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Most existing research in wireless sensor networks focuses on optimally running a single application on top of a tailor-made and deployed network. However, as sensors become an integral part of our environments, we posit that sensor networks will be increasingly viewed as platforms that will be used to run several user applications simultaneously. Concurrently executing applications requires the network's resources to be shared across applications so as to make the best long-term utilization of the constrained devices and communications network. This resource sharing entails tradeoffs in the fidelity offered to individual applications. Fidelity is an application-dependent concept that can denote a variety of operational measures including communication latency, data quality, and redundancy. In this paper, we present a principled way to define the fidelity associated with an application given a particular allocation of the available resources. Given a desired set of applications to deploy, we also explore the impact of sharing resources among the applications in terms of fidelity degradation to individual applications. To this end, we provide an algorithm that determines the optimal subset of applications to deploy given the available resources and the potential impact on fidelity and evaluate it.