Elmira College
One Park Place
Elmira, New York 14901
800-935-6472
Student Talks Abstracts
Student Talks Abstracts
2012 MAA Seaway Section Meeting, Elmira College
Student Talk Abstracts
Student Talk Abstracts
Jeremy Baron, Jennifer Cordaro, Eric Knauf, Robert Wesolowski, University at Buffalo
Hongliang Xu, Buffalo State College
Structure-Solution Determination from X-ray Powder Distraction Data at Sub-atomic Resolution
Abstract: Most of what is known about the three-dimensional molecular structures of bio-medically important compounds has been discovered through the techniques of X-ray distraction crystallography. The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimeter in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented micro-crystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern.
Direct Methods routinely solve crystal structures when single-crystal diffraction data are available at atomic resolution (1.0-1.2A), but fail to determine micro-crystal structures due to reflections overlapping and low-resolution diffraction data. By artifficially and intelligently extending the measured data to atomic resolution, we have successfully solved structures having power diffraction data at sub-atomic resolutions. The newly developed method, Powder Shake-and-Bake, is implemented in a computer program PowSnB. We are going to discuss new approach, algorithm, strategy and applications.
Research supported by the National Science Foundation CSUMS grants 0802994 and 0802964.
Tara Hudson, SUNY Fredonia
Carbon Dioxide Flux Due to Soil Respiration
Abstract: A substantial amount of carbon dioxide is emitted from the respiration of microorganisms in the soil, which unfortunately is difficult to estimate. The goal of this project was to analyze the data gathered by researchers at Harvard Forest to determine trends in the emission of carbon dioxide. Mixed-effect models were applied to the data, and then alternative characteristics such as soil drainage and site descriptions were used to suggest rationale for the clusters which appear. As a follow up analysis, a model was selected to predict the carbon dioxide flux given a location.
Eric Knauf, Robert Wesolowski, Jeremy Baron, Jennifer Cordaro, University at Buffalo
Hongliang Xu, Buffalo State College
Optimizing default parameters of Powder Shake-and-Bake
Abstract: Knowledge of the structural arrangement of atoms in solids is necessary to facilitate the study of their properties, a vital part of meeting the needs of many industries such as pharmaceuticals. However, the success applications of direct methods in the phasing of microcrystalline structures dependent on the quality and resolution of the collected experimental data. X-ray powder diffraction experiments routinely yield diffraction data at sub-atomic resolution, a resolution that many direct-method algorithms have difficulty.
The dual-spaced Powder Shake-and-Bake package, which allows for the inclusion of unmeasured reections and produces better starting models, is now used in tangent with the refinement package of EXPO2011, to aid in the microcrystalline structure determination. A new process, which combines both packages strength, begins with the extension of sub-atomic data to atomic data. It follows with the creation of potential crystal structures from Powder Shake-and-Bake and using these as input for the refinement processes of EXPO2011. Of two crystal structures that this new approach has been tested on, both crystal structures were successfully determined at more extended sub-atomic resolutions than processing the crystal structures with EXPO2011 solely. More crystal structures are currently being tested.
This research experience is supported by the National Science Foundation CSUMS grants 0802994 and 0802964.
Christian Lethbridge, SUNY Oneonta
Colorful Pascal Triangle
Abstract: The Pascal triangle is a commonly used tool that helps determine binomial coefficients, however there is a lot more to this triangle than simply that. This study began by examining Gilbert and Smith and their work with the modulo 2 version of the triangle. Interestingly, there is a nice connection between this triangle and the regular polygons constructible with ruler and compass. This study investigates the Pascal triangle in Mod "N" and how the repeating patterns are connected amongst these rows. Finally this study shows the Pascal triangle when its entries are replaced by colored dots in Mod 2,3,4, and 5.
David Cervantes Nava, Traymon Beavers, Molly Domino, Michelle Rose, SUNY Potsdam
Graphs from Beyond the Grave: Self-Stabilizing Algorithms for Minimal Double Dominating Sets
Abstract: Self-stabilizing algorithms play a key role in fault tolerant distributed computing. They account for the inevitable fact that all computers eventually fail and still allow a network to function properly. We propose two distributed self-stabilizing algorithms that result in a minimal double dominating set of nodes.
Samuel Pine, Elmira College
Bounds for Elements of the Degree Sequence of an Unknown Vertex Set in a Balanced Bipartite Graph
Abstract: Consider the set of all balanced bipartite graphs. Given the degree sequence of one vertex set in one of these graphs, we find bounds for any given position in the degree sequence of the unknown vertex set. Additionally, we establish bounds for the median of the unknown degree sequence, as well as bounds for any given percentile. We discuss the connection between this paper and the High School Prom Theorem.
Patrick Reilly, Elmira College
Triangles, Tetrahedrons, and \Tricky" Election Outcomes
Abstract: As the election approaches, the nation turns to the polls and to the vote. My focus is also on the election, but not on the winner or loser; rather, my focus is on the method of election. Our archaic election procedure survives against the evidence of economists and mathematicians such as Donald Saari. Saaris representation triangles geometrically depict 3-candidate elections. Representation triangles demonstrate how multiple outcomes arise from close elections. A step above the 3-candidate representation triangle is the 4-candidate representation tetrahedron. This presentation exhibits the creation and use of a voting tetrahedron and compares it to Tabarroks version used to illustrate the 1860 presidential election.
Michaela Stone, Alfred University
Braid-Theoretic Approach to Knot Floer Homology
Abstract: We present a braid-theoretic approach to combinatorially computing knot Floer homology and the transverse invariant. Beginning with the braid word, we algorithmically compute a nice Heegaard diagram which is adapted to this braid. We argue that this algorithm is, in general, significantly faster than the previous algorithm involving grid diagrams.
Sven Thomas, Alfred University
Prime Numbers and the Riemann Zeta Function
Abstract: Being recognized by Hilbert as one of the most important unsolved problems of our time, Problem 8- the Riemann Hypothesis{ is arguably the most famous problem in mathematics. It has withstood the efforts of the most powerful minds in mathematics for centuries. It has influences in physics, biology, chaos, probability, computer science, and, of course, mathematics, but what is it? In this talk, we will discuss the importance of prime numbers and the pivotal role they share with the Riemann Zeta function and Riemann Hypothesis. This talk is intended to be relatively accessible.
Jeremy Topolski, SUNY Fredonia
Variations on the Knight's Tour Problem
Abstract: The classic "knight's tour" problem asks whether it is possible for a knight to begin on a given square of a standard 8 by 8 chessboard, and then to make a sequence of 64 moves, landing on each square exactly once, and returning to the starting square. The problem has been generalized to m by n chessboards.
We consider a number of variations of this problem, including:
Hongliang Xu, Buffalo State College
Structure-Solution Determination from X-ray Powder Distraction Data at Sub-atomic Resolution
Abstract: Most of what is known about the three-dimensional molecular structures of bio-medically important compounds has been discovered through the techniques of X-ray distraction crystallography. The best and most detailed structural information is obtained when the diffraction pattern of a single crystal a few tenths of a millimeter in each dimension is analyzed, but growing high-quality crystals of this size is often difficult, sometimes impossible. However, many crystallization experiments that do not yield single crystals do yield showers of randomly oriented micro-crystals that can be exposed to X-rays simultaneously to produce a powder diffraction pattern.
Direct Methods routinely solve crystal structures when single-crystal diffraction data are available at atomic resolution (1.0-1.2A), but fail to determine micro-crystal structures due to reflections overlapping and low-resolution diffraction data. By artifficially and intelligently extending the measured data to atomic resolution, we have successfully solved structures having power diffraction data at sub-atomic resolutions. The newly developed method, Powder Shake-and-Bake, is implemented in a computer program PowSnB. We are going to discuss new approach, algorithm, strategy and applications.
Research supported by the National Science Foundation CSUMS grants 0802994 and 0802964.
Tara Hudson, SUNY Fredonia
Carbon Dioxide Flux Due to Soil Respiration
Abstract: A substantial amount of carbon dioxide is emitted from the respiration of microorganisms in the soil, which unfortunately is difficult to estimate. The goal of this project was to analyze the data gathered by researchers at Harvard Forest to determine trends in the emission of carbon dioxide. Mixed-effect models were applied to the data, and then alternative characteristics such as soil drainage and site descriptions were used to suggest rationale for the clusters which appear. As a follow up analysis, a model was selected to predict the carbon dioxide flux given a location.
Eric Knauf, Robert Wesolowski, Jeremy Baron, Jennifer Cordaro, University at Buffalo
Hongliang Xu, Buffalo State College
Optimizing default parameters of Powder Shake-and-Bake
Abstract: Knowledge of the structural arrangement of atoms in solids is necessary to facilitate the study of their properties, a vital part of meeting the needs of many industries such as pharmaceuticals. However, the success applications of direct methods in the phasing of microcrystalline structures dependent on the quality and resolution of the collected experimental data. X-ray powder diffraction experiments routinely yield diffraction data at sub-atomic resolution, a resolution that many direct-method algorithms have difficulty.
The dual-spaced Powder Shake-and-Bake package, which allows for the inclusion of unmeasured reections and produces better starting models, is now used in tangent with the refinement package of EXPO2011, to aid in the microcrystalline structure determination. A new process, which combines both packages strength, begins with the extension of sub-atomic data to atomic data. It follows with the creation of potential crystal structures from Powder Shake-and-Bake and using these as input for the refinement processes of EXPO2011. Of two crystal structures that this new approach has been tested on, both crystal structures were successfully determined at more extended sub-atomic resolutions than processing the crystal structures with EXPO2011 solely. More crystal structures are currently being tested.
This research experience is supported by the National Science Foundation CSUMS grants 0802994 and 0802964.
Christian Lethbridge, SUNY Oneonta
Colorful Pascal Triangle
Abstract: The Pascal triangle is a commonly used tool that helps determine binomial coefficients, however there is a lot more to this triangle than simply that. This study began by examining Gilbert and Smith and their work with the modulo 2 version of the triangle. Interestingly, there is a nice connection between this triangle and the regular polygons constructible with ruler and compass. This study investigates the Pascal triangle in Mod "N" and how the repeating patterns are connected amongst these rows. Finally this study shows the Pascal triangle when its entries are replaced by colored dots in Mod 2,3,4, and 5.
David Cervantes Nava, Traymon Beavers, Molly Domino, Michelle Rose, SUNY Potsdam
Graphs from Beyond the Grave: Self-Stabilizing Algorithms for Minimal Double Dominating Sets
Abstract: Self-stabilizing algorithms play a key role in fault tolerant distributed computing. They account for the inevitable fact that all computers eventually fail and still allow a network to function properly. We propose two distributed self-stabilizing algorithms that result in a minimal double dominating set of nodes.
Samuel Pine, Elmira College
Bounds for Elements of the Degree Sequence of an Unknown Vertex Set in a Balanced Bipartite Graph
Abstract: Consider the set of all balanced bipartite graphs. Given the degree sequence of one vertex set in one of these graphs, we find bounds for any given position in the degree sequence of the unknown vertex set. Additionally, we establish bounds for the median of the unknown degree sequence, as well as bounds for any given percentile. We discuss the connection between this paper and the High School Prom Theorem.
Patrick Reilly, Elmira College
Triangles, Tetrahedrons, and \Tricky" Election Outcomes
Abstract: As the election approaches, the nation turns to the polls and to the vote. My focus is also on the election, but not on the winner or loser; rather, my focus is on the method of election. Our archaic election procedure survives against the evidence of economists and mathematicians such as Donald Saari. Saaris representation triangles geometrically depict 3-candidate elections. Representation triangles demonstrate how multiple outcomes arise from close elections. A step above the 3-candidate representation triangle is the 4-candidate representation tetrahedron. This presentation exhibits the creation and use of a voting tetrahedron and compares it to Tabarroks version used to illustrate the 1860 presidential election.
Michaela Stone, Alfred University
Braid-Theoretic Approach to Knot Floer Homology
Abstract: We present a braid-theoretic approach to combinatorially computing knot Floer homology and the transverse invariant. Beginning with the braid word, we algorithmically compute a nice Heegaard diagram which is adapted to this braid. We argue that this algorithm is, in general, significantly faster than the previous algorithm involving grid diagrams.
Sven Thomas, Alfred University
Prime Numbers and the Riemann Zeta Function
Abstract: Being recognized by Hilbert as one of the most important unsolved problems of our time, Problem 8- the Riemann Hypothesis{ is arguably the most famous problem in mathematics. It has withstood the efforts of the most powerful minds in mathematics for centuries. It has influences in physics, biology, chaos, probability, computer science, and, of course, mathematics, but what is it? In this talk, we will discuss the importance of prime numbers and the pivotal role they share with the Riemann Zeta function and Riemann Hypothesis. This talk is intended to be relatively accessible.
Jeremy Topolski, SUNY Fredonia
Variations on the Knight's Tour Problem
Abstract: The classic "knight's tour" problem asks whether it is possible for a knight to begin on a given square of a standard 8 by 8 chessboard, and then to make a sequence of 64 moves, landing on each square exactly once, and returning to the starting square. The problem has been generalized to m by n chessboards.
We consider a number of variations of this problem, including:
- Suppose we have k knights, k > 0. Can they cooperate to "tour" the board?
- Suppose the chessboard is on some other surface besides the plane, such as a torus. What happens in this case?
Amber Voorhees, SUNY Oneonta
Linear Algebra Approach to Regression Analysis
Abstract: Using Linear Algebra methods, speciffcally Matrix Algebra, I will show how to predict the Line of Best Fit for the Statistical method of Regression Analysis. I will provide the equations for doing so as well the deffinitions and/or examples of any linear algebra techniques used.
Jennifer White, Le Moyne College
EVEN Peg Solitaire is Solvable
Abstract: Peg solitaire seems like an easy enough game where anyone can end up being a "genius." It is played by jumping a peg over another peg into an empty hole on the other side. When a peg is hopped over, it is immediately removed from the game board. If you can solve the board down to one peg remaining you are classiffied as a genius. Solving a 3x100 board seems very strenuous, but it in fact can be solved to 1 remaining
peg, in a simple pattern of moves. In this talk we will explore what types of peg boards are solvable and which ones are not.
Winona Wixon, Houghton College
A Faster Chutes and Ladders
Abstract: Mathematicians have used absorbing Markov chains to model children's games such as Chutes and Ladders and Hi Ho Cherry-O. We adapted the techniques described in \Chutes and Ladders for the Impatient by Cheteyan, Hengeveld, and Jones (The College Mathematics Journal, January 2011) to minimize the number of turns required to fnish a game of Chutes and Ladders by interchanging chutes and ladders while keeping the same number of each. We first tried this on a simplified version of the game, then we moved to the actual game board and followed the same process to find the optimal arrangement of the chutes and ladders.
Linear Algebra Approach to Regression Analysis
Abstract: Using Linear Algebra methods, speciffcally Matrix Algebra, I will show how to predict the Line of Best Fit for the Statistical method of Regression Analysis. I will provide the equations for doing so as well the deffinitions and/or examples of any linear algebra techniques used.
Jennifer White, Le Moyne College
EVEN Peg Solitaire is Solvable
Abstract: Peg solitaire seems like an easy enough game where anyone can end up being a "genius." It is played by jumping a peg over another peg into an empty hole on the other side. When a peg is hopped over, it is immediately removed from the game board. If you can solve the board down to one peg remaining you are classiffied as a genius. Solving a 3x100 board seems very strenuous, but it in fact can be solved to 1 remaining
peg, in a simple pattern of moves. In this talk we will explore what types of peg boards are solvable and which ones are not.
Winona Wixon, Houghton College
A Faster Chutes and Ladders
Abstract: Mathematicians have used absorbing Markov chains to model children's games such as Chutes and Ladders and Hi Ho Cherry-O. We adapted the techniques described in \Chutes and Ladders for the Impatient by Cheteyan, Hengeveld, and Jones (The College Mathematics Journal, January 2011) to minimize the number of turns required to fnish a game of Chutes and Ladders by interchanging chutes and ladders while keeping the same number of each. We first tried this on a simplified version of the game, then we moved to the actual game board and followed the same process to find the optimal arrangement of the chutes and ladders.
Student Talk Schedule
Basement of Library, Classroom 1
1:30 – 1:42
Jeremy Baron, University at Buffalo
Jennifer Cordaro, University at Buffalo
Eric Knauf, University at Buffalo
Robert Wesolowski, University at Buffalo
Hongliang Xu, Buffalo State College
Structure‐Solution Determination from X‐ray Powder Diffraction Data at Sub-atomic Resolution
1:30 – 1:42
Jeremy Baron, University at Buffalo
Jennifer Cordaro, University at Buffalo
Eric Knauf, University at Buffalo
Robert Wesolowski, University at Buffalo
Hongliang Xu, Buffalo State College
Structure‐Solution Determination from X‐ray Powder Diffraction Data at Sub-atomic Resolution
1:45 – 1:57
Eric Knauf, University at Buffalo
Robert Wesolowski, University at Buffalo
Jeremy Baron, University at Buffalo
Jennifer Cordaro, University at Buffalo
Hongliang Xu, Buffalo State College
Optimizing default parameters of Powder Shake‐and‐Bake
Eric Knauf, University at Buffalo
Robert Wesolowski, University at Buffalo
Jeremy Baron, University at Buffalo
Jennifer Cordaro, University at Buffalo
Hongliang Xu, Buffalo State College
Optimizing default parameters of Powder Shake‐and‐Bake
2:05 – 2:17
Tara Hudson, SUNY Fredonia
Carbon Dioxide Flux Due to Soil Respiration
Tara Hudson, SUNY Fredonia
Carbon Dioxide Flux Due to Soil Respiration
2:20 – 2:32
Michaela Stone, Alfred University
Braid‐Theoretic Approach to Knot Floer Homology
Michaela Stone, Alfred University
Braid‐Theoretic Approach to Knot Floer Homology
2:40 – 2:52
Amber Voorhees, SUNY Oneonta
Linear Algebra Approach to Regression Analysis
Amber Voorhees, SUNY Oneonta
Linear Algebra Approach to Regression Analysis
2:55 – 3:07
Sven Thomas, Alfred University
Prime Numbers and the Riemann Zeta Function
Sven Thomas, Alfred University
Prime Numbers and the Riemann Zeta Function
Basement of Library, Classroom 2
1:30 – 1:42
Christian Lethbridge, SUNY Oneonta
Colorful Pascal Triangle
Christian Lethbridge, SUNY Oneonta
Colorful Pascal Triangle
1:45 – 1:57
Samuel Pine, Elmira College
Bounds for Elements of the Degree Sequence of an Unknown Vertex Set in a Balanced Bipartite Graph
Samuel Pine, Elmira College
Bounds for Elements of the Degree Sequence of an Unknown Vertex Set in a Balanced Bipartite Graph
2:05 – 2:17
David Cervantes Nava, SUNY Potsdam
Traymon Beavers, SUNY Potsdam
Molly Domino, SUNY Potsdam
Michelle Rose, SUNY Potsdam
Graphs from Beyond the Grave: Self‐Stabilizing Algorithms for Minimal Double Dominating Sets
David Cervantes Nava, SUNY Potsdam
Traymon Beavers, SUNY Potsdam
Molly Domino, SUNY Potsdam
Michelle Rose, SUNY Potsdam
Graphs from Beyond the Grave: Self‐Stabilizing Algorithms for Minimal Double Dominating Sets
2:20 – 2:32
Patrick Reilly, Elmira College
Triangles, Tetrahedrons, and “Tricky” Election Outcomes
Patrick Reilly, Elmira College
Triangles, Tetrahedrons, and “Tricky” Election Outcomes
2:40 ‐ 2:52
Winona Wixon, Houghton College
A Faster Chutes and Ladders
Winona Wixon, Houghton College
A Faster Chutes and Ladders
2:55 – 3:07
Jennifer White, Le Moyne College
EVEN Peg Solitaire is Solvable
Jennifer White, Le Moyne College
EVEN Peg Solitaire is Solvable
3:15 – 3:27
Jeremy Topolski, SUNY Fredonia
Variations on the Knight’s Tour Problem
Jeremy Topolski, SUNY Fredonia
Variations on the Knight’s Tour Problem
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