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Talks in the Department of Mathematical Sciences
- Astronomy Club
Erika Hamden, Columbia University
Wednesday, April 9, 8:00 pm in Room RI-232
Title:
Star Formation in the
Orion Nebula
Abstract:
Erika will talk on Star Formation in the Orion Nebula Star Cluster, and the 6.5 meter telescope which gathered the spectra.
- Dept. of Mathematical Sciences Seminar
Tobias Schaefer, College of Staten Island
Tuesday, April 8, 4:00-5:00 pm in Room RI-222
Title:
Coarse-graining of noise in nonlinear systems with scale-separation
Abstract:
I will discuss three methods to coarse-grain small noise in
weakly nonlinear systems with scale-separation. The first method is based of
a method of multiple scales on the level of the stochastic equation, the
second method employs an asymptotic expansion of the associated Fokker-
Planck equation and the third method is based on a hierarchy of path
integrals. Examples from optics and fluid dynamics will illustrate the
application of the discussed methods to concrete problems.
- Dept. of Mathematical Sciences Seminar
Draga Vidakovic, Georgia State University
Tuesday, April 1, 11:00-12:00 pm in Room RI-232
Title:
Making connections between the study of linear algebra content and the study of learning theories
Abstract:
This study investigates the impact of the parallel study of learning theory and advanced undergraduate mathematics on prospective and practicing secondary mathematics teachers. Participants at a four-year public, liberal arts college studied learning theories (culminating with APOS) related to mathematics education at the same time they studied advanced undergraduate linear algebra. The researchers investigated how participants use learning theory to gain a deeper understanding of linear algebra and their own learning of content from linear algebra to help make sense of the learning theories. Additionally, the researchers explored the impact of learning theories on participants' teaching plans and perceptions of their students learning. This talk will outline the design and preliminary findings from the project as well as provide a short overview of the APOS theory of learning.
- Dept. of Mathematical Sciences Seminar
Diana Thomas, MSU
Wednesday, March 26, 2:45-3:45 pm in Room RI-222
Title: Minimal Periods and Turning Constants of Simple Closed Curves in R^n
Abstract:
In the theory of ordinary differential equations the Lipschitz
constant, L, is associated with guaranteeing uniqueness of solutions. In the
late 70's Lasota and Yorke proved that in the case of periodic solutions of
period T to an autonomous system over a Banach space TL = 4 and over a
Hilbert space TL = 2p with the Hilbert space result being sharp. In the 80's,
Busenberg and Martelli extended the Banach space result by showing TL = 6
and developed a sharp example in L1. This talk will explore the geometry of
this intriguing problem in R^n with non-Euclidean norms.
- Dept. of Mathematical Sciences Seminar
Sunil Mathur, University of Mississippi
Friday, March 14, 11:30- 12:30 pm in Room RI-232
Title: A New Statistical Test to Identify Differentially Expressed Genes from Microarray Data
Motivation: Microarray experiments contribute significantly to the progress in disease treatment by enabling a precise and early diagnosis. One of the major objectives of microarray experiments is to identify differentially expressed genes under various conditions. The statistical methods, currently available in literature to analyze microarray data are not up to the mark, mainly due to the lack of understanding of the distribution of microarray data.
Results: We present a test to identify differentially expressed genes using microarray data. The proposed test is highly robust against extreme values and does not assume the distribution of parent population. Simulation studies show that the proposed test is more powerful than some of the commonly used methods. When applied to microarray data, it is found that the proposed test identifies more differentially expressed genes than its competitors. The asymptotic distribution of the proposed test statistic and the p-value function is presented.
- Dept. of Mathematical Sciences Seminar
Daniel Cranston, DIMACS, Rutgers University
Wednesday, March 12, 3:00-4:00 pm in Room RI-222
Title: Discharging And Reducibility: An Introduction By Example
Abstract:
Many coloring results and structural results on graphs are
proved using a pair of techniques called reducibility and discharging.
The most well-known such result is the 4-Color Theorem. More generally,
to prove a hypothetical Theorem A for planar graphs, our proof has two
phases: a discharging phase and a reducibility phase. In the discharging
phase, we prove that every planar graph must contain at least one
subgraph from a specified list. The name discharging comes from the fact
that we assign a charge (an integer) to each vertex so the sum of the
charges is negative; we move the charge around (discharge it) so that
only vertices appearing in one of the specified subgraphs have negative
charge. In the reducibility phase, we prove that any counterexample to
Theorem A cannot contain any subgraph in the specified list. This implies
that there is no counterexample to Theorem A, and hence, the theorem is
true. In this talk, we illustrate the techniques of discharging and
reducibility by proving the following theorem: The vertices of a planar
graph of girth at least 14 can be partitioned into two subsets I and F
such that G[F] is a forest and I is a 2-independent set, that is: any two
vertices in I are distance at least 3 apart in G. This structural
theorem has applications to star coloring; a star coloring is a proper
coloring such that the union of any two color classes induces a forest of
disjoint stars. This is joint work with Craig Timmons and Andri K|ndgen,
both of California State, San Marcos.
- Dept. of Mathematical Sciences Seminar
Din Chen
Department of Mathematics and Statistics, South Dakota State University
and Department of Surgery, Sanford School of Medicine, University of South Dakota
Monday, March 10, 10:00-11:00 pm in Room RI-232
Title: A Simulation Study on Statistical Power to Choose Baselines in Clinical Trials
Abstract:
Multiple assessments of an efficacy variable are often conducted prior to the initiation of randomized treatment in clinical trials as baseline information. In this talk, I will describe a consulting project I have completed with a Shire Pharmaceutical on investigating 1) which baselines to be included in the analysis of covariance to increase the statistical power and 2) the magnitude of power loss by dichotomizing a continuous variable to a categorical variable for analysis and reporting in the medical society. A power analysis is developed with extensive simulations based on data from clinical trials in patients with end stage renal disease (ESRD). The findings can be easily applied in and extended to other clinical trials with similar design.
- Dept. of Mathematical Sciences Seminar
John Yap, University of Florida
Thursday, March 6, 10:30-11:30 pm in Room RI-232
Title: Nonparametric Modeling of Large Longitudinal Covariance Structure in Functional Mapping of Quantitative Trait Loci
Abstract: Estimation of the covariance structure of longitudinal processes is a fundamental prerequisite for the practical deployment of functional mapping designed to study the genetic regulation and network of quantitative variation in dynamic complex traits. We present a nonparametric estimation approach for the covariance structure of a quantitative trait measured repeatedly at a series of times. Specifically, we adopt Huang et al.'s (2006) approach of invoking the modified Cholesky decomposition and converting the problem into modeling a sequence of regressions of responses. A regularized covariance estimator is obtained using a normal penalized likelihood with an L2 penalty. This approach, embedded within the mixture likelihood framework of functional mapping, leads to enhanced power of this dynamic mapping method while preserving its biological relevance. Extensive simulation studies are performed to reveal the statistical properties and advantages of the proposed method. A real example from a mouse genome project is analyzed to illustrate the utilization of the methodology. The new method will provide a useful tool for genomewide scanning for the existence and distribution of quantitative trait loci underlying a dynamic trait important to agriculture, biology and health sciences.
- Dept. of Mathematical Sciences Seminar
Andrew Nevai, Mathematical Biosciences Institute, Ohio State University
Thursday, February 28, 11:30-12:30 pm in Room RI-232
Title: Spatial problems in mathematical ecology
Abstract: In this talk, I will introduce two spatial problems in theoretical ecology together with their mathematical solutions.
The first part of the talk concerns competition between plants for sunlight. In it, I use a mechanistic Kolmogorov-type competition model to connect plant population vertical leaf profiles (or VLPs) to the asymptotic behavior of the resulting dynamical system. For different VLPs, conditions can be obtained for either competitive exclusion to occur or stable coexistence at one or more equilibrium points.
The second part of the talk concerns the spatial spread of infectious diseases. Here, I use a family of SI-type models to examine the ability of a disease, such as rabies, to invade or persist in a spatially
heterogeneous habitat. I will discuss properties of the disease-free equilibrium and the behavior of the endemic equilibrium as the mobility of healthy individuals becomes very small relative to that of infecteds. The family of disease models consists variously of systems of difference equations (which I will emphasize), ODEs, and reaction-diffusion equations.
- Dept. of Mathematical Sciences Seminar
David Hu, Courant Institute, NYU
Tuesday, February 26, 12:00-1:00 pm in Room RI-232
Title: Snakes on a plane
Abstract: Snakes propel themselves over land using a variety of techniques, including sidewinding, lateral sinuous slithering and a unidirectional accordion-like mode. We explore these friction-based propulsion mechanisms through a combined experimental and theoretical investigation. Particular attention is given to classifying the gaits of snakes according to Froude number and the relative magnitudes of the frictional forces in the tangential and normal directions. In a simple kinematic model, we prescribe the waveform of the snake and calculate its motion as required by the torque and force balances on its body. A key feature of our model is that it allows us to rationalize the snake's gait on the basis of speed and mechanical efficiency. We also provide a historical survey of our previous work on the propulsion of water-walking insects.
- Dept. of Mathematical Sciences Seminar
Rachel E. Vincent-Finley, University of Houston
Tuesday, February 12, 11:15-12:15 pm in Room RI-232
Title: Reduced Basis Simulation
Abstract: Molecular dynamics (MD) simulation provides a powerful tool to study molecular motion with respect to classical mechanics. When considering protein dynamics, local motions, such as bond
stretching, occur within femtoseconds, while rigid body and large-scale motions, occur within a range of nanoseconds to seconds. To date, literature reports simulations of solvated
proteins on the order of nanoseconds, however, simulations of this length do not provide adequate sampling for the study of large-scale molecular motion.
In this presentation I will describe a method for performing molecular simulations with respect to a reduced coordinate space. Given a standard MD trajectory I use principal component analysis to identify k dominant characteristics of a trajectory and construct a k-dimensional (k-D) representation of the atomic coordinates with respect to these k characteristics. Using this
model I define equations of motion and perform simulations with respect to the constructed k-D representation. I apply this reduced basis simulation method to test cases and compare the
simulations to standard MD simulations of the test cases. The results indicate that the molecular activity with respect to the reduced basis simulation method is comparable to that observed in
the standard MD simulations of test cases.
- Dept. of Mathematical Sciences Seminar
Julie Silva Spitzer, San Jose State University
Monday, February 11, 11:15-12:15 pm in Room RI-232
Title: Teaching Special Needs Students Mathematics (Grades K-12)
Abstract: This talk will begin by discussing research which describes the characteristics of students with special needs and their impact on learning mathematics. Specific strategies will be presented that address these challenges. General strategies for teaching mathematics in an inclusive classroom will also be discussed.
- Dept. of Mathematical Sciences Seminar
Toni M. Smith, University of Maryland
Thursday, February 7, 11:45-12:45 pm in Room RI-232
Title: Student Understanding of Statistical Hypothesis Testing: A focus on the "Big Picture"
Abstract: In today's data driven world, the development of a statistically literate society is of value. As a result, many students are enrolling in university level introductory statistics courses and educators are promoting the development of strong understandings of the material taught in those courses. Statistical hypothesis testing, a powerful method of inferential statistics widely used in research, is taught in these introductory courses. Though algorithmic in nature, statistical hypothesis testing is supported by statistical theory. It is important that introductory students develop connected understandings of the algorithm, the concepts and logic that support it, and its uses in the real world.
In this talk, I will present a study of the degree to which undergraduate level, introductory statistics students develop the desired understandings of the overall "big picture" of statistical hypothesis testing. In order to investigate student understanding I employed a mixed methods approach, collecting both quantitative and qualitative data. In the quantitative phase I created a framework for assessing understanding of the conceptual and logical foundations of statistical hypothesis testing and its uses, constructed a multiple choice instrument with items representative of various categories from the framework, and collected data on student performance on this instrument. Additionally, I collected student scores from a course exam that assesses student ability to use the algorithm to solve traditional statistical hypothesis testing problems and compared these scores with those from the multiple choice assessment. In the qualitative phase, in order to gain more insight into student thinking, I conducted follow-up interviews with students who represent a range of performance patterns on the two quantitative assessments. Final results of the quantitative phase as well as emerging results from initial analyses in the qualitative phase will be presented. Implications of this study both for instructional design in statistics courses and for the preparation and professional development of statistics teachers will be addressed.
- Dept. of Mathematical Sciences Seminar
Hilary Smith Risser, Texas Women's University
Monday, February 4, 11:30-12:30 pm in Room RI-232
Title: Exploring what makes developmental students different from traditional students in their later coursework
Abstract: Studies have indicated that students with previous developmental mathematics coursework were less successful in their later math courses than their non-developmental counterparts. These differences could be due to differences in high school preparation (e.g. number of math courses taken, class rank) or to students' study habits (e.g. Number of hours spent on homework, tutoring received) in their most recent course. This study examines the high school records and self-reports of study habits in an effort to explain the differences in the later outcomes for developmental and non-developmental students. Approximately one third of the students had previously taken developmental coursework. Results indicated that the academic preparation of the two groups was significantly different. However, there were few significant differences in the study habits reported by the two groups.
- Dept. of Mathematical Sciences Seminar
Thomas Judson, Harvard University
Monday, January 28, 11:30-12:30 am in Room RI-232
Title: High School Calculus in Japan and the United States
Abstract:
Is high school calculus in Japan different than high school calculus in the U.S? How do high school calculus students from both countries compare? We examined and interviewed above average high school calculus students from Japan and the United States in order to determine any differences in their conceptual understanding of calculus and their ability to use algebra to solve traditional calculus problems. We will discuss the Japanese high school curriculum, some of our findings from the study, and the problems that we encountered in doing a cross-cultural investigation of Japanese and American calculus students.
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