4,693 research outputs found

    Efficient Rewirings for Enhancing Synchronizability of Dynamical Networks

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    In this paper, we present an algorithm for optimizing synchronizability of complex dynamical networks. Based on some network properties, rewirings, i.e. eliminating an edge and creating a new edge elsewhere, are performed iteratively avoiding always self-loops and multiple edges between the same nodes. We show that the method is able to enhance the synchronizability of networks of any size and topological properties in a small number of steps that scales with the network size.Although we take the eigenratio of the Laplacian as the target function for optimization, we will show that it is also possible to choose other appropriate target functions exhibiting almost the same performance. The optimized networks are Ramanujan graphs, and thus, this rewiring algorithm could be used to produce Ramanujan graphs of any size and average degree

    Topological properties and fractal analysis of recurrence network constructed from fractional Brownian motions

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    Many studies have shown that we can gain additional information on time series by investigating their accompanying complex networks. In this work, we investigate the fundamental topological and fractal properties of recurrence networks constructed from fractional Brownian motions (FBMs). First, our results indicate that the constructed recurrence networks have exponential degree distributions; the relationship between HH and canberepresentedbyacubicpolynomialfunction.Wenextfocusonthemotifrankdistributionofrecurrencenetworks,sothatwecanbetterunderstandnetworksatthelocalstructurelevel.Wefindtheinterestingsuperfamilyphenomenon,i.e.therecurrencenetworkswiththesamemotifrankpatternbeinggroupedintotwosuperfamilies.Last,wenumericallyanalyzethefractalandmultifractalpropertiesofrecurrencenetworks.Wefindthattheaveragefractaldimension can be represented by a cubic polynomial function. We next focus on the motif rank distribution of recurrence networks, so that we can better understand networks at the local structure level. We find the interesting superfamily phenomenon, i.e. the recurrence networks with the same motif rank pattern being grouped into two superfamilies. Last, we numerically analyze the fractal and multifractal properties of recurrence networks. We find that the average fractal dimension of recurrence networks decreases with the Hurst index HH of the associated FBMs, and their dependence approximately satisfies the linear formula ≈2−H \approx 2 - H. Moreover, our numerical results of multifractal analysis show that the multifractality exists in these recurrence networks, and the multifractality of these networks becomes stronger at first and then weaker when the Hurst index of the associated time series becomes larger from 0.4 to 0.95. In particular, the recurrence network with the Hurst index H=0.5H=0.5 possess the strongest multifractality. In addition, the dependence relationships of the average information dimension andtheaveragecorrelationdimension and the average correlation dimension on the Hurst index HH can also be fitted well with linear functions. Our results strongly suggest that the recurrence network inherits the basic characteristic and the fractal nature of the associated FBM series.Comment: 25 pages, 1 table, 15 figures. accepted by Phys. Rev.

    Fast Escape from Quantum Mazes in Integrated Photonics

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    Escaping from a complex maze, by exploring different paths with several decision-making branches in order to reach the exit, has always been a very challenging and fascinating task. Wave field and quantum objects may explore a complex structure in parallel by interference effects, but without necessarily leading to more efficient transport. Here, inspired by recent observations in biological energy transport phenomena, we demonstrate how a quantum walker can efficiently reach the output of a maze by partially suppressing the presence of interference. In particular, we show theoretically an unprecedented improvement in transport efficiency for increasing maze size with respect to purely quantum and classical approaches. In addition, we investigate experimentally these hybrid transport phenomena, by mapping the maze problem in an integrated waveguide array, probed by coherent light, hence successfully testing our theoretical results. These achievements may lead towards future bio-inspired photonics technologies for more efficient transport and computation.Comment: 13 pages, 10 figure
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