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SUMMARY:Rigid Graphs for Adaptive Networks\, with Data - Reiko Heckel\, Un
 iversity of Leicester
DTSTART:20141205T160000Z
DTEND:20141205T170000Z
UID:TALK55915@talks.cam.ac.uk
CONTACT:Jonathan Hayman
DESCRIPTION:\nNetworks with dynamically changing topology can modelled usi
 ng rule-based graph transformations. If we are interested in the relative 
 timing of different kinds of change\, stochastic models are required\, add
 ing rate constants to rules controlling their delay once a match has becom
 e available. A particularly case are adaptive networks where structural ne
 twork changes and updates of local states are interdependent\, especially 
 if states carry data over numerical or other infinite domains. \n\nStochas
 tic graph transformation models for complex networks are hard to construct
  and analyse. Refinements help to produce systems at the right level of ab
 straction\, enable analysis techniques and mappings to other formalisms. R
 igidity is a property of graphs introduced in Kappa to support stochastic 
 refinement\, allowing to preserve the number of matches for rules in the r
 efined system. In this talk: 1) we propose a notion of rigidity in an axio
 matic setting based on adhesive categories\; 2) we show how the rewriting 
 of rigid structures can be defined systematically by requiring matches to 
 be open maps reflecting certain structures\; and 3) we obtain in our setti
 ng a notion of refinement which generalises that in Kappa\, and allows a r
 ule to be partitioned into a set of rules which are collectively equivalen
 t to the original. \n\nWe illustrate our approach on an example of a socia
 l network with dynamic topology and discuss applications to the energy-dri
 ven approach to rewriting\, progressing from the most basic case where dat
 a states are Boolean to numerical data states\, both emerging as instances
  of the categorical framework. \n
LOCATION:Room FW26\, Computer Laboratory\, William Gates Building
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