85 citations · 285 across the 40 of their papers we have counts for
50 papers
A domain decomposition method for the directional contact angle hysteresis interval on doubly periodic rough surfaces
Zijie Lin, William M Feldman, Braxton Osting
We study wetting on a doubly periodic rough surface in three dimensions. Although the liquid-vapor interface meets the solid at the local Young's angle, microscale roughness can ca…
Maximizing the fundamental Laplace--Neumann eigenvalue on quadrilaterals
Ryoki Endo, Braxton Osting
We prove that among convex planar quadrilaterals of equal area, the square uniquely maximizes the first nonzero Laplace--Neumann eigenvalue. This is the quadrilateral case of the N…
An accelerated rearrangement method for two-phase composite optimization
Chiu-Yen Kao, Seyyed Abbas Mohammadi, Braxton Osting
We propose and analyze an Accelerated Rearrangement Method (ARM) for solving a class of nonconvex optimization problems involving two-phase composites. These problems include maxim…
Cuffless, calibration-free hemodynamic monitoring with physics-informed machine learning models
Henry Crandall, Tyler Schuessler, Filip Bělík +13
Wearable technologies have the potential to transform ambulatory and at-home hemodynamic monitoring by providing continuous assessments of cardiovascular health metrics and guiding…
Layer Potential Methods for Doubly-Periodic Harmonic Functions
Bohyun Kim, Braxton Osting
We develop and analyze layer potential methods to represent harmonic functions on finitely-connected tori (i.e., doubly-periodic harmonic functions). The layer potentials are expre…
A Semi-definite Optimization Method for Maximizing the Shared Band Gap of Topological Photonic Crystals
Chiu-Yen Kao, Junshan Lin, Braxton Osting
Topological photonic crystals (PCs) can support robust edge modes to transport electromagnetic energy in an efficient manner. Such edge modes are the eigenmodes of the PDE operator…
Partial Identification of the Average Treatment Effect with Stochastic Counterfactuals and Discordant Twins
Brian Knaeble, Braxton Osting, Placede Tshiaba
We develop a novel approach to partially identify causal estimands, such as the average treatment effect (ATE), from observational data. To better satisfy the stable unit treatment…
Targeting influence in a harmonic opinion model
Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola +2
Influence propagation in social networks is a central problem in modern social network analysis, with important societal applications in politics and advertising. A large body of w…
Harmonic functions on finitely-connected tori
Chiu-Yen Kao, Braxton Osting, Édouard Oudet
In this paper, we prove a Logarithmic Conjugation Theorem on finitely-connected tori. The theorem states that a harmonic function can be written as the real part of a function whos…
Observational Causality Testing
Brian Knaeble, Braxton Osting, Placede Tshiaba
In prior work we have introduced an asymptotic threshold of sufficient randomness for causal inference from observational data. In this paper we extend that prior work in three mai…
Escape times for subgraph detection and graph partitioning
Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola +2
We provide a rearrangement based algorithm for fast detection of subgraphs of vertices with long escape times for directed or undirected networks. Complementing other notions o…
Extremal graph realizations and graph Laplacian eigenvalues
Braxton Osting
For a regular polyhedron (or polygon) centered at the origin, the coordinates of the vertices are eigenvectors of the graph Laplacian for the skeleton of that polyhedron (or polygo…
A dynamical systems based framework for dimension reduction
Ryeongkyung Yoon, Braxton Osting
We propose a novel framework for learning a low-dimensional representation of data based on nonlinear dynamical systems, which we call dynamical dimension reduction (DDR). In the D…
Flat tori with large Laplacian eigenvalues in dimensions up to eight
Chiu-Yen Kao, Braxton Osting, Jackson C. Turner
We consider the optimization problem of maximizing the -th Laplacian eigenvalue, , over flat -dimensional tori of fixed volume. For , this problem is equivalent t…
High Spots for the Ice-Fishing Problem with Surface Tension
Nathan Willis, Chee Han Tan, Christel Hohenegger +1
In the ice-fishing problem, a half-space of fluid lies below an infinite rigid plate (``the ice'') with a hole. In this paper, we investigate the ice-fishing problem including the…
An Isoperimetric Sloshing Problem in a Shallow Container with Surface Tension
Chee Han Tan, Christel Hohenegger, Braxton Osting
In 1965, B. A. Troesch solved the isoperimetric sloshing problem of determining the container shape that maximizes the fundamental sloshing frequency among two classes of shallow c…
Probabilistic methods for approximate archetypal analysis
Ruijian Han, Braxton Osting, Dong Wang +1
Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the in…
Steklov Eigenvalues of Nearly Spherical Domains
Robert Viator, Braxton Osting
We consider Steklov eigenvalues of three-dimensional, nearly-spherical domains. In previous work, we have shown that the Steklov eigenvalues are analytic functions of the domain pe…
Quantifying Sufficient Randomness for Causal Inference
Brian Knaeble, Braxton Osting, Placede Tshiaba
Spurious association arises from covariance between propensity for the treatment and individual risk for the outcome. For sensitivity analysis with stochastic counterfactuals we in…
A non-autonomous equation discovery method for time signal classification
Ryeongkyung Yoon, Harish S. Bhat, Braxton Osting
Certain neural network architectures, in the infinite-layer limit, lead to systems of nonlinear differential equations. Motivated by this idea, we develop a framework for analyzing…
Consistency of archetypal analysis
Braxton Osting, Dong Wang, Yiming Xu +1
Archetypal analysis is an unsupervised learning method that uses a convex polytope to summarize multivariate data. For fixed , the method finds a convex polytope with vertic…
Computation of free boundary minimal surfaces via extremal Steklov eigenvalue problems
Chiu-Yen Kao, Braxton Osting, Èdouard Oudet
Recently Fraser and Schoen showed that the solution of a certain extremal Steklov eigenvalue problem on a compact surface with boundary can be used to generate a free boundary mini…
A metric on directed graphs and Markov chains based on hitting probabilities
Zachary M. Boyd, Nicolas Fraiman, Jeremy L. Marzuola +3
The shortest-path, commute time, and diffusion distances on undirected graphs have been widely employed in applications such as dimensionality reduction, link prediction, and trip…
A continuum limit for the PageRank algorithm
Amber Yuan, Jeff Calder, Braxton Osting
Semi-supervised and unsupervised machine learning methods often rely on graphs to model data, prompting research on how theoretical properties of operators on graphs are leveraged…