Scholarly Work - Computer Science
Permanent URI for this collectionhttps://scholarworks.montana.edu/handle/1/3034
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Item Reconstructing embedded graphs from persistence diagrams(2020-10) Belton, Robin Lynne; Fasy, Brittany T.; Mertz, Rostik; Micka, Samuel; Millman, David L.; Salinas, Daniel; Schenfisch, Anna; Schupbach, Jordan; Williams, LuciaThe persistence diagram (PD) is an increasingly popular topological descriptor. By encoding the size and prominence of topological features at varying scales, the PD provides important geometric and topological information about a space. Recent work has shown that well-chosen (finite) sets of PDs can differentiate between geometric simplicial complexes, providing a method for representing complex shapes using a finite set of descriptors. A related inverse problem is the following: given a set of PDs (or an oracle we can query for persistence diagrams), what is underlying geometric simplicial complex? In this paper, we present an algorithm for reconstructing embedded graphs in Rd (plane graphs in R2) with n vertices from n2 −n+d+1 directional (augmented) PDs. Additionally, we empirically validate the correctness and time-complexity of our algorithm in R2 on randomly generated plane graphs using our implementation, and explain the numerical limitations of implementing our algorithm.Item Physiological dynamic compression regulates central energy metabolism in primary human chondrocytes(2018-02) Salinas, Daniel; Mumey, Brendan M.; June, Ronald K.Chondrocytes use the pathways of central metabolism to synthesize molecular building blocks and energy for cartilage homeostasis. An interesting feature of the in vivo chondrocyte environment is the cyclical loading generated in various activities (e.g., walking). However, it is unknown whether central metabolism is altered by mechanical loading. We hypothesized that physiological dynamic compression alters central metabolism in chondrocytes to promote production of amino acid precursors for matrix synthesis. We measured the expression of central metabolites (e.g., glucose, its derivatives, and relevant co-factors) for primary human osteoarthritic chondrocytes in response to 0–30 minutes of compression. To analyze the data, we used principal components analysis and ANOVA-simultaneous components analysis, as well as metabolic flux analysis. Compression-induced metabolic responses consistent with our hypothesis. Additionally, these data show that chondrocyte samples from different patient donors exhibit different sensitivity to compression. Most importantly, we find that grade IV osteoarthritic chondrocytes are capable of synthesizing non-essential amino acids and precursors in response to mechanical loading. These results suggest that further advances in metabolic engineering of chondrocyte mechanotransduction may yield novel translational strategies for cartilage repair.