Carleman linearization is used to transform a polynomial control system with output, defined on n-dimensional space, into a linear or bilinear system evolving in the space of infinite sequences. Such a system is described by infinite matrices with special properties. Linear observability of the original system is studied. It means that all coordinate functions can be expressed as linear combina...

In this paper we prove a class of equivalences of additive functor categories that are relevant to enumerative combinatorics, representation theory, and homotopy theory. Let X denote an additive category with finite direct sums and splitting idempotents. The class includes (a) the Dold-Puppe-Kan theorem that simplicial objects in X are equivalent to chain complexes in X ; (b) the observation of...

Termination of a stochastic context-free grammar, i.e. almost sure finiteness of the random trees it produces, is shown to be equivalent to extinction of an embedded multitype branching process. We show that the maximum likelihood estimator in a saturated model based on complete or partial observation of a finite tree always gives terminating grammars. With partial observation we show that this...

This paper presents a version of the Certainty Equivalence Principle, usable for nonlinear, variable end-time, partial observation Zero-Sum Differential Games, which states that under the unicity of the solution to the auxiliary problem, optimal controllers can be derived from the solution of the related perfect observation game. An example is provided where in one region, the new extended resu...