Statistical analysis of 22 public transport networks in Poland

Public transport systems in 22 Polish cities have been analyzed. Sizes of these networks range from N=152 to N=2881. Depending on the assumed definition of network topology the degree distribution can follow a power law or can be described by an exponential function. Distributions of paths in all considered networks are given by asymmetric, unimodal functions. Clustering, assortativity and betweenness are studied. All considered networks exhibit small world behavior and are hierarchically organized. A transition between dissortative small networks N=500 is observed.Comment: 11 pages, 17 figures, 2 tables, REVTEX4 forma

Ising model on two connected Barabasi-Albert networks

We investigate analytically the behavior of Ising model on two connected Barabasi-Albert networks. Depending on relative ordering of both networks there are two possible phases corresponding to parallel or antiparallel alingment of spins in both networks. A difference between critical temperatures of both phases disappears in the limit of vanishing inter-network coupling for identical networks. The analytic predictions are confirmed by numerical simulations.Comment: 6 pages including 6 figure

Universal scaling of distances in complex networks

Universal scaling of distances between vertices of Erdos-Renyi random graphs, scale-free Barabasi-Albert models, science collaboration networks, biological networks, Internet Autonomous Systems and public transport networks are observed. A mean distance between two nodes of degrees k_i and k_j equals to =A-B log(k_i k_j). The scaling is valid over several decades. A simple theory for the appearance of this scaling is presented. Parameters A and B depend on the mean value of a node degree _nn calculated for the nearest neighbors and on network clustering coefficients.Comment: 4 pages, 3 figures, 1 tabl

External bias in the model of isolation of communities

We extend a model of community isolation in the d-dimensional lattice onto the case with an imposed imbalance between birth rates of competing communities. We give analytical and numerical evidences that in the asymmetric two-specie model there exists a well defined value of the asymmetry parameter when the emergence of the isolated (blocked) subgroups is the fastest, i.e. the characteristic time tc is minimal. This critical value of the parameter depends only on the lattice dimensionality and is independent from the system size. Similar phenomenon was observed in the multi-specie case with a geometric distribution of the birth rates. We also show that blocked subgroups in the multi-specie case are absent or very rare when either there is a strictly dominant specie that outnumbers the others or when there is a large diversity of species. The number of blocked species of different kinds decreases with the dimension of the multi-specie system.Comment: 6 pages, 4 figure

Estimation of a Noise Level Using Coarse-Grained Entropy of Experimental Time Series of Internal Pressure in a Combustion Engine

We report our results on non-periodic experimental time series of pressure in a single cylinder spark ignition engine. The experiments were performed for different levels of loading. We estimate the noise level in internal pressure calculating the coarse-grained entropy from variations of maximal pressures in successive cycles. The results show that the dynamics of the combustion is a nonlinear multidimensional process mediated by noise. Our results show that so defined level of noise in internal pressure is not monotonous function of loading.Comment: 12 pages, 6 figure

Interplay between network structure and self-organized criticality

We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free (SF) networks and how this emerging structure affects dynamics of the system. We also discuss how the observed phenomenon can be used to explain evolution of scientific collaboration.Comment: 4 pages, 4 figure

Ferromagnetic fluid as a model of social impact

The paper proposes a new model of spin dynamics which can be treated as a model of sociological coupling between individuals. Our approach takes into account two different human features: gregariousness and individuality. We will show how they affect a psychological distance between individuals and how the distance changes the opinion formation in a social group. Apart from its sociological aplications the model displays the variety of other interesting phenomena like self-organizing ferromagnetic state or a second order phase transition and can be studied from different points of view, e.g. as a model of ferromagnetic fluid, complex evolving network or multiplicative random process.Comment: 8 pages, 5 figure

Dynamics of Helping Behavior and Networks in a Small World

To investigate an effect of social interaction on the bystanders' intervention in emergency situations a rescue model was introduced which includes the effects of the victim's acquaintance with bystanders and those among bystanders from a network perspective. This model reproduces the experimental result that the helping rate (success rate in our model) tends to decrease although the number of bystanders $k$ increases. And the interaction among homogeneous bystanders results in the emergence of hubs in a helping network. For more realistic consideration it is assumed that the agents are located on a one-dimensional lattice (ring), then the randomness $p \in [0,1]$ is introduced: the $kp$ random bystanders are randomly chosen from a whole population and the $k-kp$ near bystanders are chosen in the nearest order to the victim. We find that there appears another peak of the network density in the vicinity of $k=9$ and $p=0.3$ due to the cooperative and competitive interaction between the near and random bystanders.Comment: 13 pages, 8 figure

Volatility clustering and scaling for financial time series due to attractor bubbling

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time thermal bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.Comment: For related publications see http://www.helbing.or