arXiv subjects

Stefan Thurner

Publications and source records attributed to Stefan Thurner.

At least 163 records · Page 9Linked to original sources

arXiv2006

Transport on Complex Networks: Flow, Jamming and Optimization

Many transport processes on networks depend crucially on the underlying network geometry, although the exact relationship between the structure of the network and the properties of transport processes remain elusive. In this paper we address this question by using numerical models in which both structure and dynamics are controlled systematically. We consider the traffic of information packets that include driving, searching and queuing. We present the results of extensive simulations on two classes of networks; a correlated cyclic scale-free network and an uncorrelated homogeneous weakly clustered network. By measuring different dynamical variables in the free flow regime we show how the global statistical properties of the transport are related to the temporal fluctuations at individual nodes (the traffic noise) and the links (the traffic flow). We then demonstrate that these two network classes appear as representative topologies for optimal traffic flow in the regimes of low density and high density traffic, respectively. We also determine statistical indicators of the pre-jamming regime on different network geometries and discuss the role of queuing and dynamical betweenness for the traffic congestion. The transition to the jammed traffic regime at a critical posting rate on different network topologies is studied as a phase transition with an appropriate order parameter. We also address several open theoretical problems related to the network dynamics.

physics.soc-ph↗

arXiv2006

Generalized Boltzmann factors and the maximum entropy principle

We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $Λ$ as inverses of these distribution functions, we are led to a generalization of the classical Boltzmann-Gibbs entropy, $S_{BG}= -\int d εω(ε) B(ε) \log B(ε)$ to the expression $S\equiv -\int d εω(ε) \int_0^{B(ε)} dx Λ(x)$, which contains the classical entropy as a special case. We demonstrate that this entropy has two important features: First, it describes the correct thermodynamic relations of the system, and second, the observed distributions are straight forward solutions to the Jaynes maximum entropy principle with the ordinary (not escort!) constraints. Tsallis entropy is recovered as a further special case.

cond-mat.stat-mech↗

arXiv2006

Hierarchical and mixing properties of static complex networks emerging from the fluctuating classical random graphs

The Erdos-Renyi classical random graph is characterized by a fixed linking probability for all pairs of vertices. Here, this concept is generalized by drawing the linking probability from a certain distribution. Such a procedure is found to lead to a static complex network with an arbitrary connectivity distribution. In particular, a scale-free network with the hierarchical organization is constructed without assuming any knowledge about the global linking structure, in contrast to the preferential attachment rule for a growing network. The hierarchical and mixing properties of the static scale-free network thus constructed are studied. The present approach establishes a bridge between a scalar characterization of individual vertices and topology of an emerging complex network. The result may offer a clue for understanding the origin of a few abundance of connectivity distributions in a wide variety of static real-world networks.

cond-mat.stat-mech↗

arXiv2005

Statistical Indicators of Collective Behavior and Functional Clusters in Gene Networks of Yeast

We analyze gene expression time-series data of yeast S. cerevisiae measured along two full cell-cycles. We quantify these data by using q-exponentials, gene expression ranking and a temporal mean-variance analysis. We construct gene interaction networks based on correlation coefficients and study the formation of the corresponding giant components and minimum spanning trees. By coloring genes according to their cell function we find functional clusters in the correlation networks and functional branches in the associated trees. Our results suggest that a percolation point of functional clusters can be identified on these gene expression correlation networks.

q-bio.GN↗

arXiv2005

On the derivation of power-law distributions within classical statistical mechanics far from the thermodynamic limit

We show that within classical statistical mechanics without taking the thermodynamic limit, the most general Boltzmann factor for the canonical ensemble is a q-exponential function. The only assumption here is that microcanonical distributions have to be separable from of the total system energy, which is the prerequisite for any sensible measurement. We derive that all separable distributions are parametrized by a mathematical separation constant Q which can be related to the non-extensivity q-parameter in Tsallis distributions. We further demonstrate that nature fixes the separation constant Q to 1 for large dimensionality of Gibbs Gamma-phase space. Our results will be relevant for systems with a low-dimensional Gamma-space, for example nanosystems, comprised of a small number of particles or for systems with a dimensionally collapsed phase space, which might be the case for a large class of complex systems.

cond-mat.stat-mech↗

arXiv2005

Statistical mechanics of scale-free networks at a critical point: Complexity without irreversibility?

Based on a rigorous extension of classical statistical mechanics to networks, we study a specific microscopic network Hamiltonian. The form of this Hamiltonian is derived from the assumption that individual nodes increase/decrease their utility by linking to nodes with a higher/lower degree than their own. We interpret utility as an equivalent to energy in physical systems and discuss the temperature dependence of the emerging networks. We observe the existence of a critical temperature $T_c$ where total energy (utility) and network-architecture undergo radical changes. Along this topological transition we obtain scale-free networks with complex hierarchical topology. In contrast to models for scale-free networks introduced so far, the scale-free nature emerges within equilibrium, with a clearly defined microcanonical ensemble and the principle of detailed balance strictly fulfilled. This provides clear evidence that 'complex' networks may arise without irreversibility. The results presented here should find a wide variety of applications in socio-economic statistical systems.

cond-mat.stat-mech↗

arXiv2005

Nonextensive aspects of self-organized scale-free gas-like networks

We explore the possibility to interpret as a 'gas' the dynamical self-organized scale-free network recently introduced by Kim et al (2005). The role of 'momentum' of individual nodes is played by the degree of the node, the 'configuration space' (metric defining distance between nodes) being determined by the dynamically evolving adjacency matrix. In a constant-size network process, 'inelastic' interactions occur between pairs of nodes, which are realized by the merger of a pair of two nodes into one. The resulting node possesses the union of all links of the previously separate nodes. We consider chemostat conditions, i.e., for each merger there will be a newly created node which is then linked to the existing network randomly. We also introduce an interaction 'potential' (node-merging probability) which decays with distance d_ij as 1/d_ij^alpha; alpha >= 0). We numerically exhibit that this system exhibits nonextensive statistics in the degree distribution, and calculate how the entropic index q depends on alpha. The particular cases alpha=0 and alpha to infinity recover the two models introduced by Kim et al.

cond-mat.other↗

arXiv2005

The phase transition in random catalytic sets

The notion of (auto) catalytic networks has become a cornerstone in understanding the possibility of a sudden dramatic increase of diversity in biological evolution as well as in the evolution of social and economical systems. Here we study catalytic random networks with respect to the final outcome diversity of products. We show that an analytical treatment of this longstanding problem is possible by mapping the problem onto a set of non-linear recurrence equations. The solution of these equations show a crucial dependence of the final number of products on the initial number of products and the density of catalytic production rules. For a fixed density of rules we can demonstrate the existence of a phase transition from a practically unpopulated regime to a fully populated and diverse one. The order parameter is the number of final products. We are able to further understand the origin of this phase transition as a crossover from one set of solutions from a quadratic equation to the other.

cond-mat.other↗

arXiv2005

Analytic formula for hidden variable distribution: Complex networks arising from fluctuating random graphs

In analogy to superstatistics, which connects Boltzmann-Gibbs statistical mechanics to its generalizations through temperature fluctuations, complex networks are constructed from the fluctuating Erdos-Renyi random graphs. Here, using the quantum mechanical method, the exact analytic formula is presented for the hidden variable distribution, which describes the fluctuation and generates a generic degree distribution through the Poisson transformation. As an example, a static scale-free network is discussed and the corresponding hidden variable distribution is found to decay as a power law.

cond-mat.dis-nn↗

arXiv2004

On the Derivation of power-law distributions within standard statistical mechanics

We show that within classical statistical mechanics it is possible to naturally derive power law distributions which are of Tsallis type. The only assumption is that microcanonical distributions have to be separable from of the total system energy, which is reasonable for any sensible measurement. We demonstrate that all separable distributions are parametrized by a separation constant Q which is one to one related to the q-parameter in Tsallis distributions. The power-laws obtained are formally equivalent to those obtained by maximizing Tsallis entropy under q constraints. We further ask why nature fixes the separation constant Q to 1 in so many cases leading to standard thermodynamics. We answer this with an explicit example where it is possible to relate Q to sytem size and interaction parameters, characterizing the physical system. We argue that these results might be helpful to explain the ubiquity of Tsallis distributions in nature.

cond-mat.stat-mech↗

arXiv2004

Anomalous Diffusion in View of Einstein's 1905 Theory of Brownian Motion

Einstein's theory of Brownian motion is revisited in order to formulate generalized kinetic theory of anomalous diffusion. It is shown that if the assumptions of analyticity and the existence of the second moment of the displacement distribution are relaxed, the fractional derivative naturally appears in the diffusion equation. This is the first demonstration of the physical origin of the fractional derivative, in marked contrast to the usual phenomenological introduction of it. Furthermore, Einstein's approach is generalized to nonlinear kinetic theory to derive the porous-medium-type equation by the appropriate use of the escort distribution.

cond-mat.stat-mech↗

arXiv2004

Contagion Flow Through Banking Networks

Based on an empirical analysis of the network structure of the Austrian inter-bank market, we study the flow of funds through the banking network following exogenous shocks to the system. These shocks are implemented by stochastic changes in variables like interest rates, exchange rates, etc. We demonstrate that the system is relatively stable in the sence that defaults of individual banks are unlikely to spread over the entire network. We study the contagion impact of all individual banks, meaning the number of banks which are driven into insolvency as a result of a single bank's default. We show that the vertex betweenness of individual banks is linearly related to their contagion impact.

cond-mat.other↗

arXiv2004

Traffic on complex networks: Towards understanding global statistical properties from microscopic density fluctuations

We study the microscopic time fluctuations of traffic-load and the global statistical properties of a dense traffic of particles on scale-free cyclic graphs. For a wide range of driving rates $R$ the traffic is stationary and the load timeseries exhibit anti-persistence due to the regulatory role of the super-structure associated with two hub nodes in the network. We discuss how the super-structure effects the functioning of the network at high traffic density and at the jamming threshold. The degree of correlations systematically decreases with increasing traffic density and eventually disappears when approaching a jamming density $R_c$. Already before jamming we observe qualitative changes in the global network-load distributions and the particle queuing-times. These changes are related to the occurrence of temporary crises in which the network-load increases dramatically, and then slowly falls back to a value characterizing free-flow.

cond-mat.stat-mech↗

arXiv2003

The Network Topology of the Interbank Market

We provide an empirical analysis of the network structure of the Austrian interbank market based on a unique data set of the Oesterreichische Nationalbank (OeNB). We show that the contract size distribution follows a power law over more than 3 decades. By using a novel ''dissimilarity'' measure we find that the interbank network shows a community structure that exactly mirrors the regional and sectoral organization of the actual Austrian banking system. The degree distribution of the interbank network shows two different power law exponents which are one-to-one related to two sub-network structures, differing in the degree of hierarchical organization. The banking network moreover shares typical structural features known in numerous complex real world networks: a low clustering coefficient and a relatively short average shortest path length. These empirical findings are in marked contrast to interbank networks that have been analyzed in the theoretical economic and econo-physics literature.

cond-mat↗

arXiv2003

Risk trading, network topology, and banking regulation

In the context of understanding the nature of the risk transformation process of the financial system we propose an iterative risk-trading game between several agents who build their trading strategies based on a general utility setting. The game is studied numerically for different network topologies. Consequences of topology are shown for the wealth time-series of agents, for the safety and efficiency of various types of networks. The proposed setup allows an analysis of the effects of different approaches to banking regulation as currently suggested by the Basle Committee of Banking Supervision. We find a phase transition-like phenomenon, where the Basle parameter plays the role of temperature and system safety serves as the order parameter. This result suggests the existence of an optimal regulation parameter. As a consequence a tightening of the current regulatory framework does not necessarily lead to an improvement of the safety of the banking system. Moreover, we show that banking systems with local risk-sharing cooperations have higher global default rates than systems with low cyclicality.

cond-mat↗

arXiv2003

Information Super-Diffusion on Structured Networks

We study diffusion of information packets on several classes of structured networks. Packets diffuse from a randomly chosen node to a specified destination in the network. As local transport rules we consider random diffusion and an improved local search method. Numerical simulations are performed in the regime of stationary workloads away from the jamming transition. We find that graph topology determines the properties of diffusion in a universal way, which is reflected by power-laws in the transit-time and velocity distributions of packets. With the use of multifractal scaling analysis and arguments of non-extensive statistics we find that these power-laws are compatible with super-diffusive traffic for random diffusion and for improved local search. We are able to quantify the role of network topology on overall transport efficiency. Further, we demonstrate the implications of improved transport rules and discuss the importance of matching (global) topology with (local) transport rules for the optimal function of networks. The presented model should be applicable to a wide range of phenomena ranging from Internet traffic to protein transport along the cytoskeleton in biological cells.

cond-mat.stat-mech↗

arXiv2002

Fractal noise maps reveal human brain activity: a key for unbiased fMRI analysis

Brain metabolism is controlled by complex regulation mechanisms. As part of their nature many complex systems show scaling behavior in their timeseries data. Corresponding scaling exponents can sometimes be used to characterize these systems. Here we present maps of scaling exponents derived from BOLD functional Magnetic Resonance Imaging (fMRI) data, and show that they reveal activation patterns in the human brain with very high precision. In contrast to standard model-based analysis we use no prior knowledge on the experimental stimulation paradigm for extracting activation patterns from fMRI timeseries. We demonstrate that mental activity is one-to-one related to large fractal exponents, or equivalently, to temporally highly correlated processes.

cond-mat↗

arXiv2002

Anomalous diffusion on dynamical networks: A model for interacting epithelial cell migration

We propose a model for cell migration where epithelial cells are able to detect trajectories of other cells and try to follow them. As cells move along in 2D cell culture, they mark their paths by loosing tiny parts of cytoplasm. Any cell moving on a surface where other cells have moved before faces a network of cell trajectories, which it tries to restrict its motion onto. With the Tsallis modification of classical thermodynamics one can solve the relevant Fokker-Planck like equation and obtain experimentally testable distribution functions. We compare the model to experimental data of normal mammary epithelial cells and cells which have been genetically manipulated to change their degree of cell-cell interaction.

cond-mat↗