We set up a general framework for higher order probabilities. A simple HOP (Higher Order Probability space) consists of a probability space and an operation PR, such that, for every event A and every real closed interval zL PR(A ,A) is the event that A's "true" probability lies in A. (The ' t rue" probability can be construed here either as the objective probability, or the probability assigned...

We develop a general tool to formalize and reason about languages expressed using higher-order abstract syntax in a proof-tool based on type theory (Coq). A language is specified by its signature, which consists of sets of sort and operation names and typing rules. These rules prescribe the sorts and bindings of each operation. An algebra of terms is associated to a signature, using de Bruijn n...

Michael Fowler 03/07/06 The Interaction Representation Recall that in the first part of this course sequence, we discussed the Schrödinger and Heisenberg representations of quantum mechanics here. In the Schrödinger representation, the operators are time-independent (except for explicitly time-dependent potentials) the kets representing the quantum states develop in time. In the Heisenberg repr...

We show how the abstract theory of (complete, boolean) lattices can be for-malised as a theory in the HOL theorem prover. The abstract lattice theory can be instantiated for concrete cases, providing immediate instantiations of many useful results. In particular, we treat the abstract theory of function lattices as an instantiation of the abstract lattice theory.

The majority of general purpose mechanised proof assistants support versions of typed higher order logic, even though set theory is the standard foundation for mathematics. For many applications higher order logic works well and provides, for speciication, the beneets of type-checking that are well-known in programming. However, there are areas where types get in the way or seem unmotivated. Fu...

The theory of the periodic structure of nth-order statistics of cyclostationary time-series is developed. This theory is the generalization of the existing theory of the periodic structure of second-order moments of cyclostationary time-series to orders greater than two and is therefore called the theory of higher-order cyclostationarity. The theory’s central parameters are moments and cumulant...

The present status of higher-order results in the electroweak theory is summarised, with particular emphasis on recent two-loop results for the prediction of the W-boson mass in the Standard Model and leading three-loop corrections to the rho parameter. The remaining theoretical uncertainties in the prediction for the W-boson mass and the effective weak mixing angle are discussed. PACS. 12.15.L...

We present a higher-order calculus ECC which naturally combines Coquand-Huet's calculus of constructions and Martin-LL of's type theory with universes. ECC is very expressive, both for structured abstract reasoning and for program speciication and construction. In particular , the strong sum types together with the type universes provide a useful module mechanism for abstract description of mat...

We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from Kähler potential. The classical action has s...