The second will be first: competition on directed networks

Multiple sinks competition is investigated for a walker diffusing on directed complex networks. The asymmetry of the imposed spatial support makes the system non transitive. As a consequence, it is always possible to identify a suitable location for the second absorbing sink that screens at most the flux of agents directed against the first trap, whose position has been preliminarily assigned. The degree of mutual competition between pairs of nodes is analytically quantified through apt indicators that build on the topological characteristics of the hosting graph. Moreover, the positioning of the second trap can be chosen so as to minimize, at the same time, the probability of being in turn shaded by a thirdly added trap. Supervised placing of absorbing traps on a asymmetric disordered and complex graph is hence possible, as follows a robust optimization protocol. This latter is here discussed and successfully tested against synthetic data.

[1]  Alessandro Vespignani,et al.  Dynamical Processes on Complex Networks , 2008 .

[2]  Zeno Farkas,et al.  One-dimensional drift-diffusion between two absorbing boundaries: application to granular segregation , 2001 .

[3]  S. Havlin,et al.  Structural properties of spatially embedded networks , 2008, 0804.2575.

[4]  V. Latora,et al.  Complex networks: Structure and dynamics , 2006 .

[5]  Raoul Kopelman,et al.  Reaction kinetics: Catalysis without a catalyst. , 2010, Nature chemistry.

[6]  Douglas H. Kelley,et al.  Emergent dynamics of laboratory insect swarms , 2013, Scientific Reports.

[7]  Zhongzhi Zhang,et al.  Mean first-passage time for maximal-entropy random walks in complex networks , 2014, Scientific Reports.

[8]  Aarnout Brombacher,et al.  Probability... , 2009, Qual. Reliab. Eng. Int..

[9]  O Bénichou,et al.  Geometry-controlled kinetics. , 2010, Nature chemistry.

[10]  Pierre Boulanger,et al.  Coarse-grained molecular simulation of diffusion and reaction kinetics in a crowded virtual cytoplasm. , 2008, Biophysical journal.

[11]  Radhika Nagpal,et al.  Programmable self-assembly in a thousand-robot swarm , 2014, Science.

[12]  Barbara Webb,et al.  Swarm Intelligence: From Natural to Artificial Systems , 2002, Connect. Sci..

[13]  Duccio Fanelli,et al.  Optimal search strategies on complex multi-linked networks , 2015, Scientific Reports.

[14]  George C. Boon.  Counterfeiting in Roman Britain , 1974 .

[15]  J. Deneubourg,et al.  Self-organized shortcuts in the Argentine ant , 1989, Naturwissenschaften.

[16]  Yan Lu,et al.  Thermosensitive core–shell microgels: From colloidal model systems to nanoreactors , 2011 .

[17]  Kevin Zhou.  Navigation in a small world , 2017 .

[18]  Maurizio Dusi,et al.  Estimating routing symmetry on single links by passive flow measurements , 2010, IWCMC.

[19]  G. Parisi,et al.  Interaction ruling animal collective behavior depends on topological rather than metric distance: Evidence from a field study , 2007, Proceedings of the National Academy of Sciences.

[20]  H E Stanley,et al.  Towards design principles for optimal transport networks. , 2010, Physical review letters.

[21]  Sang Hoon Lee,et al.  Exploring maps with greedy navigators , 2011, Physical review letters.

[22]  José S. Andrade,et al.  Enhanced Flow in Small-World Networks , 2013, Physical review letters.

[23]  M. Ballauff,et al.  Enhanced activity of enzymes immobilized in thermoresponsive core-shell microgels. , 2009, The journal of physical chemistry. B.

[24]  Ralf Metzler,et al.  Generalized facilitated diffusion model for DNA-binding proteins with search and recognition states. , 2012, Biophysical journal.

[25]  O Bénichou,et al.  Facilitated diffusion of proteins on chromatin. , 2010, Physical review letters.

[26]  J. S. Andrade,et al.  Optimal transport exponent in spatially embedded networks. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  Andrej Kosmrlj,et al.  How a protein searches for its site on DNA: the mechanism of facilitated diffusion , 2009 .

[29]  Arun Yethiraj,et al.  Effect of macromolecular crowding on reaction rates: a computational and theoretical study. , 2009, Biophysical journal.

[30]  P ? ? ? ? ? ? ? % ? ? ? ? , 1991 .

[31]  USA,et al.  Efficient search by optimized intermittent random walks , 2009, 0909.1048.

[32]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[33]  K. Luby-Phelps,et al.  Cytoarchitecture and physical properties of cytoplasm: volume, viscosity, diffusion, intracellular surface area. , 2000, International review of cytology.