The Rose Mathematics Seminar

Overview

The Rose-Hulman Mathematics Seminar meets on a regular basis throughout the year per the schedule below. The seminar is quite informal and so the topics are likely to vary from week to week .  Anyone --- student, faculty, or visitor --- is encouraged to give a talk or series of talks on any topic of interest.  We're especially happy to have students attend or better yet, give talks! Students can get credit for attending and giving talks, by signing up for MA450. For seminars in past years go to the seminar history page. Here is a printable campus map if needed by our off-campus visitors.

• Regular Day and Time (Fall 2012-13): Wednesday, period 7, 1:35 P.M.
• Place: G317
• Organizer: Bill Butske butske@rose-hulman.edu   (812)-877-8602

Current and Upcoming Schedule (latest first)

• Topic:  A New Information-Splitting Image Analysis Technique
• Speaker:  Mark Inlow
• Date:  01 May 2013
• Abstract:  : Important insights into various brain diseases, Alzheimer’s for example, can be obtained by correlating changes in the brain with genetic information. Detecting such correlations is complicated by the size and complexity of the data. An MRI image of a subject’s brain may consist of over 200,000 picture elements and his/her genetic data may consist of 500,000 or more pieces of information (single nucleotide polymorphisms). For such data current brain image analysis methods based on Gaussian random field theory are inadequate for various reasons. We present research on new methods which are based on a simple geometric property of the t-statistic. Thus although preliminary results indicate these methods are superior to random field methods, the theory behind them is straightforward, requiring little beyond introductory probability and statistics.

• Topic:  Robust Analysis of Metabolic Pathways: Engineering, Biology, and Math
• Speaker:  Allen Holder
• Date:  27 Mar 2013
• Abstract:  We show how topics in engineering design can aid problems in the biological sciences, and in reverse, how the engineering fields can gain from the biological application. We particularly focus on robust optimization, which has been used in several engineering fields to support optimal designs in which parameters are uncertain. We review a couple of classic examples to highlight the central modeling themes. We then adapt the robust paradigm to a popular problem in computational biology called flux balance analysis (FBA). Previous FBA models have been linear or quadratic and have assumed a static relationship between a cell's environment and its growth rate. This assumption is doubtful, and we extend the static model to a robust counterpart that accounts for the inherit uncertainty in individual variation. The robust model advances traditional FBA's validity with regard to its scientific goals since it removes the menacing shortcoming of ignoring dynamics. The biological setting leads naturally to questions about if, and if so how, solutions to robust models converge to their static counterparts as uncertain parameters become certain. One of these results argues that static solutions are robust solutions if the variation is appropriately restricted. With regard to engineering designs, this means that optimal designs created under static conditions are indeed robust under some restricted set of parametric variation. Many of the engineering models are solved efficiently with modern second-order cone solvers. However, these solvers have been unsuccessful at solving the robust FBA models. The exact reason for this failure is unknown, and we are working to enhance the numerical stability of the optimizers. We will point to some of our suspicions about why the solvers have been unfaithful in the biological setting. If we are successful in rectifying the numerics, then the engineering applications will gain more trustworthy solvers. Thankfully, we can re-model the robust FBA problem to make use of a different solver, which has proven itself worthy of the computational task.

• Topic:  Pairs of Pants and the Congruence Laws of Geometry
• Speaker:  Allen Broughton
• Date:  30 Jan 2013
• Abstract:  Many of us know that a torus can be constructed by gluing together the opposite ends of a parallelogram. Different parallelograms yield geometrically different surfaces. For surfaces of higher genus, with more holes, the surface can be constructed by gluing together hexagons with six right angles (yes that can happen in hyperbolic geometry). Then all possible surfaces arise from the gluing of some set of hexagons. The hexagons are from a "pairs of pants" decomposition of the surface which is the big idea of this talk. Understanding the possible constructions depends on the following proposed Congruence Law in Hyperbolic Geometry: If two right-angled hexagons have three corresponding sides of equal length then they are congruent. The talk will explain all concepts from the ground up. The proposed congruence law will be related to the familiar side-side-side and side-angle side congruence theorems from high school geometry.

• Topic:  Network-based Quantitative Analysis of Crossword Puzzle Difficulty
• Speaker:  John McSweeney
• Date:  16 Jan 2013
• Abstract:  What distinguishes a crossword puzzle from a simple list of trivia questions is the interlocking nature of the answers in the grid -- one solution can promote further ones in a cascading fashion. To model this mathematically, we build a network object from a puzzle: answers in the puzzle are nodes in the network, and nodes are linked via an edge if the corresponding answers cross. Each node also has a state, "solved" or "unsolved", that depends dynamically on the states of its neighbors. Motivated by analogous issues which arise in epidemiological analyses of structured populations, we consider the following general questions: what features of the distribution of the difficulties of the clues, and of the structure of the crossword network, determine whether a puzzle can be fully (or nearly fully) solved? Are impediments to full solution typically due to puzzle structure or clue difficulty? I will present rigorous results for certain puzzles with a high degree of symmetry, as well as simulation-based analyses of "real-world" puzzles from the Sunday New York Times.

• Topic:  Challenging Problems in Computational Biochemistry
• Speaker:  Yosi Shibberu
• Date:  19 Dec 2012
• Abstract:  Biochemistry is a rich source of important computational problems that should be of interest to mathematicians, computer scientists and engineers. The dramatic drop in the cost of sequencing DNA as well as progress in several structural genomics initiatives have created many new and exciting opportunities. I will begin with a review of elementary concepts in biology and biochemistry and then describe recent progress reported in the literature on solving the grand challenge problem of biochemistry - the protein folding problem. Protein molecules are the workhorses of life. An efficient solution to the protein folding problem will dramatically improve our ability to identify the function of individual proteins and go a long way towards enabling us to design proteins with new functions. I conclude with an update of ongoing research conducted in collaboration with Mark Brandt in Chemistry and Biochemistry on characterizing structural changes believed to occur in the estrogen receptor, a protein that plays an important role in breast cancer.

• Topic:  Discrete Optimization Problems at NASA Langley Research Center
• Speaker:  Rex Kincaid, Visiting Scholar from College of William and Mary
• Date:  12 Sep 2012
• Abstract:  An overview of several discrete optimization problems of interest to NASA Langley Research Center will be presented. Applications include placement of actuators for noise control in turboprops, locating truss elements for vibration control in space structures, optimizing network metrics for air transportation, and scheduling runway configuration changes at airports.