely to cause trouble if deferred until later. Most of this work used a single heuristic to measure the difficulty of a vertex. Relatively less attention has been paid to select an appropriate colour for the selected vertex. Some recent work has demonstrated the superiority of combining a number of different heuristics for vertex and colour selection. In …

Electrocardiographic Abnormalities Among Mexican Americans: Correlations With Diabetes, Obesity, And The Metabolic Syndrome, Saulette R. Queen, Beverly Smulevitz, Anne R. Rentfro, Kristina Vatcheva, David D. Mcpherson, Susan P. Fisher-Hoch, Joseph B. Mccormick, Susan T. Laing

School of Mathematical & Statistical Sciences Faculty Publications

Background: Resting ischemic electrocardiographic abnormalities have been associated with cardiovascular mortality. Simple markers of abnormal autonomic tone have also been associated with diabetes, obesity, and the metabolic syndrome in some populations. Data on these electrocardiographic abnormalities and correlations with coronary risk factors are lacking among Mexican Americans wherein these conditions are prevalent.

Objective: This study aimed to evaluate the prevalent resting electrocardiographic abnormalities among community-dwelling Mexican Americans, and correlate these findings with coronary risk factors, particularly diabetes, obesity, and the metabolic syndrome.

Methods: Study subjects (n=1280) were drawn from the Cameron County Hispanic Cohort comprised of community-dwelling Mexican Americans living …

Mapping Of Stochastic Matrices Into Polynomial Form In The Complex Plane, Jordan Emile Cates

Honors Theses

This thesis originated from a specific problem from biology. Namely we need to study probabilistic models that represent molecular interactions that take place inside living cells, such as the number of molecular heat-shock proteins present in a cell. Because of the intrinsic discrete nature of the number of molecules present in cells, the fundamental mathematical models are based on Markov processes. For such processes a transition probability matrix describes the evolution of the state of the cell, whereas the state itself, i.e. the number of molecules present at a specific time, is described by a vector. The components of this …

Generalized Borcea-Voisin Construction, Jimmy Dillies

Mathematical Sciences: Faculty Publications

C. Voisin and C. Borcea have constructed mirror pairs of families of Calabi-Yau threefolds by taking the quotient of the product of an elliptic curve with a K3 surface endowed with a non-symplectic involution. In this paper, we generalize the construction of Borcea and Voisin to any prime order and build three and four dimensional Calabi-Yau orbifolds. We classify the topological types that are obtained and show that, in dimension 4, orbifolds built with an involution admit a crepant resolution and come in topological mirror pairs. We show that for odd primes, there are generically no minimal resolutions and the …

Parameterized Special Theory Of Relativity (Pstr), Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

We have parameterized Einstein’s thought experiment with atomic clocks, supposing that we knew neither if the space and time are relative or absolute, nor if the speed of light was ultimate speed or not. We have obtained a Parameterized Special Theory of Relativity (PSTR), first introduced in 1982. Our PSTR generalized not only Einstein’s Special Theory of Relativity, but also our Absolute Theory of Relativity, and introduced three more possible Relativities to be studied in the future. After the 2011 CERN’s superluminal neutrino experiments, we recall our ideas and invite researchers to deepen the study of PSTR, ATR, and check …

Using Predictive Analytics To Detect Major Problems In Department Of Defense Acquisition Programs, Austin W. Dowling

Theses and Dissertations

This research provides program analysts and Department of Defense (DoD) leadership with an approach to identify problems in real-time for acquisition contracts. Specifically, we develop optimization algorithms to detect unusual changes in acquisition programs’ Earned Value data streams. The research is focused on three questions. First, can we predict the contractor provided estimate at complete (EAC)? Second, can we use those predictions to develop an algorithm to determine if a problem will occur in an acquisition program or subprogram? Lastly, can we provide the probability of a problem occurring within a given timeframe? We find three of our models establish …

Full Isolation Number Of Matrices: Some Extremal Results, David Tate, David E. Brown

Browse All Undergraduate research

A set of nonzero entries of a (0,1)-matrix is an isolated set if no two entries belong to the same row, no two entries belong to the same column, and no two entries belong to a submatrix of the form [1 1; 1 1]. The isolation number of a matrix is the maximum size over all isolated sets. The isolation number of a matrix is a well-known and well-used lower bound for the matrix's Boolean rank. We will discuss the isolation number of the adjacency matrix of various graphs and develop some extremal results for n x n matrices with …

Self-Assembly Of Self-Similar Structures By Active Tiles, Daria Karpenko

USF Tampa Graduate Theses and Dissertations

The natural capacity of DNA for molecular self-assembly has already been exploited to create DNA based tiles which can self-assemble into nano-scale arrays and carry out nano-scale computation. Thus far, however, all such self-assembly has been passive, in the sense that the binding capacities of a tile are never altered throughout the assembly. The idea of active tiles, tiles that can send signals to each other and activate latent binding sites, has been proposed but never incorporated into a formal model. Here, I present an extension of the existent abstract tile assembly model by defining an active tile assembly and …

Essays In The Economics Of Environmental Policy., Ashokankur Datta Dr.

Doctoral Theses

It is increasingly being accepted that the planet we live in is unable to fulfill the enormous resource demands that mankind places on it. As a result the environment we live in has undergone rapid changes in the last two centuries - changes that adversely affects human life. Long ago Thomas Malthus and more recently the Club of Rome researchers warned that rapid economic and population growth were going to be unsustainable as they are going to create an acute shortage of food and vital metals like mercury. Their predictions never passed the test of time (Sterner, 2003). However their …

A Women-Only Comparision Of The U.S. Air Force Fitness Test And The Marine Combat Fitness Test, Tarah D. Mitchell

Theses and Dissertations

In 2009, Captain Thomas Worden determined the Air Force Physical Fitness Test (AFPFT) poorly predicted combat capability for his 86 study participants. With only 5 of these 86 volunteers being women, this limited Worden's findings to primarily men. This follow-on research investigated whether these results carried over to women. We recruited 61 female volunteers and compared their performance on the AFPFT to the Marine Combat Fitness Test, the proxy for combat capability. Like Worden's research, we discovered little association between the two (R² of 0.161). However, this association significantly increased (adj R² of 0.572) when utilizing the raw …

Multiple Solutions Of The Quasi Relativistic Choquard Equation, Michael Melgaard, Frederic D. Y. Zongo

Articles

We prove existence of multiple solutions to the quasi relativistic Choquard equations with a scalar potential.

Hadamard Renormalisation Of The Stress Energy Tensor On The Horizons Of A Spherically Symmetric Black Hole Space-Time, Cormac Breen, Adrian Ottewill

Articles

We consider a quantum field which is in a Hartle-Hawking state propagating in a general spherically symmetric black hole space-time. We make use of uniform approximations to the radial equation to calculate the components of the stress tensor, renormalized using the Hadamard form of the Green's function, on the horizons of this space-time. We then specialize these results to the case of the `lukewarm' Reissner-Nordstrom-de Sitter black hole and derive some conditions on the stress tensor for the regularity of the Hartle-Hawking state

On FoxʼS M-Dimensional Category And Theorems Of Bochner Type, John Oprea, Jeff Strom

Mathematics and Statistics Faculty Publications

We show that cat M (X)=Cat (jm),where cat m(X) is Fox’s m-dimensional category, jm:X→X [m] is the mth Postnikov section of X and cat (X) is the Lusternik–Schnirelmann category of X. This characterization is used to give new “Bochner-type” bounds on the rank of the Gottlieb group and the first Betti number for manifolds of non-negative Ricci curvature. Finally, we apply these methods to obtain Bochner-type theorems for manifolds of almost non-negative sectional curvature.

Combinatorics Using Computational Methods, Derrick Stolee

Department of Mathematics: Dissertations, Theses, and Student Research

Computational combinatorics involves combining pure mathematics, algorithms, and computational resources to solve problems in pure combinatorics. This thesis provides a theoretical framework for combinatorial search, which is then applied to several problems in combinatorics. Some results in space-bounded computational complexity are also presented.

Lecture Hall Sequences, Q-Series, And Asymmetric Partition Identities, Sylvie Corteel, Carla D. Savage, Andrew Sills

Mathematical Sciences: Faculty Publications

We use generalized lecture hall partitions to discover a new pair of q-series identities. These identities are unusual in that they involve partitions into parts from asymmetric residue classes, much like the little Göllnitz partition theorems. We derive a two-parameter generalization of our identities that, surprisingly, gives new analytic counterparts of the little Göllnitz theorems. Finally, we show that the little Göllnitz theorems also involve “lecture hall sequences,” that is, sequences constrained by the ratio of consecutive parts.

Quadratic Spline Approximation Of The Newsvendor Problem Optimal Cost Function, Christina Marie Burton

Theses and Dissertations

We consider a single-product dynamic inventory problem where the demand distributions in each period are known and independent but with density. We assume the lead time and the fixed cost for ordering are zero and that there are no capacity constraints. There is a holding cost and a backorder cost for unfulfilled demand, which is backlogged until it is filled by another order. The problem may be nonstationary, and in fact our approximation of the optimal cost function using splines is most advantageous when demand falls suddenly. In this case the myopic policy, which is most often used in practice …

The National & State Context Of Stem Education: Past, Present, And Future, Henry M. Huckaby, Kamau Bobb, Charles Kutal, Judy Awong-Taylor

Interdisciplinary STEM Teaching & Learning Conference (2012-2019) (Archived)

N/A

The 1, 2-Conjecture For Graphs With Relatively Small Chromatic Number, Sogol Jahanbekam, Douglas West

Faculty Publications

No abstract provided.

Metacalibration In Geometric Optimization, Donald C. Sampson

Theses and Dissertations

A introduction to metacalibration methods and their application. This includes a new proof of the double bubble conjecture, new results in the area of equitent problems (isoperimetric problems with boundary), and comments on a mapping conjecture.

Exploring The On-Line Partitioning Of Posets Problem, Leah F. Rosenbaum

Scripps Senior Theses

One question relating to partially ordered sets (posets) is that of partitioning or dividing the poset's elements into the fewest number of chains that span the poset. In 1950, Dilworth established that the width of the poset - the size of the largest set composed only of incomparable elements - is the minimum number of chains needed to partition that poset. Such a bound in on-line partitioning has been harder to establish, and work has evalutated classes of posets based on their width. This paper reviews the theorems that established val(2)=5 and illustrates them with examples. It also covers some …

Subdivision Rules, 3-Manifolds, And Circle Packings, Brian Craig Rushton

Theses and Dissertations

We study the relationship between subdivision rules, 3-dimensional manifolds, and circle packings. We find explicit subdivision rules for closed right-angled hyperbolic manifolds, a large family of hyperbolic manifolds with boundary, and all 3-manifolds of the E^3,H^2 x R, S^2 x R, SL_2(R), and S^3 geometries (up to finite covers). We define subdivision rules in all dimensions and find explicit subdivision rules for the n-dimensional torus as an example in each dimension. We define a graph and space at infinity for all subdivision rules, and use that to show that all subdivision rules for non-hyperbolic manifolds have mesh not going to …