Abstractions of stochastic hybrid systems

Many control systems have large, infinite state space that can not be easily abstracted. One method to analyse and verify these systems is reachability analysis. It is frequently used for air traffic control and power plants. Because of lack of complete information about the environment or unpredicted changes, the stochastic approach is a viable alternative. In this paper, different ways of introducing rechability under uncertainty are presented. A new concept of stochastic bisimulation is introduced and its connection with the reachability analysis is established. The work is mainly motivated by safety critical situations in air traffic control (like collision detection and avoidance) and formal tools are based on stochastic analysis

Decision-Making Under Uncertainty: Beyond Probabilities

This position paper reflects on the state-of-the-art in decision-making under uncertainty. A classical assumption is that probabilities can sufficiently capture all uncertainty in a system. In this paper, the focus is on the uncertainty that goes beyond this classical interpretation, particularly by employing a clear distinction between aleatoric and epistemic uncertainty. The paper features an overview of Markov decision processes (MDPs) and extensions to account for partial observability and adversarial behavior. These models sufficiently capture aleatoric uncertainty but fail to account for epistemic uncertainty robustly. Consequently, we present a thorough overview of so-called uncertainty models that exhibit uncertainty in a more robust interpretation. We show several solution techniques for both discrete and continuous models, ranging from formal verification, over control-based abstractions, to reinforcement learning. As an integral part of this paper, we list and discuss several key challenges that arise when dealing with rich types of uncertainty in a model-based fashion

Systems Biology of Cancer: A Challenging Expedition for Clinical and Quantitative Biologists

A systems-biology approach to complex disease (such as cancer) is now complementing traditional experience-based approaches, which have typically been invasive and expensive. The rapid progress in biomedical knowledge is enabling the targeting of disease with therapies that are precise, proactive, preventive, and personalized. In this paper, we summarize and classify models of systems biology and model checking tools, which have been used to great success in computational biology and related fields. We demonstrate how these models and tools have been used to study some of the twelve biochemical pathways implicated in but not unique to pancreatic cancer, and conclude that the resulting mechanistic models will need to be further enhanced by various abstraction techniques to interpret phenomenological models of cancer progression