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In Dynamic Data-Driven Application Systems (DDDAS), applications must dynamically adapt their behavior in response to objectives and conditions that change while deployed. Often these applications may be safety critical or tightly resource constrained, with a need for graceful degradation when introduced to unexpected conditions. This paper begins by motivating and providing a vision for a dynamically adaptable mixed critical computing platform to support DDDAS applications. The authors then specifically focus on the need for advancements in task models and scheduling algorithms to manage the resources of such a platform.