(Advisor: Giulianna Davidoff and Margaret Robinson)

## Fall 2017 Math/Stat Club Talks

## (Held in Clapp 416: 12:15 pm-1:00 pm, unless noted)

*Friday, December 1, 2017 (held in Clapp 407)*

Speaker: **DR.ASHLEA B. MILBURN**

ASSISTANT PROFESSOR AND JOHN L. IMHOFF CHAIR, DEPARTMENT OF INDUSTRIAL ENGINEERING, UNIVERSITY OF ARKANSAS

**Worldwide disasters cause over 30,000 deaths and $100 billion in economic damages per year. Rapid delivery of support such as food, water and medical attention is critical in minimizing suffering. Effective logistics and the optimized use of scarce resources can mean the difference between life and death. A good disaster response plan will deliver the right support to the right people at the right place and time. However, developing such a plan requires understanding where impacted populations are located and what they need. Social media is accelerating the pace at which this potentially lifesaving information becomes available to emergency managers. However, the information does not come without its drawbacks. Some in the emergency response community have cited concerns over the accuracy of data posted to social platforms, and have expressed a hesitation to take action on social data without first verifying it. There is a tradeoff between the timeliness and accuracy of the data that must be evaluated. In this seminar, Dr. Milburn will present her research on whether considering, and acting on, social data prior to its absolute verification improves the efficacy of disaster response plans. Come and learn how math, computer science and engineering can be applied to answer this and related questions! Dr. Milburn will also discuss opportunities for graduate study in industrial engineering at the University of Arkansas.**

*Wednesday, November 29, 2017*

Speaker: **Shanise Walker, ****Graduate Teaching Assistant, Iowa State University, Department of Mathematics**

*Graph Coloring Problems: Proper Colorings and Injective Colorings*

In this talk, two types of graph coloring problems will be introduced. A proper coloring of a graph $G$ is an assignment of colors on $G$ such that no two adjacent vertices receive the same colors. A graph $G$ is $k$-colorable if it can be colored properly with $k$ colors. Proper colorings have applications in committee-scheduling as well as coloring the regions of a map with common boundaries different colors. We discuss various well-known theorems of proper colorings. An injective coloring of a graph $G$ is an assignment of colors to the vertices of $G$ so that any two vertices with a common neighbor have distinct colors. A graph $G$ is injectively $k$-choosable if it has an injective coloring where the color of each vertex $v$ of $G$ can be chosen from any list $L(v)$ of size $k$. Injective colorings have applications in the theory of error-correcting codes and are closely related to other notions of colorability. We show that a subcubic planar graph with girth at least 6 is injectively 5-choosable, which improves several known bounds on the injective chromatic number of planar graphs.

*Wednesday, November 15, 2017*

Speaker: ** Adam Sullivan**, PhD, Assistant Professor of Biostatistics at Brown University & director of the Master’s program in Biostatistics at Brown University

Why Statistics in The World of Data Science? and information about our Master’s program at Brown.

*Friday, November 10, 2017*

Inside information to the Stat/Biostat Graduate program at UConn

Director of Graduate admissions perspective

**Speaker: Ofer Harel, Director of admissions**

Department of Statistics, University of Connecticut

In this presentation, Ofer Harel will introduce the department of Statistics graduate programs at the University of Connecticut. He will elaborate on different types of degrees, concentrations and requirements and will give some inside information relating to your future applications. This will be an open session where you can come with your questions.

*Wednesday, November 8, 2017*

**Speaker: Kat Correia**

(Fourth year Ph.D. student in the Department of Biostatistics at Harvard School of Public Health)

A woman walks into a bar an infertility clinic. What’s the probability she walks out with a baby?

In my talk, I will use national data on in vitro fertilization cycles to motivate the estimation of the Relative Excess Risk due to Interaction (RERI) in clustered data settings. I will introduce the concept of the RERI -- which is an additive interaction measure for binary outcomes-- and explain why it is a useful measure. I will present results from simulation studies that demonstrate the difficulty in estimating the RERI using frequentist random intercept models, and propose an advantageous alternative using a Bayesian approach. Finally, I will evaluate the potential interaction between maternal age and severe obesity on the likelihood of achieving a live birth following an in vitro fertilization procedure using a national database from the Society for Assisted Reproductive Technology.

I promise there will be no complicated math formulas, and there will be cute baby pictures, fun memes, and Chef Jeff Kat cookies!

*Wednesday, November 1, 2017*

**Please join us to hear about fellow students summer research!**

**Geometries in the Absence of the Side-Angle-Side Axiom**

Speaker: ** Emily Castner**

Collaborators: Elizabeth Theta Brown, Stephen Davis, Edwin O'Shea, Edouard Seryozhenkov, and Alfredo Vargas

The story of the parallel postulate and non-Euclidean geometry has been oft-told. Less studied as an axiom of geometry is the Side-Angle-Side rule for triangle congruence. Although SAS appears as a theorem in Euclid's Elements, its proof hinges on an implicit assumption of superimposition. We survey non-SAS geometries and axiom equivalences in the context of Hilbert's modern axiomatization of Euclidean geometry. Our perspective is informed by mathematical logic. Our main result is a novel proof that Euclid's parallel postulate is not equivalent to Playfair's axiom in the non-SAS context.

**Resilience to Discrete Disturbance in Non-Autonomous Systems**

Speakers: **Spencer Daugherty and Xuzhen Xiang**

In our research, we studied the resilience of differential systems exhibiting alternative stable state behavior. Our conceptual models integrated nonautonomous shifting and repeated discrete disturbance. This type of modelling has many real-world applications, especially in ecological systems like the coral reef.

*Wednesday, October 25, 2017*

Come hear about our spring courses offered here in the math/stat department and around the 5 colleges!

*Wednesday, October 18, 2017*

*Speaker Heidi Goodson, Visiting Assistant Professor of Mathematics at Haverford Colleg e*

*Title: Elliptic Curves over Finite Fields*

Abstract: Elliptic curves are solution sets to cubic equations in two variables. Questions of how to find, count, and characterize points on elliptic curves have been studied since the days of Diophantus. Nearly 2000 years later, the great mathematician Joe Silverman wrote, "the theory of elliptic curves is rich, varied, and amazingly vast." In this talk, I will define what it means to be a point over a finite field and answer the question "How many?" We'll discuss estimates, exact values, and surprising trends as the order of the field varies.

*Wednesday, October 11, 2017*

*Speaker: Nicholas Reich-Biostatistics in Practice: Forecasting Infectious Disease Outbreaks*

Nicholas Reich is an Associate Professor of Biostatistics at UMass-Amherst. He will talk about his research that focuses on developing methods for improving forecasts of infectious disease outbreaks for diseases such as dengue fever and influenza. He will discuss how this work has arisen out of collaborations with governmental health agencies, e.g. the US Centers for Disease Control and Prevention and the Ministry of Public Health in Thailand. This work is collaborative research with new Mt. Holyoke statistics professor Evan Ray. He will also talk generally about doing data science that interfaces with public health practice, highlighting career opportunities in this rapidly growing industry.

*Wednesday, October 4, 2017*

#### PLEASE COME AND BRING YOUR FAVORITE PUZZLE!

This week we will have two parts to the meeting:

First Nikkole Spencer '19 will tell us about her summer research in the Makerspace this summer where she used the 3D printer to make hands for children who need an artificial hand. She will also help us prepare for our Big Talk ( Friday 10/13 4:00 in Gamble) and workshop (on Saturday 10/14) after break when Henry Segerman is coming to talk about 3D printing.

Then next Haylea Hubacz '18 has some of the puzzles and games that we collected in the club last year and we are hoping to share those with all of you and also hear from all of you about the other great games and puzzles that you bring with you.

*Wednesday, September 27, 2017*

**Please join us to hear about what your fellow classmates did over the summer. Part 2!**

** Rachel Bostick' 20** worked at the Fred Hutchinson Cancer Research Center in Seattle, WA on HIV Vaccine/Prevention trials creating data visualizations and working various data sets and statistical models.

**Spencer Daughtery '19 and Xuzhen Xiang ‘19 **worked with Alanna Hoyer-Leitzl on studying the resilience of non-autonomous systems to discrete disturbance, with applications to ecological systems such as coral reefs.

**Nhu Thao Do '19** "Matroid theory - REU at Georgia Tech and the non-crossing partition transform - summer research at MHC.

**Sizhen Fang' 18**: SPUR program at Cornell University; researched on fractal analysis.

**Young Yang ’18** worked with Tim Chumley at MHC on "The Random Path Generated By Sphere After Collision", which involves knowledge in Brownian Motion.

**Surabhi Sharma '18** worked at Bank of America in Charlotte NC as technology analyst.

**Ani Gelashvili '18** worked at JP Morgan in sale and trading.

*Wednesday, September 20, 2017*

**Please join us to hear about what your fellow classmates did over the summer!**

**Emily Castner '18:** Foundations of Geometry research at James Madison University, worked as a counselor at Epsilon Camp, and assisted in online classes with the Art of Problem Solving

**Gauri Ganjoo '19**: REU Program at Alburn University in Alabama

**Haylea Hubacz ’18**: Internship this summer in the Education Affairs office at UMass Medical School

**Muhammadaha Areeb Shaukat Khichi '18**: Biochemistry research

**Sophie Le '18**: SPUR program at Cornell University, doing research in Group Theory

Plus some email messages from Allison Pan '18, Swasi Khunjeli '18 and Xueying Xu '18!

*Wednesday, September 13, 2017*

#### Welcome Meeting!

This first meeting will be organizational. You will meet the math/stat faculty, hear about the student groups working on various types of problems, find out what kinds of activities the club usually has and brainstorm about new ideas! Bring lots of good, new ideas with you! All are welcome.

*Wednesday, April 4, 2017*

Cecily Santiago will introduce our Mathematician of the Month and we will have Math Taboo!

*Wednesday, March 29, 2017*

**Fall 2017 Courses!**

Come hear about our fall courses offered here in the math/stat department and around the 5 colleges!

*Wednesday, March 22, 2017*

**The Association of Women in Mathematics (AWM) Discussion**

The AWM was founded in 1971 with the purpose of encouraging women and girls to study and to have active careers in the mathematical sciences, and to promote equal opportunity and the equal treatment of women and girls in the mathematical sciences.

Come join us at lunchtime on Wednesday, March 22, to hear a bit of the history of the AWM--how it has transformed the lives of women in mathematics and statistics in the last 45 years, what it is still doing--and to discuss the issues and advantages of starting our own student chapter.

Special guest: **Victoria Day**, MHC mathematics alum, now a graduate student at the University of Massachusetts, a founder of the UMass AWM Student Chapter

*Friday, December 9, 2016*

#### Speaker: Alicia Specht

**iCC: a new method for estimating network relationships for non-Gaussian data**

Gene co-expression networks (GCNs) are widely used to understand gene regulations and infer gene functions. This talk will discuss a novel method, iCC, for constructing GCNs using RNA-Sequencing data. iCC defines a new correlation measure that can be applied to data following any known distribution to construct undirected GCNs, and is robust to the effects of outliers. iCC's effectiveness is examined using simulations and an Escherichia coli dataset, and compared to commonly used transformation techniques.

*Monday, December 5, 2016*

*Speaker: Qingcong Yuan*

**A New Class of Measures for Independence Test with Its Application in Big Data**

Abstract: A new class of measures for testing independence between two random vectors, using characteristic functions, is proposed. By choosing a particular weight function in the class, we study a new index for measuring independence and its property. Sample versions and their asymptotic properties using different estimations are developed. We demonstrate the advantage of our methods via simulations and real data analysis. In particular, we develop a two-stage sufficient variable selection procedure and a sufficient dimension reduction method to illustrate the effective use of our methods in big data analysis.

*Friday, December 2, 2016*

**Speaker Evan Ray**

**Statistical Methods for Predicting Infectious Disease **

Public health agencies like the Centers for Disease Control and Prevention (CDC) would like to have reliable predictions of future infectious disease dynamics to help plan resource allocation and interventions. In this talk, I will discuss ongoing research that has been motivated by participation in a series of disease prediction contests run by the CDC and other United States federal government agencies. In the first part of the talk, I will describe a semi-parametric prediction method that combines kernel conditional density estimation with copulas to obtain a joint predictive density for disease incidence in all future weeks of the disease season. In applications to predicting dengue fever and influenza, we demonstrate that this method outperforms commonly used approaches to disease prediction in many settings. I will then briefly outline some directions for future research in this area, including the use of ensemble methods that combine predictive distributions from many different models and exploration of models that make predictions for multiple spatial units, such as in each state in the country.

*Monday November 29, 2016*

**A General Approach to Testing for Pleiotropy with Rare and Common Variants**

*Sharon M. Lutz*

*Department of Biostatistics and Informatics*

*University of Colorado, Anschutz Medical Campus*

Through genome-wide association studies, numerous genes have been shown to be associated with multiple phenotypes. To determine the overlap of genetic susceptibility of correlated phenotypes, one can apply multivariate regression or dimension reduction techniques, such as principal components analysis, and test for the association with the principal components of the phenotypes rather than the individual phenotypes.

However, as these approaches test whether there is a genetic effect for at least one of the phenotypes, a significant test result does not necessarily imply pleiotropy. Recently, a method called Pleiotropy Estimation and Test Bootstrap (PET-B) has been proposed to specifically test for pleiotropy, (i.e. that 2 normally distributed phenotypes are both associated with the single nucleotide polymorphism (SNP) of interest). While this method examines the genetic overlap between the 2 quantitative phenotypes, the extension to binary phenotypes, 3 or more phenotypes, and rare variants is not straightforward. Two approaches to formally test this pleiotropic relationship in multiple scenarios will be presented. These approaches depend on permuting the genotype of interest and comparing the set of observed p-values to the set of permuted p-values in relation to the origin (e.g. a vector of zeros) either using the Hausdorff metric or a cut-off based approach.

These approaches are appropriate for categorical and quantitative phenotypes, more than 2 phenotypes, common variants and rare variants. These approaches are evaluated under various simulation scenarios and applied to the COPDGene study, a case-control study of Chronic Obstructive Pulmonary Disease (COPD) in current and former smokers.

*Wednesday, November 2, 2016 *

*Wednesday, November 2, 2016*

#### Raji Balasubramanian, Associate Professor @ UMass, talks about Biostatistics graduate programs at UMass-Amherst!

*Wednesday, November 9th, 2016 *

#### George Cobb, Professor of Statistics emeritus

**What is Markov Chain Monte Carlo,** **What Can It Do, and How Does It Work? ****Three Stories of Important Applications**

**Background**. In my earlier talk, I argued that Markov Chain Monte Carlo (MCMC) can be seen as one of three major developments in the 2500-year history of the integral, with “integral” defined informally as “how to add up a very large number of very small numbers.”

(1) In classical Greece, the integral was part of the attempt to understand motion, area, and the infinite.

(2) At the dawn of the Enlightenment, Newton used antiderivatives as a shortcut for computing integrals, and used integrals to explain the motion of the planets.

(3) Beginning around 1950, MCMC made it possible, for the first time, to compute integrals for applied high-dimensional problems that could not be solved using traditional methods.

**What is MCMC**?** (There are two MCs: Markov Chains and Monte Carlo.)**

(1) **Markov chains**: If you have ever played Monopoly or shuffled a deck of cards, you already know about Markov chains: random processes for which the probabilities for where you go next depend only on where you are now.

(2) **Monte Carlo** is a systematic way to use random numbers to approximate integrals that can’t be computed by traditional methods. MCMC is now widely used to compute sums, averages, probabilities, and total net change -- integrals that occur throughout the sciences but are too hard for calculus-based methods.

**Applications: **I’ll compress the history and logic of MCMC into three sets of examples.

(1) **1953**: MCMC was invented to solve a problem related to the **nuclear physics** of the hydrogen bomb. I’ll also tell the story of what must surely be the nastiest academic food fight ever about a big table of 0s and 1s, arising from a problem in **ecology** – how species distribute themselves on the islands of the Galapagos.

**(2)** **1983**. A second major development was a method called the Gibbs sampler, first applied to **image processin**g. I’ll illustrate the method using a problem from **molecular biology**.

* (3) 1990. *The third major development generalized MCMC to compute a very broad class of integrals. A study of

**lung cancer rates**and an Ohio uranium plant illustrates what are called

**multilevel statistical models**, one of the most important areas of applied data analysis of the last 20 years.

*Wednesday, November 2nd, 2016 *

Spring courses! Come hear about our spring courses offered here in the math/stat department and around the 5 colleges!

*Wednesday, October 26th, 2016: Clapp 407 (note location)*

**Joint CS/Math/Stat Club**

Come hear about the summer experiences of your fellow students. Sophia Gu will talk about an opportunity with Google during J-term, Em Castner, and Deepshikha Adhikari will present their experiences with Google and data science internships. Food will be served in 416.

*Wednesday, October 19th, 2016 *

**George Cobb, Ph.D. Markov Chain Monte Carlo and the Integral: A 2500-year Drama in Three Acts**

I plan to address my premise historically via the standard academic cliché of compare/contrast based on (a) chronology, (b) big questions, (c) available technology, and (d) mathematical theory. In my planned talk I oversimplify shamelessly, reducing the stories supporting my premise to three acts:

Act I: **Classical Greec**e (around 350 BCE): motion and area; infinite sums and adding a geometric series.

Act II: **Enlightenment** (2^{nd} half of the 1600s, after two millennia of dormancy): total net change and area; the Fundamental Theorem of Calculus tells how to convert instantaneous rate of change to total net change, allowing Newton to explain the universe.

Act III: **Computer age** (Two-and-a-half centuries later, starting around 1950): the Ergodic Theorem tells how to compute the integrals that defeat calculus. Applications include robotics, computer vision, molecular biology, and the ecology of species distribution. Don’t be put off by “Fundamental Theorem of Calculus” and “Ergodic Theorem”. If the phrase “add up a very large number of very small numbers” makes sense, you have all the mathematical background you need for my talk.

*Wednesday, October 12th, 2016 *

Come join Erin Mullin and Alex Wellnitz to learn about Big O - Little O program and to play games. It's going to be a social meeting to get to know each other and develop a stronger sense of community.

*Wednesday, October 5th, 2016 *

**Joint CS/Math/Stat Club Lunch**

*Wednesday September 21, 2016, Clapp 407 : Turan's Problem (Annie Raymond)*

*Wednesday September 21, 2016, Clapp 407 : Turan's Problem (Annie Raymond)*

What is the maximum number of edges in a graph on n vertices without triangles? Mantel's answer in 1907 that at most half of the edges can be present started a new field: extremal combinatorics. More generally, what is the maximum number of edges in a n-vertex graph that does not contain any subgraph isomorphic to H? What about if you consider hypergraphs instead of graphs? We will explore different strategies to attack such problems, calling upon combinatorics, integer programming, semidefinite programming and flag algebras. We will conclude with some recent work where we embed the flag algebra techniques in more standard methods.** This is joint work with James Saunderson, Mohit Singh and Rekha Thomas. **

*Wednesday, September 14, 2016: Welcome Meeting*

This first meeting will be organizational. You will meet math/stat faculty, hear about the student groups working on various types of problems, find out what kinds of activities the club usually has and brainstorm about what it might have. We'll let you know what is already on the agenda, but bring lots of good new ideas with you.

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