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Future networks have to accommodate an increase of 3-4 orders of magnitude in data rates with very heterogeneous session sizes and sometimes with strict time deadline requirements.The dynamic nature of scheduling of large transactions and the need for rapid actions by the Network Management and Control (NMC) system, require timely collection of network state information. Rough estimates of the size of detailed network states suggest large volumes of data with refresh rates commensurate with the coherence time of the states (can be as fast as 100 ms), resulting in huge burden and cost for the network transport (300 Gbps/link) and computation resources. Thus, judicious sampling of network states is necessary for a cost-effective network management system. In this paper, we consider a construct of an NMC system where sensing and routing decisions are made with cognitive understanding of the network states and short-term behavior of exogenous offered traffic. We have studied a small but realistic example of adaptive monitoring based on significant sampling techniques. This technique balances the need for accurate and updated state information against the updating cost and provides an algorithm that yields near optimum performance with significantly reduced burden of sampling, transport and computation. We show that our adaptive monitoring system can reduce the NMC overhead by a factor of 100 in one example. The essential spirit of the cognitive NMC is that it collects network states ONLY when they matter to the network performance.