Scaling in public transport networks

We analyse the statistical properties of public transport networks. These networks are defined by a set of public transport routes (bus lines) and the stations serviced by these. For larger networks these appear to possess a scale-free structure, as it is demonstrated e.g. by the Zipf law distribution of the number of routes servicing a given station or for the distribution of the number of stations which can be visited from the chosen one without changing the means of transport. Moreover, a rather particular feature of the public transport network is that many routes service common subsets of stations. We discuss the possibility of new scaling laws that govern intrinsic features of such subsets.Comment: 9 pages, 4 figure

Entropic equation of state and scaling functions near the critical point in scale-free networks

We analyze the entropic equation of state for a many-particle interacting system in a scale-free network. The analysis is performed in terms of scaling functions which are of fundamental interest in the theory of critical phenomena and have previously been theoretically and experimentally explored in the context of various magnetic, fluid, and superconducting systems in two and three dimensions. Here, we obtain general scaling functions for the entropy, the constant-field heat capacity, and the isothermal magnetocaloric coefficient near the critical point in scale-free networks, where the node-degree distribution exponent $\lambda$ appears to be a global variable and plays a crucial role, similar to the dimensionality $d$ for systems on lattices. This extends the principle of universality to systems on scale-free networks and allows quantification of the impact of fluctuations in the network structure on critical behavior.Comment: 8 pages, 4 figure

Critical phenomena on scale-free networks: logarithmic corrections and scaling functions

In this paper, we address the logarithmic corrections to the leading power laws that govern thermodynamic quantities as a second-order phase transition point is approached. For phase transitions of spin systems on d-dimensional lattices, such corrections appear at some marginal values of the order parameter or space dimension. We present new scaling relations for these exponents. We also consider a spin system on a scale-free network which exhibits logarithmic corrections due to the specific network properties. To this end, we analyze the phase behavior of a model with coupled order parameters on a scale-free network and extract leading and logarithmic correction-to-scaling exponents that determine its field- and temperature behavior. Although both non-trivial sets of exponents emerge from the correlations in the network structure rather than from the spin fluctuations they fulfil the respective thermodynamic scaling relations. For the scale-free networks the logarithmic corrections appear at marginal values of the node degree distribution exponent. In addition we calculate scaling functions, which also exhibit nontrivial dependence on intrinsic network properties.Comment: 15 pages, 4 figure

Network Harness: Metropolis Public Transport

We analyze the public transport networks (PTNs) of a number of major cities of the world. While the primary network topology is defined by a set of routes each servicing an ordered series of given stations, a number of different neighborhood relations may be defined both for the routes and the stations. The networks defined in this way display distinguishing properties, the most striking being that often several routes proceed in parallel for a sequence of stations. Other networks with real-world links like cables or neurons embedded in two or three dimensions often show the same feature - we use the car engineering term "harness" for such networks. Geographical data for the routes reveal surprising self-avoiding walk (SAW) properties. We propose and simulate an evolutionary model of PTNs based on effectively interacting SAWs that reproduces the key features.Comment: 5 pages, 4 figure

Public transport networks: empirical analysis and modeling

We use complex network concepts to analyze statistical properties of urban public transport networks (PTN). To this end, we present a comprehensive survey of the statistical properties of PTNs based on the data of fourteen cities of so far unexplored network size. Especially helpful in our analysis are different network representations. Within a comprehensive approach we calculate PTN characteristics in all of these representations and perform a comparative analysis. The standard network characteristics obtained in this way often correspond to features that are of practical importance to a passenger using public traffic in a given city. Specific features are addressed that are unique to PTNs and networks with similar transport functions (such as networks of neurons, cables, pipes, vessels embedded in 2D or 3D space). Based on the empirical survey, we propose a model that albeit being simple enough is capable of reproducing many of the identified PTN properties. A central ingredient of this model is a growth dynamics in terms of routes represented by self-avoiding walks.Comment: 19 pages, 23 figure

Correlated dynamics in egocentric communication networks

We investigate the communication sequences of millions of people through two different channels and analyze the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbors thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constrains (for short messages) and partly to the human behavioral features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.Comment: 7 pages, 6 figure

Component composition of organic compounds of the assimilative apparatus of different species of the genus Aesculus affected by Cameraria ohridella (Lepidoptera, Gracillariidae)

The most important disease for plants of the Aesculus genus is leaf spot caused by the leaf miner Cameraria ohridella (Lepidoptera , Gracillariidae) , which limits the use of Aesculus in landscaping in urban areas. The leaf miner C. ohridella is an insect widely spread in most European countries. The study was carried out in an urban area with six species of the genus Aesculus L. ( А e . hippocastanum L., A e . pavia L., A e . parviflora Walt., A e . flava Sol., A e . glabra Willd. and hybrid Aesculus × carnea ). The article reflects the results of research on the influence of the leaf miner C. ohridella on the peculiarities of changes in the chemical composition of chestnut leaf extracts. The component composition of the leaves of different ches t nut species was determined using chromatographic analysis. The study shows the results of the phytochemical screening of the leaves of different species from genus Aesculus , uninfested and infested with C. ohridella . A t otal of 186 chemical co m ponents were identified from the leaf extract s of Aesculus plants with six main groups of chemical components – carboh y drates, polyphenols, steroids, hydrocarbons, fatty acids and miscellaneous. The carbohydrates group is represented in the leaves of all studied Aesculus species in the maximum degree. The obtained data demonstrate significant change in the number of all chemical components under the influence of C. ohridella . The studied species showed an increase in carboh y drates content with the influence of leaf miner C. ohridella , except for such species as A e . flava and A e . parviflora . The qualitative composition of polyphenolic compounds was species-specific. The analysis of the composition of extracts of uninfested leaves established that four components were contained in extracts of Ae. hippocastanum and Ae. pavia , but they were different in their composition. In comparison with the composition of polyphenols in leaves without damage and leaves infected with C. ordidella , the absence of (2R-trans)-catechine in extracts from infected leaves of Ae. hippocastanum and Ae. glabra was found. U sing principal component analys i s , it was established that Ae. glabra shows a clear separation between chemical composition of the infested and uninfested samples. We identified two components of a phenolic nature only in extracts of infested leaves of Ae. flava , (trimethylsilyl catechollactate tris(trimethylsilyl) ether and epigallocatechin (6TMS)) , and quercetin was identified only in infected leaf extracts of Ae. glabra . Th ese results can indicate a greater pote n tial resistance of these Aesculus species to damage by the studied herbivory