57,458 research outputs found
Semi-dynamic connectivity in the plane
Motivated by a path planning problem we consider the following procedure.
Assume that we have two points and in the plane and take
. At each step we add to a compact convex
set that does not contain nor . The procedure terminates when the sets
in separate and . We show how to add one set to
in amortized time plus the time needed to find
all sets of intersecting the newly added set, where is the
cardinality of , is the number of sets in
intersecting the newly added set, and is the inverse of the
Ackermann function
Accelerator Design for the CHESS-U Upgrade
During the summer and fall of 2018 the Cornell High Energy Synchrotron Source
(CHESS) is undergoing an upgrade to increase high-energy flux for x-ray users.
The upgrade requires replacing one-sixth of the Cornell Electron Storage Ring
(CESR), inverting the polarity of half of the CHESS beam lines, and switching
to single-beam on-axis operation. The new sextant is comprised of six
double-bend achromats (DBAs) with combined-function dipole-quadrupoles.
Although the DBA design is widely utilized and well understood, the constraints
for the CESR modifications make the CHESS-U lattice unique. This paper
describes the design objectives, constraints, and implementation for the CESR
accelerator upgrade for CHESS-U
Mutation of Directed Graphs -- Corresponding Regular Expressions and Complexity of Their Generation
Directed graphs (DG), interpreted as state transition diagrams, are
traditionally used to represent finite-state automata (FSA). In the context of
formal languages, both FSA and regular expressions (RE) are equivalent in that
they accept and generate, respectively, type-3 (regular) languages. Based on
our previous work, this paper analyzes effects of graph manipulations on
corresponding RE. In this present, starting stage we assume that the DG under
consideration contains no cycles. Graph manipulation is performed by deleting
or inserting of nodes or arcs. Combined and/or multiple application of these
basic operators enable a great variety of transformations of DG (and
corresponding RE) that can be seen as mutants of the original DG (and
corresponding RE). DG are popular for modeling complex systems; however they
easily become intractable if the system under consideration is complex and/or
large. In such situations, we propose to switch to corresponding RE in order to
benefit from their compact format for modeling and algebraic operations for
analysis. The results of the study are of great potential interest to mutation
testing
Comments on a state-operator correspondence for the torus
We investigate the existence of a state-operator correspondence on the torus.
This correspondence would relate states of the CFT Hilbert space living on a
spatial torus to the path integral over compact Euclidean manifolds with
operator insertions. Unlike the states on the sphere that are associated to
local operators, we argue that those on the torus would more naturally be
associated to line operators. We find evidence that such a correspondence
cannot exist and in particular, we argue that no compact Euclidean path
integral can produce the vacuum on the torus. Our arguments come solely from
field theory and formulate a CFT version of the Horowitz-Myers conjecture for
the AdS soliton.Comment: 29 pages, 8 figure
A Growing Self-Organizing Network for Reconstructing Curves and Surfaces
Self-organizing networks such as Neural Gas, Growing Neural Gas and many
others have been adopted in actual applications for both dimensionality
reduction and manifold learning. Typically, in these applications, the
structure of the adapted network yields a good estimate of the topology of the
unknown subspace from where the input data points are sampled. The approach
presented here takes a different perspective, namely by assuming that the input
space is a manifold of known dimension. In return, the new type of growing
self-organizing network presented gains the ability to adapt itself in way that
may guarantee the effective and stable recovery of the exact topological
structure of the input manifold
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