Against Extrinsic Dispositions

McKitrick (2003) proposes that an object has a disposition if and only if there are a manifestation, the circumstances of the manifestation, a counterfactual true of the object, and an overtly dispositional locution referring to the disposition. A disposition is extrinsic if and only if an object has it, but a perfect duplicate of the object might not have it. I present an alternative definition that an object has a disposition if and only if a counterfactual is true of the object that under a certain condition, it would interact with another object in a certain manner. There are three reasons for thinking that my definition is better than her definition. 1. Ockham’s razor favors my definition over McKitrick’s definition. My definition is consistent, while her definition is not, with Lewis’s and her definitions of intrinsic and extrinsic properties. 3. My definition goes well, while her definition does not, with our intuition that an object has a disposition even in a possible world where there is nothing but that object

Extrinsic hyperspheres in manifolds with special holonomy

We describe extrinsic hyperspheres and totally geodesic hypersurfaces in manifolds with special holonomy. In particular we prove the nonexistence of extrinsic hyperspheres in quaternion-Kaehler manifolds. We develop a new approach to extrinsic hyperspheres based on the classification of special Killing forms.Comment: published versio

Extrinsic local regression on manifold-valued data

We propose an extrinsic regression framework for modeling data with manifold valued responses and Euclidean predictors. Regression with manifold responses has wide applications in shape analysis, neuroscience, medical imaging and many other areas. Our approach embeds the manifold where the responses lie onto a higher dimensional Euclidean space, obtains a local regression estimate in that space, and then projects this estimate back onto the image of the manifold. Outside the regression setting both intrinsic and extrinsic approaches have been proposed for modeling i.i.d manifold-valued data. However, to our knowledge our work is the first to take an extrinsic approach to the regression problem. The proposed extrinsic regression framework is general, computationally efficient and theoretically appealing. Asymptotic distributions and convergence rates of the extrinsic regression estimates are derived and a large class of examples are considered indicating the wide applicability of our approach

Extrinsic Curvature Embedding Diagrams

Embedding diagrams have been used extensively to visualize the properties of curved space in Relativity. We introduce a new kind of embedding diagram based on the {\it extrinsic} curvature (instead of the intrinsic curvature). Such an extrinsic curvature embedding diagram, when used together with the usual kind of intrinsic curvature embedding diagram, carries the information of how a surface is {\it embedded} in the higher dimensional curved space. Simple examples are given to illustrate the idea.Comment: 22 pages, 4 figure

Extrinsic CPT Violation in Neutrino Oscillations

In this talk, we investigate extrinsic CPT violation in neutrino oscillations in matter with three flavors. Note that extrinsic CPT violation is different from intrinsic CPT violation. Extrinsic CPT violation is one way of quantifying matter effects, whereas intrinsic CPT violation would mean that the CPT invariance theorem is not valid. We present analytical formulas for the extrinsic CPT probability differences and discuss their implications for long-baseline experiments and neutrino factory setups.Comment: 4 pages, 1 figure, aipproc LaTeX. Talk presented at the 5th International Workshop on Neutrino Factories & Superbeams (NuFact'03), Columbia University, New York, USA, June 5-11, 2003. To be published in the Proceedings of NuFact'03 (AIP Conference Proceedings