Spring 2009

[2/3] [3/3] [3/16] [3/17] [3/24] [3/31] [4/14] [4/21] [4/22] [4/24] [4/28] [4/30]


4/30: Improving the Two Color Image Prior Bayesian Demosaicing Algorithm
Ke Zhou ('09)
Dickinson College

Image demosaicing is the process of recovering truecolor images from raw data captured by color filter arrays. The research focuses on the improvement of a state-of-the-art demosaicing algorithm built upon the pivotal assumption that there exist two representative colors in an image neighborhood. Using a JAVA experimental framework, we have implemented the target algorithm and compared it with three alternative demosaicing schemes. The failure mode of the algorithm is identified and two forms of adjustment are proposed. Confirming important behaviors of the algorithm, the result points to modest improvement in demosaicing quality. Further research is necessary to fully explore the potential of the proposed forms of adjustment.

Date: 4/30
Location: Tome 117
Time: 12:00-12:50
Lunch provided

4/28: Integration of Java Generics Into The jmle Tool Within The Eclipse IDE
Adrian Kostrubiak ('09)
Dickinson College

The Java Modeling Language (JML) is a mathematical notation that can be included in Java programs, often through the use of in code annotations. JML is used to formally define the behavior of Java classes and modules. Due to their nature, formal specifications cannot actually be executed. However, the jmle tool created by Professor Tim Wahls has allowed the execution of these formal specifications through converting them into constraint programs. Unfortunately, previous to this work, neither JML nor any of the supporting tools were compatible with many of the newer Java 5 JDK features, such as generics and enum types. The goal of this research is to bring the functionality of generics into the jmle tool. Although there were numerous unexpected complications, limited generic functionality has been brought to the jmle tool. The aforementioned success has shown that the full integration of generics into the jmle tool should not be much more work at this point. However, for the jmle tool to acquire complete Java 5 JDK compatibility, much more work needs to be done.

Date: 4/28
Location: Tome 117
Time: 12:00-12:50
Lunch provided

4/24: Dynamical Effects of Non-Linearities and Time-Varying Gain Modulation in Neurally Plausible Network Models of Perceptual Decision-Making
Ritwik Niyogi ('09)
Dickinson College

Simple perceptual decision-making links sensation to action and constitutes the basis of many cognitive processes. Recent studies in neuroscience have made progress in identifying the neural systems associated with such processes. In particular, electrophysiological recordings from behaving primates have found the neuronal correlates of temporal integration of sensory information during perceptual decision-making tasks. However, less is known about how the underlying decision network operates, and how it can be adapted or modified to achieve behavioral goals.

Mathematical modeling of these decision processes seeks to provide a theoretical framework against which experimental data can be interpreted and evaluated. We use computational and analytical techniques from dynamical systems theory to study neurally plausible low-dimensional neural network models, which accumulate sensory evidence over time in order to form a categorical perceptual choice among two competing alternatives. In particular, we investigate how non-linearities in and multiplicative gain modulation of neural input-output (transfer) functions (e.g. due to attentional processes) can affect the dynamics of the decision network. Our work extends previous modeling efforts and predicts that modulation of both excitatory and inhibitory cells may be involved during temporal integration. We show how dynamic gain modulation over time can affect the temporal dynamics of the decision network, and thus enable flexible decision-making.

Date: 4/24
Location: Tome 115
Time: 12:30-1:20
Lunch provided

4/22: The Effects of Network Structure and Fitness Sharing on the Evolutionary Dynamics of Iterated Prisoner’s Dilemma Strategies
Matt Bachmann ('09)
Dickinson College

The Iterated Prisoner’s Dilemma (IPD) is a game where individuals repeatedly choose to either defect or cooperate. The game is designed such that a defector will out perform a cooperating opponent but two opponents who chose to cooperate will out perform two opponents who defect against each other. The effects of two parameters on the evolutionary dynamics of the populations of IPD strategies have been investigated.

First, a sharing parameter that forces individuals to share a portion of their fitness with all of the individuals with whom they play. When no sharing was required the population was allowed to evolve normally. As the amount of sharing increased evolution slowed down and strategies would show little change. At the highest levels evolution essentially stopped and strategies at the end of the experiment had behavior similar to ones from the beginning.

Next the structure of the network that determines which individuals play each other. Networks ranging from local networks through small world to random networks were tested. The closer the network structure was to a random network the longer defective strategies would evolve. However, this randomness also allowed the system to evolve more cooperative strategies towards the end of the experiment.

Date: 4/22
Location: Tome 117
Time: 12:30-1:20
Lunch provided

4/21: Interpreting Arithmetic in Arbitrary First Order Theories
Richard Rast ('09)
Dickinson College

The most important logical property of a mathematical structure is decidability - whether it can be solved.  A few cases have a well-known negative answer, the most famous of which is arithmetic.  In an effort to spread this result as far as possible, I have made a program which automatically identifies and describes arithmetical structure in arbitrarily-defined structures.

Date: 4/21
Location: Tome 117
Time: 12:00-12:50
Lunch provided

4/14: Polygons that Tessellate the Plane Under Reflections
Ron Umble, Ph.D.
Professor of Mathematics
Millersville University

This talk reviews current work by MU undergraduates Andrew Hall, Matthew Kirby, and Joshua York, who recently proved that exactly eight families of polygons generate a tessellation of the plane under reflections. Given such a polygon G, the goal of their project is to find, classify, and count the classes of periodic orbits of a billiard ball in motion on G. My former student Andrew Baxter and I gave a complete solution on a equilateral triangle (Am. Math. Monthly, June-July 2008).

Date: 4/14
Location: Tome 117
Time: 12:00-12:50
Lunch provided

3/31: Commonsense in Machine Ethics
Gene Rohrbaugh, Ph.D.
Associate Professor of Computer Science
Messiah College

The rapidly evolving field of Machine Ethics deals with implementing behavioral constraints in machines. As artificial intelligence technologies yield increasingly complex autonomous agents, it becomes more and more important to ensure that these agents continue to behave in acceptable ways. This is challenging, since the very features that make them useful -- their ability to learn and adapt -- entails a certain unpredictability in their behavior. A variety of frameworks have been proposed for implementing ethics in machine agents. In this talk I will explore the possibility of using OpenCyc, billed as "the world's largest and most complete general knowledge base and commonsense reasoning engine," as the basis for one such implementation.

Date: 3/31
Location: Tome 115
Time: 12:00-12:50
Lunch provided

3/24: Web content, CRUD, and You
Russell Toris ('11)
Computer Science Major
Dickinson College

If you're connected to the Web, doing basic content operations (Create, Read, Update, and Delete or CRUD) has traditionally meant using FTP or using web forms to pass data to a back-end system. But now there's a new alternative: the Java Content Repository, a standard API for interacting with storage systems. Crux is a micro-application that can pass "web clippings" to a Java Content Repository using a simple web interface. With a couple of mouse clicks, a Firefox user can select a part of a web page, apply a title and some tags ,and send the clipping to a repository via an ordinary form POST. Then you can browse the repository and retrieve the clippings for later use. This small JavaScript application leverages the power of JCR to enable "easy, reliable CRUD" over the wire, freeing the user from having to know anything about FTP or database technology. See why "remote repository" technology has the potential to make content storage easier for end-users.

Date: 3/24
Location: Tome 115
Time: 12:00-12:50
Lunch provided

3/17: Termites, Flocks of Birds, Sunflower Seeds, and the Formation of Opinions: Modeling Emerging Order with NetLogo Software
Marc Renault, Ph.D.
Associate Professor of Mathematics
Shippensburg University

In this informal talk I'll explore some of the capability of NetLogo (see http://ccl.northwestern.edu/netlogo/ for a preview).

NetLogo is a programmable modeling environment for simulating natural and social phenomena. Modelers can give instructions to hundreds or thousands of "agents" all operating independently. This makes it possible to explore the connection between the micro-level behavior of individuals and the macro-level patterns that emerge from the interaction of many individuals.

We'll play with some of the models that others have created with NetLogo, then I'll spend time discussing my own research into "continuous opinion dynamics". How are your opinions influence by those around you? During an election, why are there large contiguous regions of blue voters and red voters? We'll see how to model this with NetLogo.

Date: 3/17
Location: Tome 115
Time: 12:00-12:50
Lunch provided

3/16: What Can You Do When You Design First
Evan Wolbach
Ursinus College ('09)

Humans tend to dive into projects and design as they go. This process can be fruitful, fun and is, in fact, necessary when the domain of knowledge required for the project is unexplored. But by leveraging all information available during the design process then a solid design can yield a high-quality product. In this talk, Evan Wolbach will discuss the design process he used to develop Venatio Creo (http://www.venatiocreo.com) , an interactive game development toolkit for non-programmers. He will also discuss the lessons he had learned during the three years of its development. During the presentation the audience will be able to see and interact with the application and experience the results of the design process first hand by participating in the collaborative development of a game of their choosing using Venatio Creo. Artist Lindsey Stone will be present to create art assets requested by the audience for use in the game.

Date: 3/16
Location: Tome 117
Time: 4:45-5:45
Snacks provided

3/3: Computer Science and Math Ramifications in the U.S. Military
Bruce D Caulkins, Ph.D.
Lieutenant Colonel (Promotable)
US Army War College

Computer Science and Mathematical concepts are critical components for today's military. More than ever before, the U.S. military relies on math- and CS-based technology in its operations. In this talk I will provide examples and insight to the ongoing information-related challenges facing our military. I will conclude by discussing the role that the commercial industry plays with respect to military operations.

Date: 3/3
Location: Tome 115
Time: 12:00-12:50
Lunch provided

2/3: Cryptography, Coding Theory, and Curve Interpolation
Dr. Darren Glass
Assistant Professor
Gettysburg College

The goal of cryptography is to use mathematics to communicate secrets so that only the people you want to hear the information do in fact hear it. The goal of coding theory is to use mathematics to build redundancy into messages so that they can withstand errors that may occur in the transmission. While much of the mathematics used in these areas is extremely deep, major advancements in both of these areas have come from the simple fact that two points determine a unique line as well as higher dimensional analogues of this fact which we all learn in grade school. In this talk, I will describe these applications of curve interpolation, and discuss broader ideas that come up in the modern theory of communications.

Date: 2/3
Location: Tome 115
Time: 12:00-12:50
Lunch provided