The continued and dramatic rise in the size of data sets has meant that new methods are
required to model and analyze them. This timely account introduces topological data …

This paper describes a new approach for ascertaining the stability of stochastic dynamical
systems in their parameter space by examining their time series using topological data …

We introduce a method for automated temporal segmentation of human motion data into
distinct actions and compositing motion primitives based on self-similar structures in the …

We introduce a novel data-driven approach to discover and decode features in the neural
code coming from large population neural recordings with minimal assumptions, using …

We provide a comprehensive account of recent advances in biomedical image analysis and
classification from two complementary imaging modalities: terahertz (THz) pulse imaging …

Persistent homology is a rigorous mathematical theory that provides a robust descriptor of
data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their …

Bifurcations in dynamical systems characterize qualitative changes in the system behavior.
Therefore, their detection is important because they can signal the transition from normal …

Exercise is a prevailing topic in modern society as more people are pursuing a healthy
lifestyle. Physical activities provide significant benefits to human well-being from the inside …

This paper introduces a simple yet powerful approach based on topological data analysis for
detecting true steps in a periodic, piecewise constant (PWC) signal. The signal is a two-state …

This work introduces a novel framework for quantifying the presence and strength of
recurrent dynamics in video data. Specifically, we provide continuous measures of …