43 citations · 83 across the 21 of their papers we have counts for
22 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…
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…
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…
Learning to Simulate Aerosol Dynamics with Graph Neural Networks
Fabiana Ferracina, Payton Beeler, Mahantesh Halappanavar +3
Aerosol effects on climate, weather, and air quality depend on characteristics of individual particles, which are tremendously diverse and change in time. Particle-resolved models…
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…
Predictive Analytics of Varieties of Potatoes
Fabiana Ferracina, Bala Krishnamoorthy, Mahantesh Halappanavar +2
We explore the application of machine learning algorithms specifically to enhance the selection process of Russet potato clones in breeding trials by predicting their suitability f…
Approximate Bipartite -Matching using Multiplicative Auction
Bhargav Samineni, S M Ferdous, Mahantesh Halappanavar +1
Given a bipartite graph with vertices and edges and a function , a -matching is a subset of edges such that every verte…
Structural Validation Of Synthetic Power Distribution Networks Using The Multiscale Flat Norm
Kostiantyn Lyman, Rounak Meyur, Bala Krishnamoorthy +1
We study the problem of comparing a pair of geometric networks that may not be similarly defined, i.e., when they do not have one-to-one correspondences between their nodes and edg…
Semi-Streaming Algorithms for Weighted -Disjoint Matchings
S M Ferdous, Bhargav Samineni, Alex Pothen +2
We design and implement two single-pass semi-streaming algorithms for the maximum weight -disjoint matching (-DM) problem. Given an integer , the -DM problem is to find…
A Normalized Bottleneck Distance on Persistence Diagrams and Homology Preservation under Dimension Reduction
Nathan H. May, Bala Krishnamoorthy, Patrick Gambill
Persistence diagrams (PDs) are used as signatures of point cloud data. Two clouds of points can be compared using the bottleneck distance d_B between their PDs. A potential drawbac…
Persistent Homology to Study Cold Hardiness of Grape Cultivars
Sejal Welankar, Paola Pesantez-Cabrera, Bala Krishnamoorthy +3
Persistent homology is a branch of computational algebraic topology that studies shapes and extracts features over multiple scales. In this paper, we present an unsupervised approa…
Geometry of a Set and its Random covers
Enrique Alvarado, Bala Krishnamoorthy, Kevin R. Vixie
Let be a bounded open subset of . We study the following questions: For i.i.d. samples drawn uniformly from , what is the probability that $\…
SFCDecomp: Multicriteria Optimized Tool Path Planning in 3D Printing using Space-Filling Curve Based Domain Decomposition
Prashant Gupta, Yiran Guo, Narasimha Boddeti +1
We explore efficient optimization of toolpaths based on multiple criteria for large instances of 3D printing problems. We first show that the minimum turn cost 3D printing problem…
Pheno-Mapper: An Interactive Toolbox for the Visual Exploration of Phenomics Data
Youjia Zhou, Methun Kamruzzaman, Patrick Schnable +3
High-throughput technologies to collect field data have made observations possible at scale in several branches of life sciences. The data collected can range from the molecular le…
A Tight Max-Flow Min-Cut Duality Theorem for Non-Linear Multicommodity Flows
Matthew Broussard, Bala Krishnamoorthy
The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of M…
Stitch Fix for Mapper and Topological Gains
Youjia Zhou, Nathaniel Saul, Ilkin Safarli +2
The mapper construction is a powerful tool from topological data analysis that is designed for the analysis and visualization of multivariate data. In this paper, we investigate a…
Representations of Energy Landscapes by Sublevelset Persistent Homology: An Example With n-Alkanes
Joshua Mirth, Yanqin Zhai, Johnathan Bush +8
Encoding the complex features of an energy landscape is a challenging task, and often chemists pursue the most salient features (minima and barriers) along a highly reduced space,…
The Maximum Distance Problem and Minimal Spanning Trees
Enrique G. Alvarado, Bala Krishnamoorthy, Kevin R. Vixie
Given a compact and , the maximum distance problem seeks a compact and connected subset of of smallest one dimensional Hausdorff meas…
Continuous Toolpath Planning in Additive Manufacturing
Prashant Gupta, Bala Krishnamoorthy, Gregory Dreifus
We develop a framework that creates a new polygonal mesh representation of the sparse infill domain of a layer-by-layer 3D printing job. We guarantee the existence of a single, con…
Robust Feasibility of Systems of Quadratic Equations Using Topological Degree Theory
Krishnamurthy Dvijotham, Bala Krishnamoorthy, Yunqi Luo +1
We consider the problem of measuring the margin of robust feasibility of solutions to a system of nonlinear equations. We study the special case of a system of quadratic equations,…