I give an overview/summary of the techniques used, and the results derived, in my 1984 PhD dissertation, Reducibility and Determinateness on the Baire Space. In particular, I focus on the calculation of the order type (and structure) of the collection of degrees of Borel sets.

To most applied statisticians, a fitting procedure's degrees of freedom is synonymous with its model complexity, or its capacity for overfitting to data. In particular, it is often used to parameterize the bias-variance tradeoff in model selection. We argue that, on the contrary, model complexity and degrees of freedom may correspond very poorly. We exhibit and theoretically explore various fit...

The Prisoner's Dilemma has been widely studied as a model for the evolution of cooperation, and most of this work has dealt with agents who either cooperate or not. In this paper we look at the consequences of allowing agents to have intermediate levels of cooperation, and to update these levels over time. The familiar strategy of "tit for tat" emerges as a robust mode of behaviour, yet there a...

Interactions in the perception of motion transparency were investigated using a signal-detection paradigm. The stimuli were the linear sum of two independent, moving, random-check "signal" textures and a third texture consisting of dynamic random "noise." Performance was measured as the ratio of squared signal and noise contrasts was varied (S2/N2). Motion detectability was poorest when the two...

The present research examined two variables regarding the acquisition of a new bimanual coordination pattern: the role of previous experience and the nature of augmented feedback. Two groups of participants acquired a new coordination pattern (135 degrees relative phase) following two sessions of practice of another novel pattern (90 degrees relative phase). Transfer of learning in these groups...

We give an alternative definition of the enumeration jump operator. We prove that the class of total enumeration degrees and the class of low enumeration degrees are first order definable in the local structure of the enumeration degrees.

The Dirac structure of confinement is shown to be of timelike-vector nature in the heavy quark limit of QCD. This stands in contradiction with the phenomenological success of the Dirac scalar confining potential. A resolution is achieved through the demonstration that an effective scalar interaction is dynamically generated by nonperturbative mixing between ordinary and hybrid QQ̄ states. The re...

We prove that for many degrees in a stable range the homotopy groups of the moduli space of metrics of positive scalar curvature on S and on other manifolds are non-trivial. This is achieved by further developing and then applying a family version of the surgery construction of Gromov-Lawson to an exotic smooth families of spheres due to Hatcher.