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Ground-state properties of tubelike flexible polymers
In this work we investigate structural properties of native states of a
simple model for short flexible homopolymers, where the steric influence of
monomeric side chains is effectively introduced by a thickness constraint. This
geometric constraint is implemented through the concept of the global radius of
curvature and affects the conformational topology of ground-state structures. A
systematic analysis allows for a thickness-dependent classification of the
dominant ground-state topologies. It turns out that helical structures,
strands, rings, and coils are natural, intrinsic geometries of such tubelike
objects
Pragmatic Administrative Law and Tax Exceptionalism
This Essay responds to the 2014 Duke Law Journal Administrative Law Symposium. Its principal contention is that courts and other commentators should give due weight to the history and virtues of the evolution of administrative law in the United States—and consider embracing the pragmatism and flexibility that it enables—in applying general principles of administrative law in the tax context
Threadable Curves
We define a plane curve to be threadable if it can rigidly pass through a
point-hole in a line L without otherwise touching L. Threadable curves are in a
sense generalizations of monotone curves. We have two main results. The first
is a linear-time algorithm for deciding whether a polygonal curve is
threadable---O(n) for a curve of n vertices---and if threadable, finding a
sequence of rigid motions to thread it through a hole. We also sketch an
argument that shows that the threadability of algebraic curves can be decided
in time polynomial in the degree of the curve. The second main result is an O(n
polylog n)-time algorithm for deciding whether a 3D polygonal curve can thread
through hole in a plane in R^3, and if so, providing a description of the rigid
motions that achieve the threading.Comment: 16 pages, 12 figures, 12 references. v2: Revised with brief addendum
after Mikkel Abrahamsen pointed us to a relevant reference on "sweepable
polygons." v3: Major revisio
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