Elmira College
One Park Place
Elmira, New York 14901
800-935-6472
Contributed Talks Abstracts
Contributed Paper Sessions
Titles, abstracts, and any special equipment requests should be sent by e-mail to Dr. Marlo Brown, at Niagara University., mbrown@niagara.edu Please use Microsoft Word.
Deadline for submissions: September 28, 2012.
Deadline for submissions: September 28, 2012.
Abstracts for MAA Seaway Meeting
Elmira College
Contributed talks
Elmira College
Contributed talks
1. Ding Ding Binghamton University
Lifts and automorphisms of p-divisible groups
p-divisible groups, or more generally formal group schemes have been studied actively since mid 20th century, especially after the work of Dieudonné and Manin. After briefly reviewing the basics of formal group schemes, we focus on a particular type of p-divisible groups, namely, the canonical lifts of level 1 Barsotti-Tate groups, and study automorphisms of their truncations.
Lifts and automorphisms of p-divisible groups
p-divisible groups, or more generally formal group schemes have been studied actively since mid 20th century, especially after the work of Dieudonné and Manin. After briefly reviewing the basics of formal group schemes, we focus on a particular type of p-divisible groups, namely, the canonical lifts of level 1 Barsotti-Tate groups, and study automorphisms of their truncations.
2. Joel Dreibelbis RIT
Newton Polygons and Polynomial-Exponential Sums
Newton Polygons are useful in studying the zeroes of some functions over a certain field. There appears to be a way to, at the very least, algorithmically determine the maximum number of integer zeroes given a Polynomial-Exponential sum with integer coefficients. Polynomial-Exponential sums are finite sums and products of polynomials and exponential functions. These sums show up in studying linear recurrences. One desired goal is to determine a uniform upper bound for the number of integer zeroes of Polynomial-Exponential sums of a fixed order N. This talk is about work in progress and will contain some conjectures, known results, and open problems.
Newton Polygons and Polynomial-Exponential Sums
Newton Polygons are useful in studying the zeroes of some functions over a certain field. There appears to be a way to, at the very least, algorithmically determine the maximum number of integer zeroes given a Polynomial-Exponential sum with integer coefficients. Polynomial-Exponential sums are finite sums and products of polynomials and exponential functions. These sums show up in studying linear recurrences. One desired goal is to determine a uniform upper bound for the number of integer zeroes of Polynomial-Exponential sums of a fixed order N. This talk is about work in progress and will contain some conjectures, known results, and open problems.
3. Brad Emmons, Utica College
The Characteristic Polynomial of permuted block matrices
It is well known that the characteristic polynomial of a block diagonal matrix is the product of the characteristic polynomials of the individual blocks. That is, if M is a matrix with blocks A and B, then PM(x) = PA(x) PB(x). It might be surprising that if the blocks are permuted to the off-diagonal positions, then the characteristic polynomials can be easily computed as well. In this case PM(x) = PAB(x2). In this talk we will show how we can generalize the result to block matrices of any size.
The Characteristic Polynomial of permuted block matrices
It is well known that the characteristic polynomial of a block diagonal matrix is the product of the characteristic polynomials of the individual blocks. That is, if M is a matrix with blocks A and B, then PM(x) = PA(x) PB(x). It might be surprising that if the blocks are permuted to the off-diagonal positions, then the characteristic polynomials can be easily computed as well. In this case PM(x) = PAB(x2). In this talk we will show how we can generalize the result to block matrices of any size.
4. Charlie Jacobson, Elmira College
Using Medians to Estimate Means in Bipartite Data
A 2007 summary of data from the National Health and Nutrition Examination Survey (NHANES) reveals inconsistencies in the self-reporting of heterosexual sex partners [F]. Specifically, the mean number of different male sex partners for women, and the mean number of different female sex partners for men, disagree by a wide margin – yet, these means must agree, as a matter of mathematics. [K] It is easy to show that this need not be true for the medians. We argue that the medians are more trustworthy as measures of center for this bipartite data. Moreover, under additional assumptions about the distributions of the number of different heterosexual sex partners for each gender, we demonstrate that we might be able to use the medians to obtain an estimate of the common mean. Specifically, in the case where the distribution for women is geometric, and the men's is Poisson, we can demonstrate that the difference between the observed medians is certainly possible, and determine bounds for the common mean. We also illustrate how this technique might be sharpened.
Using Medians to Estimate Means in Bipartite Data
A 2007 summary of data from the National Health and Nutrition Examination Survey (NHANES) reveals inconsistencies in the self-reporting of heterosexual sex partners [F]. Specifically, the mean number of different male sex partners for women, and the mean number of different female sex partners for men, disagree by a wide margin – yet, these means must agree, as a matter of mathematics. [K] It is easy to show that this need not be true for the medians. We argue that the medians are more trustworthy as measures of center for this bipartite data. Moreover, under additional assumptions about the distributions of the number of different heterosexual sex partners for each gender, we demonstrate that we might be able to use the medians to obtain an estimate of the common mean. Specifically, in the case where the distribution for women is geometric, and the men's is Poisson, we can demonstrate that the difference between the observed medians is certainly possible, and determine bounds for the common mean. We also illustrate how this technique might be sharpened.
5. Keith Jones SUNY Oneonta
Self-Similarity – Games, Fractals, and Groups
The long-studied game “The Tower of Hanoi” has a fascinating connection to the famous Sierpinski Gasket fractal, which provides a clear visualization of the recursive nature of its solution. This connection is strengthened by a group structure, which exhibits the same self-similarity. The fractal nature of the group lends itself to a natural description in terms of a finite state automaton – a theoretical model for computing. In this expository talk, I will introduce the various concepts involved, and illustrate how these seemingly disparate concepts are tightly intertwined.
Self-Similarity – Games, Fractals, and Groups
The long-studied game “The Tower of Hanoi” has a fascinating connection to the famous Sierpinski Gasket fractal, which provides a clear visualization of the recursive nature of its solution. This connection is strengthened by a group structure, which exhibits the same self-similarity. The fractal nature of the group lends itself to a natural description in terms of a finite state automaton – a theoretical model for computing. In this expository talk, I will introduce the various concepts involved, and illustrate how these seemingly disparate concepts are tightly intertwined.
6. Chulmin Kim, RIT
Properties and Applications of Multivariate Antedependence Models
In many of biological studies, attributes are measured on each subject over repeated time, yielding longitudinal data. The importance of covariance modeling has been noted for analyzing longitudinal data. The goal of covariance modeling is to obtain as parsimonious a presentation of the covariance as possible, yet one that fits the data well. Antedependence (AD) models, generalization of Autoregressive (AR) models that allow the variances and same-lag correlations to vary over time, can be very useful for covariance structure for longitudinal data. We generalize the univariate AD models to multivariate AD (MAD) models and study some of their properties. Two examples in biological and in baseball are given to illustrate the usefulness of those properties of MAD.
Properties and Applications of Multivariate Antedependence Models
In many of biological studies, attributes are measured on each subject over repeated time, yielding longitudinal data. The importance of covariance modeling has been noted for analyzing longitudinal data. The goal of covariance modeling is to obtain as parsimonious a presentation of the covariance as possible, yet one that fits the data well. Antedependence (AD) models, generalization of Autoregressive (AR) models that allow the variances and same-lag correlations to vary over time, can be very useful for covariance structure for longitudinal data. We generalize the univariate AD models to multivariate AD (MAD) models and study some of their properties. Two examples in biological and in baseball are given to illustrate the usefulness of those properties of MAD.
7. Quincy Loney, Binghamton University
A look at the Lie algebra 4D and some of its subalgebras
The abstract would be: In this talk we introduce Lie algebras and some of their basic properties. We will look at the finite dimensional simple Lie algebras of types D4, B3, and G2. A familiarity with elementary linear algebra should be sufficient preparation for this talk.
A look at the Lie algebra 4D and some of its subalgebras
The abstract would be: In this talk we introduce Lie algebras and some of their basic properties. We will look at the finite dimensional simple Lie algebras of types D4, B3, and G2. A familiarity with elementary linear algebra should be sufficient preparation for this talk.
8. James Marengo, RIT
Limiting Distributions for Order Statistics
Suppose we take a random sample X1, X2, X3,…,Xn from a uniform distribution on the interval(0,1) and we put the data in ascending order to form the so-called order statistics: Y1<Y2<Y3<…<Yn. A basic result from mathematical statistics says that each of these order statistics has a Beta distribution. After discussing this result, we will investigate the limiting distribution of each order statistic as the sample size n approaches infinity.
This talk should be accessible to any student who has had a calculus- based probability course.
Limiting Distributions for Order Statistics
Suppose we take a random sample X1, X2, X3,…,Xn from a uniform distribution on the interval(0,1) and we put the data in ascending order to form the so-called order statistics: Y1<Y2<Y3<…<Yn. A basic result from mathematical statistics says that each of these order statistics has a Beta distribution. After discussing this result, we will investigate the limiting distribution of each order statistic as the sample size n approaches infinity.
This talk should be accessible to any student who has had a calculus- based probability course.
9. Barry Minemyer, SUNY Binghamton
Simplicial Isometric Embeddings of a Simplicial Complex into Rpq
In this talk we will prove that every finite n-dimensional metric simplicial complex X admits a simplicial isometric embedding into where p = q = max{d, 2n+1} and d = max{deg(v) | v is a vertex of X}. Here is endowed with the Lorentzian inner product that has p eigenvalues of 1 and q eigenvalues of -1. The proof of this theorem is existential, but if time permits I will give an alternate proof which is (somewhat) constructive (but increases dimension) which will allow for an example.
Simplicial Isometric Embeddings of a Simplicial Complex into Rpq
In this talk we will prove that every finite n-dimensional metric simplicial complex X admits a simplicial isometric embedding into where p = q = max{d, 2n+1} and d = max{deg(v) | v is a vertex of X}. Here is endowed with the Lorentzian inner product that has p eigenvalues of 1 and q eigenvalues of -1. The proof of this theorem is existential, but if time permits I will give an alternate proof which is (somewhat) constructive (but increases dimension) which will allow for an example.
10. Sam Northshield SUNY Plattsburgh
The equation a2+b2+c2= (a+b+c)2 and some friends.
The relatively prime integral solutions a,b,c of the title equation enjoy the surprising property that |a+b|, |a+c|, and |b+c| are all perfect squares. We show this along with its geometric realization in terms of Ford circles. In an upcoming Monthly Problem (posed by the speaker), one is asked to show that for a relatively prime integral solution a,b,c,d of a2+b2+c2+d2=(a+b+c+d)2, |a+b+c| is the square of the norm of an Eisenstein integer. Although we won’t prove this, we see how it is related to a type of “Ford sphere”. We will also look at some of the geometry behind the equations 2(a2+b2+c2+d2)=(a+b+c+d)2, 3(a2+b2+c2)=(a+b+c)2, and 4(a2+b2+c2+d2)=(a+b+c+d)2.
The equation a2+b2+c2= (a+b+c)2 and some friends.
The relatively prime integral solutions a,b,c of the title equation enjoy the surprising property that |a+b|, |a+c|, and |b+c| are all perfect squares. We show this along with its geometric realization in terms of Ford circles. In an upcoming Monthly Problem (posed by the speaker), one is asked to show that for a relatively prime integral solution a,b,c,d of a2+b2+c2+d2=(a+b+c+d)2, |a+b+c| is the square of the norm of an Eisenstein integer. Although we won’t prove this, we see how it is related to a type of “Ford sphere”. We will also look at some of the geometry behind the equations 2(a2+b2+c2+d2)=(a+b+c+d)2, 3(a2+b2+c2)=(a+b+c)2, and 4(a2+b2+c2+d2)=(a+b+c+d)2.
11. Jun-Koo Park, Houghton College
On coarse-grained Normal Mode Analysis and refined Gaussian Network Model for protein structure fluctuations
Functions of bio-structures are related to the dynamics, especially various kinds of large-amplitude motions. With some assumptions, those motions can be investigated by Normal Mode Analysis and Gaussian Network Model. However, despite their contributions to many applications, the relationship between NMA and GNM requires a further discussion. In this work, we review the NMA and GNM and evaluate GNM, based on how well it predicts the structural fluctuations, compared to experimental data. Then, we propose ways of coarse-graining for NMA on protein residue-level structural fluctuations by choosing different approaches to represent the amino acids and the forces between them. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, and also agree better with the B-factors. B-factor correlations are comparable or better than with those estimated with conventional GNM. The extracted force constants are surveyed for different pairs of residues with different extents of separation in sequence. The statistical averages are used to build a finer-grained GNM, which is able to predict fluctuations better than GNM.
On coarse-grained Normal Mode Analysis and refined Gaussian Network Model for protein structure fluctuations
Functions of bio-structures are related to the dynamics, especially various kinds of large-amplitude motions. With some assumptions, those motions can be investigated by Normal Mode Analysis and Gaussian Network Model. However, despite their contributions to many applications, the relationship between NMA and GNM requires a further discussion. In this work, we review the NMA and GNM and evaluate GNM, based on how well it predicts the structural fluctuations, compared to experimental data. Then, we propose ways of coarse-graining for NMA on protein residue-level structural fluctuations by choosing different approaches to represent the amino acids and the forces between them. The residue mean-square-fluctuations and their correlations with the experimental B-factors are calculated for a large set of proteins. The coarse-grained methods perform more efficiently than all-atom normal mode analysis, and also agree better with the B-factors. B-factor correlations are comparable or better than with those estimated with conventional GNM. The extracted force constants are surveyed for different pairs of residues with different extents of separation in sequence. The statistical averages are used to build a finer-grained GNM, which is able to predict fluctuations better than GNM.
12. Joseph Petrillo, Alfred University
The Alfred University Calculus Initiative: A Progress Report
The Alfred University Calculus Initiative (AUCI) is a multi-faceted project that combines a new and distinctive first-semester calculus curriculum with classroom transformation, video lessons, online homework, and web-based implementation into a comprehensive calculus experience. We are currently piloting the full AUCI course package in our Calculus I classes. In this talk, we will give a progress report on the AUCI and discuss some lessons learned by the instructors. This project is funded by the National Science Foundation (DUE-1140437).
The Alfred University Calculus Initiative: A Progress Report
The Alfred University Calculus Initiative (AUCI) is a multi-faceted project that combines a new and distinctive first-semester calculus curriculum with classroom transformation, video lessons, online homework, and web-based implementation into a comprehensive calculus experience. We are currently piloting the full AUCI course package in our Calculus I classes. In this talk, we will give a progress report on the AUCI and discuss some lessons learned by the instructors. This project is funded by the National Science Foundation (DUE-1140437).
13. Gabriel Prajitura, SUNY Brockport
Self similarity of sets in the plane under the power functions
An advanced problem in Operator Theory lead to a question in elementary math: which sets of complex numbers are self similar under the square function. We will present several approaches to this problem as well as to some versions of it in which the set under consideration is subject to some topological restrictions.
Self similarity of sets in the plane under the power functions
An advanced problem in Operator Theory lead to a question in elementary math: which sets of complex numbers are self similar under the square function. We will present several approaches to this problem as well as to some versions of it in which the set under consideration is subject to some topological restrictions.
14. Gary Raduns, Roberts Wesleyan college
Seventy three is a palindrome
Musings prompted by a house number, or a light introduction to palindromic and strictly non-palindromic numbers.
Seventy three is a palindrome
Musings prompted by a house number, or a light introduction to palindromic and strictly non-palindromic numbers.
15. Paul Seaburger, Monroe Community College
Making Calculus Come Alive with Dynamic Visualization Tools
A tour of several Java applets developed by the presenter to help students visualize calculus. Although the presenter has developed over 100 applets for various calculus textbooks, all of the applets demonstrated in this presentation can be found on the presenter’s webpage. Illustrated concepts include piece-wise functions, tangent lines, sketching derivative graphs from the graph of a function, Riemann sums, accumulation/area functions and the Fundamental Theorem of Calculus, slope fields, washer and shell methods, volumes with a common cross-section, 3D graphs of functions of two variables, parametric curves and surfaces, etc. In addition to his work on applets for visualizing single variable calculus, the presenter is also the PI of an NSF funded project that focuses on helping students visualize multivariable calculus. See http://web.monroecc.edu/calcNSF.
Making Calculus Come Alive with Dynamic Visualization Tools
A tour of several Java applets developed by the presenter to help students visualize calculus. Although the presenter has developed over 100 applets for various calculus textbooks, all of the applets demonstrated in this presentation can be found on the presenter’s webpage. Illustrated concepts include piece-wise functions, tangent lines, sketching derivative graphs from the graph of a function, Riemann sums, accumulation/area functions and the Fundamental Theorem of Calculus, slope fields, washer and shell methods, volumes with a common cross-section, 3D graphs of functions of two variables, parametric curves and surfaces, etc. In addition to his work on applets for visualizing single variable calculus, the presenter is also the PI of an NSF funded project that focuses on helping students visualize multivariable calculus. See http://web.monroecc.edu/calcNSF.
16. Paul Seaburger, Monroe Community College
Visually Verifying Homework Problems in Multivariable Calculus
Multivariable Calculus involves many concepts that require three-dimensional visualization to fully understand. Using CalcPlot3D, an online applet, students can view & print visual verifications for a variety of multivariable calculus homework problems. Examples include the plane determined by three points, the intersection of two surfaces, contour plots, directional derivatives, tangent planes, level surfaces, Lagrange multiplier optimization, and Riemann sums of rectangular prisms. CalcPlot3D is part of an NSF-funded grant project called Dynamic Visualization Tools for Multivariable Calculus (DUE- CCLI #0736968). See http://web.monroecc.edu/calcNSF/.
Visually Verifying Homework Problems in Multivariable Calculus
Multivariable Calculus involves many concepts that require three-dimensional visualization to fully understand. Using CalcPlot3D, an online applet, students can view & print visual verifications for a variety of multivariable calculus homework problems. Examples include the plane determined by three points, the intersection of two surfaces, contour plots, directional derivatives, tangent planes, level surfaces, Lagrange multiplier optimization, and Riemann sums of rectangular prisms. CalcPlot3D is part of an NSF-funded grant project called Dynamic Visualization Tools for Multivariable Calculus (DUE- CCLI #0736968). See http://web.monroecc.edu/calcNSF/.
17. Hossein Shahmohamad, RIT
The Millennium Problems, Part I &II of VII
In the year 2000, The Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of the seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money. These Millennium Problems encompass many of the fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. This talk will introduce the first Millennium problem, The Riemann Hypothesis, and the second Millennium problem and any recent progress made towards it.
The Millennium Problems, Part I &II of VII
In the year 2000, The Clay Foundation of Cambridge, Massachusetts, announced a historic competition: Whoever could solve any of the seven extraordinarily difficult mathematical problems, and have the solution acknowledged as correct by the experts, would receive $1 million in prize money. These Millennium Problems encompass many of the fascinating areas of pure and applied mathematics, from topology and number theory to particle physics, cryptography, computing and even aircraft design. This talk will introduce the first Millennium problem, The Riemann Hypothesis, and the second Millennium problem and any recent progress made towards it.
Print This Page
Email This Page
