Related papers: Boundary Discontinuity Designs: Theory and Practic…
We consider the problem of computing bounds for causal queries on causal graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such…
Experimental continuation encompasses a set of methods that combine control and continuation to obtain the full bifurcation diagram of a nonlinear system experimentally, including responses that would be unstable in the system without…
We prove that nonlocal minimal graphs in the plane exhibit generically stickiness effects and boundary discontinuities. More precisely, we show that if a nonlocal minimal graph in a slab is continuous up to the boundary, then arbitrarily…
Nonlinear regression models addressing both efficacy and toxicity outcomes are increasingly used in dose-finding trials, such as in pharmaceutical drug development. However, research on related experimental design problems for corresponding…
A theoretical, and potentially also practical, problem with stochastic gradient descent is that trajectories may escape to infinity. In this note, we investigate uniform boundedness properties of iterates and function values along the…
We develop a cross-sectional research design to identify causal effects in the presence of unobservable heterogeneity without instruments. When units are dense in physical space, it may be sufficient to regress the "spatial first…
Diffusion-based trajectory optimization has emerged as a powerful planning paradigm, but existing methods require either learned score networks trained on large datasets or analytical dynamics models for score computation. We introduce…
We discuss methods for visualizing neural network decision boundaries and decision regions. We use these visualizations to investigate issues related to reproducibility and generalization in neural network training. We observe that changes…
This paper addresses one of the most prevalent problems encountered by political scientists working with difference-in-differences (DID) design: missingness in panel data. A common practice for handling missing data, known as complete case…
Biharmonic distance (\bd) is a powerful graph distance metric with many applications, including identifying critical links in road networks and mitigating over-squashing problem in \gnn. However, computing \bd\ is extremely difficult,…
The adaptive BDDC method is extended to the selection of face constraints in three dimensions. A new implementation of the BDDC method is presented based on a global formulation without an explicit coarse problem, with massive parallelism…
Mistakes in binary conditions are a source of error in many software systems. They happen when developers use, e.g., < or > instead of <= or >=. These boundary mistakes are hard to find and impose manual, labor-intensive work for software…
Neural operators have emerged as powerful surrogates for the solution of partial differential equations (PDEs), yet their ability to handle general, highly variable boundary conditions (BCs) remains limited. Existing approaches often fail…
Practitioners in diverse fields such as healthcare, economics and education are eager to apply machine learning to improve decision making. The cost and impracticality of performing experiments and a recent monumental increase in electronic…
Boundary labeling is a well-known method for displaying short textual labels for a set of point features in a figure alongside the boundary of that figure. Labels and their corresponding points are connected via crossing-free leaders. We…
In reliability engineering, we need to understand system dependencies, cause-effect relations, identify critical components, and analyze how they trigger failures. Three prominent graph models commonly used for these purposes are fault…
This paper extends backstepping to higher-dimensional PDEs by leveraging domain symmetries and structural properties. We systematically address three increasingly complex scenarios. First, for rectangular domains, we characterize boundary…
The case-crossover design (Maclure, 1991) is widely used in epidemiology and other fields to study causal effects of transient treatments on acute outcomes. However, its validity and causal interpretation have only been justified under…
Structure-based drug design (SBDD) aims to design small-molecule ligands that bind with high affinity and specificity to pre-determined protein targets. Generative SBDD methods leverage structural data of drugs in complex with their protein…
Assessing the boundedness and stability of vector nonlinear systems with variable delays and coefficients remains a challenging problem with broad applications in science and engineering. Existing methods tend to produce overly conservative…