759,673 research outputs found
The Maximum Exposure Problem
Given a set of points P and axis-aligned rectangles R in the plane, a point p in P is called exposed if it lies outside all rectangles in R. In the max-exposure problem, given an integer parameter k, we want to delete k rectangles from R so as to maximize the number of exposed points. We show that the problem is NP-hard and assuming plausible complexity conjectures is also hard to approximate even when rectangles in R are translates of two fixed rectangles. However, if R only consists of translates of a single rectangle, we present a polynomial-time approximation scheme. For general rectangle range space, we present a simple O(k) bicriteria approximation algorithm; that is by deleting O(k^2) rectangles, we can expose at least Omega(1/k) of the optimal number of points
Secluded Connectivity Problems
Consider a setting where possibly sensitive information sent over a path in a
network is visible to every {neighbor} of the path, i.e., every neighbor of
some node on the path, thus including the nodes on the path itself. The
exposure of a path can be measured as the number of nodes adjacent to it,
denoted by . A path is said to be secluded if its exposure is small. A
similar measure can be applied to other connected subgraphs, such as Steiner
trees connecting a given set of terminals. Such subgraphs may be relevant due
to considerations of privacy, security or revenue maximization. This paper
considers problems related to minimum exposure connectivity structures such as
paths and Steiner trees. It is shown that on unweighted undirected -node
graphs, the problem of finding the minimum exposure path connecting a given
pair of vertices is strongly inapproximable, i.e., hard to approximate within a
factor of for any (under an
appropriate complexity assumption), but is approximable with ratio
, where is the maximum degree in the graph. One of
our main results concerns the class of bounded-degree graphs, which is shown to
exhibit the following interesting dichotomy. On the one hand, the minimum
exposure path problem is NP-hard on node-weighted or directed bounded-degree
graphs (even when the maximum degree is 4). On the other hand, we present a
polynomial algorithm (based on a nontrivial dynamic program) for the problem on
unweighted undirected bounded-degree graphs. Likewise, the problem is shown to
be polynomial also for the class of (weighted or unweighted) bounded-treewidth
graphs
Parameterized Complexity of Secluded Connectivity Problems
The Secluded Path problem models a situation where a sensitive information
has to be transmitted between a pair of nodes along a path in a network. The
measure of the quality of a selected path is its exposure, which is the total
weight of vertices in its closed neighborhood. In order to minimize the risk of
intercepting the information, we are interested in selecting a secluded path,
i.e. a path with a small exposure. Similarly, the Secluded Steiner Tree problem
is to find a tree in a graph connecting a given set of terminals such that the
exposure of the tree is minimized. The problems were introduced by Chechik et
al. in [ESA 2013]. Among other results, Chechik et al. have shown that Secluded
Path is fixed-parameter tractable (FPT) on unweighted graphs being
parameterized by the maximum vertex degree of the graph and that Secluded
Steiner Tree is FPT parameterized by the treewidth of the graph. In this work,
we obtain the following results about parameterized complexity of secluded
connectivity problems.
We give FPT-algorithms deciding if a graph G with a given cost function
contains a secluded path and a secluded Steiner tree of exposure at most k with
the cost at most C.
We initiate the study of "above guarantee" parameterizations for secluded
problems, where the lower bound is given by the size of a Steiner tree.
We investigate Secluded Steiner Tree from kernelization perspective and
provide several lower and upper bounds when parameters are the treewidth, the
size of a vertex cover, maximum vertex degree and the solution size. Finally,
we refine the algorithmic result of Chechik et al. by improving the exponential
dependence from the treewidth of the input graph.Comment: Minor corrections are don
National Space Transportation Systems Program mission report
The STS 41-C National Space Transportation Systems Program Mission Report contains a summary of the major activities and accomplishments of the eleventh Shuttle flight and fifth flight of the OV-099 vehicle, Challenger. Also summarized are the significant problems that occurred during STS 41-C, and a problem tracking list that is a complete list of all problems that occurred during the flight. The major objectives of flight STS 41-C were to successfully deploy the LDEF (long duration exposure facility) and retrieve, repair and redeploy the SMM (Solar Maximum Mission) spacecraft, and perform functions of IMAX and Cinema 360 cameras
Optimization of Reconfigurable Intelligent Surfaces with Electromagnetic Field Exposure Constraints
This work tackles the problem of maximizing the achievable rate in a
reconfigurable intelligent surface (RIS)-assisted communication link, by
enforcing conventional maximum power constraints and additional constraints on
the maximum exposure to electromagnetic radiations of the end-users. The RIS
phase shift matrix, the transmit beamforming filter, and the linear receive
filter are jointly optimized, and two provably convergent and low-complexity
algorithms are developed. One algorithm can be applied to general system
setups, but does not guarantee global optimality. The other is shown to be
provably optimal in the special case of isotropic electromagnetic exposure
constraints. The numerical results show that RIS-assisted communications can
ensure high data rate transmissions while guaranteeing users' exposure
constraints to radio frequency emissions
GaP betavoltaic cells as a power source
Maximum power output for the GaP cells of this study was found to be on the order of 1 microW. This resulted from exposure to 200 and 40 KeV electrons at a flux of 2 x 10(exp 9) electrons/sq cm/s, equivalent to a 54 mCurie source. The efficiencies of the cells ranged from 5 to 9 percent for 200 and 40 KeV electrons respectively. The lower efficiency at higher energy is due to a substantial fraction of energy deposition in the substrate, further than a diffusion length from the depletion region of the cell. Radiation damage was clearly observed in GaP after exposure to 200 KeV electrons at a fluence of 2 x 10(exp 12) electrons/sq cm. No discernable damage was observed after exposure to 40 KeV electrons at the same fluence. Analysis indicates that a GaP betavoltaic system would not be practical if limited to low energy beta sources. The power available would be too low even in the ideal case. By utilizing high activity beta sources, such as Sr-90/Y-90, it may be possible to achieve performance that could be suitable for some space power applications. However, to utilize such a source the problem of radiation damage in the beta cell material must be overcome
Dose, exposure time, and resolution in Serial X-ray Crystallography
The resolution of X-ray diffraction microscopy is limited by the maximum dose
that can be delivered prior to sample damage. In the proposed Serial
Crystallography method, the damage problem is addressed by distributing the
total dose over many identical hydrated macromolecules running continuously in
a single-file train across a continuous X-ray beam, and resolution is then
limited only by the available molecular and X-ray fluxes and molecular
alignment. Orientation of the diffracting molecules is achieved by laser
alignment. We evaluate the incident X-ray fluence (energy/area) required to
obtain a given resolution from (1) an analytical model, giving the count rate
at the maximum scattering angle for a model protein, (2) explicit simulation of
diffraction patterns for a GroEL-GroES protein complex, and (3) the frequency
cut off of the transfer function following iterative solution of the phase
problem, and reconstruction of an electron density map in the projection
approximation. These calculations include counting shot noise and multiple
starts of the phasing algorithm. The results indicate counting time and the
number of proteins needed within the beam at any instant for a given resolution
and X-ray flux. We confirm an inverse fourth power dependence of exposure time
on resolution, with important implications for all coherent X-ray imaging. We
find that multiple single-file protein beams will be needed for sub-nanometer
resolution on current third generation synchrotrons, but not on fourth
generation designs, where reconstruction of secondary protein structure at a
resolution of 0.7 nm should be possible with short exposures.Comment: 19 pages, 7 figures, 1 tabl
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