Metric Dimension for Gabriel Unit Disk Graphs is NP-Complete

We show that finding a minimal number of landmark nodes for a unique virtual addressing by hop-distances in wireless ad-hoc sensor networks is NP-complete even if the networks are unit disk graphs that contain only Gabriel edges. This problem is equivalent to Metric Dimension for Gabriel unit disk graphs. The Gabriel edges of a unit disc graph induce a planar O(\sqrt{n}) distance and an optimal energy spanner. This is one of the most interesting restrictions of Metric Dimension in the context of wireless multi-hop networks.Comment: A brief announcement of this result has been published in the proceedings of ALGOSENSORS 201

Kinematics of gas and stars in circumnuclear star-forming regions of early type spirals

(Abbr.) We present high resolution (R~20000) spectra in the blue and the far red of cicumnuclear star-forming regions (CNSFRs) in three early type spirals (NGC3351, NGC2903 and NGC3310) which have allowed the study of the kinematics of stars and ionized gas in these structures and, for the first time, the derivation of their dynamical masses for the first two. In some cases these regions, about 100 to 150 pc in size, are seen to be composed of several individual star clusters with sizes between 1.5 and 4.9 pc estimated from Hubble Space Telescope (HST) images. The stellar dispersions have been obtained from the Calcium triplet (CaT) lines at $\lambda\lambda$ 8494,8542,8662 \AA, while the gas velocity dispersions have been measured by Gaussian fits to the H$\beta$ and [OIII] $\lambda\lambda$ 5007 \AA lines on the high dispersion spectra. Values of the stellar velocity dispersions are between 30 and 68 km/s. We apply the virial theorem to estimate dynamical masses of the clusters, assuming that systems are gravitationally bounded and spherically symmetric, and using previously measured sizes. The measured values of the stellar velocity dispersions yield dynamical masses of the order of 10$^7$ to 10$^8$ solar masses for the whole CNSFRs. Stellar and gas velocity dispersions are found to differ by about 20 to 30 km/s with the H$\beta$ emission lines being narrower than both the stellar lines and the [OIII] $\lambda\lambda$ 5007 \AA lines. The twice ionized oxygen, on the other hand, shows velocity dispersions comparable to those shown by stars, in some cases, even larger. We have found indications of the presence of two different kinematical components in the ionized gas of the regions...Comment: 4 pages, proceeding of the meeting "Young massive star clusters - Initial conditions and environments", Granada, Spain, 200

Enhanced Parallel Generation of Tree Structures for the Recognition of 3D Images

Segmentations of a digital object based on a connectivity criterion at n-xel or sub-n-xel level are useful tools in image topological analysis and recognition. Working with cell complex analogous of digital objects, an example of this kind of segmentation is that obtained from the combinatorial representation so called Homological Spanning Forest (HSF, for short) which, informally, classifies the cells of the complex as belonging to regions containing the maximal number of cells sharing the same homological (algebraic homology with coefficient in a field) information. We design here a parallel method for computing a HSF (using homology with coefficients in Z/2Z) of a 3D digital object. If this object is included in a 3D image of m1 × m2 × m3 voxels, its theoretical time complexity order is near O(log(m1 + m2 + m3)), under the assumption that a processing element is available for each voxel. A prototype implementation validating our results has been written and several synthetic, random and medical tridimensional images have been used for testing. The experiments allow us to assert that the number of iterations in which the homological information is found varies only to a small extent from the theoretical computational time.Ministerio de Economía y Competitividad MTM2016-81030-