In this wIn this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace spanned by specially chosen observable functions. The Koopman operator is an infinite-dimensional linear operator that evolves functions of the state of a dynamical system. Dominant terms in the Koopman expansion are typically co...

Subjective Logic (SL) is a type of probabilistic logic, which is suitable for reasoning about situations with uncertainty and incomplete knowledge. In recent years, SL has drawn a significant amount of attention from the multi-agent systems community as it connects beliefs and uncertainty in propositions to a rigorous statistical characterization via Dirichlet distributions. However, one seriou...

Preventive diagnostics and maintenance of complex dynamic systems such as chemical plants and aircraft engines benefit from knowledge of the system components. The conditions of the components are often represented by the parameters of the system, in which case the current conditions of the components can be deduced from the variations of the system parameters about their nominal values. This p...

Planning in partially-observable dynamical systems (such as POMDPs and PSRs) is a computationally challenging task. Popular approximation techniques that have proved successful are point-based planning methods including pointbased value iteration (PBVI), which works by approximating the solution at a finite set of points. These point-based methods typically are anytime algorithms, whereby an in...

An algebraic scheme is suggested in which discretized spacetime turns out to be a quantum observable. As an example, a toy model producing spacetimes of four points with diierent topologies is presented. The possibility of incorporating this scheme into the framework of non-commutative diierential geometry is discussed.