A New Distribution-Free Concept for Representing, Comparing, and Propagating Uncertainty in Dynamical Systems with Kernel Probabilistic Programming

This work presents the concept of kernel mean embedding and kernel probabilistic programming in the context of stochastic systems. We propose formulations to represent, compare, and propagate uncertainties for fairly general stochastic dynamics in a distribution-free manner. The new tools enjoy sound theory rooted in functional analysis and wide applicability as demonstrated in distinct numerical examples. The implication of this new concept is a new mode of thinking about the statistical nature of uncertainty in dynamical systems

A comparative study of formalisms for programming language definition : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Computer Science at Massey University

This study looks at a number of methods for defining the full syntax and semantics of computer programming languages. The syntax, especially the nature of context-dependent conditions in it, is first examined, then some extensions of context-free grammars are compared to see to what extent they can encompass the full context-conditions of typical programming languages. It is found that several syntax extensions are inadequate in this regard, and that the ability to calculate complicated functions and conditions, and to eventually delete the values of such functions, is needed. This ability may be obtained either by allowing unrestricted rules and meta-variables in the phrase-structure, or by associating mathematical functions either with individual production rules or with the whole context-free structure, to transform it into an 'abstract syntax'. Since the form of a definition of a programming language semantics depends critically on how one conceives "meaning", five main types of semantics are considered: these are called 'natural', 'prepositional', 'functional', and 'structural' semantics, as well as a semantics based on string rewriting rules. The five types are compared for their success in defining the semantics of computing languages, of the example Algol-like language ALEX in particular. Among other conclusions, it is found that the semantics of structures and computations on structures is the only type sufficiently comprehensive, precise, and readable