@conference {
	title = {Compositional Analysis of Dynamic Bayesian Networks and Applications to Complex Dynamic System Decomposition},
	author = {Yang, Shahan., Zhou, Yuchen., Baras, John S.},
	year = {2013},
	month = {03/2013},
	abstract = {Dynamic Bayesian networks (DBNs) can be effectively used to model various problems in complex dynamic systems. We perform an empirical investigation on compositional analysis of DBNs using abstraction. In static systems and hidden Markov models, computation of a metric called treewidth induces a tree decomposition that can be used to perform logical or probabilistic inference and max + optimizations in time exponential in treewidth and linear in overall system size. Intuitively, the linear scaling means that very large systems can be analyzed as long as they are sufficiently sparse and well structured. In these simple cases, summary propagation, which uses two operations, summation (projection) and product (composition), suffices to perform the inference or optimization. Here, we begin an extension of this to structured networks of communicating dynamic systems. We define generalizations of projection and composition operators that treat labeled Markov chains as primitive objects. The projection operation, corresponding to summation, is implemented as label deletion followed by exact state reduction for Markov chains, similar to Hopcroft{\textquoteright}s DFA minimization algorithm, with O(n log m) complexity. The composition operation is the product of state machines. We use canonical MDDs, similar to BDDs, to capture logical dependencies symbolically. Combining symbolic representations with Markov chain lumping algorithms is a novel contribution. Using this approach, we have created a tool leveraging model based systems engineering technologies. The communicating Markov chains are specified using UML Statecharts via Papyrus extended using an ANTLR parsed domain specific language (DSL). The tool reduces the number of states in networks of Markov chains by several orders of magnitude. In one example, a network having a product state space of more than 600 million states is reduced to about 500 states. A feature of this technique is that the state space is examined incrementally, meaning that the full state space is never explicitly represented, even as an input to the reduction algorithm. The primary reduction appears to come from symmetry which is surprising because the technique includes no explicit symmetry handling. We note that composition is efficient at least for systems with high symmetry. We describe applications to a hospital intensive care unit (ICU) from a systems engineering perspective.},
	address = {Atlanta, GA},
	booktitle = {Conference on Systems Engineering Research (CSER{\textquoteright}13),},
	pages = {pp. 167-176}
}
@conference {
	title = {Interactive Tree Decomposition Tool for Reducing System Analysis Complexity},
	author = {Yang, Shahan., Wang, Baobing., Baras, John S.},
	year = {2013},
	month = {03/2013},
	abstract = {We present a graphical tool for the calculation of treewidth, a metric on the parametric structure of a system that is intimately tied to the complexity of system analysis. For many graphically describable systems, such as systems of parametric equations, as in a SysML Parametric diagram, or Bayesian networks or even mind maps and writing term papers, analysis of the system is exponential in treewidth and linear in system size. A tool facilitating comprehensive analysis can serve to bring competitive advantage to a systems engineering workflow by reducing costly unanticipated behaviors. Furthermore, a byproduct of computing treewidth is a framework for enumerating computationally compatible distributed algorithms. In this paper, we pose this NP-complete problem from the perspective of finding satisficing solutions, exposing choices that can influence the complexity of the resulting system to the designer. A designer can contribute two important things to the structure of the system: a visual intuition about the relationships between the underlying objects and the ability to change the relationships themselves at design time to reduce analysis complexity. Having a visual tool that provides instant feedback will help designers achieve an intuitive grasp of the relationship between design decisions and system complexity. As complexity is the root of almost every systems engineering problem, and also something not easily understood, incorporating complexity analysis into a design process should improve resulting system designs. The tool uses a randomized, anytime algorithm for interactive optimization of treewidth. It presents a sequence of choices to a designer and incrementally lowers an upper bound on system treewidth over time. This algorithm is novel, as few algorithms are targeted at interactivity with a human user. We present a number of simple examples for using the tool. We show how our tool helps to decompose some example systems, including a quadrotor optimization, a sensor network optimization, a Bayesian network, and a mind map.},
	address = {Atlanta, GA},
	booktitle = {Conference on Systems Engineering Research (CSER{\textquoteright}13),},
	pages = {pp. 138-147}
}
