When controlling an autonomous system, it is inefficient or sometimes impossible for the human operator to specify detailed commands. Instead, the field of AI autonomy has developed goal-directed systems, in which human operators specify a series of goals to be accomplished. Increasingly, the control of autonomous systems involves performing a mix of discrete and continuous actions. For example...

The goal here is to recover an apocryphal result on the structure of holomorphic discrete series representations of symplectic groups Spn(R) and unitary groups U(p, q) for sufficiently high highest weight of the lowest K-type. The same sort of argument applies to other groups of hermitian type, for example the classical groups O(n, 2) and O∗(2n). For Sp(n), the maximal compact is isomorphic to ...

Let {Xn} be a stationary and ergodic time series taking values from a finite or countably infinite set X . Assume that the distribution of the process is otherwise unknown. We propose a sequence of stopping times λn along which we will be able to estimate the conditional probability P (Xλn+1 = x|X0, . . . , Xλn) from data segment (X0, . . . , Xλn) in a pointwise consistent way for a restricted ...

The design of a complete expansion that allows for compact representation of certain relevant classes of signals is a central problem in signal processing applications. Achieving such a representation means knowing the signal features for the purpose of denoising, classification, interpolation and forecasting. Multilayer Neural Networks are relatively a new class of techniques that are mathemat...