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We have created a logic-based, Turing-complete language for stochastic modeling. Since the inference scheme for this language is based on a variant of Pearl's loopy belief propagation algorithm, we call it Loopy Logic. Traditional Bayesian networks have limited expressive power, basically constrained to finite domains as in the propositional calculus. Our language contains variables that can capture general classes of situations, events and relationships. A first-order language is also able to reason about potentially infinite classes and situations using constructs such as hidden Markov models(HMMs). Our language uses an Expectation-Maximization (EM) type learning of parameters. This has a natural fit with the Loopy Belief Propagation used for inference since both can be viewed as iterative message passing algorithms. We present the syntax and theoretical foundations for our Loopy Logic language. We then demonstrate three examples of stochastic modeling and diagnosis that explore the representational power of the language. A mechanical fault detection example displays how Loopy Logic can model time-series processes using an HMM variant. A digital circuit example exhibits the probabilistic modeling capabilities, and finally, a parameter fitting example demonstrates the power for learning unknown stochastic values.

We demonstrate through numerical simulation the modification of the thermal emission spectrum by a metallic photonic crystal (PhC). Here the radiation is funneled into a narrow emission band in contrast to the broad spectrum associated with a Planckian-distribution. A detailed quantitative evaluation of the spectral, power, and angular efficiencies of a PhC thermal emitter and its portability across IR spectral bands is provided. We show that an optimized tungsten PhC possesses a predominant narrow-band forward emission profile with an emitter efficiency that is more than double that of an ideal blackbody and ∼65–75% more power-efficient across the IR spectrum.

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