2,087 research outputs found
Complexity of the General Chromatic Art Gallery Problem
In the original Art Gallery Problem (AGP), one seeks the minimum number of
guards required to cover a polygon . We consider the Chromatic AGP (CAGP),
where the guards are colored. As long as is completely covered, the number
of guards does not matter, but guards with overlapping visibility regions must
have different colors. This problem has applications in landmark-based mobile
robot navigation: Guards are landmarks, which have to be distinguishable (hence
the colors), and are used to encode motion primitives, \eg, "move towards the
red landmark". Let , the chromatic number of , denote the minimum
number of colors required to color any guard cover of . We show that
determining, whether is \NP-hard for all . Keeping
the number of colors minimal is of great interest for robot navigation, because
less types of landmarks lead to cheaper and more reliable recognition
Energy bursts in fiber bundle models of composite materials
As a model of composite materials, a bundle of many fibers with
stochastically distributed breaking thresholds for the individual fibers is
considered. The bundle is loaded until complete failure to capture the failure
scenario of composite materials under external load. The fibers are assumed to
share the load equally, and to obey Hookean elasticity right up to the breaking
point. We determine the distribution of bursts in which an amount of energy
is released. The energy distribution follows asymptotically a universal power
law , for any statistical distribution of fiber strengths. A similar
power law dependence is found in some experimental acoustic emission studies of
loaded composite materials.Comment: 5 pages, 4 fig
Insider Liability for Short-Swing Profits Pursuant to Mergers and Related Transactions
This article considers the problems presented by the application of section 16(b) of the Securities Exchange Act of 1934 to corporate merger transactions. Mr. Hemmer argues that the matching across proposal, which has been suggested by some commentators, should not be applied to the merger situation. Instead, the author advocates that the possibility of abuse test, which the courts have applied to conversion transactions, should also. be applicable to the corporate merger. Mr. Hemmer feels this approach will prevent the abuses for which section 16(b) was enacted and, at the same time, provide the courts with a flexible test for this complex area
Crossover Behavior in Burst Avalanches of Fiber Bundles: Signature of Imminent Failure
Bundles of many fibers, with statistically distributed thresholds for
breakdown of individual fibers and where the load carried by a bursting fiber
is equally distributed among the surviving members, are considered. During the
breakdown process, avalanches consisting of simultaneous rupture of several
fibers occur, with a distribution D(Delta) of the magnitude Delta of such
avalanches. We show that there is, for certain threshold distributions, a
crossover behavior of D(Delta) between two power laws D(Delta) proportional to
Delta^(-xi), with xi=3/2 or xi=5/2. The latter is known to be the generic
behavior, and we give the condition for which the D(Delta) proportional to
Delta^(-3/2) behavior is seen. This crossover is a signal of imminent
catastrophic failure in the fiber bundle. We find the same crossover behavior
in the fuse model.Comment: 4 pages, 4 figure
A Parallel Distributed Strategy for Arraying a Scattered Robot Swarm
We consider the problem of organizing a scattered group of robots in
two-dimensional space, with geometric maximum distance between robots. The
communication graph of the swarm is connected, but there is no central
authority for organizing it. We want to arrange them into a sorted and
equally-spaced array between the robots with lowest and highest label, while
maintaining a connected communication network.
In this paper, we describe a distributed method to accomplish these goals,
without using central control, while also keeping time, travel distance and
communication cost at a minimum. We proceed in a number of stages (leader
election, initial path construction, subtree contraction, geometric
straightening, and distributed sorting), none of which requires a central
authority, but still accomplishes best possible parallelization. The overall
arraying is performed in time, individual messages, and
travel distance. Implementation of the sorting and navigation use communication
messages of fixed size, and are a practical solution for large populations of
low-cost robots
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