A
Aaron Abrams
Researcher at Washington and Lee University
Publications - 43
Citations - 560
Aaron Abrams is an academic researcher from Washington and Lee University. The author has contributed to research in topics: Dehn function & Polynomial. The author has an hindex of 11, co-authored 39 publications receiving 522 citations. Previous affiliations of Aaron Abrams include Emory University & University of California, Davis.
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Circles minimize most knot energies
TL;DR: In this article, the authors define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle.
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Finding topology in a factory: configuration spaces
Aaron Abrams,Robert Ghrist +1 more
TL;DR: A class of topological spaces related to motion-planning on graphs that arise naturally in this very context, arising simultaneously in two seemingly disparate fields are described.
Journal ArticleDOI
State Complexes for Metamorphic Robots
Aaron Abrams,Robert Ghrist +1 more
TL;DR: In this article, the authors introduce a mathematical framework for defining and analyzing general metamorphic robots, combining with ideas from geometric group theory, and define a new type of configuration space called state complex, which is especially adapted to parallelization.
Posted Content
Circles Minimize most Knot Energies
TL;DR: In this paper, the authors define a new class of knot energies (known as renormalization energies) and prove that a broad class of these energies are uniquely minimized by the round circle.
Posted Content
State complexes for metamorphic robots
Aaron Abrams,Robert Ghrist +1 more
TL;DR: A new type of configuration space for metamorphic robots—the state complex—which is especially adapted to parallelization, and an algorithm for optimizing an input reconfiguration sequence with respect to elapsed time is presented.