20152016 Academic Year Colloquium Schedule 

September 9, 2015
Title: 
Counting Without Seeing

Speaker:  Eric Kamischke
Mathematics and Engineering
Jackson College
Jackson, MI

Abstract: 
The National Park Service asked for an estimate of the number of elk taken by the wolves introduced to the park. As there was no method guaranteed to find all the kills in the wilds of the park, a design was created to estimate what was not seen. The estimate involved a double count procedure, logistic regression modeling and parameter approximation. Once the estimate was found, the search and verification of the standard error involved delta methods, bootstrapping, and simulation.

Location: 
Palenske 227

Time: 
3:30 PM

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September 17, 2015
September 24, 2015
Title: 
Symmetry Groups: The mathematical connection between patterns in Moorish architecture and the artwork of M.C. Escher

Speaker:  David A. Reimann
Associate Professor
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
The mathematical structure of symmetrical patterns can be studied using group theory. The Moors built many magnificent buildings richly decorated with geometric patterns during their rule of the Iberian peninsula (7111492). The graphic artist M.C. Escher visited southern Spain in 1922 and was captivated by the patterns that richly decorate the architecture of the Alhambra, Alcazar, and other Moorish buildings. After a second visit to Spain in 1935, Escher became obsessed with creating patterns of interlocking figures based on these elaborate tiling patterns. While Escher had no formal mathematical training, he used mathematical methods grounded in scientific literature to study these patterns. We will view these patterns through the lens of group theory, one of the great mathematical accomplishments of the 19th century. This talk will be highly visual with many pictures of Escher's works and Moorish architecture.

Location: 
Palenske 227

Time: 
3:30 PM

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October 1, 2015
Title: 
Finding the Best Way From Here to There — A Primer on Variational Calculus

Speaker:  Darren Mason
Professor
Mathematics & Computer Science
Albion College
Albion, MI

Abstract: 
Given a task to accomplish, it is natural to ask what is the best way to achieve your goal? Maybe you are flying from Beijing to London and need the shortest flight path. Or you are selling fuel and you want to find the optimal time t to sell it so that you can maximize your profit. Or you are crossing a river with a strong current and want to determine a propeller direction (as a function of time) so that you cross the river in the least amount of time. The number of possible questions of this type seems endless. During this lecture we will discuss some of the above problems, a famous brainteaser called the brachistochrone problem, and illustrate how to find solutions to these problems using a version of calculus that makes sense in infinite dimensions — the interesting field of variational calculus!

Location: 
Palenske 227

Time: 
3:30 PM

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October 8, 2015
Title: 
Spider Craps: Mathematical Development of a New Casino Game

Speaker:  Mark Bollman>
Professor and Chair, Department of Mathematics and Computer Science
Mathematics and Computer Science
Albion College
Albion, MI

Abstract: 
Games of chance have been found in the relics of ancient cultures for as far back as one cares to look. The popular game of craps, played with two sixsided dice, traces its origins to the Old English game of Hazard, which was then transplanted to New Orleans by French settlers and evolved into one of the most popular casino table games. This talk will describe research in both theoretical and experimental probability that modified craps to use eightsided dice, leading to the invention of a new game called "Spider Craps". Mathematical points of interest for casino game developers including reasonable win probabilities, a meaningful house advantage, and efficient gameplay will be described. This research was carried out under a grant from Albion College's Foundation for Undergraduate Research, Scholarship, and Creative Activity (FURSCA) with recent Albion alumnus Jacob Engel.

Location: 
Palenske 227

Time: 
3:30 PM

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October 22, 2015
Title: 
Building Better Biological Models

Speaker:  Elizabeth Skubak Wolf
Assistant Professor
Mathematics and Computer Science
Saint Mary's College
Notre Dame, IN

Abstract: 
Randomness is inherent in many biological processes, from the dynamics of the populations in an ecosystem down to the systems of biochemical reactions occurring within a single cell. Therefore, when trying to analyze these processes, we might consider using a stochastic model — that is, one that includes some form of randomness.
Can stochastic models behave significantly differently from deterministic models? (Yes!) What might a stochastic model look like? How exactly does one use a stochastic model to say anything useful? We'll look at a few biological examples, introduce a particular stochastic model called a Markov chain, and see how, using a tool called Monte Carlo simulation, we can gain some insight into the biological systems we model.

Location: 
Palenske 227

Time: 
3:30 PM

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October 29, 2015
Title: 
The weak cop number of a graph

Speaker:  Robert Bell
The weak cop number of an infinite graph
Lyman Briggs College & Department of Mathematics
Michigan State University
East Lansing, MI

Abstract: 
The cop number of a finite graph G is defined as the minimal number of cops a player needs to capture an opponent's robber in a game of cops and robbers on G. In this game, the cop player places each of her cop pawns on vertices of G; and then the opponent places his robber pawn on a vertex of G. Both players have complete information about G and the location of the pawns. The players alternate turns, with the cop player playing first, by moving any number of his or her pawns along edges of G to adjacent vertices. If a cop is moved to the same vertex as the robber, then the robber is captured.
In this talk, we explore the notion of a weak cop number due to
Florian Lehner. Suppose G is a possibly infinite graph. The weak cop
number of G is the minimal number of cops needed to either capture the robber or prevent the robber from visiting any vertex of G infinitely often. We compute the weak cop numbers of several families of infinite graphs, extend several theorems to this new setting, and give examples of how some of the foundational theorems for finite graphs fail to extend to infinite graphs. In particular, we will outline how one can bound the weak cop number of a connected, countable, locally finite planar graph. This is joint work with undergraduate participants in the 2015 summer REU program at MSU.

Location: 
Palenske 227

Time: 
3:30 PM

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November 5, 2015
Title: 
Random Chess: Piece Strength; End Games; and Large Sparse Eigenvalue Problems.

Speaker:  Allan Struthers
Professor
Mathematical Sciences
Michigan Technological University
Houghton, Michigan

Abstract: 
Chess books all include an assessment of the relative strength of pieces and a detailed analysis of various end game situations. Modern computer algebra systems make it easy to build transition matrices for random walks by various pieces on chess boards. The eigenvectors of these large
sparse matrices quantify piece strength and provide interesting endgame information. The talk will provide
all necessary background in both Chess and Linear Algebra.

Location: 
Palenske 227

Time: 
3:30 PM

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November 12, 2015
Title: 
TwoColored Motzkin Paths, Set
Partitions and Restricted Growth Functions

Speaker:  Samantha Dahlberg
Mathematics
Michigan State University
East Lansing, MI

Abstract: 
This talk is based on the research done with a Research Experience for Undergraduates (REU) group at Michigan State University in the summer of 2014. The goal of this talk is to first introduce three commonly studied objects in combinatorics: set partitions, restricted growth functions (RGFs) and twocolored Motzkin paths. We will introduce and explore these seemingly different objects, but we will find that they are actually closely related to each other. This is joint work with Robert Dorward, Jonathan Gerhard, Thomas Grubb, Carlin Purcell, Lindsey Reppuhn, and Bruce Sagan.

Location: 
Palenske 227

Time: 
3:30 PM

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November 19, 2015
Title: 
Tennis Rankings over Time

Speaker:  Michael A. Jones
Associate Editor
Mathematical Reviews
Ann Arbor, MI

Abstract: 
In 2010, Kim Clijsters won the U.S. Open, but had her world ranking drop from #3 to #5 by the Women's Tennis Assocation (WTA). How can a tennis player win a tournament but drop in the rankings? The WTA uses a moving window to determine the rankings. We explain how discounting older results in the window can prevent such counterintuitive behavior and consider geometric and arithmetic discounting methods. We examine real data from the WTA, and comment on discounting methods already in use by the Federation Internationale de Football Association (FIFA) for ranking national teams for the World Cup and by the Professional Golf Association for ranking golfers.
This talk is based on joint work with Alex Webb (undergraduate at Macalaster College) and Jennifer Wilson (Eugene Lang College, New School University).

Location: 
Palenske 227

Time: 
3:30 PM

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February 4, 2016
Title: 
Forms resulting from replacing edges with flexible plates in convex equilateral polyhedra

Speaker:  David A. Reimann
Professor
Mathematics and Computer Science
Albion College
Albion, Michigan

Abstract: 
The convex equilateral polyhedra include Platonic Solids, Archimedean solids, prisms, antiprisms, and Johnson solids. Additionally, the class of nearmiss Johnson solids have faces that are almost regular. The edges in these polyhedra can be replaced with flexible twodimensional shapes (plates). The connection points at the ends of the edges are replaced with four holes located in the corners of the plates.
Faces and vertices are transformed into open space, while edges
become solid plates, resulting in open lattice structures that simultaneously provide a sense of lightness and enclosure.
Examples will be shown with edges replaced by squares, rectangles, and annulus sectors.
A wide variety of materials can be used for the plates such as paper, cardboard, wood veneer, and corrugated plastic.
Forms have been made using found objects such as business cards, coffee cup sleeves, and package condoms.
A material's stiffness, weight, and flexibility all contribute to the final form.
Fasteners such as split pin brads and cable ties have been used.
These constructions yield surprising and visually interesting forms that are
significantly different from the underlying base polyhedra.
Finally, the audience will build their own structures using playing cards.

Location: 
Palenske 227

Time: 
3:30 PM

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March 3, 2016
Title: 
Follow The Bouncing Ball: Keno and Lotteries

Speaker:  Mark Bollman
Professor of Mathematics and Chair, Department of Mathematics and Computer Science
Mathematics & Computer Science
Albion College
Albion, MI

Abstract: 
Keno, as played in casinos, is a descendant of an ancient Chinese game and an ancestor of Powerball and similar lotteries. In this talk, we shall look at the combinatorial mathematics behind keno and lotteries and detourbrieflyinto the world of integer programming to examine some tricky questions behind what appear to be very simple games.

Location: 
Palenske 227

Time: 
3:30 PM

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March 24, 2016
April 7, 2016
Title: 
Title: Improving Collection with Forecasting

Speaker:  John Greer
Program Manager, NGA
Research
National GeospatialIntelligence Agency
Springfield, VA

Abstract: 
I will discuss recent work using mathematical models to understand and predict event data ??? data labeled with a place, time, and type of activity. The work builds on SelfExciting Point Process (SEPP) models used for pattern analysis and prediction in seismology and crime prevention. In addition to giving intuitive descriptions of different types of point processes, I will show how to use them to forecast, and how to evaluate those forecasts. One of the applications for this work is to drive image collection by satellites. I will also give a brief overview of the National GeospatialIntelligence Agency (NGA) and some of its biggest scientific challenges.

Location: 
Palenske 227

Time: 
3:30 PM

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April 28, 2016
Title: 
The Calculus Behind Generic Drug Equivalence

Speaker:  Michael A. Jones
Associate Editor
Mathematical Reviews
American Mathematical Society
Ann Arbor, MI

Abstract: 
Motivated by an interview on National Public Radio's Science Friday, I look at the calculus behind the bioequivalence of generic and name brand drugs. To show bioequivalence, the Federal Drug Administration (FDA) requires a statistical comparison of three values related to the concentration of the drugs. These three values are related to calculus. I show that there is good reason why the FDA considers these values, as any two of the three is enough to recover the concentration of the drug over time for an orally taken, singlecompartment drug. The results hinge on applications of the Lambert W function. We revisit the biostatistics problem and explain how bioequivalence is determined in practice.
This talk is based on a paper of the same title, coauthored with Stanley R. Huddy of Farleigh Dickinson University.

Location: 
Palenske 227

Time: 
3:30 PM

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