We consider a class of stochastic models for which the performance measure is deened as a mathematical expectation that depends on a parameter , say (), and we are interested in constructing estimators of in functional form (i.e., entire functions of), which can be computed from a single simulation experiment. We focus on the case where is a continuous parameter, and also consider estimation of...

Emotional states of consciousness, or what are typically called emotional feelings, are traditionally viewed as being innately programmed in subcortical areas of the brain, and are often treated as different from cognitive states of consciousness, such as those related to the perception of external stimuli. We argue that conscious experiences, regardless of their content, arise from one system ...

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...