# Spring 2013 Abstracts

**Rigid or flexible?***Jessica Sidman*, Department of Mathematics and Statistics.

**Abstract** : Suppose you are building a structure out of solid bars attached at flexible joints. Will your structure be rigid or flexible? We will focus on the special case of bars and joints lying in a plane, where Laman's theorem gives a good answer to this question. In three dimensions, the question is still open and has implications for understanding protein folding.

**What is Biostatistics?***Haley Hedlin*, Department of Mathematics and Statistics, UMass Amherst

**Abstract** : Ever wondered what's the difference between biostatistics and statistics? Are you curious what exactly a biostatistician does or what types of careers are available to biostatisticians? Would you like to see an application of statistics to neuroscience? If you answered yes to any of these questions, this is the talk for you. The first part of this talk will describe what biostatistics is and what you can do with it. The second part will be a non-technical overview of a biostatistics research project I conducted in collaboration with neuroscientists. In the work, we propose an extension to Granger causality as it's typically applied to electroencephalography (EEG) data.

**Statistical Analysis of Network Data***Weston Viles*, Boston University

**Abstract** : The analysis of network data is widespread across scientific disciplines. The technological and infrastructure, social, biological, and information sciences are a few which have enjoyed such analyses. Mathematicians, statisticians, physicists, sociologists, and biologists, for example, have made extensive use of network data analysis, however, much work remains to more fully develop the theory and methods of statistical analysis of network data.

New, non-classical, methods require further development to fully address statistical network inference and network characterization for real-world problems. For example, if a sociologist observes a high school cafeteria and the social behavior therein, how accurately can he/she construct a model of the friendship network within the school? For another example, with measured voltage readings from electrodes on the cortical surface of an epileptic seizure patient's brain, can a neuroscientist, by inferring a brain-activity functional network, infer the origin of the seizure? Such questions exist on the frontier of the analysis of network data.

I will discuss the mathematical, statistical, and algorithmic challenges associated with network data analysis, some existing problems and some problems on which I have worked (as those above) as well as future problems. My discussion will include the probabilistic and statistical theory behind solutions to such problems and will address the mathematical, biological, and physical applications.

**Ambulance Travel Time Estimation using Bayesian Models***Bradford Westgate*, Cornell University

**Abstract** : Travel time estimates for ambulances are useful for deciding which ambulance should respond to a new emergency, and for optimizing ambulance base locations. In this talk, I will discuss using Bayesian statistical models and GPS data to estimate the distribution of ambulance travel times between any two locations in a city. I will introduce Bayesian statistics in general, and give examples of how prior beliefs are combined with evidence from the data to make statistical conclusions. I will show how Bayesian models are used to estimate unobserved data. I will compare our Bayesian travel time estimation methods to alternative methods, and give some surprising results about the variability of ambulance travel times across the day.

**A New Approach for Constrained Bayesian Analysis**,*Michelle Danaher*, Eunice Kennedy Shriver, National Institute of Child Health and Human Development

**Abstract** : The role of a statistician is to reveal the underlying story of data. Before beginning analysis, understanding the processes which yield data may help to inform which solutions are possible. For example, well-understood complex feedback mechanisms drive reproductive hormonal patterns during the menstrual cycle. Effectively incorporating these known relationships is important for proper statistical inference and it may increase model efficiency. I will begin my talk by discussing the BioCycle Study, a cohort study of healthy regularly menstruating women. Next, I will give a brief introduction to Bayesian statistics, and discuss previous Bayesian methods for incorporating these known biological relationships. Subsequently, I will discuss a proposed new approach, which uses Minkowski-Weyl decomposition of polyhedral regions. Lastly, I will apply the new approach to the BioCycle Study and discuss the results.

KEY WORDS: Bayesian inference; Extreme directions; Extreme points; Parameter restriction; Parameter constraints; Polyhedral region

**Detecting Gamma-Ray Bursts Using Cyclic Dierence Sets**,*Harriet Pollatsek*, Department of Mathematics and Statistics

**Abstract** : Astronomers study high-energy radiation such as X-rays and gamma rays with instruments mounted on satellites, to avoid blocking of the radiation by the earth's atmosphere. Gamma ray bursts are extremely powerful explosions. They occur very briefly but almost daily. So far, it is not well-understood what causes the bursts and what they mean. Are they evidence of the birth of a black hole? the product of the collision of two neutron stars? The space observatory SWIFT was launched in 2004 to study gamma ray bursts with a new level of precision. Among the instruments on the orbiting SWIFT spacecraft was one using a "coded mask". Coded masks can be created using a mathematical object called a "cyclic difference set."

In this talk I'll describe how a coded mask works, what a cyclic difference set is, and why using a difference set produces a coded mask with desirable properties. The emphasis will be on concrete examples.This talk has no prerequisites, but familiarity with modular arithmetic will be helpful.

**Digit Sums and Harshad Numbers**,*Helen G. Grundman*, Bryn Mawr College

**Abstract** : A Harshad number is a positive integer that is divisible by the sum of its digits. A b-Harshad number is a number that is divisible by the sum of the digits in its base b expansion. I will begin with definitions, examples, and a number of simple questions concerning these numbers. Then I will focus on strings of consecutive b-Harshad numbers, proving that for any b, a string of consecutive b-Harshad numbers consists of at most 2b numbers. This talk is suitable for students and faculty of all levels, who enjoy numbers.