6,462 research outputs found
Locked and Unlocked Chains of Planar Shapes
We extend linkage unfolding results from the well-studied case of polygonal
linkages to the more general case of linkages of polygons. More precisely, we
consider chains of nonoverlapping rigid planar shapes (Jordan regions) that are
hinged together sequentially at rotatable joints. Our goal is to characterize
the families of planar shapes that admit locked chains, where some
configurations cannot be reached by continuous reconfiguration without
self-intersection, and which families of planar shapes guarantee universal
foldability, where every chain is guaranteed to have a connected configuration
space. Previously, only obtuse triangles were known to admit locked shapes, and
only line segments were known to guarantee universal foldability. We show that
a surprisingly general family of planar shapes, called slender adornments,
guarantees universal foldability: roughly, the distance from each edge along
the path along the boundary of the slender adornment to each hinge should be
monotone. In contrast, we show that isosceles triangles with any desired apex
angle less than 90 degrees admit locked chains, which is precisely the
threshold beyond which the inward-normal property no longer holds.Comment: 23 pages, 25 figures, Latex; full journal version with all proof
details. (Fixed crash-induced bugs in the abstract.
Program management model study
Two models, a system performance model and a program assessment model, have been developed to assist NASA management in the evaluation of development alternatives for the Earth Observations Program. Two computer models were developed and demonstrated on the Goddard Space Flight Center Computer Facility. Procedures have been outlined to guide the user of the models through specific evaluation processes, and the preparation of inputs describing earth observation needs and earth observation technology. These models are intended to assist NASA in increasing the effectiveness of the overall Earth Observation Program by providing a broader view of system and program development alternatives
Generic Global Rigidity in Complex and Pseudo-Euclidean Spaces
In this paper we study the property of generic global rigidity for frameworks of graphs embedded in d-dimensional complex space and in a d-dimensional pseudo-Euclidean space R with a metric of indefinite signature). We show that a graph is generically globally rigid in Euclidean space iff it is generically globally rigid in a complex or pseudo-Euclidean space. We also establish that global rigidity is always a generic property of a graph in complex space, and give a sufficient condition for it to be a generic property in a pseudo-Euclidean space. Extensions to hyperbolic space are also discussed.Engineering and Applied Science
Characterizing the universal rigidity of generic frameworks
A framework is a graph and a map from its vertices to E^d (for some d). A
framework is universally rigid if any framework in any dimension with the same
graph and edge lengths is a Euclidean image of it. We show that a generic
universally rigid framework has a positive semi-definite stress matrix of
maximal rank. Connelly showed that the existence of such a positive
semi-definite stress matrix is sufficient for universal rigidity, so this
provides a characterization of universal rigidity for generic frameworks. We
also extend our argument to give a new result on the genericity of strict
complementarity in semidefinite programming.Comment: 18 pages, v2: updates throughout; v3: published versio
Only connect: addressing the emotional needs of Scotland's children and young people
A report on the SNAP (Scottish Needs Assessment Programme) Child and Adolescent Mental Health Phase Two survey. It describes a survey of a wide range of professionals working with children and young people in Scotland, and deals with professional perspectives on emotional, behavioural and psychological problems. Conclusions and recommendations are presented
Localizability of Wireless Sensor Networks: Beyond Wheel Extension
A network is called localizable if the positions of all the nodes of the
network can be computed uniquely. If a network is localizable and embedded in
plane with generic configuration, the positions of the nodes may be computed
uniquely in finite time. Therefore, identifying localizable networks is an
important function. If the complete information about the network is available
at a single place, localizability can be tested in polynomial time. In a
distributed environment, networks with trilateration orderings (popular in real
applications) and wheel extensions (a specific class of localizable networks)
embedded in plane can be identified by existing techniques. We propose a
distributed technique which efficiently identifies a larger class of
localizable networks. This class covers both trilateration and wheel
extensions. In reality, exact distance is almost impossible or costly. The
proposed algorithm based only on connectivity information. It requires no
distance information
- …