<p>This dissertation extends the theory of persistent homology to time varying systems. Most of the previous work has been dedicated to using this powerful tool in topological data analysis to study static point clouds. ...

2008’s Democratic Presidential Primary will go down as one of the most competitive races in recent history. Two candidates, Senators Barack Obama (Illinois) and Hillary Clinton (New York), fought a see-saw battle to obtain ...

Wikipedia is known as a convenient source of user generated information for a wide range of topics, but is it able to compete in quality with a print encyclopedia? In this paper, I formulate a theoretical framework to ...

Firm self-regulation with regards to illegal and unethical labor practices has become a significant trend recently, as firms face possible negative exposure from the investigatory media. This paper provides a theoretical ...

The purpose of this paper is to investigate methods for analyzing networks from an algebraic perspective. The main focus will be on the dominant eigenpair of the adjacency matrix representing a graph, as many different ...

In the past thirty years, academia and the marketplace have devoted signi cant e ort and resources toward gaining a better understanding of how volatility changes over time in the nancial markets and how changes in one ...

Two standard invariants used to study the fundamental group of the complement X of a hyperplane arrangement are the Malcev completion of its fundamental group G and the cohomology groups of X with coefficients in rank one ...

During periods of market dislocation, which can be characterized by high asset volatility, correlations between assets generally tend to increase. However, there has been little research on the behavior of correlations ...

<p>Machine learning is a powerful branch of mathematics and statistics that allows the automation of tasks that would otherwise require humans a long time to perform. Two particular fields of machine learning that have ...