Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies.   use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular,  derive condence sets for persistence diagrams and condence bands for persistence landscapes.
['Frédéric Chazal', 'Brittany Terese Fasy', 'Fabrizio Lecci', 'Alessandro Rinaldo', 'Aarti Singh', 'Larry Wasserman']
I am writing a research paper on a idea On the Bootstrap for Persistence Diagrams and Landscapes
[{"from": "human", "value": "I am writing a research paper on a idea On the Bootstrap for Persistence Diagrams and Landscapes"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Persistent homology probes topological properties from point clouds and functions. By looking at multiple scales simultaneously, one can record the births and deaths of topological features as the scale varies.   use a statistical technique, the empirical bootstrap, to separate topological signal from topological noise. In particular,  derive condence sets for persistence diagrams and condence bands for persistence landscapes."}]