Completed Research Projects
Here are samples of some of my previous research projects and expository presentations.
Integer Distances on a Circle
This project started by solving the following problem posed by Stanley Rabinowitz in the Pi Mu Epsilon Journal. "Let ABC be an equilateral triangle with edge length c inscribed in a circle. Let N be a point on minor arc AB. Let NB = a and NA = b. Is it possible for a, b, and c to all be distinct positive integers?"
This work afirms the problem and classifies all such a, b, and c.
This work afirms the problem and classifies all such a, b, and c.
IntegerDistancesSlides.pdf |
Duplicate Bug Detection Machine Learning Project
Open source software projects can sometimes get hundreds of "bug reports" each day. Inevitably, some of these reports describe the same issue. It is often infeasible for software developers to read and fix the problems mentioned each report. Additionally, once an issue has been fixed all other reports about the same issue should be flagged as complete. This project aimed to develop a method that automatically classifies bug reports as duplicates, so that developers can spend their time efficiently. This was done by data mining these bug reports, prepossessing the data, and implementing machine learning algorithms to flag duplicate reports. This project was done under Youngstown State University's Collaborative Research Experience for Undergraduates (CREU).
DuplicateBugsSeniorThesis.pdf |
DupBugsSlides.pdf |
Modeling Butanol Production
Although fossil fuels are currently the most economically sensible source of energy, many other alternative energy sources are being explored as replacements for fossil fuels. Butanol, a promising alternative biofuel, has similar energy content when compared to gasoline. The genus Clostridium is known for its ability to produce butanol. A mathematical model was developed using the known metabolic pathway of xylose to butanol, as well as basic Michaelis-Menten kinematics. Experiments were conducted using the bacterium Clostridium beijerinckii in bench-top fermentors to calibrate the parameter of the model so other products could be determined analytically and protein expression could be studied. The goal of this research was to develop methods to obtain optimum yields of butanol production. To achieve this goal, two separate but complementary approaches were undertaken. First, the development and verification of a model to guide the selection of parameters that optimize butanol production. Second, to identify proteins and associated enzymes that are activated at various stages of the fermentation process, which can be targeted for enhanced protein expression in future research. This project was done under Youngstown State University's Mathematics and Biology Undergraduate Research (MBUR).
ButanolProductionPoster.pdf |
ButanolProductionFinalPaperMBUR.pdf |
Residue Number Systems to Check Computer Algebra
Residue Number systems are ways of representing numbers, where each number is stored as an array of remainders mod different bases. This is a possible alternative method to perform arithmetic calculations on large numbers. It takes advantage of the fact that computers have parallel processors since arithmetic operations can be performed component-wise on each element in the residue set at the same time. It may be more efficient than traditional number systems and only using a fraction of computational power. Because only the residue set is stored in a computers memory, new techniques are needed to handle conversion in and out of RNS, overflow detection, parity checking, and signed number. This project looks into overcoming some of these challenges.
ResidueNumberSystemsSlides.pdf |
Prime Generation
Generating large prime numbers is important for many application including cryptography. In 1947, W. H. Mills proved the following theorem. "There exists a constant A such that [A^(3^n)] is a prime for every positive integer n." Here is the first 600 digits of the smallest such A.
1.3063778838 6308069046 8614492602 6057129167 8458515671 3644368053 7599664340 5376682659 8821501403 7011973957 0729696093 8103086882 2388614478 1635348688 7133922146 1943534578 7110033188 1405093575 3558319326 4801721383 2361522359 0622186016 1085667905 7215197976 0951619929 5279707992 5631721527 8412371307 6584911245 6317518426 3310565215 3513186684 1550790793 7238592335 2208421842 0405320517 6890260257 9344300869 5290636205 6989687262 1227499787 6664385157 6619143877 2844982077 5905648255 6091500412 3788524793 6260880466 8815406437 4425340131 0736114409 4137650364 3793012676 7211713103 0265228386 6154666880 4874760951 4410790754 0698417260 3473107746
The first 10,000 digits have been calculated and are available at OEIS website! But how much accuracy is needed to actually generate primes? This project looked into the practicality of generating primes using this Mil's Theorem.
1.3063778838 6308069046 8614492602 6057129167 8458515671 3644368053 7599664340 5376682659 8821501403 7011973957 0729696093 8103086882 2388614478 1635348688 7133922146 1943534578 7110033188 1405093575 3558319326 4801721383 2361522359 0622186016 1085667905 7215197976 0951619929 5279707992 5631721527 8412371307 6584911245 6317518426 3310565215 3513186684 1550790793 7238592335 2208421842 0405320517 6890260257 9344300869 5290636205 6989687262 1227499787 6664385157 6619143877 2844982077 5905648255 6091500412 3788524793 6260880466 8815406437 4425340131 0736114409 4137650364 3793012676 7211713103 0265228386 6154666880 4874760951 4410790754 0698417260 3473107746
The first 10,000 digits have been calculated and are available at OEIS website! But how much accuracy is needed to actually generate primes? This project looked into the practicality of generating primes using this Mil's Theorem.
PrimeGeneratorEncryptionSlides.pdf |
Thinning the Harmonic Series
It is common knowledge that the Harmonic series diverges. Does the series still diverge if you remove the reciprocal of all prime numbers? What if you remove numbers according to a pattern? How about all numbers with the digit 9? The results of this expose project may surprise you!
HarmonicSeriesThinningSlides.pdf |