This research concerns complex dynamical systems based on networks of logical gates updated and observed at discrete time intervals. Examples of such systems in contemporary technology abound, including digital logic systems, digital communication systems, and more. This is also the case, notably, of many biochemical systems, such as DNA regulatory circuits. In fact, Norbert Wiener, one of the pioneers of the modern information age, famously wrote about ?the essential unity of the set of problems centering about communication, control, and statistical mechanics, whether in the machine or in living tissue.?
This research studies a novel signal model, and corresponding optimal estimation methods, for Boolean dynamical system models under noisy observational conditions. The optimal recursive MMSE estimator for the proposed model is called the Boolean Kalman Filter (BKF). The terminology comes from the fact that this estimator is reminiscent of the (extended, unscented) Kalman filter for continuous state-spaces. The BKF also has similarities with the forward (and backward) algorithm used for state estimation in Hidden Markov Models (HMM). The methodology is applied to the inference of biochemical regulatory networks, in collaboration with the Translational Genomics Research Institute (TGen), the University of Pittsburgh, and the Oswaldo Cruz Foundation (FIOCRUZ), in Brazil.
