Simulations, along with other similar applications like virtual worlds and video games, require computational models of intelligence that generate realistic and credible behavior for the participating synthetic characters. Cognitive architectures, which are models of the fixed structure underlying intelligent behavior in both natural and artificial systems, provide a conceptually valid common basis, as evidenced by the current efforts towards a standard model of the mind, to generate human-like intelligent behavior for these synthetic characters. Developments in the field of artificial intelligence, mainly in probabilistic graphical models and neural networks, open up new opportunities for cognitive architectures to make the synthetic characters more autonomous and to enrich their behavior. Sigma (Σ) is a cognitive architecture and system that strives to combine what has been learned from four decades of independent work on symbolic cognitive architectures, probabilistic graphical models, and more recently neural models, under its graphical architecture hypothesis. Sigma leverages an extended form of factor graphs towards a uniform grand unification of not only traditional cognitive capabilities but also key non-cognitive aspects, creating unique opportunities for the construction of new kinds of cognitive models that possess a Theory-of-Mind and that are perceptual, autonomous, interactive, affective, and adaptive. In this paper, we will introduce Sigma along with its diverse capabilities and then use three distinct proof-of-concept Sigma models to highlight combinations of these capabilities: (1) Distributional reinforcement learning models in a simple OpenAI Gym problem; (2) A pair of adaptive and interactive agent models that demonstrate rule-based, probabilistic, and social reasoning in a physical security scenario instantiated within the SmartBody character animation platform; and (3) A knowledge-free exploration model in which an agent leverages only architectural appraisal variables, namely attention and curiosity, to locate an item while building up a map in a Unity environment.