A note on domination in bipartite graphs

DOMINATING SET remains NP-complete even when instances are restricted to bipartite graphs, however, in this case VERTEX COVER is solvable in polynomial time. Consequences to VECTOR DOMINATING SET as a generalization of both are discussed

Optimization-based Secure Multi-hop Localization in Wireless Ad Hoc Networks

The problem of localizing nodes without GPS based on a small fraction of anchor nodes which are aware of their positions is considered to be an important service for applications in wireless ad hoc networks. With an adversary trying to mislead nodes about their estimated locations, several approaches aiming to defeat attackers by means of robustness instead of cryptographic measures have been proposed in the past. Nevertheless, these robust techniques focus on single-hop based localization. Hence, we investigate the impact of employing the well-known Least Median of Squares (LMS) algorithm in the context of the multi-hop based DV-hop approach. We argue that in this case LMS is no longer able to meet its requirements. We examine the source of this behavior and show that LMS leads to more accurate results when using the median to obtain average hop lengths in DV-hop. Furthermore, we investigate the feasibility of performing lateration using the l1-norm instead of the typically employed l2-norm, as well as the possibility of enhancing the robustness of LMS using lateration based on the l1-norm. Contrary to our expectations, the l1-norm only results in a slight, neglectable advantage compared to the computationally less expensive l2-norm lateration

Ordered and linked chordal graphs

A graph G is called k-ordered if for every sequence of k distinct vertices there is a cycle traversing these vertices in the given order. In the present paper we consider two novel generalizations of this concept, k-vertex-edge-ordered and strongly k-vertex-edge-ordered. We prove the following results for a chordal graph G: (a) G is (2k-3)-connected if and only if it is k-vertex-edge-ordered (k ≥ 3). (b) G is (2k-1)-connected if and only if it is strongly k-vertex-edge-ordered (k ≥ 2). (c) G is k-linked if and only if it is (2k-1)-connected

ATLAS Pixel Detector Timing Optimisation with the Back of Crate Card of the Optical Pixel Read out System

As with all detector systems at the Large Hadron Collider (LHC), the assignment of data to the correct bunch crossing, where bunch crossings will be separated in time by 25 ns, is one of the challenges for the ATLAS pixel detector. This document explains how the detector system will accomplish this by describing the general strategy, its implementation, the optimisation of the parameters, and the results obtained during a combined testbeam of all ATLAS subdetectors

Characterization of proper optimal elements with variable ordering structures

In vector optimization with a variable ordering structure the partial ordering defined by a convex cone is replaced by a whole family of convex cones, one associated with each element of the space. As these vector optimization problems are not only of interest in applications but also mathematical challenging, in recent publications it was started to develop a comprehensive theory. In doing that also notions of proper efficiency where generalized to variable ordering structures. In this paper we study the relations between several types of proper optimality notions, among others based on local and global approximations of the considered sets. We give scalarization results based on new functionals defined by elements from the dual cones which allow characterizations also in the nonconvex case

On classes of set optimization problems which are reducible to vector optimization problems and its impact on numerical test instances

Set optimization with the set approach has recently gained increasing interest due to its practical relevance. In this problem class one studies optimization problems with a set-valued objective map and defines optimality based on a direct comparison of the images of the objective function, which are sets here. Meanwhile, in the literature a wide range of theoretical tools as scalarization approaches and derivative concepts as well as first numerical algorithms are available. These numerical algorithms require on the one hand test instances where the optimal solution sets are known. On the other hand, in most examples and test instances in the literature only set-valued maps with a very simple structure are used. We study in this paper such special set-valued maps and we show that some of them are such simple that they can equivalently be expressed as a vector optimization problem. Thus we try to start drawing a line between simple set-valued problems and such problems which have no representation as multiobjective problems. Those having a representation can be used for defining test instances for numerical algorithms with easy verifiable optimal solution set

Optical Readout in a Multi-Module System Test for the ATLAS Pixel Detector

The innermost part of the ATLAS experiment at the LHC, CERN, will be a pixel detector. The command messages and the readout data of the detector are transmitted over an optical data path. The readout chain consists of many components which are produced at several locations around the world, and must work together in the pixel detector. To verify that these parts are working together as expected a system test has been built up. In this paper the system test setup and the operation of the readout chain is described. Also, some results of tests using the final pixel detector readout chain are given.Comment: 6 pages, 10 figures, Pixel 2005 proceedings preprin

Diversity and Ecological Correlates of Red Fluorescence in Marine Fishes

Marine environments at depths below -10 to -25 m are almost devoid of ambient red sunlight because water quickly attenuates long wavelengths. This stenospectral light environment presents unique opportunities for organisms that can transform ambient blue-green light into red light by fluorescence. Numerous marine fish species display intricate patterns of fluorescence. Because color vision is a key component of fish sensory ecology, several putative visual functions of red fluorescence have been proposed but are difficult to test experimentally. Here, we follow a comparative approach to assess the consistency between the phylogenetic distribution of red fluorescence with its presumed functions. We collected and analyzed the largest data set of red fluorescence in fishes to date, consisting of confirmed cases in 272 primarily diurnal fish species from 49 out of 90 surveyed fish families and 12 out of 21 surveyed fish orders, contrasted to 393 fish species with confirmed absence of red fluorescence. Based on a priori hypotheses on adaptive function, we compare the prevalence of red fluorescence among pre-defined sets of species based on ecological or biological characteristics while controlling for shared ancestry. When comparing between species, we find no evidence that red fluorescence is more prevalent in deep-water species, contrasting with our recent finding that fluorescence brightness increases with depth within species. There is also no evidence for a role in group-driven communication. Phylogenetic patterns are consistent, however, with three other predictions. First, fluorescence with a rather patchy distribution across the body occurred significantly more often among sit-and-wait predators or otherwise sedentary fish than in more mobile species, consistent with background matching for camouflage. Second, small, predatory fishes tended to show red fluorescent irides disproportionally often consistent with a proposed function in prey localization. Finally, sexually dimorphic species showed fluorescent fins more often, as predicted if relevant in sexual communication. From these findings, we derive predictions for experimental investigations of the presumed functions of red fluorescence

Molecular Beam Epitaxy Growth and Characterization of Germanium-Doped Cubic AlxGa1−xN

In cubic (c-)GaN Ge has emerged as a promising alternative to Si for n-type doping, offering the advantage of slightly improved electrical properties. Herein, a study on Ge doping of the ternary alloy c-AlxGa1−xN is presented. Ge-doped c-AlxGa1−xN layers are grown by plasma-assisted molecular beam epitaxy. In two sample series, both the Al mole fraction x and the doping level are varied. The incorporation of Ge is verified by time-of-flight secondary ion mass spectrometry. Ge incorporation and donor concentrations rise exponentially with increasing Ge cell temperature. A maximum donor concentration of 1.4 × 1020 cm−3 is achieved. While the incorporation of Ge is almost independent of x, incorporation of O, which acts as an unintentional donor, increases for higher x. Dislocation densities start increasing when doping levels of around 3 × 1019 cm−3 are exceeded. Also photoluminescence intensities begin to drop at these high doping levels. Optical emission of layers with x > 0.25 is found to originate from a defect level 0.9 eV below the indirect bandgap, which is not related to Ge. In the investigated range 0 ≤ x ≤ 0.6, Ge is a suitable donor in c-AlxGa1−xN up to the low 1019 cm−3 range