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Physical Sciences and Mathematics Commons™
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Articles 1 - 5 of 5
Full-Text Articles in Physical Sciences and Mathematics
Lazy Golfing, Didar Ashkerbekov, Max Hougas
Lazy Golfing, Didar Ashkerbekov, Max Hougas
Symposium on Undergraduate Research and Creative Expression (SOURCE)
Walking golfers are expected to leave their golf bags just outside the edge of the green while they are putting the ball. We construct a simple model of this situation, in which the green is assumed to be a circle with the hole at the center and the golfer one-putts the ball. (He or she is a great golfer!) We construct a function to determine the distance that the golfer walks from his or her approach shot on the green and then to the next tee box. Given this model, we determine the optimal location for leaving the golf bag …
Circle The Cat: Developing Intelligent Strategies For A Simple Two-Player Game, Kirk Baly, Micheal Lay, Owen Prough
Circle The Cat: Developing Intelligent Strategies For A Simple Two-Player Game, Kirk Baly, Micheal Lay, Owen Prough
Symposium on Undergraduate Research and Creative Expression (SOURCE)
Circle the Cat is an adaptation of the classic mathematical puzzle Qudraphage in which a cat attempts to escape a hexagonal board, but after each move one hexagon is blocked. We have coded a simulation of this classic puzzle. The result of our development allows for the implementation of varying strategies to computationally examine their effectiveness. The code itself, though extensive, is open enough for additions/extensions to be added fairly easily. Analysis of simpler strategies has allowed for improvement of both Cat and Player AI systems. We are currently looking at implementing more advanced systems, perhaps turning to machine learning.
Computer Monitored Problem Solving Dialogues, Lisa Dion, Jeremy Jank, Nicole Rutt
Computer Monitored Problem Solving Dialogues, Lisa Dion, Jeremy Jank, Nicole Rutt
Symposium on Undergraduate Research and Creative Expression (SOURCE)
This project looks over the shoulder at students collaboratively engaged in a math problem-solving activity. One task we looked at was mechanically classifying the students current activity or knowledge state, of which we have identified 15 different categories. We have produced an automatic classifier that examines student sentences and is 55% accurate in identifying utterances as containing certain bits of knowledge or evidence of certain activities. The classifier was built from a corpus of student-written reports. Treating each sentence as a bag of words, we built vector space models of the word co-occurrence matrix using both non-negative matrix factorization (NMF) …
Non-Contiguous Pattern Avoidance In Binary Trees, Michael Dairyko, Samantha Tyner, Casey Wynn
Non-Contiguous Pattern Avoidance In Binary Trees, Michael Dairyko, Samantha Tyner, Casey Wynn
Symposium on Undergraduate Research and Creative Expression (SOURCE)
We consider the enumeration of binary trees avoiding non-contiguous binary tree patterns. We begin by modifying a known algorithm that counts binary trees avoiding a single contiguous tree pattern. Next, we use this algorithm to prove several theorems about the generating function whose nth coefficient gives the number of n-leaf trees avoiding a pattern. In addition, we investigate and structurally explain the recurrences that arise from these generating functions. Finally, we examine the enumeration of binary trees avoiding multiple tree patterns.
Modeling Infectious Diseases : Two Strain Diseases In Metapopulations, Daniel Rossi, Sydney Philipps, Rachel Vonarb
Modeling Infectious Diseases : Two Strain Diseases In Metapopulations, Daniel Rossi, Sydney Philipps, Rachel Vonarb
Symposium on Undergraduate Research and Creative Expression (SOURCE)
Infectious diseases often mutate and are carried between regions. We consider a mathematical model which begins to account for these factors. We assume two disjoint populations that only occasionally comingle, and two strains of a disease present in these populations. Of interest are the equations describing the dynamics of this system, the conditions under which epidemics will occur, and the long term behavior of the system under various initial conditions. We find that in many ways this system is similar to a simpler one-population model. However, we find evidence that there may be conditions under which both disease strains can …