supported by the National Science Foundation (DMS-0353880)

Summer 2005- Thanks for a great summer!



Rahul Bansal              University of Texas
Rien Beal                     Bethune-Cookman College
Omar  Chilous            Alabama A&M
Atoshi Chowdhury      Princeton University
Patrick  Corbin            Tulane University
David Eisenstat          University of Rochester
Sylvia  Fanous             Iowa State University
Aleka McAdams         DePauw University
Kelly McConville         St. Olaf College
Tracy McKay                Bowdoin College
Jude Melancon           Louisiana State University
Christina Monford       Florida A&M
Danielle Newton        Benedict College
Justin P. Peters         Wartburg College
Nathan Ray                 Southeast Missouri State
David Watson             Carleton College



  • Stegnalysis: An Exploration of Methods Prof. Jennifer Davidson, Prof. Clifford Bergman, Eric Hansen, Aleka McAdams, Tracy McKay

  • The chi-square attack is a steganalytic method developed by Westfeld and Pfitzmann (1999) in order to recognize some types of steganographic embedding in the least significant bits (LSBs) of an image's pixel values.  When the chi-square attack is applied to a JPEG image, it  produces a graph of the probability of steganographic embedding vs. the sample size of the image's quantized DCT coefficients. By examining this graph an analyst can determine whether or not an image contains steganographic embedding. We explored the chi-square attack and used Receiver Operating Characteristic (ROC) curves to develop an automated method that objectively evaluates the results of the chi-square attack and determines whether or not a JPEG image contains an embedded Jsteg message.  Although our research was done on images embedded using Jsteg, the methods we used could also be applied to other stego-algorithms with predictable embedding schemes.  Furthermore, the feature we used to automate this test can be used along with other features in Artificial Neural Network pattern classification of steganographic images.
  • Performance Analysis of Numerical Software for Stiff Ordinary Differential Equations Prof. Roger Alexander , Jangwoon Lee, Omar Chilous, Sylvia Fanous, Nathan Ray

  • The purpose of this project is to apply a new method to evaluate the performance of numerical solvers of stiff ordinary differential equations. We evaluate the performance of the numerical software by comparing computed solutions with analytic approximations obtained by the method of matched asymptotic expansions.
  • Rational realization of nonzero rational eigenvalues for trees and symmetric tree sign patterns Prof. Leslie Hogben, Rana Mikkelson, Atoshi Chowdhury, Jude Melancon

  • A sign  pattern is a  matrix  whose entries  are elements of {+, -,0}; it describes the set of real matrices whose entries have the signs in the pattern. A graph (that allows loops but not multiple edges) describes  the set of symmetric matrices  having a zero-nonzero pattern of entries determined by  the absence or presence of edges in the graph. DeAlba, Hardy, Hentzel, Hogben Wangsness gave algorithms for the computation of maximum multiplicity and minimum rank of matrices associated with a tree sign pattern or tree, and an algorithm to obtain an integer matrix realizing minimum rank.  We extend these results by giving algorithms to obtain a symmetric rational matrix realizing the maximum multiplicity of a rational eigenvalue among symmetric matrices associated with a symmetric tree sign pattern or tree. The group's paper has appeared in Linear Algebra and Its Applications. Iowa State University Combinatorial Matrix Theory Research Group
  • Strongly Regular Graphs Prof. Sung Yell Song, Joohyung Kim David Eisenstat, Dave Watson
  • We define strongly regular graphs and give some constructions for some strongly regular graphs with specific parameters, namely v=64,k=28,\lambda =12,\mu =12.  Our goal is to characterize these constructions by using the structure of the combinatorial objects from which they come.
  • Mathematical Systems Theory  Prof. Wolfgang Kliemann, Prof. Justin Peters, Chris Kurth, Jose Reyes, Rien Beal, Patrick Corbin, Kelly McConville, Christina Monford, Danielle L. Newton  The Mathematical Systems Theory group at Iowa State University consists of 13 faculty members from the departments of Mathematics, Statistics, Physics, and several engineering departments. The group collaborates on various interdisciplinary research projects in the areas of control theory, nanotechnology, national infrastructure, bioinformatics, and stochastic systems.  Increasingly, the role of an applied mathematician is that of a collaborator in large interdisciplinary teams, and students who join this team will have experiences in collaborative research that should make the transition to becoming a research mathematician easier.  In 2005, five studetns worked in on several projects in dynamical systems:
    • Global Behavior of Dynamical Systems- Patrick Corbin, Kelly McConville  In the analysis of dynamical systems, the most central concept is that of the system's limit sets.  Traditionally, two distinct methods are employed in the characterization of these limit sets: chain recurrence, and attractor-repeller theory.  In this paper, we will show that these two methods yield the same description of the limit sets, and thus are equivalent.  More specifically, assuming a finest Morse Decomposition on the system, the minimal attractors andrepellers are chain recurrent.  A paper has appeared.
    • Relating Groups To Dynamical Systems- Rien Beal The purpose of this project is to analyze groups, and if given all of the properties of a group try to determine the properties of an associated dynamical system. Since a dynamical system is a group itself, in this research we hope to find properties of a dynamical system such as fixed points, periodic orbits, and cyclic orbits from
    • <>only the knowledge of the group. Finding the properties for this special dynamical system is slightly different than finding the properties of a traditional dynamical system mainly because in this special case we will be dealing with discrete time.  Continuity does not apply when dealing with group structures.
    • Mathematics of the Heart Beat Cycle- Christina Monford, Danielle L. Newton  The purpose of this research project is to analyze a mathematical model that reflects the behavior of the heart beat cycle by applying various mathematical methods. This research project should accomplish three main objectives. The first objective is to analyze and prove that the mathematical model should exhibit an equilibrium
    • <>or relaxed state corresponding to diastole which is the rhythmic expansion of the chambers of the heart at each heartbeat, duringwhich they fill with blood. Secondly, to show that there must be a threshold for triggering the electrochemical waves emanating from
      arteries. Lastly, to demonstrate that the mathematical model must reflect a rapid return to an equilibrium state.
  • Modeling Cancer Mathematically Prof. Khalid Boushaba, Prof. Howard Levine, Fernando Miranda-Mendoza, Rahul Bansal, Justin Peters.  Metastases are the main cause of mortality in cancer.  The surgical removal of a primary tumor is often followed by a rapid growth of secondary tumors (metastases) that may have been dormant in a distant organ for many years. This project models this phenomena using a model that focuses on the idea that secreted growth factors from the primary tumor have a rather short half life and thus cannot diffuse very far without degrading or binding to the extra cellular matrix (ECM) and becoming deactivated whereas secreted inhibitors have a much longer half life and thus able to diffuse over longer distances.  This project had two parts:
    • Simulations in one dimension on a model for the regulation of tumor dormancy- Rahul Bansal

    • In this paper, we present simulations on the model for the regulation of tumor dormancy established by K. Boushaba, H. A. Levine and M. Nilsen-Hamilton. There the authors studied the interaction between a mother tumor and a daughter tumor through the tracking of biochemicals in the bloodstream in a two-compartment model described by a system of twelve ODEs. Here we wish to include the notion of spatial distribution of cell density and thus we consider the more general model described by a system of six PDEs.
    • A Mathematical Model for Fibroblast Growth Factor Competition Based on Enzyme Kinetics (Mathematical Biosciences and Engineering, October 2005 see also cover)- Khalid Boushaba and Justin P. Peters

    • In this paper, we develop a mathematical model for the competition of two species of fibroblast growth factor, FGF-1 and FGF-2, for the same cell surface receptor.  We provide pathways for this interaction using experimental data obtained by Neufeld and Gospodarowicz in \textit{Basic and Acidic Fibroblast Growth Factors Interact with the Same Cell Surface Receptors} as a guide. These pathways demonstrate how the interaction of two fibroblast growth factors affects cell proliferation.  Upon development of these pathways, we use simulations in MATLAB and optimization to extrapolate the values of a variety of biochemical parameters
      imbedded within the model. Furthermore, it should be possible to use the model as the basis for a testable hypothesis. We explore this predictive ability with further simulations in MATLAB.

Useful Links

Latex slides

Matlab Information has links to Matlab guides

Young Mathematicians Conference at Ohio State- Rahul, Justin, Tracy, Jude, and Patrick particpated

Mathematics Department Homepage
Web page maintained by Leslie Hogben
Last Update: 4-May-07