Search results for "Planar"
showing 10 items of 412 documents
Approximation Algorithms for Multicoloring Planar Graphs and Powers of Square and Triangular Meshes
2006
A multicoloring of a weighted graph G is an assignment of sets of colors to the vertices of G so that two adjacent vertices receive two disjoint sets of colors. A multicoloring problem on G is to find a multicoloring of G. In particular, we are interested in a minimum multicoloring that uses the least total number of colors. The main focus of this work is to obtain upper bounds on the weighted chromatic number of some classes of graphs in terms of the weighted clique number. We first propose an 11/6-approximation algorithm for multicoloring any weighted planar graph. We then study the multicoloring problem on powers of square and triangular meshes. Among other results, we show that the infi…
Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2
2009
AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.
Curve packing and modulus estimates
2018
A family of planar curves is called a Moser family if it contains an isometric copy of every rectifiable curve in $\mathbb{R}^{2}$ of length one. The classical "worm problem" of L. Moser from 1966 asks for the least area covered by the curves in any Moser family. In 1979, J. M. Marstrand proved that the answer is not zero: the union of curves in a Moser family has always area at least $c$ for some small absolute constant $c > 0$. We strengthen Marstrand's result by showing that for $p > 3$, the $p$-modulus of a Moser family of curves is at least $c_{p} > 0$.
Planar Cell Polarity Signaling in Collective Cell Movements During Morphogenesis and Disease
2012
Collective and directed cell movements are crucial for diverse developmental processes in the animal kingdom, but they are also involved in wound repair and disease. During these processes groups of cells are oriented within the tissue plane, which is referred to as planar cell polarity (PCP). This requires a tight regulation that is in part conducted by the PCP pathway. Although this pathway was initially characterized in flies, subsequent studies in vertebrates revealed a set of conserved core factors but also effector molecules and signal modulators, which build the fundamental PCP machinery. The PCP pathway in Drosophila regulates several developmental processes involving collective cel…
Exploiting multivalent nanoparticles for the supramolecular functionalization of graphene with a nonplanar recognition motif.
2013
The supramolecular modification of planar graphene with the geometri- cally mismatched, curved 9,10-di(1,3-dithiole-2-ylidene)-9,10-dihydroanthracene (exTTF) molecule is demonstrated. The exTTF-graphene interaction is governed by p-p and CH-p interactions, with a negligible contribution from charge transfer. We amplified these weak forces through multivalent gold nanoparticles. Our re- sults show that planarity is not a prerequisite for recognition motifs for graphene.
A novel hardware accelerator for the HEVC intra prediction
2015
International audience; A novel hardware accelerator for the High Efficiency Video Coding (HEVC) intra prediction is presented in this paper in order to reduce the computation complexity within this standard and to accelerate the concerned calculations. We propose a new pipelined structure that we called Processing Element (PE) to execute all angular modes, and we repeat it in five paths that our architecture composed of. We present also another structure to carry out the Planar mode. This architecture supports all intra prediction modes for all prediction unit sizes. The synthesis results show that our design can run at 213 MHz for Xilinx Virtex 6 and is capable to process real time 120 10…
Solvent impact on the planarity and aromaticity of free and monohydrated zinc phthalocyanine: a theoretical study
2017
A theoretical investigation on the planarity of molecular structure of zinc phthalocyanine (ZnPc) and its aromaticity has been performed using B3LYP and M06-2X density functionals combined with selected Pople-type basis sets. The effect of the applied calculation method on the optimized structure of ZnPc and ZnPc∙∙∙H2O, both in the gas phase and in the polar solvent, was analyzed. To quantify the aromaticity of the ZnPc and ZnPc∙∙∙H2O complexes, both the geometric and magnetic criteria, i.e., Harmonic Oscillator Model of Aromaticity (HOMA) index and the nucleus-independent chemical shift (NICS) values at the centers or 1 A above the centers of structural subunits, were calculated. The energ…
Estimating the Best Reference Homography for Planar Mosaics From Videos
2015
This paper proposes a novel strategy to find the best reference homography in mosaics from video sequences. The reference homography globally minimizes the distortions induced on each image frame by the mosaic homography itself. This method is designed for planar mosaics on which a bad choice of the first reference image frame can lead to severe distortions after concatenating several successive homographies. This often happens in the case of underwater mosaics with non-flat seabed and no georeferential information available. Given a video sequence of an almost planar surface, sub-mosaics with low distortions of temporally close image frames are computed and successively merged according to…
Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections
2018
We present the powerful module-intersection integration-by-parts (IBP) method, suitable for multi-loop and multi-scale Feynman integral reduction. Utilizing modern computational algebraic geometry techniques, this new method successfully trims traditional IBP systems dramatically to much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by explicitly carrying out the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to a basis of 73 master integrals.
Orientational analysis of planar fibre systems observed as a Poisson shot-noise process
2007
Summary We consider two-dimensional fibrous materials observed as a digital greyscale image. The problem addressed is to estimate the orientation distribution of unobservable thin fibres from a greyscale image modelled by a planar Poisson shot-noise process. The classical stereological approach is not straightforward, because the point intensities of thin fibres along sampling lines may not be observable. For such cases, Karkkainen et al. (2001) suggested the use of scaled variograms determined from grey values along sampling lines in several directions. Their method is based on the assumption that the proportion between the scaled variograms and point intensities in all directions of sampl…