New Research on Old Subject Draws Interest

Reposted from the Penn State Harrisburg News Archive.

Students are creating software to display the logical connections between the theorems of The Elements, a discourse on geometry.

Students at Penn State Harrisburg are gaining national attention from research they hope will bring new insights to the age-old study of geometry.

The group is creating software that displays the logical connections between the theorems of The Elements, the oldest written discourse on the study of geometry. The students are the first to extensively display these relationships using a visual technique, according to Dr. Eugene Boman, associate professor of mathematics, who is overseeing the project.

Siddharth Dahiya, of Camp Hill, and Tyler Brown, of Elizabethtown, both computer science and mathematical sciences double majors, received a Penn State Summer Discovery Grant for the project. The students, including Joseph Roberge, a graduate student in the Computer Science program, also received funding from Pi Mu Epsilon, the national mathematics honor society, and the college’s Mathematical Sciences program to complete their work, which began at the beginning of the year. Students Alexandra Milbrand, a mathematical sciences major, and Viplav Patel, a computer science major, also contributed significantly to the work. The students have presented their research in Madison, Wis. at MathFest, an annual nationwide mathematics conference, and at the regional Student Mathematics Conference at Moravian College, and will present at the Eastern Pennsylvania and Delaware sectional meeting of the Mathematical Association of America this fall.

The Elements, written in about 300 BC by Greek mathematician Euclid, begins by introducing five basic postulates, or foundational laws, that serve as the building blocks for later theorems. The students have gone through The Elementstheorem by theorem, mapped out the connections between them, and written the software that displays these connections in a visual and interactive form.

“I’m very proud of the progress [the students] have made,” said Boman. “Last January we started with nothing but an idea and now we have a fairly sophisticated piece of software that displays Euclid’s work in a completely original manner. Every colleague I’ve shown this to has been impressed, and we’re not finished with it yet.”

The software can be altered to display the connections of any set of interconnected ideas, according to Boman, who said the program can be generalized for applications in industry as well as in science and mathematics.

Integrated Undergraduate-Graduate Program in Computer Science

Integrated Undergraduate-Graduate Program in Computer Science:  Earn both a Bachelor's and Master's Degree in five years.

The Computer Science Integrated Undergraduate-Graduate (IUG) Program offers a limited number of academically superior Bachelor of Science candidates the opportunity to enroll in an integrated, continuous program of study leading to both the Bachelor of Science and the Master of Science in Computer Science. The ability to coordinate as well as concurrently pursue the two degree programs enables the student to earn the two degrees in five years.

As many as 12 of the credits required for the master's degree may be applied to both undergraduate and graduate degree programs. A minimum of 50 percent of the courses proposed to count for both degrees must be at the 500 level. Thesis credits may not be double counted.

Students have the choice of receiving the BS degree at the end of the fourth year or waiting until the end of the fifth year to receive both degrees. 

See the IUG page on the CS Program website for more information. 

Master's Thesis Defense: "SALIENT: Stochastic, Adaptive Latency Improvement for Event Notification Trees"

You are invited to attend Jason Long's Master's Thesis defense on Friday, September 7th at 2pm.  The defense will be held in Olmsted W231.  Details about Jason's thesis can be found below.

Title:  SALIENT: Stochastic, Adaptive Latency Improvement for Event Notification Trees

Author:  Jason Long

Thesis Adviser:  Jeremy Blum, D.Sc.

Abstract

A challenge in massively multiplayer online games (MMOGs) is the need for game event information to be quickly disseminated to all participants. Because of the cost and scalability limitations of centralized servers, peer-to-peer technologies have been adopted in which peers serve both to reconcile conflicting actions and to broadcast the events to other peers. This paper describes and evaluates a new algorithm, Stochastic, Adaptive Latency Improvement for Event Notification Trees (SALIENT). SALIENT provides for the efficient broadcast of event dissemination in peer-to-peer MMOGs through a distributed algorithm for constructing and maintaining a peer-to-peer broadcast tree.

SALIENT consists of am MMOG event dissemination model requiring a zone coordinator to be chosen from all participants. Each participant sends their event data to that zone coordinator for the zone coordinator to serialize and then broadcast through a broadcast tree to all participants.

The aim of SALIENT is to decrease the experienced average latency of all participants. In order to accomplish this goal, SALIENT employs a number of independent mechanisms that work over time to incrementally make improvements to the structure of the broadcast tree. SALIENT incorporates randomized algorithms to continually explore alternate tree structures that might reduce average latency and evaluate those alternate tree structures. When an improved structure is found, SALIENT adopts the new structure.

SALIENT was found to greatly reduce experienced latency, typically as much as 30-50% reduction in event delays, as compared to a simple base case where the broadcast tree is randomly assembled. In addition, SALIENT has bandwidth management strategies that help increase the number of nodes that can be supported for nodes with very limited bandwidth. Compared to a base case where a flat broadcast tree is used and can only support 12 participants in total, SALIENT allows 60 or more participants to be supported.