Two Forms of Inconsistency in Quantum Foundations

Recently, there has been some discussion of how Dutch Book arguments might be used to demonstrate the rational incoherence of certain hidden variable models of quantum theory (Feintzeig and Fletcher 2017). In this paper, we argue that the 'form of inconsistency' underlying this alleged irrationality is deeply and comprehensively related to the more familiar 'inconsistency' phenomenon of contextuality. Our main result is that the hierarchy of contextuality due to Abramsky and Brandenburger (2011) corresponds to a hierarchy of additivity/convexity-violations which yields formal Dutch Books of different strengths. We then use this result to provide a partial assessment of whether these formal Dutch Books can be interpreted normatively.Comment: 26 pages, 5 figure

Preference-Theoretic Weak Complementarity: Getting More with Less

A preference-theoretic characterization of weak complementarity is provided based on an explicit representation of revealed preference. Weak complementarity is defined in terms of the observable property of nonessentiality and the unobservable property of no existence value. Preference-theoretic characterizations of these properties facilitate a precision and intuition that is not generally available within the existing calculus-based literature. An exact welfare measure is specified that does not require a continuous nonmarket good or monotonic preference on the nonmarket good, and which can be easily generalized to accommodate infinite choke prices. It is shown that no existence value can be rejected by revealed preference, contradicting a widely stated assertion within the literature. Even though no existence value is unobservable, it does require an observable condition that is nontrivial with three or more market goods.

The cardiac bidomain model and homogenization

We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To allow for some relevant nonlinear membrane models, we make essential use of the boundary unfolding operator. There are several complications preventing the application of standard homogenization results, including the degenerate temporal structure of the bidomain equations and a nonlinear dynamic boundary condition on an oscillating surface.Comment: To appear in Networks and Heterogeneous Media, Special Issue on Mathematical Methods for Systems Biolog