(& Special Events)

Missing data is a common problem in epidemiologic studies. Informative missing data can have a profound impact on study findings. Missing data not only result in less information but it may also lead to non-significant findings resulting from reduced power. Missing data can also introduce bias if dropouts have characteristics that are absent among respondents. We examined the performance of several imputation methods for handling missing cross sectional and longitudinal data on renal function from the Strong Heart Study (SHS). SHS is an ongoing study of cardiovascular disease (CVD) in American Indians, a population with high rates of diabetes and renal dysfunction. Methods of data imputation appropriate for each type of data were compared for robust estimates of means and standard errors. Mean, Adjacent value,, single imputation, multiple imputation and complete case data were examined. The outcome variables considered for imputation were a measure of serum creatinine (Scr) and estimated glomerular filtration rate (eGFR) as calculated by the modification of diet in renal disease study (MDRD) formula. Cox hazard models were used to predict fatal and non-fatal CVD events using imputed Scr and GFR. The hazard ratios of both outcomes were compared with one another and evidence showing that imputing eGFR was superior to imputing Scr is presented.

While conventional tomography is associated to the Radon transform in Euclidean spaces, electrical impedance tomography, or EIT, is associated to the Radon transform in the hyperbolic plane. I will discuss about some recent work on network tomography that can be associated to a problem similar to EIT on graphs. A strategy is developed to determine the weight w for the case of general weighted graphs. I begin by considering relatively simple graphs and suitable choices for the data of the w-Neumann boundary value problem to produce a linear system of equations for the values of w.

This is a special event that is co-sponsored by the Mathematical Association of America. The talk is at 7:30 in the Katzen Center Recital Hall. Full details are available at Halloween Talk/Party.

Did you ever notice how often mathematics seems to pop up on the popular TV show, the Simpsons? Sarah Greenwald did! And she and her colleague Andrew Nestor have made names for themselves finding and publicizing these mathematical cameos through their webpage Simpsons Math . Com, as well as dozens of public lectures and appearances in the media. Dr. Greenwald knows about all the inside math jokes. She has met and interviewed the writers for the Simpsons and Futurama, exploring their mathematical backgrounds. She is the acknowledged expert in this field, and she is coming to American University! Come and find out: What logo of a well known mathematical organization was prominently featured in a scene with Lisa and Maggie? What curious mathematical object is used as a bottle for Klein Beer in the 31st century? What is a Frinkahedron? And much much more. Following the performance, there will be a Halloween themed reception in Gray Hall. Costumes (especially Simpsons and Futurama related costumes) are encouraged at both events!

I will introduce the quantum mechanical notion of entanglement between subsystems. Einstein pointed to the "problem" of entanglement to claim that quantum mechanics was not a complete theory. Now we know that entanglement is actually found in nature and is one of the most important signatures of quantum mechanics. The crucial idea is that a system cannot be completely described as a product of its subsystems. Examples of these concepts in particle systems will be presented, and different choices of subsystems will be discussed.

The cohomology ring of the Grassmannian X=G(k,n) has been studied for well over 100 years, but the last decade has seen surprising new twists to the story. I will explain the beautiful puzzle rule of Knutson-Tao-Woodward for the triple intersection numbers on X, and an extension of this rule that conjecturally computes all 3-point, genus zero Gromov-Witten invariants on X. These numbers are the structure constants of the quantum cohomology ring of X. Only linear algebra is required to follow most of this talk.

As advertised, I am planning to make this talk accessible to a general math audience, so I am not going to be very ambitious in terms of content. But hopefully people will be able to appreciate what quantum cohomology is all about after listening.

With special guest Blair Jones, A distinguished alumna and long time friend of the department.

Presentations at 5:30 by Dan Kalman, I-Lok Chang, Ali Enayat, Meghan Emilio and Kent Miller. Dinner to follow.

Most people are familiar with (non-random) fractals, where some geometric construction is repeatedly applied to generate finer and finer detail. While it is less well known, there is also a field of random fractals, where shapes are generated by combining a geometric construction with a random component.

This talk will start with some common fractals, and then show how one can use randomness to construct similar random fractals. Examples include random Cantor sets, the Chaos game, random walks, random ferns, and random mountains. Pictures will be used to illustrate the ideas and unique, never before seen random constructions will be drawn in real time!

Most of the talk will be accessible to a general audience.

Statistical Properties of Exchange-Rate Fluctuations at Minute-by-Minute Frequencies: An Econometric Analysis in the Spirit of Benoit Mandelbrot
Mico Loretan, Federal Reserve Board

Recently, data on actual transactions prices and trading volumes in the wholesale foreign exchange market have become available, at sampling frequencies as high as second-by-second. The new data are generally of much higher quality and, in
particular, have a better economic information content that those used in previous studies of properties of exchange rate fluctuations at high frequencies. Earlier studies of the high-frequency characteristics of foreign exchange rates have typically been based on readings of “indicative quotes,” and are generally sampled at frequencies of only once per five minute at best. In contrast, the exchange rate dataset compiled by Electronic Broking Services, Inc., (EBS) contains transactions prices at second-by-second (and potentially even higher) frequencies. The data are available as far back as the beginning of 1999, i.e., since the commencement of trading in the euro as a separate currency.

We use the high-frequency EBS dataset to compute minute-by-minute on returns for the yen-dollar and dollar-euro exchange rate pairs from January 1999 to December 2004, yielding about 2.25 million observations. We estimate characteristics of the underlying data generating processes, such as their maximal moment exponents, that were first popularized in the economics literature by Benoit Mandelbrot in several papers he wrote in the 1960s and 1970s. We also test whether these characteristics of the data can be regarded as reasonably constant over time. These estimates allow us to discern how importantly the data deviate from ordinary maintained (statistical) hypotheses about the data generating processes, such as finiteness of low-order moments. We also test whether the statistical findings are invariant (over reasonable scales) to the choice of sampling frequency. We further examine whether robust estimators, such as Kendall’s τ, of contemporaneous dependence among the exchange rate series would suggest different inferences about the data than those that are based on the “standard” correlation estimator, viz., Pearson’s ρ.

This is a special event in Ward Hall Room 1 followed by an April Fool's Day party in Bentley Lounge in Gray Hall. Colin Adams (of Williams College) presents Sir Randolph Bacon III in a tale of adventure on the high seas involving great risk to the tale teller, and how an understanding of the mathematical theory of knots saved his bacon. No nautical or mathematical background assumed. For full details, click here.

A Gentle Introduction To Algebraic Geometry
Artur Elezi, AU

We will discuss the objects studied in Algebraic Geometry, the methods that are used to study them and some of the most important problems in the field. Similarities and differences with other kinds of geometries (or math disciplines) will be pointed out. Undergraduate students should be able to understand the majority of this talk.