Talks in the Department of Mathematical Sciences (Spring 2009)

• Dept. of Mathematical Sciences Seminar
  Michael A. Jones, American Mathematical Society
  Wednesday, April 15, 2:45 - 3:45 pm in Room RI-222
  
  Title:Minimal Requirements for Representation under Apportionment Methods: Cutoffs and Thresholds in the Democratic Primary
  Abstract: For the Democratic Primary, the Democratic Delegate Selection Rules stipulate that delegates be awarded based on a candidate's share of the popular vote at local district levels, as long as the candidate receives at least 15% of the popular vote. I will examine the consequences of such a 15% cutoff by analyzing the conditions under which a candidate with minimal support can receive a delegate. In any apportionment method, the number of delegates a candidate receives depends not only on his or her share of the popular vote but also on the distribution of votes among the other candidates. In fact, three situations may occur: 1) A candidate's popular vote may be insufficient to earn a delegate regardless of how the popular vote is split; 2) A candidate's popular vote may be sufficient to earn a delegate if the popular vote is split in a particular way; and 3) A candidate's popular vote is sufficient to earn a delegate regardless of how the vote is split. For the candidate with the least support, these categories are bounded by two quantities: the minimal popular support necessary for the candidate to receive a delegate, denoted by TI (the threshold of inclusion), and the minimal popular support sufficient for the candidate to receive a delegate, denoted by TE (the threshold of exclusion). I will determine the thresholds of inclusion and exclusion for different apportionment methods and explain how the choice of an apportionment method could preclude the use of a cutoff. Along the way, there will be time for a geometric perspective on apportionment and the application of an intuitive convexity result.
  
  
• Dept. of Mathematical Sciences Seminar
  Amir Golnabi, Thayer School of Engineering, Dartmouth College
  Monday, March 23, 3 – 4 pm in Room RI-224
  
  Title: Microwave Imaging for Breast Cancer Detection
  Abstract: Breast cancer is a significant health problem in the U.S. and it accounts for about 32% of all cancers in women and roughly 40,460 deaths annually. Researchers have shown that the best way to improve patient’s long term prognosis is to detect the cancer at its early stage. Today, the most common method for detection in clinical practice is X-ray mammography which is generally quite effective for a broad population of women with various breast types. However, screening mammography has substantial limitations, primarily the high false-positive rate (ranging from 1% to 29% with the mean of 10%), which can result in unnecessary and costly surgical interventions. Breast cancer detection is a particularly challenging problem for younger women and those with radiographically higher density breasts. In these cases, the increased levels of fibroglandular tissue can easily obscure small tumors, and as a result, the overall sensitivity of mammography can be significantly reduced. Mammography has other drawbacks from patient’s perspective, including uncomfortable and painful breast compression, and exposure to ionizing radiation. Other clinical standards, such as ultrasound and magnetic resonance imaging (MRI), have also been used to detect breast cancer; however, while both can achieve high spatial resolution, they do not provide information about molecular-level changes in breast tissue. In response to these shortcomings, alternative and/or complementary medical imaging modalities are being developed to improve both sensitivity and specificity of current imaging tools, and to supply more functional information about the breast tissue health. Microwave imaging spectroscopy (MIS) for breast cancer detection is one these alternative imaging approaches. Our early clinical microwave imaging studies on patients with suspected tumors demonstrated significant discrimination between those with malignant tumors versus those with benign lesions and other normal tissues. In addition to this, the non-ionizing and non-compressive nature of microwave imaging makes this technique attractive for cancer screening.
  
  
• Dept. of Mathematical Sciences Seminar
  Ashwin Vaidya, University of North Carolina at Chapel Hill
  Friday, March 13, 10:45-11:45 am in Room RI-232
  
  Title: Mathematical Theory of Fluid-Solid Interaction with Application to Particle Sedimentation
  Abstract: The interaction of fluids with solids has given rise to some very interesting mathematical and physical problems on pattern formations, stability and bifurcations. One can point to applications in a variety of fields such as engineering flow problems and those in biological systems such as aggregation phenomena of cells in blood flow. We will look at the simplest version of the general class of such problems; the motion of a single rigid body immersed in a fluid which can be Newtonian or non-Newtonian. In particular, we examine the orientational dynamics of a symmetric body moving in a fluid. Experiments show that the attitude that a particle assumes when immersed in a fluid depends upon the material properties of the fluid as well as the shape of the body. As the inertial effects in the fluid increase, vortex shedding in the wake of the body gives rise to some very interesting dynamics and transitions. In this talk we present an overview of some mathematical, experimental and numerical work that we have done regarding this problem.
  
  
• Dept. of Mathematical Sciences Seminar
  Carmen Tekwe, University of Buffalo
  Tuesday, March 10, 10:45-11:45 am in Room RI-232
  
  Title: Adjusting for Uncertainty in Estimated Radiation Dose Among Atomic Bomb Survivors
  Abstract: The survivors of the atomic bombs in Hiroshima and Nagasaki, Japan provide a study cohort for studying the effects of exposure to ionizing radiation at both low and high levels. In estimating the radiation dosage received by the survivors, several factors need to be accounted for such as the uncertainty due to classical measurement error which occurs due to imperfect recall by the survivors of their location and shielding at the time of exposure. Recent literature has pointed out the need to also account for Berkson error in estimating radiation dose among the survivors which results from the assignment of estimated group doses to individuals within a certain distance away from the hypocenter as well as imperfect system calculations. This seminar focuses on some statistical models which have been used in the past for adjusting uncertainties related to dose estimation. We propose the generalized multiple-indicators multiple-causes measurement error (G-MIMIC ME) models as a means to adjust for dose uncertainty and to also assess the effects of radiation dose on several outcomes such as chromosome aberration, glycophorin gene A mutation and epilation. Multiple-indicators multiple-causes (MIMIC) models are useful for studying the effects of a latent variable on several outcomes, when causes of the explanatory latent variable are observed. Classical measurement error is uncorrelated with the latent variable; while a Berkson error is uncorrelated with its estimate. The error in the MIMIC model with perfectly observed causes is a Berkson error and the classical Berkson error model is a special case of the MIMIC model. Previous work has focused on linear MIMIC models, where the causes of the latent variable are observed without error. We generalize the MIMIC model to allow non-linear relationships and also allowing both classical measurement error and Berkson error in the causal model, proposing the G-MIMIC ME model. We propose estimation procedures based on the Monte Carlo EM algorithm and apply our results to data collected on A-bomb survivors.
  
  
• Dept. of Mathematical Sciences Seminar
  Haiyan Su, University of Rochester Medical Center
  Monday, March 9, 10:45-11:45 am in Room RI-232
  
  Title: Comparison of Treatment Effects--An Empirical Likelihood-Based Method
  Abstract: In epidemiologic, biomedical, economic research, a common concern that often arises is how to evaluate the difference between two treatments/groups. Many methods have been proposed for evaluating the difference of the parameters in two linear models under assumptions such as normally distributed and homogeneous errors, and equal sample sizes, for example, by Chow (1960, Econometrica), Weerahandi (1987, Econometrica), and Bhuyan and Majumder (1996, Biometrical Journal). These assumptions may not be satisfied or at least need to be diagnosed. To avoid making these assumptions, we proposed a more efficient approach for treatment comparison based on the empirical likelihood, and showed that the resulting statistic is chi-squared asymptotically, which can be used to make inference and to derive confidence intervals for the difference. The Bartlett correction was applied to obtain the adjusted confidence interval. Simulation experiments illustrate that our method outperforms the published ones. Our method is used to analyze a data set from a drug study.
  
  
• Dept. of Mathematical Sciences Seminar
  Dr. Donald A. Outing, United States Military Academy
  Wednesday, March 4, 2:45-3:45 pm in Room RI-222
  
  Title: Parabolic Equation Techniques for Range-Dependent Seismo-Acoustics
  Abstract: The parabolic equation method is useful for solving non-separable wave propagation problems that are dominated by outgoing energy. It is an important method because such problems are very common; applications include seismology, ocean acoustics, atmospheric acoustics, gravity waves, electromagnetic waves, waves in porous media, and nonlinear waves. Parabolic equation techniques provide large efficiency gains and make it possible to routinely solve problems that would otherwise be difficult. Parabolic equation techniques are also very accurate provided the outgoing assumption holds. In this presentation, the speaker will provide an overview of parabolic equation techniques and discuss recent progress made in resolving some of the issues in the development of parabolic equation techniques.
  
  
• Dept. of Mathematical Sciences Seminar
  Alex Alexakis, Ecole Normale Superieure
  Tuesday, March 3, 11:00-12:00 pm in Room RI-223
  
  Title: Shear flow instabilities and mixing in strongly stratified media
  Abstract: The generation of turbulence and enhanced mixing in the presence of strong stratification is a problem that appears in many physical systems like the ocean, or accretion processes in compact stars. In such systems strong stratification is expected to suppress turbulence and thus result in minimal mixing, that is however much smaller than what is observed in nature. I will review some of the difficulties that are met when dealing with such systems and the attempts to model them. I will present some recent results that suggest a mechanism for shear flow instabilities, and the generation of turbulence. These results will be supported by numerical simulations that are carried at unprecedented large values of stratification. Conclusions on the topic and open questions will be discussed.
  
  
• Dept. of Mathematical Sciences Seminar
  Evan Fuller, University of California, San Diego
  Tuesday, March 3, 10:15-11:15 am in Room RI-232
  
  Title: In-Service Teachers’ Proof Schemes in Transition
  Abstract: Research has shown that many in-service teachers “prove” by finding a pattern from several examples. I will describe a summer professional development institute that was designed to help in-service teachers enhance their understanding of mathematical proof. I will discuss the notion of proof scheme and our approach of focusing on the explanatory power of different proofs. In particular, I will analyze teaching practices that the instructor of the institute used in order to facilitate changes in participants' understanding of proof.
  
  
• Dept. of Mathematical Sciences Seminar
  Shahriar Afkhami, Virginia Tech
  Friday, February 27, 10:45-11:45 am in Room RI-232
  
  Title: Computational investigation of interfacial dynamics in complex fluids
  Abstract: Fluids with small-scale inhomogeneities (microstructure) include suspensions, emulsions, polymer blends and surfactant solutions. Applications range from coating and extrusion to microfluidic flows. Flows of these complex fluids display features that are not found in simple flows. These novel flow phenomena can be traced back to the influence of the fluid microstructure on the stresses that develop within the flow. These flows are further complicated by the presence of a contact line, where the fluid/fluid interface intersects with a solid boundary such as controlled droplet motion by electrowetting. This talk focuses on the computational study of drop deformation in systems with two immiscible liquids such as in polymer processing, ferrohydrodynamics and moving contact line phenomena. I will briefly describe numerical methodologies I have developed for incorporating some complex features of interfacial dynamics. I will also present direct numerical simulations of the microstructure of immiscible polymer blends, combined numerical and experimental study of droplet ferrohydrodynamics and multiscale computational simulations of dynamic contact lines.
  
  
• Dept. of Mathematical Sciences Seminar
  Ling Chen, University of Missouri – Columbia
  Thursday, February 26, 10:00-11:00 am in Room RI-232
  
  Title: A Multiple Imputation Approach to the Analysis of Interval-censored Failure Time Data with the Additive Hazards Model
  Abstract: This talk will discuss regression analysis of interval-censored failure time data which occur in many fields including demographical, epidemiological and medical studies. We proposed a general semiparametric method based on multiple imputation for inference under the additive hazards model. This multiple imputation converts the analysis of interval-censored failure time data to that of right-censored failure time data. A major advantage of the approach is its simplicity and it can be easily implemented by using the existing software packages for right-censored failure time data. Extensive simulation studies are conducted and indicate that the approach performs well for practical situations and is comparable to the existing methods. The methodology is applied to a set of interval-censored failure time data arising from an AIDS clinical trial.
  
  
• Dept. of Mathematical Sciences Seminar
  Nermin Bayazit, Florida State University
  Friday, February 13, 11:30-12:30 pm in Room RI-232
  
  Title: Prospective Mathematics Teachers' Views about Mathematics, Proof and Definitions, and Their Use of Definitions in Constructing Proof
  Abstract: In this study, prospective mathematics teachers' conception of mathematics, proof and mathematical definitions, and how those conceptions may inform their proof construction approaches were investigated. Moreover, their approaches to assess the validity of a given proof were discussed. The study provided evidence that a prospective teacher who has an instrumentalist view of mathematics tended to use a heuristic approach while the one with Platonist view have a tendency to use a procedural approach.
  
  
• Physics Club Seminar/Welcome back party
  Kaitlyn Murphy
  Wednesday, February 11, 2009, 4:30 - 5:30 pm in Room RI-261
  
  Title: My Summer of REU Research in San Diego: A Jersey Girl Survives an Earthquake While Doing Math
  Audience: Physics majors, physics minors, physics and math faculty, friends of physics