🍩 Database of Original & Non-Theoretical Uses of Topology
(found 3 matches in 0.001287s)
Using Persistent Homology to Reveal Hidden Information in Neural Data (2015)Gard Spreemann, Benjamin Dunn, Magnus Bakke Botnan, Nils A. Baas
AbstractWe propose a method, based on persistent homology, to uncover topological properties of a priori unknown covariates of neuron activity. Our input data consist of spike train measurements of a set of neurons of interest, a candidate list of the known stimuli that govern neuron activity, and the corresponding state of the animal throughout the experiment performed. Using a generalized linear model for neuron activity and simple assumptions on the effects of the external stimuli, we infer away any contribution to the observed spike trains by the candidate stimuli. Persistent homology then reveals useful information about any further, unknown, covariates.
Topological Analysis of Gene Expression Arrays Identifies High Risk Molecular Subtypes in Breast Cancer (2012)Javier Arsuaga, Nils A. Baas, Daniel DeWoskin, Hideaki Mizuno, Aleksandr Pankov, Catherine Park
AbstractGenomic technologies measure thousands of molecular signals with the goal of understanding complex biological processes. In cancer these molecular signals have been used to characterize disease subtypes, signaling pathways and to identify subsets of patients with specific prognosis. However molecular signals for any disease type are so vast and complex that novel mathematical approaches are required for further analyses. Persistent and computational homology provide a new method for these analyses. In our previous work we presented a new homology-based supervised classification method to identify copy number aberrations from comparative genomic hybridization arrays. In this work we first propose a theoretical framework for our classification method and second we extend our analysis to gene expression data. We analyze a published breast cancer data set and find that that our method can distinguish most, but not all, different breast cancer subtypes. This result suggests that specific relationships between genes, captured by our algorithm, help distinguish between breast cancer subtypes. We propose that topological methods can be used for the classification and clustering of gene expression profiles.