Abstract: Bioinformatics is a field in which computer systems are used to process experimental data from biological experiments. Working with members of the Biology Department, I have constructed a relational database system to aid in processing the data from gene expression experiments done using a microarray or DNA chip. The Anoxia Gene Expression Group is specifically interested in genes expressed in neurons and mitochondria in the nematode C. elegans when it is raised in an environment devoid of oxygen. To identify these genes easily from among over 22,500 candidates, I mined data from the existing SAGE and Mitores databases to construct two relational databases: one detailing all of the genes expressed in neurons, and the other detailing the genes expressed in mitochondria. Once experimental data has been loaded into the database, the biologists use a web interface to access and query the databases. These queries involve selecting experimental data for genes expressed in neurons, mitochondria, or both that are either up-regulated or down-regulated around a cutoff value specified by the user.

Abstract: Can we trace The Mona Lisa to Leonardo DaVinci, or demonstrate how a certain wing span can mean it’s a deadly midge or even evaluate if seeing viagra in an email title means it’s spam? Is it possible to use numerical characteristics of a painting to determine its creator, or measurements of an insect to distinguish its species, or titles of emails to separate spam from legitimate messages? Linear Discriminant Analysis (LDA) is a statistical method used to identify group membership using a linear combination of features. The techniques extend concepts from ANOVA (Analysis of Variance) and Regression Analysis. We examine methods for producing a linear combinition that best distinguishes between the groups using univariate and multivariate sets of predictors.

Abstract : Software engineers and computer scientists alike frequently come upon a problem of how to store and easily retrieve large quantities of data. The most common method is to rely upon structures such as binary trees, linked lists, and vectors. But when it comes to displaying the data found within these graphs, those engineers have to conceive of a method to search through a graph and display the contents stored within.

Scientific computing is requiring greater and greater processing power. Cluster computing provides a inexpensive means of creating powerful parallel processing computers. We construct a Beowulf Linux cluster for Bioinformatics work and show the research and construction of the cluster as well as the mechanics of how parallel processing systems are used to tackle large scale problems.able of Contents

Table of Contents

Chapter 1 – An introduction to the project………………………………………….…..1
Chapter 2 – Single Variable data analysis………………………………………………5
Chapter 3 – Multi Variable data analysis……………………………………………….11
Chapter 4 – Regression analysis and the draft pick value chart….……….……….……25
Works Cited……………………………………………………………………………..33

Abstract: Within this paper the topic of clustering coefficients is examined. This is introduced in relation to social networking theory as a subtopic of graph theory. We show that any graph is triangle free if and only if it has a clustering coefficient of zero. Many basic classes of graphs are examined and their clustering coefficients determined. A clustering coefficient of zero is proven for bipartite, cycle, path, and grid graphs as well as trees. Formulas to easily compute the clustering coefficient of wheel graphs and radial street networks are shown. We define a new class of graphs for which interesting results occur. This new class of graphs is examined in analysis of the relationship between clustering coefficients and the density of edges. Finally, we discuss an array of applications of clustering coefficients.

Introduction:

Long before I discovered a relationship with regular space-division through the Moorish artists of the Alhambra, I had already recognized it in myself. At the beginning I had no notion of how I might be able to build up my figures systematically. I knew no rules of the game and I tried, also without knowing what I was about, to fit together congruent surfaces to which I tried to give animal shapes…later the designing of new motifs gradually came with rather less struggle that in the early days, and yet this has remained a very strenuous occupation, a real mania to which I became enslaved and from which I can only with difficulty free myself.

(Escher 1958, Ernst, 1994, p. 41)

M. C. Escher was interested in tessellations long before he even understood the concept of them. He was never known as an exemplar student but began his art career at a young age beginning with training as an architect. Beyond school, he became even more fascinated with repeating patterns and interlocking pieces that span over infinite space. His fascination motivated him to bridge the gap between mathematics and art throughout his career.

This paper will study the legacy that M. C. Escher has left in the mathematical world. To do this, it will first explain the fundamentals of group theory and the special topics of symmetry groups, frieze groups and crystallographic groups. The 17 classified crystallographic groups will explain the early artwork that inspired Escher in his tessellations. Then the paper will explore the development of Escher’s tessellations. Lastly, it will discuss the influence Escher has had on other scholars, artists, and scientists.

Abstract: A biometric authentication system matches physiological characteristics to a database of such characteristics. In biometric authentication, genuine users are generally those that the system should accept and imposters are those that the system should reject. One methodology for evaluating the matching performance of biometric authentication systems is the receiver operating characteristics (ROC) curve. The ROC curve graphically illustrates the relationship between type I and type II statistical classification errors when varying a threshold across a genuine and an imposter match score distributions. The performance of each biometric system can be estimated via a confidence region for a ROC curve of that system's performance. In this project ROC confidence regions will be created using radial sweep method. Radial sweep is based on converting the type I and type II errors to polar coordinates. The technique of bootstrapping will be utilized to estimate the variability of each point on an individual ROC curve. Simulations will be performed using real biometric match score data. A radial sweep method for comparing two ROC curves will be discussed.

Abstract:

A survival curve shows the proportion of a population at risk which survives up tp a certain time. Such curves can be described by theoretical parametric models (such as expoential, lognormal, or Weibull) as well as nonparametric methods (such as Kaplan Meier). We investigate methods for determining if survival curves from two populations to treatments are significantly different with applications to real data.

Abstract: Ranking college sports teams that play in leagues of different strengths can be challenging. A number of methods have been proposed to calibrate teams while accounting for performance and strength of schedule. We use Monte Carlo simulations of hundreds of seasons to compare several existing models, such as raw winning percentage, rating percentage index (RPI), Bradley-Terry (KRACH) and Poisson scoring rates (CHODR), for rating college ice hockey teams. By using these simulations we can examine common questions such as what are the pros and cons of being a strong team in a weak league versus being an average team in a strong league.

Introduction:

Dr. Jeff Han is a researcher based at the Courant Institute at NYU. With a strong background in electrical engineering, Dr. Han found inspiration in a glass of water. The way the light changed when entering the glass gave him the idea to invent multitouch screens using frustrated total internal reflection (FTIR). These are screens that have been outfitted to have infrared light bouncing within a translucent screen. When pressure is applied to a point on the screen, an infrared (IR) camera will pick up the frustrated IR light on that point and relay this information to a computer. After processing, the computer will then project the desired result back onto the screen.

Dr. Han has created the company Perceptive Pixels to market his product. Other companies have taken the same technology, but used it differently, whether it be using a matrix of force-sensitive-resistors, known as FSRs, or using estimations of distance from a wall from stereo with Visual Touchpad and TouchLight, or strength of intensity with Holowall. The object of this paper is to explore the mathematics behind Dr. Han’s multitouch display, and how to use this knowledge to create a multitouch display.

Penenburg, Adam L. “Can’t Touch This”, Fast Company, no. 112 (2007): 86.

Han, Jefferson Y. Low-Cost Multi-Touch Sensing through Frustrated Total Internal Reflection. Seattle, 2005: 115.

Abstract: One of the results given in [3] shows that for , there exists a unique degree sequence of length , no gaps, and one degree repeated twice. In this paper, we will investigate the question of when degree sequences that contain a unique degree repeated three times are graphical. For example, we will show that for there exists graphical degree sequences with a unique degree repeated three times. However, they are not unique as in the unique pair case. The preliminary sections will review essential material needed to investigate this hypothesis. We will present a review of pertinent graph theory and will begin by reinforcing important theorems, algorithms, and definitions. Then we will investigate when degree sequences with one degree repeated three times are always graphical.

Abstract: I decided to develop a unit based on cooperative learning and peer interaction because so oftenmathematics classes are conducted in a very traditional teaching style. It is important to make mathematics as interesting and as fun as other content areas. This unit is one example of how hands-on activities and tangible examples can revolutionize the way modern mathematics is tuaght. By creating this lesson I hope to entertain and inspire even the most uninspired students.

This unit is designed for 11th grade Math B class (Algebra II/Trigonometry). "Regression Equations and Reality" has students work with the many types of regression equations, including linear, expoential and lograithmic regressions. It is aligned with New York State MST Standard 3 Commencement level Math B standards.

"Regression Equations and Reality" consists of a variety of labs and games and a final project as an alternative assessment. "Reression Equations and Reality" brings a Constructivist attidtude to th e classromm and inspires students who struggle with mathematic concepts.