8 papers
Existence of Minimal Homotopies for Immersed Planar Curves
Lia Buchbinder, Yunjia Kou, Bala Krishnamoorthy +1
We study the existence of area-minimizing homotopies between homotopic curves in the plane. While the classical Plateau problem establishes the existence of least-area surfaces spa…
Minimal Homotopies in Three Dimensions: A Cable System Approach
Lia Buchbinder, Bala Krishnamoorthy, Kevin R. Vixie
We study null homotopies of immersed spheres in and the volume they sweep during contraction. For a smooth immersion with finitely many transverse self-intersections…
A Stable Measure of Chaos in Dynamical Systems using Persistent Homology
Bala Krishnamoorthy, Elizabeth Thompson
Many real-world dynamics exhibit chaos, a phenomenon in which neighboring trajectories in the state space of a dynamical system diverge exponentially over time. A common measure us…
A Stable Measure of Similarity for Time Series using Persistent Homology
Bala Krishnamoorthy, Elizabeth P. Thompson
Persistent homology, the study of holes that appear in data as one thickens balls centered around its points over time, has theoretically guaranteed stability. That is, small data…
Weighted MCC: A Robust Measure of Multiclass Classifier Performance for Observations with Individual Weights
Rommel Cortez, Bala Krishnamoorthy
Several performance measures are used to evaluate binary and multiclass classification tasks. But individual observations may often have distinct weights, and none of these measure…
Box Filtration
Enrique Alvarado, Prashant Gupta, Bala Krishnamoorthy
We define a new framework that unifies the filtration and mapper approaches from TDA, and present efficient algorithms to compute it. Termed the box filtration of a PCD, we grow bo…