1,721,030 research outputs found
The spectral dimension and geometrical universality on graphs
No full textThe spectral dimension d̄ of an infinite graph, defined according to the asymptotic behavior of the Laplacian operator spectral density, seems to be the right generalization of the Euclidean dimension d of lattices to non translationally invariant networks when dealing with dynamical and thermodynamical properties. In fact d̄ exactly replaces d in most laws where dimensional dependence explicitly appears: the spectrum of harmonic oscillations, the average autocorrelation function of random walks, the critical exponents of the spherical model, the low temperature specific heat, the generalized Mermin-Wagner theorem, the infrared singularities of the Gaussian model and many other. Still, d̄ would be a rather unsatisfactory generalization of d if it hadn't a second fundamental property: the independence of geometrical details at any finite scale (or geometrical universality). Here we show that d̄ is invariant under all geometrical transformations affecting only finite scale topology. In particular we prove that d̄ is left unchanged by any quasi-isometry (including coarse-graining and addition of finite range couplings), by local rescaling of couplings and by addition of infinite range of couplings provided they decay faster than a given power law
An energy window study of light transmission-disorder relationship in 1D photonic structures
No full textWhile the light transmission of photonic crystals is characterized by the photonic band gap, the one of disordered photonic structures is typified by a multiplicity of transmission depths. The total transmission over a range of wavelengths is related to the width of such range, but also to the type of disorder. Less homogeneous disordered structures transmit more light than the ordered counterpart regardless of the wavelengths range width. More homogeneous disordered structures transmit more light than the ordered counterpart only above a certain value of the width. We studied this behaviour with a statistical analysis over 5000 permutations of structures for six wavelength widths and for two different homogeneity degrees (Shannon-Wiener index)
The heterogeneity in link weights may decrease the robustness of real-world complex weighted networks
Full text linkHere we report a comprehensive analysis of the robustness of seven high-quality real-world complex weighted networks to errors and attacks toward nodes and links. We use measures of the network damage conceived for a binary (e.g. largest connected cluster LCC, and binary efficiency Effbin) or a weighted network structure (e.g. the efficiency Eff, and the total flow TF). We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binary-topological connectedness are almost unaffected. These findings unveil a problematic response-state where the attack toward a small fraction of nodes-links returns the real-world complex networks in a connected but inefficient state. Our findings unveil how the robustness may be overestimated when focusing on the connectedness of the components only. Last, to understand how the networks robustness is affected by link weights heterogeneity, we randomly assign link weights over the topological structure of the real-world networks and we find that highly heterogeneous networks show a faster efficiency decrease under nodes-links removal: i.e. the robustness of the real-world complex networks against nodes-links removal is negatively correlated with link weights heterogeneity
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No full textDynamical dimension splitting on fractals: Structures with different diffusive and vibrational spectral dimensions
No full textOn fractals and inhomogeneous structures that have been studied up to now, a single parameter, the spectral dimension, rules diffusion and vibrational dynamics. However, in principle, two distinct parameters could be necessary to describe the two physical phenomena. In this paper we show the existence of fractal structures where two different spectral dimensions are required. Random walks and vibrational spectrum are studied by renormalization group as well as alternative techniques to obtain the exact values of the dimensions and to clarify the origin of such dynamical dimension splitting. © World Scientific Publishing Company
A comparative analysis of link removal strategies in real complex weighted networks
Full text linkIn this report we offer the widest comparison of links removal (attack) strategies efficacy in impairing the robustness of six real-world complex weighted networks. We test eleven different link removal strategies by computing their impact on network robustness by means of using three different measures, i.e. the largest connected cluster (LCC), the efficiency (Eff) and the total flow (TF). We find that, in most of cases, the removal strategy based on the binary betweenness centrality of the links is the most efficient to disrupt the LCC. The link removal strategies based on binary-topological network features are less efficient in decreasing the weighted measures of the network robustness (e.g. Eff and TF). Removing highest weight links first is the best strategy to decrease the efficiency (Eff) in most of the networks. Last, we found that the removal of a very small fraction of links connecting higher strength nodes or of highest weight does not affect the LCC but it determines a rapid collapse of the network efficiency Eff and the total flow TF. This last outcome raises the importance of both to adopt weighted measures of network robustness and to focus the analyses on network response to few link removals
COVID-19 diffusion and its impact on dental practice in distant countries with similar ethnic background
No full textConditional attack strategy for real-world complex networks
No full textWhen attacking a real-world complex network, the removing strategy based on recalculated nodes betweenness centrality (Bet) is usually the best strategy for reducing the size of the largest connected component (LCC). In particular during the early stage of the removing process, the Bet strategy can reduce the size of LCC by a order of magnitude smaller than all other common strategies. However, near the end of this process, it can be less efficient and fail to completely break the network before other strategies. We found that this limit has origin from the nature of the betweenness centrality's definition: when a subgraph is very well connected, the betweenness of their nodes is very small and if it is a complete subgraph (a clique), the betweenness centrality of all nodes is zero. In consequence, when the network becomes fragmented and the largest connected component is (or closed to) a complete graph, the betweenness strategy will almost ignore it and remove nodes elsewhere, thus making the size of the LCC unchanged. Therefore, we propose a modified strategy that remove the highest betweenness node (global) conditioned on whether the node is in the LCC. If it is not, the strategy will seek inside the LCC and remove the one with the highest betweenness (local). We analyzed the efficacy of this strategy for several real-world complex networks and found that it is consistently the most efficient for all networks and for all time during the attacking process. Finally, we analyze the relationship between the relative efficiency of the betweenness centrality with respect to other strategies and the network's clustering structure. We found that real-world complex networks owing to higher clustering are more vulnerable to the Bet attack strategy. We show this relation by comparing different social networks, and then comparing two financial networks (SP500) sampled at different times that present the same number of nodes but different clustering coefficient level. This work sheds light on the design of a more robust network and as an initial speculative example, we propose a "toy model network" that after an initial node attack presents peculiar robustness properties against to both degree and betweenness attack. (C) 2019 Elsevier B.V. All rights reserved
New Betweenness Centrality Node Attack Strategies for Real-World Complex Weighted Networks
Full text linkIn this work, we introduce a new node attack strategy removing nodes with the highest conditional weighted betweenness centrality (CondWBet), which combines the weighted structure of the network and the node's conditional betweenness. We compare its efficacy with well-known attack strategies from literature over five real-world complex weighted networks. We use the network weighted efficiency (WEFF) like a measure encompassing the weighted structure of the network, in addition to the commonly used binary-topological measure, i.e., the largest connected cluster (LCC). We find that if the measure is WEFF, the CondWBet strategy is the best to decrease WEFF in 3 out of 5 cases. Further, CondWBet is the most effective strategy to reduce WEFF at the beginning of the removal process, whereas the Strength that removes nodes with the highest sum of the link weights first shows the highest efficacy in the final phase of the removal process when the network is broken into many small clusters. These last outcomes would suggest that a better attacking in weighted networks strategy could be a combination of the CondWBet and Strength strategies
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