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09/05/2023
Observational Causality Testing
In prior work we have introduced an asymptotic threshold of sufficient r...
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12/25/2022
Escape times for subgraph detection and graph partitioning
We provide a rearrangement based algorithm for fast detection of subgrap...
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10/25/2022
Wasserstein Archetypal Analysis
Archetypal analysis is an unsupervised machine learning method that summ...
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06/20/2022
Extremal graph realizations and graph Laplacian eigenvalues
For a regular polyhedron (or polygon) centered at the origin, the coordi...
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04/18/2022
A dynamical systems based framework for dimension reduction
We propose a novel framework for learning a low-dimensional representati...
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02/16/2022
Flat tori with large Laplacian eigenvalues in dimensions up to eight
We consider the optimization problem of maximizing the k-th Laplacian ei...
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11/12/2021
High Spots for the Ice-Fishing Problem with Surface Tension
In the ice-fishing problem, a half-space of fluid lies below an infinite...
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08/12/2021
Probabilistic methods for approximate archetypal analysis
Archetypal analysis is an unsupervised learning method for exploratory d...
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03/09/2021
Quantifying Sufficient Randomness for Causal Inference
Spurious association arises from covariance between propensity for the t...
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11/22/2020
A non-autonomous equation discovery method for time signal classification
Certain neural network architectures, in the infinite-layer limit, lead ...
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10/16/2020
Consistency of archetypal analysis
Archetypal analysis is an unsupervised learning method that uses a conve...
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06/25/2020
A metric on directed graphs and Markov chains based on hitting probabilities
The shortest-path, commute time, and diffusion distances on undirected g...
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01/24/2020
A continuum limit for the PageRank algorithm
Semi-supervised and unsupervised machine learning methods often rely on ...
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08/22/2019
Regression Analysis of Unmeasured Confounding
When studying the causal effect of x on y, researchers may conduct regre...
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05/22/2019
Coarse Quad Layouts Through Robust Simplification of Cross Field Separatrix Partitions
Streamline-based quad meshing algorithms use smooth cross fields to part...
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02/08/2018
A diffusion generated method for computing Dirichlet partitions
A Dirichlet k-partition of a closed d-dimensional surface is a collectio...
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11/03/2017
A generalized MBO diffusion generated motion for orthogonal matrix-valued fields
We consider the problem of finding stationary points of the Dirichlet en...
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08/28/2017
Towards Spectral Sparsification of Simplicial Complexes Based on Generalized Effective Resistance
As a generalization of the use of graphs to describe pairwise interactio...
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08/18/2017
Consistency of Dirichlet Partitions
A Dirichlet k-partition of a domain U ⊆R^d is a collection of k pairwise...
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08/07/2017
An Approach to Quad Meshing Based on Harmonic Cross-Valued Maps and the Ginzburg-Landau Theory
A generalization of vector fields, referred to as N-direction fields or ...
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02/28/2015
Analysis of Crowdsourced Sampling Strategies for HodgeRank with Sparse Random Graphs
Crowdsourcing platforms are now extensively used for conducting subjecti...
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08/22/2013
Minimal Dirichlet energy partitions for graphs
Motivated by a geometric problem, we introduce a new non-convex graph pa...
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07/26/2012
