A multiobjective optimization approach to obtain decision thresholds for distributed detection in wireless sensor networks.

For distributed detection in a wireless sensor network, sensors arrive at decisions about a specific event that are then sent to a central fusion center that makes global inference about the event. For such systems, the determination of the decision thresholds for local sensors is an essential task. In this paper, we study the distributed detection problem and evaluate the sensor thresholds by formulating and solving a multiobjective optimization problem, where the objectives are to minimize the probability of error and the total energy consumption of the network.

Characterization of a Class of Sigmoid Functions with Applications to Neural Networks.

We study two classes of sigmoids: the simple sigmoids, defined to be odd, asymptotically bounded, completely monotone functions in one variable, and the hyperbolic sigmoids, a proper subset of simple sigmoids and a natural generalization of the hyperbolic tangent. We obtain a complete characterization for the inverses of hyperbolic sigmoids using Euler's incomplete beta functions, and describe composition rules that illustrate how such functions may be synthesized from others. These results are applied to two problems.