Edge Colourings of Graphs Avoiding Monochromatic Matchings of a Given Size

Let k and l be positive integers. With a graph G, we associate the quantity c(k,l)(G), the number of k-colourings of the edge set of G with no monochromatic matching of size l. Consider the function c(k,l) : N --> N given by c(k,l)(n) = max {c(k,l)(G): vertical bar V(G)vertical bar = n}, the maximum of c(k,l)(G) over all graphs G on n vertices. In this paper, we determine c(k,l)(n) and the corresponding extremal graphs for all large n and all fixed values of k and l.

Analyzing the Complexity and Reliability of Switch-Frequency-Reconfigurable Antennas Using Graph Models

This paper addresses the functional reliability and the complexity of reconfigurable antennas using graph models. The correlation between complexity and reliability for any given reconfigurable antenna is defined. Two methods are proposed to reduce failures and improve the reliability of reconfigurable antennas. The failures are caused by the reconfiguration technique or by the surrounding environment. These failure reduction methods proposed are tested and examples are given which verify these methods.

Connections between the Sznajd model with general confidence rules and graph theory

The Sznajd model is a sociophysics model that is used to model opinion propagation and consensus formation in societies. Its main feature is that its rules favor bigger groups of agreeing people. In a previous work, we generalized the bounded confidence rule in order to model biases and prejudices in discrete opinion models. In that work, we applied this modification to the Sznajd model and presented some preliminary results. The present work extends what we did in that paper. We present results linking many of the properties of the mean-field fixed points, with only a few qualitative aspects of the confidence rule (the biases and prejudices modeled), finding an interesting connection with graph theory problems. More precisely, we link the existence of fixed points with the notion of strongly connected graphs and the stability of fixed points with the problem of finding the maximal independent sets of a graph. We state these results and present comparisons between the mean field and simulations in Barabasi-Albert networks, followed by the main mathematical ideas and appendices with the rigorous proofs of our claims and some graph theory concepts, together with examples. We also show that there is no qualitative difference in the mean-field results if we require that a group of size q > 2, instead of a pair, of agreeing agents be formed before they attempt to convince other sites (for the mean field, this would coincide with the q-voter model).

Properly coloured copies and rainbow copies of large graphs with small maximum degree

Let G be a graph on n vertices with maximum degree ?. We use the Lovasz local lemma to show the following two results about colourings ? of the edges of the complete graph Kn. If for each vertex v of Kn the colouring ? assigns each colour to at most (n - 2)/(22.4?2) edges emanating from v, then there is a copy of G in Kn which is properly edge-coloured by ?. This improves on a result of Alon, Jiang, Miller, and Pritikin [Random Struct. Algorithms 23(4), 409433, 2003]. On the other hand, if ? assigns each colour to at most n/(51?2) edges of Kn, then there is a copy of G in Kn such that each edge of G receives a different colour from ?. This proves a conjecture of Frieze and Krivelevich [Electron. J. Comb. 15(1), R59, 2008]. Our proofs rely on a framework developed by Lu and Szekely [Electron. J. Comb. 14(1), R63, 2007] for applying the local lemma to random injections. In order to improve the constants in our results we use a version of the local lemma due to Bissacot, Fernandez, Procacci, and Scoppola [preprint, arXiv:0910.1824]. (c) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 425436, 2012

Comparison between the C5 or C6-Cz electrode assembly and C3 or C4-Cz assembly for transcranial electric motor activation of muscular response of the contralateral facial nerve

We used an assembly of electrodes C3 and C4-Cz in order to activate the motor cortical area of the corticobulbar tract to elucidate the motor-evoked potential of the contralateral mentalis muscle. We compared this setup to that of an assembly with electrodes C5 or C6-Cz using a train of electrical pulses and a single electrical pulse. This analysis was made in 23 consecutive patients who underwent several varied surgeries and were prospectively operated on at Santa Paula Hospital between January and June 2011. The results showed that the assembly with C5 or C6-Cz produced a multisynaptic motor-evoked potential in the contralateral mentalis muscle in 86.9 % of the patients, whereas 82.6 % of patients stimulated at points C3 or C4-Cz presented the same response. However, both assemblies showed similar behavior with the use of a single electrical pulse for peripheral contralateral nerve stimulation. We concluded that the C5 or C6-Cz assembly was similar to C3 or C4-Cz in obtaining a multisynaptic response in the contralateral mentalis muscle, although it required less intensive stimulation than the C3 or C4- Cz assembly.

Comparative study on the far-field spectra and near-field amplitudes for silver and gold nanocubes irradiated at 514, 633 and 785 nm as a function of the edge length

We describe a systematic investigation by the discrete dipole approximation on the optical properties of silver (Ag) and gold (Au) nanocubes as a function of the edge length in the 20-100 nm range. Our results showed that, as the nanocube size increased, the plasmon resonance modes shifted to higher wavelengths, the contribution from scattering to the extinction increased, and the quadrupole modes became more intense in the spectra. The electric field amplitudes at the surface of the nanocubes were calculated considering 514, 633 and 785 nm as the excitation wavelengths. While Ag nanocubes displayed the highest electric field amplitudes (vertical bar E vertical bar(max)) when excited at 514 nm, the Au nanocubes displayed higher vertical bar E vertical bar(max) values than Ag, for all sizes investigated, when the excitation wavelength was either 633 or 785 nm. The variations in vertical bar E vertical bar(max) as a function of size for both Ag and Au nanocubes could be explained based on the relative position of the surface plasmon resonance peak relative to the wavelength of the incoming electromagnetic wave. Our results show that not only size and composition, but also the excitation wavelength, can play an important role over the maximum near-field amplitudes values generated at the surface of the nanocubes.

Fuzzy Connectedness Image Segmentation in Graph Cut Formulation: A Linear-Time Algorithm and a Comparative Analysis

A deep theoretical analysis of the graph cut image segmentation framework presented in this paper simultaneously translates into important contributions in several directions. The most important practical contribution of this work is a full theoretical description, and implementation, of a novel powerful segmentation algorithm, GC(max). The output of GC(max) coincides with a version of a segmentation algorithm known as Iterative Relative Fuzzy Connectedness, IRFC. However, GC(max) is considerably faster than the classic IRFC algorithm, which we prove theoretically and show experimentally. Specifically, we prove that, in the worst case scenario, the GC(max) algorithm runs in linear time with respect to the variable M=|C|+|Z|, where |C| is the image scene size and |Z| is the size of the allowable range, Z, of the associated weight/affinity function. For most implementations, Z is identical to the set of allowable image intensity values, and its size can be treated as small with respect to |C|, meaning that O(M)=O(|C|). In such a situation, GC(max) runs in linear time with respect to the image size |C|. We show that the output of GC(max) constitutes a solution of a graph cut energy minimization problem, in which the energy is defined as the a"" (a) norm ayenF (P) ayen(a) of the map F (P) that associates, with every element e from the boundary of an object P, its weight w(e). This formulation brings IRFC algorithms to the realm of the graph cut energy minimizers, with energy functions ayenF (P) ayen (q) for qa[1,a]. Of these, the best known minimization problem is for the energy ayenF (P) ayen(1), which is solved by the classic min-cut/max-flow algorithm, referred to often as the Graph Cut algorithm. We notice that a minimization problem for ayenF (P) ayen (q) , qa[1,a), is identical to that for ayenF (P) ayen(1), when the original weight function w is replaced by w (q) . Thus, any algorithm GC(sum) solving the ayenF (P) ayen(1) minimization problem, solves also one for ayenF (P) ayen (q) with qa[1,a), so just two algorithms, GC(sum) and GC(max), are enough to solve all ayenF (P) ayen (q) -minimization problems. We also show that, for any fixed weight assignment, the solutions of the ayenF (P) ayen (q) -minimization problems converge to a solution of the ayenF (P) ayen(a)-minimization problem (ayenF (P) ayen(a)=lim (q -> a)ayenF (P) ayen (q) is not enough to deduce that). An experimental comparison of the performance of GC(max) and GC(sum) algorithms is included. This concentrates on comparing the actual (as opposed to provable worst scenario) algorithms' running time, as well as the influence of the choice of the seeds on the output.

Flow Visualization with Quantified Spatial and Temporal Errors Using Edge Maps

Robust analysis of vector fields has been established as an important tool for deriving insights from the complex systems these fields model. Traditional analysis and visualization techniques rely primarily on computing streamlines through numerical integration. The inherent numerical errors of such approaches are usually ignored, leading to inconsistencies that cause unreliable visualizations and can ultimately prevent in-depth analysis. We propose a new representation for vector fields on surfaces that replaces numerical integration through triangles with maps from the triangle boundaries to themselves. This representation, called edge maps, permits a concise description of flow behaviors and is equivalent to computing all possible streamlines at a user defined error threshold. Independent of this error streamlines computed using edge maps are guaranteed to be consistent up to floating point precision, enabling the stable extraction of features such as the topological skeleton. Furthermore, our representation explicitly stores spatial and temporal errors which we use to produce more informative visualizations. This work describes the construction of edge maps, the error quantification, and a refinement procedure to adhere to a user defined error bound. Finally, we introduce new visualizations using the additional information provided by edge maps to indicate the uncertainty involved in computing streamlines and topological structures.

Algebraic-graph method for identification of islanding in power system grids

In this paper, a new algebraic-graph method for identification of islanding in power system grids is proposed. The proposed method identifies all the possible cases of islanding, due to the loss of a equipment, by means of a factorization of the bus-branch incidence matrix. The main features of this new method include: (i) simple implementation, (ii) high speed, (iii) real-time adaptability, (iv) identification of all islanding cases and (v) identification of the buses that compose each island in case of island formation. The method was successfully tested on large-scale systems such as the reduced south Brazilian system (45 buses/72 branches) and the south-southeast Brazilian system (810 buses/1340 branches). (C) 2011 Elsevier Ltd. All rights reserved.

EDGE-PRESERVING SPECKLE TEXTURE REMOVAL BY INTERFERENCE-BASED SPECKLE FILTERING FOLLOWED BY ANISOTROPIC DIFFUSION

Ultrasonography has an inherent noise pattern, called speckle, which is known to hamper object recognition for both humans and computers. Speckle noise is produced by the mutual interference of a set of scattered wavefronts. Depending on the phase of the wavefronts, the interference may be constructive or destructive, which results in brighter or darker pixels, respectively. We propose a filter that minimizes noise fluctuation while simultaneously preserving local gray level information. It is based on steps to attenuate the destructive and constructive interference present in ultrasound images. This filter, called interference-based speckle filter followed by anisotropic diffusion (ISFAD), was developed to remove speckle texture from B-mode ultrasound images, while preserving the edges and the gray level of the region. The ISFAD performance was compared with 10 other filters. The evaluation was based on their application to images simulated by Field II (developed by Jensen et al.) and the proposed filter presented the greatest structural similarity, 0.95. Functional improvement of the segmentation task was also measured, comparing rates of true positive, false positive and accuracy. Using three different segmentation techniques, ISFAD also presented the best accuracy rate (greater than 90% for structures with well-defined borders). (E-mail: fernando.okara@gmail.com) (C) 2012 World Federation for Ultrasound in Medicine & Biology.

Cutting Edge: Brazilian Pemphigus Foliaceus Anti-Desmoglein 1 Autoantibodies Cross-React with Sand Fly Salivary LJM11 Antigen

The environmental factors that contribute to the development of autoimmune diseases are largely unknown. Endemic pemphigus foliaceus in humans, known as Fogo Selvagem (FS) in Brazil, is mediated by pathogenic IgG4 autoantibodies against desmoglein 1 (Dsg1). Clusters of FS overlap with those of leishmaniasis, a disease transmitted by sand fly (Lutzomyia longipalpis) bites. In this study, we show that salivary Ags from the sand fly, and specifically the LJM11 salivary protein, are recognized by FS Abs. Anti-Dsg1 monoclonal autoantibodies derived from FS patients also cross-react with LJM11. Mice immunized with LJM11 generate anti-Dsg1 Abs. Thus, insect bites may deliver salivary Ags that initiate a cross-reactive IgG4 Ab response in genetically susceptible individuals and lead to subsequent FS. Our findings establish a clear relationship between an environmental, noninfectious Ag and the development of potentially pathogenic autoantibodies in an autoimmune disease. The Journal of Immunology, 2012, 189: 1535-1539.

Self-organized criticality in MHD driven plasma edge turbulence

We analyze long-range time correlations and self-similar characteristics of the electrostatic turbulence at the plasma edge and scrape-off layer in the Tokamak Chauffage Alfven Bresillien (TCABR), with low and high Magnetohydrodynamics (MHD) activity. We find evidence of self-organized criticality (SOC), mainly in the region near the tokamak limiter. Comparative analyses of data before and during the MHD activity reveals that during the high mHD activity the Hurst parameter decreases. Finally, we present a cellular automaton whose parameters are adjusted to simulate the analyzed turbulence SOC change with the MHD activity variation. (C) 2011 Published by Elsevier B.V.

Weak quasi-randomness for uniform hypergraphs

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs. Moreover, let K(k) be the complete graph on k vertices and M(k) the line graph of the graph of the k-dimensional hypercube. We will show that the pair of graphs (K(k),M(k)) has the property that if the number of copies of both K(k) and M(k) in another graph G are as expected in the random graph of density d, then G is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to d. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 1-38, 2012

On the optical properties of copper nanocubes as a function of the edge length as modeled by the discrete dipole approximation

This Letter reports an investigation on the optical properties of copper nanocubes as a function of size as modeled by the discrete dipole approximation. In the far-field, our results showed that the extinction resonances shifted from 595 to 670 nm as the size increased from 20 to 100 nm. Also, the highest optical efficiencies for absorption and scattering were obtained for nanocubes that were 60 and 100 nm in size, respectively. In the near-field, the electric-field amplitudes were investigated considering 514, 633 and 785 nm as the excitation wavelengths. The E-fields increased with size, being the highest at 633 nm. (c) 2012 Elsevier B.V. All rights reserved.

Electronics and Optics of Graphene Nanoflakes: Edge Functionalization and Structural Distortions

The effects of edge covalent functionalization on the structural, electronic, and optical properties of elongated armchair graphene nanoflakes (AGNFs) are analyzed in detail for a wide range of terminations, within the framework of Hartree-Fock-based semiempirical methods. The chemical features of the functional groups, their distribution, and the resulting system symmetry are identified as the key factors that determine the modification of strutural and optoelectronic features. While the electronic gap is always reduced in the presence of substituents, functionalization-induced distortions contribute to the observed lowering by about 35-55% This effect is paired with a red shift of the first optical peak, corresponding to about 75% of the total optical gap reduction. Further, the functionalization pattern and the specific features of the edge-substituent bond are found to influence the strength and the character of the low-energy excitations. All of these effects are discussed for flakes of different widths, representing the three families of AGNFs.