The complexity class of Πpk-Polynomial Local Search (PLS) problems with Πp` -goal is introduced, and is used to give new characterisations of definable search problems in fragments of Bounded Arithmetic. The characterisations are established via notations for propositional proofs obtained by translating Bounded Arithmetic proofs using the Paris-Wilkie-translation. For ` ≤ k, the Σ`+1-definable ...

Title of dissertation: MICROTURBULENT TRANSPORT OF NON-MAXWELLIAN ALPHA PARTICLES George John Wilkie, Doctor of Philosophy, 2015 Dissertation directed by: Professor William Dorland Department of Physics A burning Deuterium-Tritium plasma is one which depends upon fusion-produced alpha particles for self-heating. Whether a plasma can reach a burning state requires knowledge of the transport of a...

This paper studies environments where individuals allocate resources across relationships with others, creating a weighted, directed network. Value is achieved both through an exogenous factor and maintaining close connections to high-value individuals. We consider two cases corresponding to the direction benefits flow along links. In Model A (for “asking”) agents receive benefits through the l...

The paper reports micro-econometric evidence on the factors that influence self-employment choice, earnings and the ability of the self-employed to generate employment for others. It uses recent longitudinal data for the UK, and is therefore able to exploit multiple observations on the same individual to control for unobserved heterogeneity, and mitigate problems of endogeneity which trouble cr...

In this thesis, I explore Isaacson’s thesis and Wilkie’s theorem, providing philosophical and formal results on how they relate to each other. At a first approximation, Isaacson’s thesis claims that Peano arithmetic is sound and complete with respect to genuinely arithmetical statements. Using internalist notions familiar from recent work on internal categoricity theorems, I provide a formal de...

1 Drawing borders Logic arose in Antiquity from two sources: the study of real argumentation in the dialectical tradition, and that of axiom-based proof patterns organizing scientific inquiry. Over the centuries that followed, the discipline turned abstract and eventually, profoundly mathematical. Is logic still about human reasoning? Or is it, as Kant and Bolzano said, about an abstraction in ...

We study a family of diffusion models for risk reserves which account for the investment income earned and for the inflation experienced on claim amounts. After we defined the process of the conditional probability of ruin over finite time and imposed the appropriate boundary conditions, classical results from the theory of diffusion processes turn the stochastic differential equation to a spec...

We discuss the data available for the TSE 300 and S&P 500 total return indexes. We consider a number of models, including the Wilkie model and regime switching models. We discuss calibration by maximum likelihood and by Markov chain Monte Carlo for the regime switching lognormal model. We then show how to use this model to price and hedge simple segregated fund maturity guarantees. keywords: Re...

We study a model of common value auctions in which bidders’ private information are independently and asymmetrically distributed. We provide two sufficient conditions under which a first-price auction generates higher revenue than a second-price auction (for a selected equilibrium). A necessary condition is given for this revenue-ranking result to hold in general. We illustrate that in a first-...

Financial literacy and cognitive capabilities are convincingly linked to the quality of financial decision-making, influencing savings, stock-picking, and avoidance of outright financial mistakes. Yet, there is little evidence that education intended to improve financial decision-making is successful. Using plausibly exogenous variation in exposure to state-mandated personal finance and mathema...