Knowledge Acquisition by Networks of Interacting Agents in the Presence of Observation Errors

arXiv:0807.2031v2 [physics.soc-ph] 1 May 2009 Knowledge Acquisition by Networks of Interacting Agents in the Presence of Observation Errors J. B. Batista and L. da F. Costa Institute of Physics at S˜ao Carlos, University of S˜ao Paulo, P.O. Box 369, S˜ao Carlos, S˜ao Paulo, 13560-970 Brazil (Dated: 24th April 2009) In this work we investigate knowledge acquisition as performed by multiple agents interacting as they infer, under the presence of observation errors, respective models of a complex system. We focus the specific case in which, at each time step, each agent takes into account its current observation as well as the average of the models of its neighbors. The agents are connected by a network of interaction of Erd˝os-R´enyi or Barab´asi-Albert type. First we investigate situations in which one of the agents has a different probability of observation error (higher or lower). It is shown that the influence of this special agent over the quality of the models inferred by the rest of the network can be substantial, varying linearly with the respective degree of the agent with different estimation error. In case the degree of this agent is taken as a respective fitness parameter, the effect of the different estimation error is even more pronounced, becoming superlinear. To complement our analysis, we provide the analytical solution of the overall behavior of the system. We also investigate the knowledge acquisition dynamic when the agents are grouped into communities. We verify that the inclusion of edges between agents (within a community) having higher probability of observation error promotes the loss of quality in the estimation of the agents in the other communities. PACS numbers: 07.05.Mh, 64.60.aq, 01.40.Ha ‘Knowledge is of two kinds: we know a subject our- selves, or we know where we can find information upon it.’ (S. Johson) I. INTRODUCTION Several important systems in nature, from the brain to society, are characterized by intricate organization. Being naturally related to such systems, humans have been trying to understand them through the construc- tion of models which can reasonably reproduce and pre- dict the respectively observed properties. Model building is the key component in the scientific method. The de- velopment of a model involves the observation and mea- surement of the phenomenon of interest, its representa- tion in mathematical terms, followed by simulations and respective confrontation with further experimental evi- dences. Because of the challenging complexity of the re- maining problems in science, model building has become intrinsically dependent on collaboration between scien- tists or agents. The problem of multiple-agent knowl- edge acquisition and processing has been treated in the literature (e.g. [1, 2]), but often under assumption of simple schemes of interactions between the agents (e.g. lattice or pool). Introduced recently, complex networks ( [3, 4, 5, 6, 7]) have quickly become a key research area mainly because of the generality of this approach to rep- resent virtually any discrete system, allied to the possi- bilities of relating network topology and dynamics. As such, complex networks stand out as being a fundamental resource for complementing and enhancing the scientific method. The present study addresses the issue of modeling how one or more agents (e.g. scientists) progress while mod- eling a complex system. We start by considering a sin- gle agent and then proceed to more general situations involving several agents interacting through networks of relationships (see Figure 1). The agents investigating the system (one or more) are allowed to make observations and take measurements of the system as they develop and complement their respective individual models. Er- rors, incompleteness, noise and forgetting are typically involved during a such model estimation. The main fea- tures of interest include the quality of the obtained mod- els and the respective amount of time required for their estimation. The plural in ‘models’ stands for the fact that the models obtained respectively by each agent are not necessarily identical and will often imply in substan- tial diversity. Though corresponding to a largely simpli- fied version of real scientific investigation, our approach captures some of the main elements characterizing the in- volvement of a large number of interacting scientists who continuously exchange information and modify their re- spective models and modeling approaches. As a matter of fact, in some cases the development of models may even affect the system being modeled (e.g. the perturbation implied by the measurements on the analyzed systems). Because interactions between scientists can be effec- tively represented in terms of complex networks (e.g. [8, 9, 10, 11, 12, 13, 14]), it is natural to resource to such an approach in our investigation. It is interesting to observe that the agents may not be limited to scien- tists, but can also include intelligent m

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