Efficiency of informational transfer in regular and complex networks

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study non-clustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small-worlds that includes {\it declustered} networks, and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.Comment: 10 pages and 9 figure

Urban road networks -- Spatial networks with universal geometric features? A case study on Germany's largest cities

Urban road networks have distinct geometric properties that are partially determined by their (quasi-) two-dimensional structure. In this work, we study these properties for 20 of the largest German cities. We find that the small-scale geometry of all examined road networks is extremely similar. The object-size distributions of road segments and the resulting cellular structures are characterised by heavy tails. As a specific feature, a large degree of rectangularity is observed in all networks, with link angle distributions approximately described by stretched exponential functions. We present a rigorous statistical analysis of the main geometric characteristics and discuss their mutual interrelationships. Our results demonstrate the fundamental importance of cost-efficiency constraints for in time evolution of urban road networks.Comment: 16 pages; 8 figure

Model calculation of the optical properties of

The marked difference between the optical absorption of dissolved PTCDA monomers and crystalline films is analysed in terms of the deformation of an effective internal vibrational mode of the molecule and transfer of Frenkel excitons between different molecular sites in the crystal. It is shown in detail that the coupling between equivalent molecules in different crystal unit cells, especially among stack neighbours, dominates over exciton transfer between the two different molecules in the crystal basis. The first type of interaction leads to a pronounced deformation of the expected Poisson progression over subsequent vibrational levels while the latter is responsible for a small Davydov splitting and, consequently, different absorption lineshapes along different crystal axes

Performance of excitable small-world networks of Bonhoeffer-van der Pol-FitzHugh-Nagumo oscillators

We investigate how performance (i.e. activity of the nodes and their subsequent synchronization) of excitable small-world networks depends on network topology. Network elements are described by Bonhoeffer-van der Pol-FitzHugh-Nagumo oscillators assumed to be close to the oscillating threshold. Global oscillations are induced by introducing a small amount of diversity. In homogeneous networks, it is found that the system performance is mainly determined by the average path length, no matter what the local properties are. The network undergoes a transition from low to high activity regimes at a critical path length. This transition, also found in regular networks, is shown to be caused by the dependence of the critical coupling strength between network units on the average path length

Quantum size effects in the optical properties of organic superlattices containing 3, 4, 9, 10 perylene tetracarboxylic dianhydride (PTCDA)

71.35.Aa Frenkel excitons and self-trapped excitons, 33.20.-t Molecular spectra, 78.20.Bh Theory, models, and numerical simulation, 78.55.Kz Solid organic materials,