## Spring 2013

### Tuesday, January 29th

Professor Dick Forrester, Dickinson College

"Optimization Modeling"

Abstract: Operations Research (OR) is a scientific approach to analyzing problems and making decisions, usually under conditions requiring the allocation of scarce resources. In this talk, we focus on optimization modeling, which involves minimizing or maximizing a function (such as costs or profits) given that the solution must satisfy certain restrictions and requirements. We will learn about the modeling process, and about some of the most common types of models, such as resource allocation, scheduling, blending, and fixed-charge models.

Noon-1:00 p.m.

Tome 115

Lunch provided

### Tuesday, February 19th

Dr. Todd Neller, Gettysburg College

"The Poker Squares Challenge"

Abstract: In this interactive talk, we will introduce the game of Poker Squares (a.k.a. Poker Solitaire, Poker Square), where a player sequentially places random playing cards into a 5-by-5 grid in order to maximize the score of Poker hands in each of the grid's 5 rows and 5 columns. We will then play a game together using a common card deck draw. From this experience of the game, we will discuss possible strategies for human and computer play. A semester-long potential Poker Squares programming contest will be outlined, and we will overview a few approaches one might take in creating strong Poker Squares computer players. Please join us to plant seeds for creative solutions to this interesting, fun, and open problem.

Noon-1:00 p.m.

Tome 115

Lunch provided

### Saturday, February 23rd

Computer Programming Contest

Hosted by Penn State Harrisburg, Messiah College and the IEEE Susquehanna Section

For more information, email Jeremy Blum at blum@psu.edu

11:00 a.m.-5:30 p.m.

Tome Hall

Lunch provided

### Thursday, February 28th

Dr. Whitney George, West Chester University of Pennsylvania

"Chekanov's DGA: A Legendrian Knot Invariant"

Abstract: In this talk, we will look at a specific type of knot in the standard contact structure on R^3 called a Legendrian knot. We will look at two projections of Legendrian knots that are very easy to understand and work with. In particular, we will use one such projection to investigate a Legendrian knot invariant developed by Chekanov in the late 90's and will show how this invariant can distinguish two Legendrian knots that could not be distinguished by other methods.

Noon-1:00 p.m.

Tome 117

Lunch provided

### Tuesday, March 26th

Professor Jennifer Schaefer, Dickinson College

"Tower of Hanoi Graphs"

Abstract: How is this graph related to this graph? Come find out at this week's Math Chat!

Noon-1:00 p.m.

Tome 115

Lunch provided

### Tuesday, April 9th

Dr. Thang Bui, Penn State Harrisburg

"Using Ants to Solve NP-hard Combinatorial Optimization Problems"

Abstract: Combinatorial optimization problems appear in many areas of science and engineering. Many of these problems turn out to be NP-hard. It is conjectured that NP-hard problems do not have polynomial time exact algorithms. In this talk we first describe an ant-based heuristic that is suitable for a number of NP-hard graph optimization problems. Here ants are used to explore the problem search space and identify promising regions in the search space. This exploration has the effect of reducing the search space significantly. Fast local optimization algorithms are then used to find a solution in the reduced search space. Our ant-based optimization technique has provided competitive results for several different graph optimization problems when compared against other algorithms including evolutionary algorithms.

We next describe an ant-based algorithm for the degree-constrained minimum cost spanning tree problem. Extensive experiments show that the ant-based algorithm is robust and yields many improvements over existing algorithms.

### Tuesday, April 16th

Elyn Rykken, Muhlenberg College

"Graphical Sequences: Havel-Hakimi versus Wolfe"

Abstract: Mathematics is full of problems that come in pairs. For example, in calculus, we first learn to differentiate functions and then seek to find their anti-derivatives. As in that case, one often finds one direction to be very straightforward while the inverse process proves to be much more daunting. The topic of degree sequences in graph theory is another such example. In this talk we will discuss both the Havel-Hakimi theorem as well as a little known algorithm for realizing graphs given by Wolfe.

Noon-1:00 p.m.

Tome 115

Lunch provided

### Tuesday, April 30th

Math & Computer Science Majors Dinner

Professor Michelle Lastrina will present "Can You Paint Yourself into a Corner? Coloring and List Coloring Extensions on Planar Graphs."

Abstract: For a planar graph G and a subset P of its vertices, we look at what happens if we first color the vertices in P and then try to extend the coloring to the remaining vertices. C. Thomassen and M.O. Albertson initiated this question in regards to coloring and list coloring, respectively. In this talk, we explore the following two questions: If the vertices of P are precolored, under what conditions on P can G be 5-colored? If the vertices of P are precolored and all other vertices are assigned lists of size 5, under what conditions on P is there a proper coloring of G from the lists? We will look at some conditions that allow such precolorings to extend, as well as some that do not.

HUB Social Hall West

6:00 p.m.

### Tuesday, April 30th

Math Senior Research Talks

Natalie Stanley

"Using a Naïve Bayes Model to Predict Gene Expression Based on Promoter Structure in Acute Myeloid Leukemia"

Acute myeloid leukemia (AML) is a hematopoietic cancer, characterized by the rapid growth of aberrant white blood cells in the bone marrow. To model this cancer, we study the HL-60 cell line. Specifically, we treat the cells with a chemical agent (PMA), which allows them to differentiate into a macrophage-like state. Through the differentiation process, there are numerous changes in gene expression, which we quantify with gene microarray analysis. In our initial analysis, we are able to cluster genes together that exhibit similar temporal expression patterns. After generating expression clusters, we analyze the promoters of co-regulated genes in search of transcriptional regulatory mechanisms that allow the genes to have similar expression. To investigate this phenomenon, we are using a Naïve Bayes model to predict expression patterns, based on over-represented subsequences (motifs) in gene promoters. Essentially, we seek to use the Bayes model to recapitulate the expression clusters, based on promoter structure.

and

Miguel Rodriguez

"Optimal Crop Rotation and the Dickinson College Farm"

Crop rotation is an important component of organic farming because it can help maintain healthy soil and provides a mechanism for weed and pest control. Dickinson College has a certified organic farm consisting of 24 different fields that grow 13 different crop groups. Currently, the crop rotation plan at Dickinson is determined by a manual process on a yearly basis. Our research is concerned with using optimization modeling to develop an optimal crop rotation plan for the Dickinson Farm. Specifically, we develop a mixed-integer program that determines a four-year crop rotation schedule that takes into account crop’s irrigation type, weed and pest control, feeding habits, and crop yield requirements.

Noon-1:00 p.m.

Tome 115

Lunch provided

**Thursday, May 2nd**

Mathematics Honors Thesis Defense by Yujia Zhou

"Classification of Symbolic Dynamics for One-Dimensional Dynamical Systems with Overlapping Regions"

When studying a dynamical system, it is common to partition the space (or a subset of the space) into a finite number of disjoint regions.

Associated to each orbit is its itinerary, the sequence of regions it passes through. If the regions in the space overlap, a single orbit can have multiple itineraries. Hence, the itineraries are ambiguous. In order to study such systems, we need a bank of examples. We can represent the example via a directed graph (the transition graph from the dynamical system) and an undirected graph (the intersection graph from the intervals). We will discuss which pairs of transition and intersection graphs can be realized by continuous one-dimensional dynamical systems (on and on ). Moreover, we can generate a realization in the form of a piecewise linear function for every such pair of intersection graph and transition graph. We will use techniques from graph coloring, combinatorics, algorithms, and dynamical systems theory.

Noon-1:00 p.m.

Rector Lecture Room

Lunch provided

**Wednesday, May 8th**

### Mathematics & Computer Science Majors BBQ

Noon-2pm

Rector Courtyard (Rain Location: Rector Atrium)

Math & CS professors will grill hot dogs, hamburger and veggie burgers and will provide side dishes.

Computer Science Senior Symposium

Tome 115

2:00-4:00 p.m.

2:00pm. Chris Pianko: Program For Cutting Stock Problem

2:20pm. Lally Boright: Changing Room

2:40pm. Chris Melusky: ICONIAC: A Web-Based Image-Sharing Application

3:00pm. Nick Davis: Detection of Emotional Secondary Trauma

3:20pm. Blake Atwell: eFit – iOS Fitness Application

3:40pm. Qi Wang: Translating Event-B Specifications to Database Applications

Please join us for drinks, snacks, and computer science! The times above are approximate, as presentations will run continuously.