Math Sciences

Upcoming Activities - Fall 2013

November 21, 11:00 am - 12:00 pm in KOM 206.

Professor Guoliang Yu, Powell Chair professor in Mathematics,  Texas, A&M University, will present "Large scale geometry and its applications" .
Abstract: I will give a survey on large scale geometry and discuss its applications to topology and analysis.  I will make an effort for this talk to be accessible to students and non-experts.
Professor Yu is the leader in the field of geometric topology and non-commutative geometry (
His exceptional accomplishments in this regard were recognized with an invitation to present an invited address at the International Congress of Mathematicians in Madrid in 2006 -- an event held only every four years and widely viewed as the single most prestigious venue in global mathematics.
November 14, 11:00 am - 12:00 pm, KOM 206
Dr. Craig Larson,
from Virginia Commonwealth University, will present "Eigenvalues of Saturated Hydrocarbons".
Abstract: We discuss the use of graph theory in representing molecular structure, gently introduce the calculation of the determinant of a graph, and then propose a simplified Hückel-type molecular-orbital (MO) model for the valence electrons of saturated hydrocarbons and consider the consequent eigenvalue spectrum. We obtain a first foundational result, which every chemist "knows'', namely that: alkanes are stable, with half their (Hückel-type MO) eigenvalues positive and half negative. We leave open the conjecture that this is also true for the full class of saturated hydrocarbons with a specific interaction constant.

Dr. Larson's research interests are in Discrete Mathematics and Mathematical Chemistry. His researches currently involve graph theory, fullerenes and artificial intelligence. He published over 20 research papers in high quality journals, and he was a Fulbright Research Scholar at Ghent University, Belgium.

Recent Activities - Fall 2013

November 7, 11:00 am - 12:00 pm, KOM 206
Professor Robert Aldred
from the University of Otago, New Zealand will present "Edge proximity and matching extensions in triangulations of surfaces" (joint work with Mike Plummer and Jun Fujisawa), in the Discrete Mathematics seminar.
Abstract: The extendability of graphs embedded in surfaces is bounded above by the genus of the surface. We consider extendability of graphs embedded in the plane, projective plane, torus and Klein bottle and look at some interesting properties of matching extension in triangulations of these surfaces.

Dr. Aldred's research interests are in Discrete Mathematics and Graph Theory. His current researches involve paths, cycles, matchings and colourings in graphs. Dr. Aldred is Editor-in-chief of Journal Combinatorial Mathematics and Combinatorial Computing, and an associate editor of Electronic Journal of Combinatorics.

November 8, 2:00 pm - 3:00 pm, KOM 206
Dr. Guannan Zhang
from Oak Ridge National Laboratory will present "Adaptive Hierarchical Stochastic Collocation Methods for High-Dimensional Approximation, Discontinuity Detection and Parameter Estimation".
Abstract:  We will discuss an adaptive hierarchical stochastic collocation (AHSC) framework that ad- dresses several challenges arising in uncertainty quantication (UQ) including: quantication of high-dimensional quantities of interest; high-dimensional discontinuity detection; and reducing com- putational complexity of parameter estimation. For high-dimensional approximation, we extended the conventional AHSC method by incorporating the wavelet basis into the sparse-grid framework. Second-generation wavelets are used constructed from a lifting scheme which allow us to preserve the framework of the multi-resolution analysis, compact support, as well as the necessary interpo- latory and Riesz property of the hierarchical basis. For high-dimensional discontinuity detection, We developed a hyper-spherical stochastic collocation method for identifying jump discontinuities by incorporating a hyper-spherical coordinate system (HSCS) into the sparse-grid approximation framework. An approximate discontinuity surface is constructed directly in the hyper-spherical system with a greatly reduced number of sparse grid points compared to existing methods. For parameter estimation problems with computationally expense physical simulations, we incorporate the AHSC approach with high-order hierarchical basis into Bayesian inference framework to reduce computational complexity in MCMC sampling. A surrogate of the posterior probability density function (PPDF) is constructed using the AHSC methods. High-order local hierarchical polynomi- als (e.g. quadratic, cubic basis) are used to further improve the accuracy and cost of the surrogate. Moreover, to eciently approximate PPDFs with multiple signicant modes, we also incorporate optimization into our new approaches.

October 22, 2013: Honors Building Room 202 2:00 pm
Mr. Brandon Banes,
candidate for the degree of Doctor of Philosophy in Mathematics and Science Education will defend his thesis "A Study of Pre-service Elementary Teachers Learning Mathematics through Problem-based Learning and Problem Solving"
Abstract: This doctoral defense presents a study of pre-service elementary teachers learning mathematics through problem-based learning (PBL) and problem solving.  Qualitative data were collected and analyzed using grounded theory methodology to study how pre-service elementary teachers constructed mathematics content knowledge using PBL and problem solving.  Quantitative data were analyzed to compare two control groups and an experimental group to determine the potential benefits of learning mathematics through PBL and problem solving on mathematics content knowledge, attitudes toward mathematics, and mathematics anxiety.

Mr. Banes dissertation committee is: Dr. Diane Miller (Chair), Dr. Angela Barlow, Dr. Terry Goodin, Dr. Ginger Holmes Rowell, Dr. Jeremy Strayer.
The dissertation defense is is open and may be attended by MTSU faculty, staff, and students.

October 18 2013: KOM 206 2:00 pm - 3:00 pm
Dr. Ying Guo,
Emory University will present "A hierarchical group ICA model for studying brain functional networks in fMRI studies" at the COMS seminar.
Abstract: Functional magnetic resonance imaging (fMRI) is a powerful non-invasive tool for studying behavior-, clinical- and cognitive-related neural activity. Observed fMRI data represent the combination of spatiotemporal processes from neural signals generated by various brain functional networks. A major goal in fMRI studies is to identify and characterize the underlying functional networks. Independent component analysis (ICA) is a computational technique that has been widely applied for this purpose. In this talk, I present a new hierarchical group ICA regression model that can directly model subjects' covariate effects in decomposition of multi-subject imaging data. The proposed model fills an important gap in the ICA literature by providing a formal statistical method to model subjects' characteristics on underlying source signals. A maximum likelihood estimation method via the EM algorithm is developed for the proposed model. Simulation studies show that our method provides more accurate estimation for brain functional networks on both the population- and individual- level compared to existing approaches. The hierarchical ICA regression model can potentially have important applications in fMRI studies to examine how spatial distributed patterns of functional networks vary with subjects' clinical and demographical variables. I will illustrate our method with an fMRI data example.

October 17, 2013; KOM 206 9:30 am - 10:30 am.  Mathematical Biology Seminar.  The group will continue its analysis of "Modeling with Ito Stochastic Differential Equations".  For more information, please contact Dr. Rachel Leander, Department of Mathematical Sciences, MTSU.

October 8, 2013: KOM 206 1:00 pm - 2:00 pm
Professor Dingxuan Zhou,
City University of Hong Kong, will present "Learning Theory and Some Applications in Data Analysis"
Abstract: Analyzing and processing big data has been an important and challenging task in various fields of science and technology. Learn- ing theory has wide applications in data analysis for handling big data. It aims at learning function relations or data structures from samples. In this talk I will briefly describe some topics in learning theory and their applications in data analysis. Some learning algorithms including least squares regularized regression, support vector machine classification, kernel PCA for sparsity, and minimum error entropy principle will be demonstrated.

Professor Zhou is a well known expert in the field of machine learning and approximation theory and is a chair professor of the the Department of Mathematics, City University of Hong Kong. He serves on the editorial boards of many prestigious journals such as Journal of Approximation Theory, Applied and Computational Harmonic Analysis, Advances in Computational Mathematics, J. of Intelligent Learning Systems and Applications, etc. He served as the Chair of the Department of Mathematics, City University of Hong Kong from 2006-2012.   

October 4, 2013: KOM 206 2:00 pm - 3:00 pm
Mr. JJ Lay
will present "Forecasting and Modeling with Hadoop" at the COMS seminar this Friday 2-3pm in KOM 206.
Abstract:Hadoop is a distributed computing platform developed at Yahoo in 2005 to address the issues surrounding "Big Data". Big Data refers to a computational problem that taxes the limitation of traditional computing paradigms. A key component of Hadoop is the MapReduce algorithm patented by Google in 2004. MapReduce involves dividing large problems into smaller units that can then be solved by the nodes within a cluster and aggregating the results once all nodes are finished. Unlike MPI, Hadoop has levels of fault-tolerance built-in that make it resilient to one or more node failures. This presentation will cover two projects underway that apply Hadoop to industry problems. The first is the challenge of accurately forecasting inventory needs. By using the widely accepted Holt-Winters method and applying it simultaneously to thousands of inventory items across a cluster, the ability to forecast in near realtime becomes a reality. The second problem involves using Monte Carlo simulations to project cash flow needs for a startup company. In this project a manufacturing startup must project cash flow demand for investors until a steady revenue stream can be established. This presentation will provide an overview of Hadoop and MapReduce within the context of these two problems and describe future research directions. 

September 30, 2013:  KOM 206 1:00 pm - 2:00 pm
Le Yin, MS student,  MTSU Department of Mathematical Sciences, will present: "Demonstrating the use of the medial trend analysis software "Trend Calculator" ".
Abstract: The MTSU actuarial science program has developed a medical trend analysis software package called "Trend Calculator".  It integrates four different methods for trend calculation: average ratio method, linear regression, exponential regression, and the authoregressive model.  In this talk, we will demonstrate in detail how to use this software.

September 26, 2013:  KOM 206 11:00 pm - 12:00 pm
Dr. Xiaoya Zha, MTSU Department of Mathematical Sciences, will present: "Order Dimension of Graphs" in the Discrete Mathematics Seminar Series.

September 26, 2013:  KOM 206 1:00 pm - 2:00 pm
Dr. Qiang Wu,
MTSU Department of Mathematical Sciences, will present: "Medical Trend Analysis – Methods, Software, and Research"
Abstract: In this talk I will review trend analysis techniques and discuss their applications in medical cost forecasting and trend factor calculation. The algorithms include average ratio, linear regression, exponential regression, and autoregressive model. A software package called "Trend Calculator" that integrates all the four methods was developed in EXCEL using VBA. I will also discuss some techniques and adjustments that can help to refine the trend calculation. They include rolling average smoothing, outlier detection, and credibility adjustments. Their utility in medical trend analysis could be the potential research topics for our graduate students.

September 18, 2013:  KOM 206 1:00 pm - 2:00 pm
Dr. Baxter Rogers, Research Associate Professor, Radiology & Radiological Sciences, Research Associate Professor of Psychiatry, Research Assistant Professor of Biomedical Engineering Institute of Imaging Science, Vanderbilt University, presented "Practical applications and practical concerns for learning and prediction with functional MRI".  The research colloquium is jointly sponsored by the Department of Mathematical Sciences and the Computational Sciences Ph.D. program.

September 11, 2013:  KOM 206  12:30 pm - 1:30 pm
Jeremy Richardson,
ACAS, MAAA, Senior Actuarial Analyst, Willis Casualty Actuarial Practice; gave a talk to AMSA students and faculty.

September 11 and 18, 2013:  KOM 206  11:00 pm - 12:00 pm
Dr. Dong Ye,
MTSU Department of Mathematical Sciences, presented "Unique 3-edge coloring and unique perfect matching" in the Discrete Mathematics Seminar SeriesThe abstract of his talk can be found by following the title hyperlink.

September 10, 2013:  MTSU Honors Building, Room 106 6:00pm - 7:00 pm
Dr. Alyson Lischka, presented  "The Development of a Mathematics Teacher Beliefs Instrument: An Application of Item Response Theory"  The talk is focused on Dr. Lischka's dissertation research.

August 27:
Mr. Brandon Banes
(MS 2010, current MSE Ph.D. student) presented a seminar for STEM faculty and students on campus.  The talk, "A Study of how Pre-service Elementary Teachers Learn Mathematics through Problem-based Learning and Problem Solving", focused on his dissertation research

August 28:  KOM 206  12:30 pm - 1:30 pm
Ms. Ye Ye
, MS graduate student in the Dept. of Mathematical Sciences at MTSU, reported on the presentation she gave at the 2013 Actuarial Research Conference (ARC) held at Temple University in Philadelphia; July 31 - August 3, 2013.  The title of her talk is "Trend Analysis Algorithms and Applications to health rate review".

Abstract: Under the Affordable Care Act (ACA), consumers will receive more value for their premium dollar because insurance companies are required to spend 80% (individual and small group markets) or 85% (larger group markets) of premium dollars on medical care and health care quality improvement, rather than on administrative costs. If they don't, the insurance companies must provide a rebate to their customers.  ACA and the health rate review regulation also require HHS or State to review the reasonableness of premium increases of 10% or more proposed by insurance carriers.  The trend analysis based on historical data is an important factor for health insurance rate evaluation and rate increase justification.  In this talk, we would like to introduce some trend analysis algorithms including methods of linear regression, exponential regression, and time series analysis.  Then we will present an Excel package, which includes all the methods mentioned above.  Finally, we will show trend results of premiums and claims based on some real data sets collected in Tennessee, as an application.

The project and corresponding software package development was led by Dr. Qiang Wu, and graduate students supported under the TDCI cycle-II grant awarded to MTSU.


Previous Activities - Academic Year 2012 - 2013

November 27, 2012  KOM 206  1:30pm-2:30pm
Richard Waggoner, FSA, MAAA Senior Actuary from Sterling Insurance, Bellingham WA and Windsor Health Plans, Brentwood, TN will speak to Actuarial Science students.

November 30, 2012  KOM 206  2:00pm-3:00pm
Dr. Thomas Yankeelov, Ingram Associate Professor of Cancer Research, Associate Professor of Radiology and Radiological Sciences, Biomedical Engineering, Physics, and Cancer Biology; Director of Cancer Imaging Research, Vanderbilt University Institute of Imaging Science, Vanderbilt-Ingram Cancer Center will present the abstract, "Integrating Quantitative Imaging and Biophysical Models to Predict Tumor Growth".  Abstract:  While elaborate mathematical models of tumor growth may exist, they are not of the form that can be applied to clinical data.  We will argue that clinically relevant mathematical modeling of tumor growth can be achieved by incorporation of non-invasive, quantitative imaging. After introducing the audience to a limited set of common, clinically available imaging techniques, we will proceed to present a series of examples displaying how these data can be incorporated into predictive models.  The overall goal is to have accurate models that can be populated by patient specific imaging data to provide an accurate prediction of how a particular therapeutic regimen will work in an individual patient.

March 21, 2013  KOM 200  2:30pm-4:00pm
Dr. Emiliano Valdez, Professor of Actuarial Science, Department of Mathematics, University of Connecticut, will be presenting two abstracts. His first talk will be  "Multivariate Binomial Models for Insurance Claim Counts" which will be for a technical based audience.  His second talk will be  "Health Care Issues and Reform: An Informative Discussion" which will be for a broader, non-technical audience. 

May 24-26, 2013
Sponsored by Middle Tennessee State University
26th Cumberland Conference on Combinatorics, Graph Theory, and Computing

MTSU Department of Mathematical Sciences
Murfreesboro, Tennessee 37132
Phone: (615) 898-2669
Fax: (615) 898-5422