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Let F be a family of n pairwise intersecting circles in the plane. We show that the number of lenses, that is convex digons, in the arrangement induced by F is at most 2n - 2. This bound is tight. Furthermore, if no two circles in F touch, then the geometr ...
In this article, we propose a dynamical system to avoid obstacles which are star shaped and simultaneously converge to a goal. The convergence is almost-global in a domain and the stationary points are identified explicitly. Our approach is based on the id ...
We study the hitting probabilities of the solution to a system of d stochastic heat equations with additive noise subject to Dirichlet boundary conditions. We show that for any bounded Borel set with positive (d-6)\documentclass[12pt]{minimal} \usepackage{ ...
Decision-making permeates every aspect of human and societal development, from individuals' daily choices to the complex decisions made by communities and institutions. Central to effective decision-making is the discipline of optimization, which seeks the ...
Image information about the state of a building after an earthquake, which can be collected without endangering the post-earthquake reconnaissance activities, can be used to reduce uncertainties in response predictions for future seismic events. This paper ...
In this paper, we propose a reduced-order modeling strategy for two-way Dirichlet-Neumann parametric coupled problems solved with domain-decomposition (DD) sub-structuring methods. We split the original coupled differential problem into two sub-problems wi ...
Molecular quantum dynamics simulations are essential for understanding many fundamental phenomena in physics and chemistry. They often require solving the time-dependent Schrödinger equation for molecular nuclei, which is challenging even for medium-sized ...
DEMO will have a limited diagnostic set for optimization of reactor performance, and limited diagnostic coverage due to challenging reactor conditions. This poses challenges for control, especially for detachment control which is planned to be performed wi ...
Diffusion-based generative methods have proven effective in modeling trajectories with offline datasets. However, they often face computational challenges and can falter in generalization, especially in capturing temporal abstractions for long- horizon tas ...
Conventional techniques for purifying macromolecular conjugates often require complex and costly installments that are inaccessible to most laboratories. In this work, we develop a one-step micropreparative method based on a trilayered polyacrylamide gel e ...