All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don’t need to think about it ...

Physics and Python stuff. Most of the videos here are either adapted from class lectures or solving physics problems. I really like to use numerical calculations without all the fancy programming ...

ABSTRACT: For a simple undirected graph G, let A( G ) be the (0, 1) adjacency matrix of G. The Seidel matrix of G, is defined as S( G )=J−I−2A( G ) , where J is the all-one matrix and I is the ...

According to mathematical legend, Peter Sarnak and Noga Alon made a bet about optimal graphs in the late 1980s. They’ve now both been proved wrong. It started with a bet. In the late 1980s, at a ...

Jane JaeYeon Pyo, a third-year Tepper School of Business doctoral student, has developed a way to measure the distances between financial statements and a novel method of interpreting them, offering a ...

Graph theory is an integral component of algorithm design that underlies sparse matrices, relational databases, and networks. Improving the performance of graph algorithms has direct implications to ...

Abstract: The huge development of social networks opens the need for their analysis. The visualization of social networks is an important and powerful tool for such kind of analysis. There are many ...

Introduction: The electronic health record (EHR) has greatly expanded healthcare communication between patients and health workers. However, the volume and complexity of EHR messages have increased ...

ABSTRACT: Let G be a connected graph with vertex set V( G ) . Then the degree resistance distance of G is defined as D R ( G )= ∑ { u,v }⊆V( G ) ( d( u )+d( v ) )R( u,v ) , where d( u ) is the degree ...