variational analysis for linear circuits [4]. new, improved interval algebra that extends the classical affine form Unfortunately, not every variational problem we seek to solve has a to a more rigorous statistical foundation. Range uncertainties now tractable analytical form. What then? Monte Carlo analysis

markets. Such algorithms are desirable due to their conceptual simplicity, ease of implementation and practical-ity. This paper takes a significant step towards this goal by presenting the first Simplex-like algorithms for these mar-kets assuming a positive resolution of an algebraic problem of Cucker

for temporal reasoning and provide a complete classification of computational tractability for different time models. We also develop more general methods which can be used for proving tractability and intractability of other relational algebras. Even though most of the thesis pertains to qualitative reasoning

Abstract. We show that every biorthogonal wavelet determines a representation by operators on Hilbert space satisfying simple identities, which captures the established relationship between orthogonal wavelets and Cuntz-algebra representations in that special case. Each of these representations

of constraints, such that all the solutions to these constraints correspond to non-linear (algebraic) loop invariants of the program. We discuss some trade-offs between the completeness of the technique and the tractability of the constraint-solving problem generated. The application of the technique

The author is to be commended on the development of this new piece of methodology, which they name DoIt. We believe that the method, or later versions of the method, has the potential to be an important element in the kit-bag of non-MCMC based methods for approximate Bayesian inference. Throughout

Models are of central importance in many scientific contexts. The centrality of models such as the billiard ball model of a gas, the Bohr model of the atom, the MIT bag model of the nucleon, the Gaussian-chain model of a polymer, the Lorenz model of the atmosphere, the Lotka-Volterra model

, this research shows that machine learning can be tractably applied towards concurrent computations. This may lead to new semi-automated methodologies founded in machine learning technology for synthesizing and testing concurrent and distributed systems.

Commutative, idempotent groupoids and the

In this project, we work towards a continuous and spatial extension of stochastic π calculus. The continuous semantics is a useful alternative to the discrete semantics and has been recently provided for other process algebras. Ability to express spatial properties of the models is an important