Why Christians Should Not Be Kaneans about Freedom

Abstract: In this paper we argue that Robert Kane’s theory of free will cannot accommodate the possibility of a sinless individual who faces morally significant choices because a sinless agent cannot voluntarily accord value to an immoral desire, and we argue that Kane’s theory requires this. Since the Jesus of the historic Christian tradition is held to be sinless, we think Christians should reject Kane’s theory because it seems irreconcilable with historic Christian Christology. We consider two objections to our argument and argue that both fail

Bose-Hubbard model with attractive interactions

We consider the Bose-Hubbard model of atoms in an optical lattice potential when the atom-atom interactions are attractive. If the lowest energy lattice sites are degenerate (such as in the homogeneous case), then, at a critical value of the interaction strength, a phase-coherent condensate becomes unstable to a quantum superposition such that the number distribution of each of the degenerate sites becomes double peaked. In the limit when the interaction dominates, the superposition becomes macroscopic and has the form $|\psi>\propto\sum_{j} e^{i\phi_{j}}\hat{b}^{\dagger N}_{j}|{\rm vac}>$, where $N$ is the total number of atoms and the sum ranges over the energy-degenerate sites.Comment: 4 pager, 5 figures, accepted for publication in PR

Income Shifting, Investment, and Tax Competition: Theory and Evidence from Provincial Taxation in Canada

We study corporate income tax competition when firms operating in multiple jurisdictions can shift income using financial planning strategies. Several such strategies, particularly intra-corporate lending, appear to be actively pursued by companies to reduce subnational corporate taxes in Canada. A simple theoretical model shows how interjurisdictional tax planning can give rise to asymmetries in jurisdictions’ tax policies, with one jurisdiction becoming a “tax haven” to attract taxable income through financial transactions, while others set higher statutory rates. Further, increased competition from tax havens may paradoxically lead to tax increases by high-tax jurisdictions. Analysis of data from administrative tax records suggests income shifting has pronounced effects on provincial tax bases in Canada. According to our preferred estimate, the elasticity of taxable income with respect to tax rates for "tax shifting" firms is 4.3, compared to 1.6 for other, comparable firms.

Limiting geodesics for first-passage percolation on subsets of Z2\mathbb{Z}^2

It is an open problem to show that in two-dimensional first-passage percolation, the sequence of finite geodesics from any point to $(n,0)$ has a limit in $n$. In this paper, we consider this question for first-passage percolation on a wide class of subgraphs of $\mathbb {Z}^2$: those whose vertex set is infinite and connected with an infinite connected complement. This includes, for instance, slit planes, half-planes and sectors. Writing $x_n$ for the sequence of boundary vertices, we show that the sequence of geodesics from any point to $x_n$ has an almost sure limit assuming only existence of finite geodesics. For all passage-time configurations, we show existence of a limiting Busemann function. Specializing to the case of the half-plane, we prove that the limiting geodesic graph has one topological end; that is, all its infinite geodesics coalesce, and there are no backward infinite paths. To do this, we prove in the Appendix existence of geodesics for all product measures in our domains and remove the moment assumption of the Wehr-Woo theorem on absence of bigeodesics in the half-plane.Comment: Published in at http://dx.doi.org/10.1214/13-AAP999 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org