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Upper Bounds For The Number Of Lattice Edges Needed To Represent 4-Regular Graphs As Lattice Graphs, Shenze Li
Upper Bounds For The Number Of Lattice Edges Needed To Represent 4-Regular Graphs As Lattice Graphs, Shenze Li
Senior Projects Spring 2019
A lattice graph is a graph whose drawing, embedded in Euclidean space R2, has vertices that are the points with integer coecients, and has edges that are unit length and are parallel to the coordinate axes. A 4-regular graph is a graph where each vertex has four edges containing it; a loop containing a vertex counts as two edges. The goal for my senior project is to find upper bounds for the number of lattice edges needed to represent 4-regular graphs as lattice graphs.
Polygonal Analogues To The Topological Tverberg And Van Kampen-Flores Theorems, Leah Leiner
Polygonal Analogues To The Topological Tverberg And Van Kampen-Flores Theorems, Leah Leiner
Senior Projects Spring 2019
Tverberg’s theorem states that any set of (q-1)(d+1)+1 points in d-dimensional Euclidean space can be partitioned into q subsets whose convex hulls intersect. This is topologically equivalent to saying any continuous map from a (q-1)(d+1)-dimensional simplex to d-dimensional Euclidean space has q disjoint faces whose images intersect, given that q is a prime power. These continuous functions have a Fourier decomposition, which admits a Tverberg partition when all of the Fourier coefficients, except the constant coefficient, are zero. We have been working with continuous functions where all of the Fourier coefficients except the constant and one other coefficient are zero. …
Credit Risk Analysis In Peer To Peer Lending Data Set: Lending Club, Mohammad Mubasil Bokhari
Credit Risk Analysis In Peer To Peer Lending Data Set: Lending Club, Mohammad Mubasil Bokhari
Senior Projects Spring 2019
This project studies the classification variable ‘default’ in Peer to Peer lending dataset known as Lending Club. The project improved on existing work in terms of accuracy, F-1 measure, precision, recall, and root mean squared error. We explored balancing techniques such as oversampling the minority class, undersampling the majority class, and random forests with balanced bootstraps. We also analyzed and proposed new features that improve the Learner performance.
The Conditional Probability That An Elliptic Curve Has A Rational Subgroup Of Order 5 Or 7, Meagan Kenney
The Conditional Probability That An Elliptic Curve Has A Rational Subgroup Of Order 5 Or 7, Meagan Kenney
Senior Projects Spring 2019
Let E be an elliptic curve over the rationals. There are two different ways in which the set of rational points on E can be said to be divisible by a prime p. We will call one of these types of divisibility local and the other global. Global divisibility will imply local divisibility; however, the converse is not guaranteed. In this project we focus on the cases where p=5 and p=7 to determine the probability that E has global divisibility by p, given that E has local divisibility by p.
Factorization Lengths In Numerical Monoids, Maya Samantha Schwartz
Factorization Lengths In Numerical Monoids, Maya Samantha Schwartz
Senior Projects Spring 2019
A numerical monoid M generated by the natural numbers n_1, ..., n_k is a subset of {0, 1, 2, ...} whose elements are non-negative linear combinations of the generators n_1, ..., n_k. The set of factorizations of an element in M is the set of all the different ways to write that element as a linear combination of the generators. The length of a factorization of an element is the sum of the coefficients of that factorization. Since an element in a monoid can be written in different ways in terms of the generators, its set of factorization lengths may …
Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske
Analysing Flow Free With One Pair Of Dots, Eliot Harris Roske
Senior Projects Spring 2019
Flow Free is a smartphone puzzle game where the player is presented with an m by m grid containing multiple pairs of colored dots. In order to solve the puzzle, the player must draw a path connecting each pair of points so that the following conditions are met: each pair of dots is connected by a path, each square of the grid is crossed by a path, and no paths intersect. Based on these puzzles, this project looks at grids of size m by n with only one pair of dots to determine for which configurations of dots a solution …
Does Aerobic Exercise Or Cardiovascular Exercise Facilitate Explicit Memory?, Nicole Paige Ellin
Does Aerobic Exercise Or Cardiovascular Exercise Facilitate Explicit Memory?, Nicole Paige Ellin
Senior Projects Spring 2019
This study examined whether cardiovascular or aerobic exercise aids in explicit memory. Five male and twenty-four females on the Bard College campus either engaged in cardiovascular or aerobic exercise (experimental condition) or watched a video (control condition). Before beginning these tasks, participants read a list of 15 words. After the task, participants recalled as many words as they could from the previous list. The participants’ test scores did not indicate that a specific condition aided in their received score, meaning memory did not differ across conditions, F(2,29)= .420, p>.05. Future directions would implement a longer period of time for …
A Strength Test For The Borda Count, Jade Monroe Waring
A Strength Test For The Borda Count, Jade Monroe Waring
Senior Projects Spring 2019
When running an election with more than two candidates, there are many ways to choose the winner. A famous theorem of Arrow states that the only mathematically fair way to choose is to do so at random. Because this is not a desirable way to choose a winner of an election, many mathematicians have devised alternate ways of aggregating ballots. In my project I consider one of these ways -- the Borda Count, considered to be one of the most desirable from both the point of view of mathematics and economics -- and came up with a method to test …
From Constant To Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models, Hsin-Fang Wu
From Constant To Stochastic Volatility: Black-Scholes Versus Heston Option Pricing Models, Hsin-Fang Wu
Senior Projects Spring 2019
The Nobel Prize-winning the Black-Scholes Model for stock option pricing has a simple formula to calculate the option price, but its simplicity comes with crude assumptions. The two major assumptions of the model are that the volatility is constant and that the stock return is normally distributed. Since 1973, and especially in the 1987 Financial Crisis, these assumptions have been proven to limit the accuracy and applicability of the model, although it is still widely used. This is because, in reality, observing a stock return distribution graph would show that there is an asymmetry or a leptokurtic shown in the …
Predicting How People Vote From How They Tweet, Rao B. Vinnakota
Predicting How People Vote From How They Tweet, Rao B. Vinnakota
Senior Projects Spring 2019
In 2016 Donald Trump stunned the nation and not a single pollster predicted the outcome. For the last few decades, pollsters have relied on phone banking as their main source of information. There is reason to believe that this method does not present the complete picture it once did due to several factors--less landline usage, a younger and more active electorate, and the rise of social media. Social media specifically has grown in prominence and become a forum for political debate. This project quantitatively analyzes political twitter data and leverages machine learning techniques such as Naive-Bayes to model election results. …