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SUMMARY:Entropy Rate of Diffusion Processes on Complex Networks - Vito Lat
 ora (Universita' di Catania\, Italy)
DTSTART:20080807T130000Z
DTEND:20080807T140000Z
UID:TALK13033@talks.cam.ac.uk
CONTACT:Eiko Yoneki
DESCRIPTION:In the realm of complex networks the concept of entropy has be
 en used as a measure to characterize properties of the topology\, such as 
 the degree distribution of a graph. Alternatively\, various authors have s
 tudied the entropy associated with ensembles of graphs and provided\, via 
 the application of the maximum entropy principle\, the best prediction of 
 network properties subject to the constraints imposed by a given set of ob
 servations.  The main theoretical and empirical interest in the study of c
 omplex networks is in understanding the relations between structure and fu
 nction. Many of the interaction dynamics that takes place in social\, biol
 ogical and technological systems can be analyzed in terms of diffusion pro
 cesses on top of complex networks\, e.g.  data search and routing\, inform
 ation and disease spreading.  In this talk\, we show how to associate an e
 ntropy rate to a diffusion process on a graph. In this context\, the entro
 py rate is a quantity more similar to the Kolmogorov-Sinai entropy rate of
  a dynamical system\, than to the entropy of a statistical ensemble\, and 
 measures what is\, on average\, the shortest per step description of the d
 iffusion on the network. Therefore\, a high entropy rate indicates a large
  randomness\, or easiness of propagating from one node to another\, and ca
 n be related to an efficient spreading over the network Differently from t
 he network entropies previously defined\, the entropy rate of a diffusion 
 depends both on the dynamical process and on the graph topology. This allo
 ws us to use the entropy rate in two different ways: i) to characterize wi
 th a single measure various structural properties of real-world networks\,
  and ii) to design optimal diffusion processes which maximize the entropy.
  As an example of the powerful possibilities of the introduced measure\, w
 e study the diffusion of random walkers whose motion is biased on the node
  degrees.\nJ. Gomez-Gardenes\, V. Latora\, http://xxx.lanl.gov/abs/0712.02
 78\n\n\nVito Latora: Dipartimento di Fisica\, Universita' di Catania\, and
  INFN Italy \n\nhttp://www.ct.infn.it/~latora/bio.html
LOCATION:FW26\, Computer Laboratory\, William Gates Builiding
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