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Donatello Telesca - UCLA, April 23, 2010
Modeling Dependent Gene Expression

We propose a Bayesian modeling approach for inference about dependence of high throughput gene expression. Our goals are to use prior knowledge about pathways to anchor inference about dependence among genes; to account for this dependence while making inferences about differences in mean expression across phenotypes; and to explore differences in the dependence itself across phenotypes. Useful features of the proposed approach are a model-based parsimonious representation of expression as an ordinal outcome, a novel and flexible representation of prior information on the nature of dependencies, and the use of a coherent probability model over both the structure and strength of the dependencies of interest. We evaluate our approach through simulations and in the analysis of data on expression of genes in the Complement and Coagulation Cascade pathway in ovarian cancer.

David Bressoud - Macalester College, June 3, 2010
Issues of the Transition to College Mathematics

Over the past quarter century, 2- and 4-year college enrollment in first semester calculus has remained constant while high school enrollment in calculus has grown tenfold, from 60,000 to 600,000, and continues to grow at 6% per year. We have passed the cross-over point where each year more students study first semester calculus in US high schools than in all 2- and 4-year colleges and universities in the United States. In theory, this should be an engine for directing more students toward careers in science, engineering, and mathematics. In fact, it is having the opposite effect. This talk will present what is known about the effects of this growth and what needs to happen in response within our high schools and universities.

Robert Ellis - Illinois Institute of Technology, April 9, 2010
An Improved Liar Game Starategy from a Deterministic Random Walk

A liar game is a 2-person perfect information played by Paul and Carole in which Paul uses Yes-No questions to find a distinguished element known by Carole, and Carole is allowed to lie a prescribed number of times. Liar games were introduced by Renyi and Ulam, and in an equivalent form, by Berlekamp. In the pathological variant, Paul plays to preserve possibilities for the distinguished element, while Carole plays to disqualify all possibilities. The original and pathological variants are equivalent to adaptive error-correcting and adaptive covering codes, respectively. We describe a deterministic random walk called the "liar machine," compare its behavior to the simple random walk on the integers, and use the result to improve the best-known strategy for Paul in the pathological variant when the number of lies is a constant fraction of the total number of questions. Joint work with Joshua Cooper.

Lynn Russell - UCSD, April 8, 2010
Climate/Aerosol Colloquium
UCSD Scipps Institute of Oceanography,
Bulletin, Atmospheric Aerosol Group, SDSUniverse, video

The Russell group develops models and analyzes observations to understand the microphysical and chemical evolution of aerosol particles in the atmosphere. Their aim is to characterize the role of atmospheric aerosols on the Earth's climate.

Tim McMurry - DePaul University, March 5, 2010
Functional Clustering for Time-Course Gene Expression Experiments Using ARMA(p,q)

Functional gene clustering is a statistical approach for identifying the temporal patterns of gene expression measured at a series of time points. I will discuss two approaches for functional clustering, one designed to estimate periodic transcriptional profiles using Fourier series, and the second relying on wavelets for dimension reduction. The covariance matrix of the serial measurements over time for each gene is flexibly modeled through an autoregressive moving-average process of order (p, q). An EM algorithm is used to estimate the unknown parameters, and the model is chosen through a selection criterion. The methods are shown to be effective in simulation studies and on recent yeast data.

Loki Natarajan - USCD, May 1, 2009
Identifying outlier genes via capture-recapture across multiple microarray gene expression studies

Antonio Palacios - SDSU, April 29, 2009
A Mathematical Model of Motor Neuron Dynamics in the Heartbeat of the Medicinal Leech

The heartbeat of the medicinal leech is driven by direct contact between two arrays of motorneurons and two lateral blood vessels. At any given time, motorneurons exhibit one of two alternating states so that, on one side of the animal, the heart beats in a rear-to-front fashion (peristaltic), while on the other side the heart beats synchronously. Every 20 heartbeats, approximately, the two sides switch modes. Although it is known that the heartbeat rhythm is generated through bursts of oscillatory activity produced by a Central Pattern Generator (CPG) network of neurons, the mechanism that translates the CPG activity into peristaltic and synchronous rhythms and transitions between them is yet unknown.

In this work, we combine experimental results with analysis and computer simulations of symmetric systems of differential equations that resemble the leech anatomy, to investigate possible mechanisms for reproducing the dynamical behavior of the motor neurons, including transitions between peristaltic and synchronous rhythms.

Juanjuan Fan - SDSU, April 24, 2009
Tree Methods for Correlated Survival Data

Carmelo Interlando - SDSU, April 22, 2009
Algebraic Decoding of Non-Binary Quadratic Residue Codes

Quadratic residue (QR) codes of length up to 137 are competitively optimal in terms of rate and minimum distance, but they are hard to decode. The difficulty lies in the lack of known, consecutive syndromes. Determining certain unknown syndromes is the major task when decoding QR codes. In this talk, I will show that a method used in the binary case for determining unknown syndromes can be extended to the non-binary case. It will then be illustrated by the complete decoding of the ternary QR code of length 23 and minimum distance equal to 9.

Kagba Suaray - CSU Long Beach, April 21, 2009
A New Trick for the Old Dog of Survival Analysis

The problem of estimating survival probabilities has been of utmost importance to statisticians, engineers, and epidemiologists alike. The occurrence of censoring renders classical statistical inference infeasible. We briefly discuss the major solutions to this problem, starting with the work of Kaplan and Meier (1958), and introduce a new, smoothed estimator. Simulations and actual data analysis show important advantages of the new method.

Peter Blomgren, SDSU, April 15, 2009
Structure Enhancement Diffusion and Contour Extraction for Electron Tomography of Mitochondria

Joint work with: Carlos Bazan, SDSU, & Michelle Miller, Illumina Inc.

The interpretation and measurement of the structural architecture of mitochondria depend heavily upon the availability of good software tools for filtering, segmenting, extracting, measuring and classifying the features of interest. Images of mitochondria contain many flow-like patterns and they are usually corrupted by large amounts of noise. Thus, it becomes necessary to enhance them by denoising and closing interrupted structures.

We introduce a new approach based on anisotropic nonlinear diffusion and bilateral filtering for electron tomography of mitochondria. It allows noise removal and structure closure at certain scales, while preserving both the orientation and magnitude of discontinuities. This technique facilitates image enhancement for subsequent segmentation, contour extraction, and improved visualization of the complex and intricate mitochondrial morphology.

We perform the extraction of the structure-defining contours by employing a variational level set formulation. The propagating front for this approach is an approximate signed distance function which does not require expensive re-initialization. The behavior of the combined approach is tested for visualizing the structure of a HeLa cell mitochondrion and the results we obtain are very promising.

Chi-Hong Tseng, UCLA, April 10, 2009
Joint Modeling of Survival Data and Longitudinal Measurements
Under Nested Case-Control Sampling

Vanamamalai Seshadri, McGill University,March 26, 2009
When is the sum of the first N integers a perfect square?

This talk arises from a simple conversation between Ramanujan, the famous Indian prodigy and Mahalanobis, a famous Indian statistician during their Cambridge days as reported by Kanigal in his book on Ramanujan - the man who knew infinity. Mahalanobis was intrigued by a problem he had heard and said to Ramanujan, "Now here is a problem for you." "What problem? Tell me." said Ramanujan still stirring. And Mahalanobis read it to him. "I was talking the other day," said William Rogers to the other villagers gathered around the fire, "to a gentleman about the place called Louvain what the Germans have burnt down. He said he knew it well- used to visit a Belgian friend there. He said the house of his friend was in a long street numbered on this side one two three and so on and that all the numbers on one side added up exactly the same as all the numbers on the other side of him. Funny thing that! He said he knew there were more than fifty houses on that side of the street but not so many as five hundred. I made mention of this to the parson and he took a pencil and worked out the number of the house where the Belgian lived. I don't know how he did it." I will discuss this problem, its connection to Pell's (or more appropriately Brahmagupta's ) equation and offer an algorithm for solving the problem.

Mark Dunster, SDSU, March 25, 2009
Prolate Spheroidal Wave Functions

These waves aren’t for surfing or riding,
Tho’ the wavelets can look quite inviting.
Give me prolate spheroids,
The oblate’s for the boids.
The football shape’s one to take pride in!

Hector Lemus, SDSU, March 20, 2009
Modeling Multivariate Biomedical Data with Polynomial Smoothing Splines

Biostatisticians are frequently asked to perform inference for data sets with multivariate repeated or longitudinal measurements. Investigators typically will ask questions such as, "are measures X and Y correlated?" or "did either of measures X and Y exceed clinically important thresholds?" We have extended previous to develop a Bayesian multivariate smoothing spline model in a state space framework. The key advance is that our model allows for incorporation of substantial inter-subject heterogeneity in a parsimonious manner. The model is applied to two data sets from the UCLA Brain Injury Research Center to make statistical inference about correlation of measures and threshold exceedance.

Ricardo Carretero, SDSU, March 18, 2009
Faraday Waves in Bose-Einstein Condensates

Traditional Faraday waves appear in a layer of liquid that is shaken vertically. These patterns can take the form of horizontal stripes, close-packed hexagons, or even squares or quasiperiodic patterns. Faraday waves are commonly observed as fine stripes on the surface of wine in a wineglass that is ringing like a bell when periodically forced.

Motivated by recent experiments on Faraday waves in Bose-Einstein condensates we investigate both analytically and numerically the dynamics of cigar-shaped Bose-condensed gases subject to periodic modulation of the strength of the transverse confinement's trap. We offer a fully analytical explanation of the observed parametric resonance yielding the pattern periodicity versus the driving frequency. These results, corroborated by numerical simulations, match extremely well with the experimental observations.

This research involves wine and cigars
And patterns concocted in bars.
When you make the glass jiggle,
With just the right wiggle,
you'll see patterns like Penrose's Star.

Don Lutz, SDSU, March 4, 2009
Asymptotic factorization for differential equations; some new results on old problems.

This talk will concern an approach to asymptotic integration of differential equations and its application to some classes of second order equations previously treated by ad hoc methods. It will be shown how the classical results follow more systematically using the concept of asymptotic factorization and this also leads to some improvements and generalizations. On this, the only date which is a command, the Literary Group remembers our friend Edgar Howard, our expert on abelian groups.

An abelian groupie named Claire
Loved to commute everywhere.
She thought Galois Ideal,
And that Zorn had appeal,
But the best was to do it with Baire.

Michael O'Sullivan, SDSU, February 25, 2009
The Sum-Product Algorithm On Some Simple Graphs

One of the recent great achievements in coding theory is the use of graphs to define codes and decoding algorithms. The sum-product algorithm, which is one of these algorithms, is similar to an algorithm used in statistics and computer science for probabilistic reasoning, which is called belief propagation. In coding theory, the algorithm is employed on graphs with cycles, whereas the validity of the algorithm is only established for graphs without cycles, i.e. trees.

Even though there is no good theoretical justification for the sum-product algorithm (SPA), the performance of the SPA as a decoder is very impressive. Asymptotically it can be shown to achieve the Shannon bound, and experimental results have yielded performance very near the bound.

This talk will report on my work with SDSU graduate Shayne Vargo and other collaborators to analyze the SPA. We have worked with some simple graphs on which we can analyze the SPA algebraically.

Milne Anderson, University College, London, February 19, 2009
Univalence Criteria and Quasicircles

A mathematical Brit
Has a talk that is surely a hit.
Why a map's one-to-one,
as must always be done
on domains that have never been slit.

Peter Salamon, SDSU, February 11, 2009
Pumping a Swing

This topic's not quantum mechanics,
But a problem in Playground Dynamics.
To get the swing high,
With a minimal try
Requires thinking with higher mathematics.

Daniel Herrlin & Jonathan Wilson, SDSU, February 6, 2009
A Double Header

1st Half with Jonathan Wilson
"Simulating NFL Game Score Differentials"

An algorithm is presented which estimates point differential distributions for upcoming football games. Opponent adjusted data is simulated through Monte Carlo simulations and analyzed with methods including mixed linear models, pseudo random forest methods, and neural networks. Results are presented from the 2006-2008 NFL seasons.

2nd Half with Daniel Herrlin
"MCMC Baseball Simulations"

In this presentation I will discuss the applications of Markov Chain Monte Carlo methods in a baseball framework. Using a Bayesian approach I will look at the distribution of production for individual players and how each players abilities fit into the framework of the Entire team. A nonlinear approach to player ability will also be introduced and the results discussed from a sampling of teams for the 2008 season.

Vadim Ponomarenko, SDSU, February 4, 2009
The Joys of LaTex

LaTeX is a typesetting language in standard use throughout mathematics and rapidly gaining adoption throughout the scientific and academic community. If you plan to write mathematics or long documents (like theses) you should learn how to use this free software. This talk is intended primarily for those new to LaTex.

Steve Hui, SDSU, January 28, 2009
A Differential Equation from Unknown Input Observer Design

A mathematics professor named Steve
Studies problems you wouldn’t believe.
Inputs are unknown!
But their cover is blown,
By clever ideas he conceives.

Chi-Hse Teng, Amylin Pharmaceuticals, December 12, 2008
Statistical Power Considerations of Dichotomizing Continuous Outcome Variables

Dichotomizing continuous outcome variables has been a practice in certain areas. The loss of statistical power is one of the scientific community‘s major concerns about dichotomizing a continuous outcome variable. To address this concern, this presentation compares the statistical power of t-tests with the statistical power of the z-scores statistics of 2x2 table analyses under different scenarios. If the outcome distribution in both the placebo group and treatment groups is normal, and the treatment effect is a location shift, and inference is on the mean, then a two-sample t-test is the uniformly most powerful test. Dichotomization will never yield a more powerful test as long as the above assumptions are valid. However, when the distribution is not normal, then this mathematical guarantee is no long there. In order to compare the statistical power of analyzing the continuous variable as is vs. analyzing via a dichotomized variable, the “corresponding” hypotheses in two different tests settings were established. The “power” is defined as the ability to claim there is a treatment effect when there is indeed one. In some cases, dichotomization could yield higher statistical power. Some pitfalls of the practice will be discussed.

Imre Tuba, SDSU IVC, December 11, 2008
The braid group and topological quantum computers

Aram Galstyan, USC Information Sciences Institute, December 5, 2008
Modeling and Tracking Activities with Event-Coupled HMMs

Plan, activity, and intent recognition (PAIR) is concerned with inferring hidden states of agents based on an observable sequence of their actions. Although PAIR has been an active area of research for more than a decade, most studies so far has been limited to systems with a single agent, or a handful of them. In this talk I will present our work on activity recognition on a much larger scale, where thousands of agents interact with each other by engaging in abstract "attribute trades". Those interactions induce an evolving network, where the nodes and the edges represent the agents and their transactions, respectively. I will demonstrate that the collective dynamics of this network can be naturally modeled through a novel type of interacting hidden Markov models (HMM), which we call Event-Coupled HMMs. I will also discuss our approach to scalable inference-making with EC-HMM, which involves pruning the network trough semi-supervised learning, and utilizing an approximate and scalable representation of the hidden process on the reduced network.

Bio: Dr. Aram Galstyan received his Ph.D. in theoretical condensed matter physics from University of Utah, in 2000. He then joined USC Information Sciences Institute where he currently works as a research scientist at the Intelligent Systems Division. Dr. Galstyan's current research focuses on learning and discovering patterns in large-scale sequential data, statistical network analysis, and semi-supervised learning with graphs. His other research interests include mathematical modeling of complex adaptive systems, emergent coordination in robotic swarms, and learning in multi-agent systems. Dr. Galstyan has authored and co–authored more than 40 scientific papers in various journals and conferences. More information is available at http://www.isi.edu/~galstyan.

Craig Tillman, Weather Predict Consulting, Raleigh NC, December 5, 2008
WPC Science for Managing Risks

This talk will introduce the science and engineering capabilities of Weather Predict Consulting (WPC) in risk management. The topics will include WPC resources and capabilities, modeling tropical cyclone risk, simulating tropical cyclone hazards, hurricane vulnerability modeling, seasonal and intra-seasonal precipitation prediction, real-time operational meteorology, super ensemble forecasts of weather, storm prediction and post-storm analysis, and global digital agricultural products.

Thokala Raju, Birla Institute of Technology and Science, Pilani, November 25, 2008
Nonlinear Compression of Chirped Similariton Pulses of Generalized Cubic-quintic Nonlinear Schrodinger Equation Model.

We present a new analytic chirped similariton pulses for the generalized cubic-quintic nonlinear Schrodinger equation with varying dispersion, nonlinearity, gain or absorption, and nonlinear gain, using a recently developed fractional transform. It is reported that these chirped similariton pulses can be precisely piloted by appropriately tailoring the dispersion profile. This fact is profitably exploited to achieve optimal compression of these chirped similariton pulses.

Jianwei Chen, SDSU, November 21, 2008
A New ANOVA in Inference for Nonparametric Local Polynomial Regression

This talk provides ANOVA inference for nonparametric local polynomial regression (LPR) in analogy with ANOVA tools for the classical linear regression model. A simple and exact local ANOVA decomposition is established, and local R-squared quantity is defined to measure the proportion of local variation explained by fitting LPR. A global ANOVA decomposition is obtained by integrating local counterparts, and a global R-squared and a symmetric projection matrix are defined. We show that the proposed projection matrix is asymptotically idempotent and asymptotically orthogonal to its complement, naturally leading to an F-test for testing for no effect. Numerical results illustrate the behaviors of the proposed R-squared and F-test.

Richard Somerville, UCSD, November 20, 2008
Global Warming: What Do We Know and What Should We Do?

Richard C. J. Somerville is a theoretical meteorologist and an expert on computer simulations of the atmosphere. He received the Ph. D. in meteorology from New York University in 1966 and has been a professor at Scripps since 1979. Richard Somerville's research is on the physics of clouds and their role in the climate system. His interests include all aspects of climate, including climate science outreach and the interface between science and public policy. He comments frequently on climate and environmental issues for the media. Somerville has received awards from the American Meteorological Society for both his research and his popular book, "The Forgiving Air: Understanding Environmental Change" - a new edition of which was recently published in 2008. Among many honors, he is a Fellow of both the American Association for the Advancement of Science and the American Meteorological Society. He is a Coordinating Lead Author for the 2007 Fourth Assessment Report of the Intergovernmental Panel on Climate Change (IPCC). The IPCC shared the 2007 Nobel Peace Prize equally with Al Gore.
Bulletin, Somerville website, podcast, video

Cameron Parker, USD, November 7, 2008
Pulling Yourself Up by the Bootstrap: A Versatile Statistical Technique and Its Use in Time Series

The bootstrap has been a quite versatile and ubiquitous technique in statistics for the past three decades. In this talk we look at the basic original setup for the bootstrap in the independent, identically distributed setting. We then see three ways this technique can be modified for use in the study of stationary time series. Finally, a detailed example on how the method can be used to test for a particular type of non-stationary processes called unit root is given.

Jim Lackritz, SDSU, October 10, 2008
The only thing I like about attorneys is working for them: A statistician talks about his work as an expert witness.

After receiving his Ph.D. in statistics, Jim took the traditional route pursuing an academic career. Jim will discuss his path on how he got involved in expert witness work and some of the things that it entails. He has been involved in more than 40 cases in the past 15 years. He will discuss some of the cases on which he has worked, and come of the pitfalls and obstacles that he has faced. In dealing with attorneys and prospective judges/juries, it is critical that results can be communicated in a simple manner.

Jonq Juang, National Chiao Tung U, September 18, 2008
Stable Synchrony in Globally-Coupled Integrate-and-Fire Oscillators

We will present a model of integrate-and-fire oscillators, a special case of which is the Mirollo and Strogatz model under the assumption of identical oscillators [SIAM J. Appl. Math, 50 (1990), pp.1645-1662]. It is assumed in our model that each oscillator evolves according to a map . It has been shown that the concavity structure of plays an important role in determining whether Peskin's second conjecture holds. We have also proved the following: (i) The system of convex oscillators (i.e., < 0 for all ) in general synchronizes when the oscillators are not quite identical, (ii) the system of a certain class of concave oscillators (i.e., > 0 for all ) will not achieve synchrony for initial conditions in a set of positive measure when the oscillators are nearly identical; and (iii) the system of concave oscillators may achieve synchrony under certain sufficient conditions provided that the oscillators are not quite non-identical and that its concavity is small.

REUT, SDSU, August 11, 2008
Matrix Factorization Group and Cell Migration Group - Final Presentations
http://www.sci.sdsu.edu/math-reu/projects.html

Jeff Remmel, August 11, 2008
The Combinatorics of Pattern Avoidance in Permutations and Words
Abstract

Glenn Tesler, UCSD, August 5, 2008
Reconstructing the Genomic Architecture of Ancestral Mammals

In addition to frequent single-nucleotide mutations, mammalian and many other genomes undergo rare and dramatic changes called genome rearrangements. These include inversions, fissions, fusions, and translocations. Although analysis of genome rearrangements was pioneered by Dobzhansky and Sturtevant in 1938, we still know very little about the rearrangement events that produced the existing varieties of genomic architectures. Recovery of mammalian rearrangement history is a difficult combinatorial problem that I will cover in this talk. Our data sets have included sequenced genomes(human, mouse, rat, and others), as well as radiation hybrid maps of additional mammals.

I-Yuan Liu, SDSU, August 1, 2008
Tests for Homogeneity of the Risk Ratio between a Secondary Infection, Given a Primary Infection, and the Primary Infection

A multi-center design is a commonly used experimental design in clinical trials. Because each center may have specific characteristics that give rise to an interaction effect between treatments and centers on a patient's response, it is essential to test the homogeneity of the risk ratio before combining the data from different centers. Therefore, it is very important and useful to find a good test statistic to test the homogeneity of risk ratio across centers. In this thesis, we focus on testing the homogeneity of the risk ratio in a special situation where the set of contingency tables containing structural zeroes. A structural zero is defined as one of the cells in a contingency table contains a structural, or a priori, zero, which happens when it is theoretically impossible to contain an observation in this cell.

The goal of this thesis is to construct test procedures for testing the homogeneity of risk ratios in a series of contingency tables with structural zeroes. We primarily focus on the risk ratio between a secondary infection, given a primary infection, and the primary infection. We are testing the null hypothesis H0:RR1=RR2=RR3=....=RRI against the alternative hypothesis Ha : not all risk ratios are equal to each other. In addition to the classical weighted least square statistic (CWLS), we developed three weighted least square procedures from transformation of the CWLS and the other three asymptotically weighted test procedures by large sample theory. The other objective of this research is to investigate the performance of these procedures in testing the homogeneity of the risk ratio. Monte Carlo simulation was performed to investigate and compare the performance of these procedures with respect to Type? errors and powers.

Scott Nelson, SDSU, July 29, 2008
Econometric Forecasting

Modeling and Forecasting Time Varying Correlation. Univariate GARCH models are a popular method for modeling and forecasting the time varying variance of financial asset returns. We discuss the extension to multivariate GARCH, which are methods for modeling the time-varying covariance/correlation structure between assets. These correlation forecasts provide important information for assessing the overall risk of a portfolio. In general, high-dimensional correlation forecasting is a difficult problem due to the curse of dimensionality. We discuss some models which attempt to overcome these problems, and illustrate their use through an application.

Kimberly Armbrust, SDSU, July 24, 2008
A Statistical Decoding Algorithm for General Linear Block Codes

Linear codes are used to transmit digital information. Finding good codes and efficient decoding algorithms for those codes has become a very important problem. Decoding algorithms need to be set in place to detect and correct errors that inevitably occur while messages are being sent through a digital channel. Yet, many of the decoding algorithms that are being utilized today are complex or require much storage space. The best known algorithm for decoding general linear codes increases in complexity at exponential rate with the length of the code. Other decoding algorithms specialize in specific codes and are ineffective on others. The problem of designing robust decoding algorithms that are efficient with regards to the amount of storage and computation they require is an important challenge for coding theorists. In this work, an algorithm to decode general linear codes is developed in which the statistical nature of syndrome decoding is utilized to obtain results in a very straightforward manner. Details are given as to how this algorithm relates to other well-known algorithms, and comparison of the complexity of these algorithms is given. Examples of the application of the proposed algorithm to several well-known codes are given and theoretical hypotheses are backed with experimental data. The applications of the algorithm extend to codes such as the (7,4,3) Hamming code, the (23,12,7) Golay code, the (31,11,11) BCH code, a (32,16,5) random code, and several different quadratic residue codes. The work ends with some very exciting results in regards to the quadratic residue code of length 89. This is a cyclic code which has the potential of being used for data transmission because it has a high rate and distance. Yet, there are no known algorithms for it in the literature. We conclude the work by applying our algorithm to the decoding of this code.

Mayra Hernandez, SDSU, July 22, 2008
Road to NSF Fellowship

NSF's Graduate Research Fellowship is a prestigious award given to less than 1000 recipients world wide per year. Such us make us think that it's easier to win the lottery than an NSF GRF; or that such fellowships are not won, that they some how come to select few from the sky. In this talk, we will show how in fact the key to success may just be mentorship and strong ties within the community of interest, we will focus on the mathematical research community, but this can well be abstracted to any such community. It will be shown that personal believe in ones work, and tenacity are keys to success, even for people with unlikely life-paths. Internships and research experiences will be shown to be keys to securing financial support, via fellowship, to complete graduate education at the highest level. "Every loss is a learning experience. The only failure is when you stop getting up after a fall. When fear keeps you from the next level"--Maurice Ashley, Chess Grand Master.
Essay Criteria
Research Plan
Previous Research

Shiqi Li, CRMSE, July 21, 2008
Variation: A Distinctive and Effective Teaching Strategy

Students from East Asian countries often top the list in international assessments of mathematics education. But classroom observation shows that mathematics teaching there is quite traditional and conservative. Some scholars have an impression of a “paradox” of mathematics education: traditional ways of teaching make excellent performance by students. It may be a misunderstanding. A distinctive and effective teaching strategy, variation, as a case of practical teaching in China, will be shown in a videotaped lesson. Based on four episodes in the lesson, the characteristics of variation and their underlying beliefs are analyzed.

REUT, SDSU Research Experience for Undergraduates and Teachers, July 15, 2008
Theoretical Studies in Cell Migration (biomathematics), Dr. Diana Verzi, and Matrix Factorization (number theory), Dr. Vadim Pnomarenko
http://www.sci.sdsu.edu/math-reu/projects.html

Dan Lanier, SDSU, July 8, 2008
Fractal Geometery and the Escape-Time Algorithms as Graphic Art Tools

Nowadays, with the computational power of the home computer, you can create pretty pictures of fractal, utilizing Matlab, in as fast as 23 seconds. This talk will explore the complex function behind the escape-time algorithm to create the Julia set and the Mandelbrot set. It will also discuss the Matlab codes responsible for creating such art.
Fractal Paper - Fractal Geometry and the Escape-time Algorithm as Graphic Art Tools

Peter Salamon, SDSU, July 1, 2008
Mathematical Modeling of Bacteriophages

The talk will begin with motivation expounding why phage and metagenomes are interesting. It will then describe some mathematical tools we have created in San Diego for the comparison and characterization of phage metagenomes. Finally it will conclude with some future directions for research in this area.

Vadim Ponomarenko, SDSU, June 24, 2008
The Joys of LaTex

LaTeX is the worldwide standard in the mathematical and scientific communities for writing things like papers, books, theses, and presentations. It has many benefits over things like Office – for example, it's free. This talk will present the basics, some handy tips and tricks, and give lots of sample code to steal. If you'll be writing a thesis in the future, and you're not already an expert, you should definitely attend.

Hojin Moon, CSULB, May 2, 2008
Ensemble methods for classification of patients for personalized medicine using
high-dimensional biomarkers

Personalized medicine is defined by the use of genomic signatures of patients in a target population for assignment of more effective therapies as well as better diagnosis and earlier interventions that might prevent or delay disease. The personalized medicine is needed because different groups of patients have different characteristics. Classification algorithms can be used for prediction of response to therapy to help individualize clinical assignment of treatment. The algorithms are required to be highly accurate for optimal treatment on each patient. Typically, there are numerous genomic and clinical variables over a relatively small number of patients, which presents challenges for most traditional classification algorithms to avoid over-fitting the data. An ensemble classifier built from the optimal number of random partitions of the feature space is presented. Our classification algorithm can overcome the problem of having fewer samples than predictors, called curse of dimensionality. Our algorithm is applied to several published genomic datasets to classify patients into risk/benefit categories. Based on cross validated results for several high-dimensional data sets, our algorithm is a consistently one of the best classification algorithms. Finally, we discuss issues on variable importance and on building the most diversified classifiers.

Florin Vaida, UCSD, April 25, 2008
Model focus and Bayesian model selection

The Deviance Information Criterion (DIC) has entered in common usage for Bayesian model selection. The criterion has the advantage of simple, direct interpretability, ease of computation, and availability in the most commonly used MCMC-based statistical package for Bayesian inference, WinBUGS.

An interesting feature of DIC is that it depends on the model focus, or subset of parameters of interest, with different focuses leading to different DIC values. However, only one particular such focus is easy to compute and reported when using MCMC (or in WinBUGS), which is the one conditional on all model parameters. We show that for other model focuses more complex computations are necessary. We show how to compute DIC for a general model focus, based on the MCMC output, and we illustrate the methods on several examples.

Farshid Arjomandi, SDSU, April 24, 2008
An Introduction to Kalman Filtering

An efficient recursive filter that estimates the state of a dynamic system from a series of noisy measurements was developed by Rudolf Kalman et al. in the late 1950's. The filter and its later developments found a great deal of usage in NASA's Apollo program of the 1960's. Since then, the list of applications has grown from radar tracking and navigation to also include areas such as economics and weather forecasting.

The original Kalman filter is modeled on a Markov chain built on linear operators which are perturbed by Gaussian noise. It can be shown that among all filters, it's the one that minimizes the variance of the estimation error. In this talk, I plan to present the theory and algorithms behind the construction of this important control systems gadget. A couple of examples encompassing applications will also be presented.

Jo Hardin, Pomona College, Apr. 18, 2008
Biweight Correlation as a Measure of Distance Between Genes on a Microarray

The underlying goal of microarray experiments is to identify genetic patterns across different experimental conditions. Genes that are contained in a particular pathway or that respond similarly to experimental conditions should be co-regulated and show similar patterns of expression on a microarray. Using clustering methods we can partition the genes of interest into groups or clusters based on measures of similarity. Typically, one of Euclidean distance or Pearson correlation is used to measure distance (or similarity) in creating gene clusters. Both Euclidean distance and Pearson correlation are quite susceptible to outliers, however, an unfortunate characteristic when dealing which microarray data (well known to be quite noisy.)

We propose a robust similarity metric based on Tukey's biweight estimation of multivariate scale and location. The robust metric, the biweight correlation, is simply the correlation obtained from a robust covariance matrix of scale. We provide results demonstrating the robustness and improvement of the correlation method. As well, our method gives an outlier identification procedure which is valuable when dealing with such massive amounts of data. Used in clustering algorithms, it is clear that the biweight correlation gives more meaningful clusters of genes.

Werner Balser, Institute for Applied Analysis, University of Ulm, Mar. 24, 2008
Why are divergent power series useful?

Power series with radius of convergence equal to zero frequently occur as solutions of ordinary as well as partial differential equations. Several such examples shall be presented, and it shall be shown that one can still use them to compute a true solution of the corresponding equation.

Zhaoxia Yu, UC Irvine, Mar. 21, 2008
Genotype determination in the presence of linkage disequilibrium

Genome-wide association studies with single nucleotide polymorphisms (SNPs) show great promise to identify genetic variations that are responsible for complex disorders. Traditionally, genotypes of SNPs are determined one at a time, based on relative signal intensities of two fluorescent dyes. Although different clustering strategies have been applied, when the allele signal of SNPs is not perfectly separated, missing values are generated. This poses a serious problem, as a complete set of genotypes is required in many studies, especially in multi-locus analyses. Recently, two methods have been considered to handle missing genotypes: (1) incorporate genotype uncertainty into association tests by using “fuzzy” calls from raw signal intensities; (2) impute missing genotypes based on the underlying linkage disequilibrium (LD) structure of SNPs. Although they both aim to extract as much information as possible from different perspectives, neither of them makes full use of data. In this talk, I will propose a novel genotype clustering method that simultaneously considers signal intensities and the underlying LD structure among SNPs. We observed that incorporating local LD information can not only strengthen the confidence of correct genotype assignments, but also correct wrong assignments that are based on signal intensities alone. In addition, our new method increases both call rate and genotyping accuracy. Finally, our results also suggest that the new method gives more accurate estimation of haplotype frequencies than traditional methods that only use called genotypes.

Goong Chen, Texas A&M University, Mar. 7, 2008
An Introduction to Mathematical Study of Greenhouse Gas Molecules and Greenhouse Effects

The threat of global warming and climate changes is now very real, and greenhouse gas effects have been strongly identified as the major culprit. Such gases emit and absorb infrared (IR) radiation in their molecular spectra, trapping heat in the atmosphere and causing its temperature to rise.

In this talk, the speaker will introduce PDE models for a rigorous mathematical study aiming at problems directly or intimately related to these greenhouse effects. He will first introduce the Schrödinger equation from laser physics as a basic model. The symmetries of the molecular structures will then be presented. Numerical results will be illustrated. Important issues such as spectral broadening and interesting problems for research will be discussed.

Vanamamalai Seshadri, McGill University, Feb. 29, 2008
Some new results on the inverse Gaussian distribution

We begin with a short explanation of the term "inverse" appearing in the name of this distribution. This adjective was originally proposed by Tweedie who introduced this distribution to the statistical world as early as 1957. However even as early as 1915 this distribution appears to have been quite well known among the physicists and probabilists as the first passage time distribution of Brownian motion with positive drift . But Tweedie's justification has merit as will be explained in the talk.

Among the many results obtained by Tweedie about this distribution there is one which stands out uniquely that has a lot of resemblance to a parallel result for the Gaussian distribution. We will use the notation IG ( at , at^2) to denote the inverse Gaussian distribution with parameters (at) and (at^2), the first denoting the mean of the distribution, where a > 0 and t > 0. Suppose that we have a random sample of n observations Y_i from IG ( at_i , a t_i^2 ) then Tweedie showed that

Q = a[ { (t_1^2) / y_1 +.... +(t_n^2) /y_n } - ( T^2 / S ) ]

has a distribution which is independent of S = y_1 +....+ y_n (T is the sum of the t_i's). He also showed that Q has a chi-squared distribution with (n-1) degrees of freedom. In this talk we will propose a prior distribution for the parameter t and see what happens.

Daniel Pick, Pick Data Mining, Feb. 22, 2008
Gene Expression Profiling as a Biomedical Research Tool

cDNA microarrays have enabled researchers to perform whole genome studies of expression profiles in cancer. The statistical methods used to perform the data analysis of such experiments has been an active area of research over the last decade, and many different algorithms have been proposed. More recent papers have attempted to perform benchmark studies comparing the performance of these algorithms.

After a brief introduction to oncology and the biology of gene expression profiling, this talk will survey the different methods proposed for data analysis of gene expression studies, discuss the software tools available for such analysis, and present the state-of-the-art in the field.

Roger Barnard, Texas Tech University, Feb. 8, 2008
How far can you deform a disk under a convex map?

We will discuss how we apply variational techniques and special function theory to verify some conjectures of C. Pommerenke and D. Minda on the sharp bound for the Schwarzian derivative of hyperbolically convex maps. This completes the classification of the extremal domains for the Schwarzian in all three classical geometries, hence answering the question first posed in the 50's as to how far one can distort a disk under a convex map in Euclidean, spherical and hyperbolic geometries. We will mention how these ideas are used to verify a number of other conjectures by Pommerenke.

Vitaly Skachek, University College, Dublin, Ireland, Jan. 30, 2008
Linear-Programming Decoding of Non-Binary Linear Codes

A framework for linear-programming (LP) decoding of non-binary linear codes over quasi-Frobenius rings is developed. It is proved that the resulting LP decoder has the maximum likelihood certificate property. It is also shown that the decoder output is the lowest cost pseudocodeword. Equivalence between pseudocodewords of the linear program and pseudocodewords of graph covers is proved. Different polytopes for use with linear-programming decoding are studied, and it is shown that for many classes of codes these polytopes yield a complexity advantage for decoding. These representations lead to polynomial-time decoders for a wide variety of classical non-binary linear codes.

LP decoding performance is illustrated for the $(11,6,5)$ ternary Golay code with ternary PSK modulation over AWGN, and in this case it is shown that the LP decoder performance is comparable to codeword-error-rate-optimum hard-decision based decoding.

Douglas Nychka, National Center for Atmospheric Research, Jan. 25, 2008
Challenges of regional climate modeling and validation.

As attention shifts from broad global summaries of climate change to more specific regional results there is a need for statistics to analyze observations and model output that have significant variability and also to quantify the uncertainty in regional projections. This talk will survey some work on interpreting regional climate experiments. In large multi-model studies one challenge is to understand the contributions of different global and regional model combinations to the simulated climate. This is difficult because the runs tend to be short in length and with a limited number of ensemble members. We suggest some spatial models for the climate fields based on sparse approximations to the covariance matrix and derive an ANOVA like decomposition for the fields. The decomposition into main effects and interactions helps to isolate the effects of different models. The spatial models also provide a rigorous framework for assessing statistical significance and comparing simulations to observed climate. This approach is illustrated for output from the PRUDENCE program and we also discuss the newer NARCCAP experiments for regional climate of North America.
Joint work with Cari Kaufman, Stephen Sain, and Linda Mearns.

Don Lutz, SDSU, Jan. 25, 2008
On some exponentially asymptotically constant difference equations with an application to nonlinear systems near a hyperbolic equilibrium.

R. Agarwal and M. Pituk have recently considered some scalar linear difference equations with coefficients that are asymptotically constant with exponentially small perturbations. Using the method of generating functions and elementary methods from complex analysis, they derived an asymptotic representation for solutions, which was then applied to study the behavior of some nonlinear autonomous scalar difference equations near a hyperbolic equilibrium. Here, we (S. Bodine and D. A. L.) show that using standard methods of asymptotic matrix analysis, their results can not only be modestly generalized to systems, but the error estimates can also be made more precise. An analogous result can also be applied to nonlinear autonomous systems.

Peter Blomgren, SDSU, Dec. 7, 2007
Simulations and Measurements of Time-Reversal in an Indoor Environment Using Wide-angle Antennas

We report on measurements and simulation results of time-reversal in the 2.4\,GHz regime.  The measurements were made in indoor environments using wide angle directional antenna arrays; and the corresponding numerical simulations computed using a full 3D-waveguide propagation code.

John Brevik, CSU Long Beach, Nov. 30, 2007
Curves on Surfaces in Projective Space

In studying algebraic surfaces in projective 3-dimensional space, one wishes to classify  the curves lying on a particular surface. I will first discuss the background necessary to frame the issue precisely and give relatively complete results for surfaces of low degree. A good general solution to the problem is provided by the  Noether-Lefschetz Theorem, stated by Noether in the late 19th century and proved by Lefschetz in the 1920s. Griffiths and Harris gave a different proof of the theorem in the 1980s; their approach has allowed generalizations in a number of directions. I will discuss some of these generalizations, my current work with Scott Nollet (TCU) on related problems, and topics for future work.

Colleen Kelly, Exponent, Nov. 19, 2007
My life as a Consulting Statistician

Colleen Kelly will talk about how Exponent, a leading engineering and scientific consulting firm, uses statistics to help their clients solve technical problems.  Examples of statistical problems encountered will be given as well as a discussion of technical and personal skills required to be successful in consulting.  A question and answer period will be held following the presentation.

Changxuan Mao, UC Riverside, Nov. 16, 2007
Population size estimation from multiple lists

The Rasch model is adopted to estimate the unknown population size in multi-list disease surveillance studies. It takes both the list effectiveness and case heterogeneity into account. A stepwise approach is proposed in which optimization problems are solved conveniently.  The sharpest lower bound to the odds that a case is unseen is introduced, which can be calculated by linear programming. There are also some less sharp lower bounds. Estimating a lower bound leads to an estimator for the population size. Real examples are investigated for the purpose of illustration.

Mark Dunster, SDSU, Nov. 16, 2007
Resonance and "almost" nonuniqueness in the scattered field of a dielectric circular cylinder

We look at the classical modal expansion for the scattered field of a plane wave from a circular dielectric cylinder. Using classical WKBJ approximations for Bessel functions, a new uniform asymptotic approximation is presented for the late coefficients in this expansion, valid for the entire region exterior to the cylinder. These approximations predict the location of a certain critical Regge pole, which can lead to at least one dramatic resonant modal term at certain critical values.

We also show that the mean square measure, over all space, of the difference of the scattered field from two distinct values of the dielectric constant of the cylinder can sometimes be very small; this can have consequences in inverse scattering, and we analyze this phenomenon, again using properties of Bessel functions.

Serkan Hosten, SFSU, Nov. 9, 2007
An Introduction to Algebraic Statistics

This will be a gentle introduction to the applications of algebraic geometry to statistics. The main goal of the talk is to present statistical models, i.e. sets of probability distributions (defined parametrically most of the time), as algebraic varieties.  I will give examples where defining equations of such statistical model varieties have been successfully computed: various graphical models and models for DNA sequence evolution.  I will also talk about the algebraic degree of maximum likelihood estimation with old and new examples.

Peter Salamon, SDSU, Nov., 2, 2007
Quantum Cooling

Cooling physical systems to extremely low temperatures is important for quantum computing, for improved MRI, and for producing new states of matter known as Bose-Einstein condensates.  The talk will present several simple mathematical problems posed by such cooling.

Oh Nam Kwon, Seoul National University, Nov. 1, 2007
Inquiry-Oriented Differential Equations: Its Impact and Prospects

Research on the relationship between different teaching methods and students’ understanding of mathematics at the university level is essential for cumulative improvement in mathematics.  However, a number of researchers have reported that there is the gap between what is taught and what is learned in mathematics in traditional modes of teaching.  This talk explores more effective teaching method at the university level.  An example of inquiry-oriented mathematics teaching at the university will be discussed and illustrated how to enhance students’ authentic understanding in an ordinary differential equations course.

Todd Coffey, Amylin Pharmaceuticals, Oct. 30, 2007
How to think like a Statistician: Providing value in the Pharmaceutical Industry

Many students in statistics or biostatistics have heard of professional opportunities in the pharmaceutical industry to design and analyze clinical studies. Most students, however, are unaware of the wide variety of opportunities for statisticians in the nonclinical areas of drug discovery and nonclinical development. In this talk I will discuss the process of drug discovery, show examples of how statisticians can provide value, and give advice on the preparation needed while in school to succeed as a nonclinical statistician.

Gerald R. North, Texas A&M University, Oct. 18, 2007
Climate Change: State of the Art
Fox 6 News (text, TV), SDSUniverse, Daily Aztec, lecture notes, movie (see note below)
You will need the RealPlayer installed on your computer in order to view this movie.
The RealPlayer is free and available for download at: http://www.realplayer.com/

Estimates of climate change over the last millennium indicate that the Earth’s temperature has increased dramatically over the last century and the pace of the warming is increasing as well. There are several ways of assessing the state of the science, including surveys, expert panel assessments and finally the Intergovernmental Panel on Climate Change. The scientific consensus is that the climate of the last few decades has been warming in an unusually rapid manner and that most of the warming is attributable to humans. The primary reason of this consensus is the emergence of several revolutionary approaches to the problem: Global Observing Systems and Analysis Techniques (satellites, routine weather observations, special field programs, etc.), Integrated Studies Across Disciplines (coupling model components, etc.), and finally the Development of Computer Intensive Simulations Systems (global climate models). While the climate system is incredibly complicated perhaps comparable to a biological system, there has been a steady accumulation of evidence supporting the hypothesis that excess anthropogenic emissions of greenhouse gases and other materials into the air are the primary drivers of recent climate change. The lecture will include some results of recent studies on future climates we might expect for the Earth and in particular the contiguous United States.

Andre Kundgen, CSU San Marcos, Oct. 12, 2007
Graph minors and reliable single message transmission

We consider the problem of sending a message from a sender S to a receiver R through an unreliable network (given by a graph G) in which edges may fail, but cannot recover.

Our aim is to design a protocol that ensures that a message sent by Swill be received by R as long as some SR-path remains (even if we don't know what path it is) without generating an infinite number of message traffic in the process.

We explicitly characterize the family of networks in which this is possible in terms of forbidden rooted minors, and we give the protocol.  We also show that there is a forbidden rooted minor characterization fort he case when we can attach a header (containing routing information) of fixed length to the message, and we discuss the algorithmic consequences of these characterizations. We also discuss the case when we can assume that at most k edges can fail.

Xin Lu, UCSD, Oct. 12, 2007
Statistical Issues in Microarray Gene Selections: False Discovery Control and Selection Reproductibility

I'll discuss two statistical issues in microarray based gene selections, the False Discovery Rate (FDR) control and the reproducibility of selection procedures.

To control the FDR and maintain a better power in gene selection, we need to estimate the proportion of true null hypothesis (PI0) based on the pooled statistics of all genes. Current methods usually assume genes are independent with each other or only weakly correlated. We showed that when strong correlation exists among the data, which is common in microarray datasets, the estimation of the proportion of null hypotheses could be highly variable resulting in a high level of variation in the FDR control. Therefore, we developed a re-sampling strategy to reduce the variation by breaking the correlations between gene expression values, then using a conservative strategy of using the upper quartile of the re-sampling estimates to obtain a strong control of FDR. With simulation studies and perturbations on actual microarray datasets, our method, compared to competing methods such as q-value, generated slightly biased estimates on the proportion of null hypotheses but with lower mean square errors. When selecting genes with controlling the same FDR level, our methods have on average a significantly lower false discovery rate at the price of a minor reduction in the power.

Another related problem is to evaluate the gene selection procedures based on their reproducibility. We proposed a non-parametric Re-Discovery Curve (RDCurve) method, to estimate the probability of re-discovery of genes selected from a microarray data set. Given a selection procedure and a data set, the RDCurve method applies the selection procedure repeatedly to bootstrapped data, select the important genes, and then estimate the expected frequency of re-discovery of the selected subset of genes. We also proposed a permutation method to estimate the confidence band of RDCurve under null hypothesis to test the significance of the RDCurve. The method we proposed is a complement to traditional FDR method. It is non-parametric and model independent. With the RDCurve method, we can evaluate the signal-noise ratio of a give data set, compare the performance between selection procedures in term of them expected reproducibility, or select the number of genes to be reported.

Farshid Arjomandi, SDSU, Oct. 5, 2007
Frobenius' Theorem and Nonlinear Geometric Control

In mathematics, Frobenius' theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an underdetermined system of first-order homogeneous linear partial differential equations. Frobenius' original version of the theorem was stated in terms of Pfaffian systems, however today it can be restated more economically in the modern language of differential forms and vector fields. This nice geometric result can be utilized to yield a criterion for determining whether a given control system is nonholonomic, i.e., whether the constraints of the system depend on parameters other than the coordinates of the system and time (such as the velocity or momentum). In this talk we will introduce the mathematical machinery, and then describe and explore the usage of this theorem to a few problems from the area of nonlinear geometric control theory.

Scott Nelson, SDSU, Oct. 2, 2007
Careers in Statistics: An Intro to Energy Forecasting

Statistical forecasting methods play a vital role in the electric power industry.  In this talk I will give an introduction to the electric power industry, and discuss some of its unique characteristics.  Specific, real world examples of short-term, long-term and financial forecasting problems will be presented, along with innovative methodology and software designed to address these problems.     Persons who are interested in pursuing careers in the energy industry are encouraged to attend.  The talk will be aimed at undergraduate and graduate statistics, math, and business majors.

Subir Ghosh, UC Riverside, Sept. 27, 2007
Model Search, Identification, and Discrimination in Factorial Experiments.

In fractional factorial experiments, we run a fraction of treatments for generating the data and assume that some or all factors do not interact with each other.  For example, in a Resolution 3 plan we assume that the factors do not interact at all and in a Resolution 4 or a Resolution 5 plan we assume that the 3-factor and higher order interactions are negligible.  Such assumptions may or may not be true in reality in the sense that a few of such interactions assumed to be negligible may in fact be non-negligible.  We consider a class of models for 2^m factorial experiments with the common parameters being the general mean, the main effects and the uncommon parameters in any two models being two 2-factor interactions one from each model.  We want to identify all the models within the class, discriminate between any two models within the class, and search for the best model for describing the data.  Both design and inference issues are discussed for this purpose.

Rich Levine, SDSU, Sept. 21, 2007
Climate Change Uncertainties: Is global warming really our fault?

Over the past few months, the United Nations Fourth Intergovernmental Panel on Climate Change (IPCC) reorted that "the observed increase in globally averaged temperatures since the mid-20th century is very likely due to the observed increase in anthropogenic greenhouse gas concentrations," a statement strengthening previous IPCC assessment reports, but leaving policymakers with tough decisions due to the uncertainties involved.  In this talk, we will present the statistical issues and research underlying and influencing the IPCC assessment of global warming and the future public health policy implications.

David Whitman, SDSU, Sept. 14, 2007
The Nature of Now.

The concept of simultaneity has an interesting history from Newton until now.  We present an anstraction of space time defined axiomatically by principles of simultaneity.

Kung-Jong Lui, SDSU, May 2, 2007
Interval estimation of the risk difference in non-compliance of randomized trials.

In a randomized clinical trial (RCT), we often come across the situations in which there are patients who do not comply with their assigned treatments or whose outcomes are missing due to their refusal or loss to follow-up.  Because noncompliance and missing outcomes do not generally occur completely at random, analyzing data as treated or excluding patients with missing outcomes from our analysis can produce a biased estimate a treatment effect.  In this paper, we consider estimation of the risk difference (RD) in the presence of both noncompliance and missing outcomes under a RCT.  On the basis of a constant risk additive model proposed elsewhere, we derive the maximum likelihood estimator (MLE) and develop three asymptotic interval estimators in closed form for the RD.  We apply Monte Carlo simulation to evaluate and compare the performance of these estimators in a variety of situations.  We note that all interval estimators developed here can perform well with respect to the coverage probability in all the situations considered here.  We find that the interval estimator using tanh -1 (x) transformation is generally more precise than the other estimators with respect to the average length.  Finally, we use the data taken from a randomized trial studying the association between flu vaccine and the risk of flu-related hospitalization to illustrate the practical use of these interval estimators.  

Valdimir Rotar, SDSU, April 6, 2007
On asymptotic proximity of probability distributions and the non-classical invariance principle

Usually, a limit theorem of Probability Theory is a theorem that concerns convergence of a sequence of distributions P_n to a distribution P. However, there is a number of works where the traditional setup is modified, and the object of study is two sequences of distributions, P_n and Q_n, and the goal consists in establishing conditions implying the convergence 

           P_n - Q_n -> 0      (1)     

In particular problems,P_n and Q_n are,  as a rule, the distributions of the r.v.'s f(X_1,...,X_n)   and f(Y_1,...,Y_n) , where f(.)  is a function, and  X_1,X_2,... and  Y_1,Y_2,... are two sequences of r.v.'s. The aim here is rather to show that different random arguments X_1,...,X_n may generate close distributions of f(X_1,...,X_n) , than to prove that the distribution of f(X_1,...,X_n) $ is close to some fixed distribution (which, above else, may be not true).

Clearly, such a framework is more general than the traditional one. First, as was mentioned, the distributions P_n and Q_n, themselves do not have to converge. Secondly, the sequences P_n and Q_n are not assumed to be tight, and the convergence in (1)  covers situations when a part of ``the probability mass or the whole distributions move away to infinity'' while the distributions P_n and Q_n, are approaching each other. 

We consider a theory on this point, including the very definition of convergence (1), and a particular example of the invariance principle (convergence to Brownian motion) in the general non-classical setup.

Vadim Ponomarenko, SDSU, April 5, 2007
Two simple ways to rig an election: an introduction to voting theory

Democracy's most fundamental ideal is for society to make choices that reflect the desires of the individuals living in it.  Many voting mechanisms have been proposed to achieve this.  All are deficient, due to a Nobel-prize-winning theorem by Kenneth Arrow -- those designing the election can manipulate the outcome.  Furthermore, due to a theorem of Gibbard and Satterthwaite, individual voters can also manipulate the outcome by voting dishonestly.

Kristin Duncan, SDSU, April 2, 2007
Parametric and nonparametric Bayesian models for items response.

Item response theory is a body of research directed at the assessment of an underlying trait or ability.  In its simplest form, it allows one to use the results of a multiple choice exam or questionnaire both to rank-order a batch of subjects and to decide which subjects exceed a threshold level of the trait or ability.  In this talk, we give an introduction to the most commonly used item response models and present a nonparametric Bayesian approach to item response theory.  Under this approach, a Dirichlet process prior distribution is placed on each item characteristic curve.  The resulting model has full support among models for which there is a one-dimensional trait underlying exam response.  Features of the model will be described. Results from fitting the new model and traditional, parametric models to responses from an undergraduate statistics exam will be presented and contrasted.

Steve Baer, Arizona State U, March 23, 2007
Slow passage through a Hopf bifurcation: New insights into the memory effect with application to neuronal bursting

In many biological, chemical and physical systems modeled mathematically as bifurcation problems, the bifurcation parameter may vary naturally and slowly with time or the parameter may be slowly varied by the experimenter.  Mathematically, these are called slow passage or ramp problems.  Of particular interest is when a parameter passes slowly through a Hopf bifurcation and the system's response changes from a slowly varying steady state to slowly varying oscillations. The interesting phenomenon is that the transition may not occur until the parameter is considerably beyond the value predicted from a static bifurcation analysis, no matter how slow the parameter is varied, and the delay in onset is dependent on the initial state of the system (memory effect). Previous studies have focused on linear or constant speed ramps [Baer, Erneux & Rinzel (1988,1989), Su (1991)]. In this talk I will introduce the problem of slow accelerating and de-accelerating ramps, obtain new results using numerical and asymptotic methods, and apply the results to problems in nerve membrane accommodation and neuronal bursting.

Sigrun Bodine, U of Puget Sound, March 15, 2007
On dichotomies, weaker and stronger, in asymptotic integration of linear differential systems

This talk will concern “almost diagonal” systems of non-autonomous linear differential equations and the asymptotic behavior of their solutions. In order to achieve a so-called “asymptotic integration” of the system, a certain balance is needed between a kind of separation (dichotomy) condition on the diagonal terms and a growth condition on the perturbation. An overview of some classical methods will be presented along with some new results. A parallel theory also exists for linear difference equations, but in this talk differential equations will be the main focus.

Martin Haenggi, U of Notre Dame, March 14, 2007
Coverage and sentry selection in wireless sensor networks

One basic application of wireless sensor networks is the surveillance or monitoring of large areas: Assuming n sensor nodes are randomly deployed and each sensor can cover a circular area of a certain radius r, what fraction of the total area of interest can be expected to be covered (as a function of n and r)? This question has been answered for certain cases.

In this talk a related problem, the so-called sentry selection problem, and a recent result will be presented. In practical applications, it is desirable to turn most of the sensor nodes off to conserve energy and only have a subset of nodes active acting as sentries. After a certain period of time, the sentry duty is moved to a new, disjoint set of nodes, and so on.

Mathematically, it can be described as:

Find the minimum radius r such that (with high probability) there exists a partition of the node set into k subsets that each provide a cover of the area.

Gilbert Walter, U of Wisconsin, Milwaukee, March 8, 2007
Prolate Spheroidal Waves and Wavelets and their remarkable properties

The prolate spheroidal wave functions go back to the 19th century.  Their use in signal processing goes back almost 50 years. But the optimization problem to which they are the solution is finding new applications in sampling and imaging.  In this talk we review some of their unique properties which make them useful in these applications. We also discuss wavelets based on them which have many nice properties lacking in other wavelets.

Adolfo J. Rumbos, Pomona College, March 1, 2007
Resonance in nonlinear elliptic boundary value problems

In this talk we survey existence results for a general class of boundary value problems of the form

Q(u) -λ a(x,u)u = g(u) + h(x)              x in Ω 

where Ωis a domain in N-dimensional Euclidean space; u is a real valued function defined on Ω and lying in an appropriate function space; Q(u) is a second order elliptic differential operator (linear or nonlinear); λ is a real parameter; a and g are continuous functions; and h is measurable function lying in some L^p class. We focus on what has been traditionally called a resonance problem; that is, the situation in which the parameter λ is an eigenvalue of the differential operator Q(u); or λ is a value for which

Q(u) -λ a(x,u)u=0 

has a non-zero solution.  Prototypes for the differential operator Q(u) are the Laplacian, Δu, in the semi-linear case, and the p-Laplacian, Δ_pu, in the quasi-linear case. 

Andres Valloud, Cincon Systems, Feb. 23, 2007
A pattern of perception

The pattern describes a way to make explicit a model by which one can explain how the interaction between observers and their environments occurs. The pattern applies to a complex system, or information manifold, under observation and a player interacting with it. A game is an example of such an information manifold. A program playing the game is an example of a player. An adaptive compiler (player) observing the execution of a program (information manifold) to modify the performance of the program is another example.

Without an observer, the information manifold is nothing but a blob. The player, however, is able to make sense of that blob by following a sequential approach of perception, processing, and action. The processing is based on the individualization of distinctions that capture relevant pieces of information. These distinctions are evaluated and a strategy is applied so that the objectives can be met. As a result, the player reacts, influencing the manifold, and the cycle starts again.

The player is divided into an interface, eyes, hands and strategy. The eyes of the player discover some few relevant distinctions (the ball, other players, etc).  Based on his strategy, the player selects some objectives to be met. Finally, his hands perform some action as throwing the ball in some direction, guided by the objectives.

Andres Valloud, until recently a consultant at JP Morgan in New York City and now lead Smalltalk virtual machine engineer at Cincom Systems, will describe the pattern of perception. He will also discuss a framework in Smalltalk that implements the pattern that has been used in games and an adaptive approach to garbage collection self-tuning.

Kristin Lauter, Microsoft Research, February 15, 2007
Cryptographic hash functions from expander graphs

In this talk I will explain the importance of collision-resistant hash functions for cryptography and survey some important new developments. Next I will explain the central role of expander graphs in various branches of mathematics. Finally I will connect the two by presenting a new construction of provable collision resistant hash functions from expander graphs.

As examples, I will give two specific families of optimal expander graphs for hash function constructions: the families of Ramanujan graphs constructed by Lubotzky-Phillips-Sarnak and Pizer respectively. When the hash function is constructed from one of Pizer's Ramanujan graphs, (the set of supersingular elliptic curves in characteristic p with l-isogenies, l a prime different from p), then collision resistance follows from the hardness of computing isogenies between supersingular elliptic curves. This is joint work with Denis Charles and Eyal Goren.

Bio: Kristin Lauter earned her Ph.D. in mathematics at the University of Chicago in 1996. She was a T.H. Hildebrandt Research Assistant Professor at the University of Michigan from 1996-1999. She has been at Microsoft Research since 1999, where she specializes in cryptography, number theory, algebraic geometry and coding theory.

Bernd Sturmfels, UC Berkeley, February 7, 2007
Algebraic Statistics for Computational Biology

This lecture gives an introduction to a recent book with this title.  It concerns interactions between algebra and statistics and their emerging applications to computational biology. Statistical models of independence and sequence alignment will be illustrated by means of a fictional character, DiaNA, who rolls tetrahedral dice with face labels "A", "C", "G" and "T".

Mark Dunster, SDSU, February 2, 2007
The Incomplete Zeta Function

No abstract provided for this talk.

Bob Grone, SDSU, January 26, 2007
An Iterative Method of Solving a Game

Julia Robinson was a mathematics major at SDSU for 3 years, from 1936 to 1939.  She transferred to UC Berkeley to obtain her BA degree in 1940.  She worked in Mathematical Logic and earned her Ph.D. at Berkeley as well. Her later work was instrumental in solving Hilbert’s Tenth Problem, and she was the first woman mathematician elected to the National Academy of Sciences, as well as the first woman President of the American Mathematical Society.

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