Expedition in Data and Harmonic Analysis on Graphs

The graph Laplacian operator is widely studied in spectral graph theory largely due to its importance in modern data analysis. Recently, the Fourier transform and other time-frequency operators have been defined on graphs using Laplacian eigenvalues and eigenvectors. We extend these results and prove that the translation operator to the i’th node is invertible if and only if all eigenvectors are nonzero on the i’th node. Because of this dependency on the support of eigenvectors we study the characteristic set of Laplacian eigenvectors. We prove that the Fiedler vector of a planar graph cannot vanish on large neighborhoods and then explicitly construct a family of non-planar graphs that do exhibit this property. We then prove original results in modern analysis on graphs. We extend results on spectral graph wavelets to create vertex-dyanamic spectral graph wavelets whose support depends on both scale and translation parameters. We prove that Spielman’s Twice-Ramanujan graph sparsifying algorithm cannot outperform his conjectured optimal sparsification constant. Finally, we present numerical results on graph conditioning, in which edges of a graph are rescaled to best approximate the complete graph and reduce average commute time.

Crime in College Park: understanding crime levels, perceptions, and environmental design in an off-campus student-occupied neighborhood

Gemstone Team Crime Prevention and Perception

Developing Quantitative Methodologies for the Digital Humanities: A Case Study of 20th Century American Commentary on Russian Literature

Using scientific methods in the humanities is at the forefront of objective literary analysis. However, processing big data is particularly complex when the subject matter is qualitative rather than numerical. Large volumes of text require specialized tools to produce quantifiable data from ideas and sentiments. Our team researched the extent to which tools such as Weka and MALLET can test hypotheses about qualitative information. We examined the claim that literary commentary exists within political environments and used US periodical articles concerning Russian literature in the early twentieth century as a case study. These tools generated useful quantitative data that allowed us to run stepwise binary logistic regressions. These statistical tests allowed for time series experiments using sea change and emergency models of history, as well as classification experiments with regard to author characteristics, social issues, and sentiment expressed. Both types of experiments supported our claim with varying degrees, but more importantly served as a definitive demonstration that digitally enhanced quantitative forms of analysis can apply to qualitative data. Our findings set the foundation for further experiments in the emerging field of digital humanities.