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Full-Text Articles in Physical Sciences and Mathematics
The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker
The Document Similarity Network: A Novel Technique For Visualizing Relationships In Text Corpora, Dylan Baker
HMC Senior Theses
With the abundance of written information available online, it is useful to be able to automatically synthesize and extract meaningful information from text corpora. We present a unique method for visualizing relationships between documents in a text corpus. By using Latent Dirichlet Allocation to extract topics from the corpus, we create a graph whose nodes represent individual documents and whose edge weights indicate the distance between topic distributions in documents. These edge lengths are then scaled using multidimensional scaling techniques, such that more similar documents are clustered together. Applying this method to several datasets, we demonstrate that these graphs are …
Line-Of-Sight Pursuit And Evasion Games On Polytopes In R^N, John Phillpot
Line-Of-Sight Pursuit And Evasion Games On Polytopes In R^N, John Phillpot
HMC Senior Theses
We study single-pursuer, line-of-sight Pursuit and Evasion games in polytopes in $\mathbb{R}^n$. We develop winning Pursuer strategies for simple classes of polytopes (monotone prisms) in Rn, using proven algorithms for polygons as inspiration and as subroutines. More generally, we show that any Pursuer-win polytope can be extended to a new Pursuer-win polytope in more dimensions. We also show that some more general classes of polytopes (monotone products) do not admit a deterministic winning Pursuer strategy. Though we provide bounds on which polytopes are Pursuer-win, these bounds are not tight. Closing the gap between those polytopes known to be …