Stochastic resonance for information flows on hierarchical networks

A simple model of information flows represented by package delivery on networks with hierarchical structures is considered. The packages should be transferred from one network node to another and the delivery process is influenced by two types of noise. The first type of noise is related to a partially false knowledge of network topology (topological noise), i.e. membership of nodes in communities in a shipping algorithm include a number of errors corresponding to a random rewiring of a fraction of network links. The second type of noise (dynamical noise) is related to a diffusive part in packet dynamics, i.e. package paths do not follow from completely deterministic rules. In the case of a pure topological noise and in the case of combination of both types of noises, we observe a resonance-like phenomenon for communication efficiency. The system performance measured as a fraction of packages that are delivered in a certain time period or as an inverse of time of a package delivery is maximal for intermediate levels of noise. This effect resembles the phenomenon of stochastic resonance that exists in many complex systems where a noise can enhance the information transfer.

[1]  Alex Arenas,et al.  Scaling of fluctuations in traffic on complex networks. , 2006, Physical review letters.

[2]  A. Fuliński.  Active Transport in Biological Membranes and Stochastic Resonances , 1997 .

[3]  D Cassi,et al.  Universal features of information spreading efficiency on d-dimensional lattices. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Bernhard Voelkl,et al.  Simulation of information propagation in real-life primate networks: longevity, fecundity, fidelity , 2010, Behavioral Ecology and Sociobiology.

[5]  R. Pastor-Satorras,et al.  Mean-field diffusive dynamics on weighted networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Gregoire Nicolis,et al.  Stochastic resonance , 2007, Scholarpedia.

[7]  D. Fell,et al.  The small world inside large metabolic networks , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[8]  A. Díaz-Guilera,et al.  Efficiency of informational transfer in regular and complex networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[9]  Ernesto Estrada,et al.  Information mobility in complex networks. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Wiesenfeld,et al.  Stochastic resonance on a circle. , 1994, Physical review letters.

[11]  Ginestra Bianconi,et al.  Entropy measures for networks: toward an information theory of complex topologies. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  R. Albert,et al.  The large-scale organization of metabolic networks , 2000, Nature.

[13]  Roy,et al.  Observation of stochastic resonance in a ring laser. , 1988, Physical review letters.

[14]  Alex Arenas,et al.  Impact of community structure on information transfer. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[15]  A. Barabasi,et al.  Evolution of the social network of scientific collaborations , 2001, cond-mat/0104162.

[16]  Jiao Gu,et al.  The effect of the forget-remember mechanism on spreading , 2008, 1011.3684.

[17]  J. Gómez-Gardeñes,et al.  Maximal-entropy random walks in complex networks with limited information. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[18]  Albert-László Barabási,et al.  Internet: Diameter of the World-Wide Web , 1999, Nature.

[19]  G. J. Rodgers,et al.  Packet Transport on Scale-Free Networks , 2002, Adv. Complex Syst..

[20]  M. Newman,et al.  The structure of scientific collaboration networks. , 2000, Proceedings of the National Academy of Sciences of the United States of America.

[21]  Ying-Cheng Lai,et al.  Information propagation on modular networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[22]  Alessandro P. S. de Moura,et al.  Fermi-Dirac statistics and traffic in complex networks. , 2005 .

[23]  M. Rosvall,et al.  Self-assembly of information in networks , 2006 .

[24]  Jason Lloyd-Price,et al.  Mutual information in random Boolean models of regulatory networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[25]  François Chapeau-Blondeau,et al.  Stochastic resonance and the benefit of noise in nonlinear systems , 2000 .

[26]  Yinghai Wang,et al.  The effect of human rhythm on packet delivery , 2010 .

[27]  Albert-László Barabási,et al.  Hierarchical organization in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  Jesús Gómez-Gardeñes,et al.  Local Empathy provides Global Minimization of Congestion in Communication Networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  R P Morse,et al.  Enhanced information transmission with signal-dependent noise in an array of nonlinear elements. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[30]  François Chapeau-Blondeau,et al.  Suprathreshold stochastic resonance and noise-enhanced Fisher information in arrays of threshold devices. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  A Díaz-Guilera,et al.  Communication in networks with hierarchical branching. , 2001, Physical review letters.

[32]  Vito Latora,et al.  Entropy rate of diffusion processes on complex networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  A. Krawiecki,et al.  Stochastic resonance as a model for financial market crashes and bubbles , 2003 .

[34]  D. Cory,et al.  Simulations of information transport in spin chains. , 2007, Physical review letters.

[35]  Junjie Wu,et al.  Weak ties: subtle role of information diffusion in online social networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Yamir Moreno,et al.  Theory of Rumour Spreading in Complex Social Networks , 2007, ArXiv.

[37]  Derek Abbott,et al.  An analysis of noise enhanced information transmission in an array of comparators , 2002 .

[38]  Tun-Wen Pai,et al.  Inhibition of the interactions between eosinophil cationic protein and airway epithelial cells by traditional Chinese herbs , 2010, BMC Systems Biology.

[39]  A. Sutera,et al.  The mechanism of stochastic resonance , 1981 .

[40]  M E J Newman,et al.  Finding and evaluating community structure in networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Yamir Moreno,et al.  Dynamics of rumor spreading in complex networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Yasuo Kuniyoshi,et al.  Information transfer at multiple scales. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[43]  M E Newman,et al.  Scientific collaboration networks. I. Network construction and fundamental results. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Thomas M. Cover,et al.  Elements of Information Theory: Cover/Elements of Information Theory, Second Edition , 2005 .

[45]  A. Wagner.  The yeast protein interaction network evolves rapidly and contains few redundant duplicate genes. , 2001, Molecular biology and evolution.

[46]  N G Stocks,et al.  Information transmission in parallel threshold arrays: suprathreshold stochastic resonance. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  K Sneppen,et al.  Communication boundaries in networks. , 2005, Physical review letters.

[48]  K Sneppen,et al.  Networks and cities: an information perspective. , 2005, Physical review letters.

[49]  Dominique M. Durand,et al.  Enhancement of information transmission of sub-threshold signals applied to distal positions of dendritic trees in hippocampal CA1 neuron models with stochastic resonance , 2010, Biological Cybernetics.

[50]  K Sneppen,et al.  Time walkers and spatial dynamics of aging information. , 2009, Physical review letters.

[51]  A Krawiecki,et al.  Noisefree stochastic multiresonance near chaotic crises. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[52]  Ilya Shmulevich,et al.  Critical networks exhibit maximal information diversity in structure-dynamics relationships. , 2008, Physical review letters.

[53]  Roy,et al.  Stochastic resonance in a bistable ring laser. , 1989, Physical review. A, General physics.

[54]  Dirk Helbing,et al.  Information Flows in Hierarchical Networks and the Capability of Organizations to Successfully Respond to Failures, Crises, and Disasters , 2006 .

[55]  M. Karnani,et al.  The physical character of information , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[56]  Jon M. Kleinberg,et al.  Tracing information flow on a global scale using Internet chain-letter data , 2008, Proceedings of the National Academy of Sciences.

[57]  Brian Karrer,et al.  Message passing approach for general epidemic models. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Marián Boguñá,et al.  Navigating ultrasmall worlds in ultrashort time. , 2008, Physical review letters.

[59]  G. Giacomelli,et al.  Noise-assisted transmission of binary information: theory and experiment. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  Petr Lánský,et al.  Information transfer with small-amplitude signals , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[61]  A. Barabasi,et al.  Lethality and centrality in protein networks , 2001, Nature.

[62]  Xiang Ling,et al.  Pheromone routing protocol on a scale-free network. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[63]  Leon O. Chua,et al.  STOCHASTIC RESONANCE IN CHUA’S CIRCUIT DRIVEN BY AMPLITUDE OR FREQUENCY MODULATED SIGNALS , 1994 .

[64]  Yasushi Yokoya.  Dynamics of traffic flow with real-time traffic information. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[65]  Peter M. A. Sloot,et al.  Identifying potential survival strategies of HIV-1 through virus-host protein interaction networks , 2010, BMC Systems Biology.

[66]  Corrado Priami,et al.  Snazer: the simulations and networks analyzer , 2010, BMC Systems Biology.

[67]  S. Thurner,et al.  Information super-diffusion on structured networks , 2003, cond-mat/0307670.

[68]  D Cassi,et al.  Efficiency of information spreading in a population of diffusing agents. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  A. Fronczak,et al.  Biased random walks in complex networks: the role of local navigation rules. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[70]  K Sneppen,et al.  Navigating networks with limited information. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[71]  Tao Zhou,et al.  Traffic dynamics based on local routing protocol on a scale-free network. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[72]  Peter Sheridan Dodds,et al.  Universal behavior in a generalized model of contagion. , 2004, Physical review letters.

[73]  Marc Barthelemy,et al.  Spatial structure of the internet traffic , 2003 .

[74]  Renato Germano,et al.  Traffic of particles in complex networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.