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Mixup Barcodes: Quantifying Geometric-Topological Interactions between Point Clouds
In particular, we introduce: (1) a mixup barcode, which captures geometric-topological interactions (mixup) between two point sets in arbitrary dimension; (2) simple summary statistics, total mixup and total percentage mixup, which quantify the complexity of the interactions as a single number; (3) a software tool for playing with the above.
Modular Control of Biological Networks
This paper presents an approach to model-based control that exploits two common features of biological networks, namely their modular structure and canalizing features of their regulatory mechanisms.
Activation Landscapes as a Topological Summary of Neural Network Performance
We use topological data analysis (TDA) to study how data transforms as it passes through successive layers of a deep neural network (DNN).
