The Markowitz Category

We give an algebraic definition of a Markowitz market and classify markets up to isomorphism. Given this classification, the theory of portfolio optimization in Markowitz markets without short selling constraints becomes trivial. Conversely, this classification shows that, up to isomorphism, there is little that can be said about a Markowitz market that is not already detected by the theory of portfolio optimization. In particular, if one seeks to develop a simplified low-dimensional model of a large financial market using mean--variance analysis alone, the resulting model can be at most two-dimensional.Comment: 1 figur

The twistor discriminant locus of the Fermat cubic

We consider the discriminant locus of the Fermat cubic under the twistor fibration $CP^3 \longrightarrow S^4$. We show that it has a conformal symmetry group of order $72$ and use this to identify its topology.Comment: 30 pages, 4 figure

Gothic Matters of De-Composition: The Pastoral Dead in Contemporary American Fiction

Against the backdrops of Terry Gifford’s post-pastoral and Fred Botting’s Gothic understanding of the literary corpse as “negative[ly] sublime,” this essay explores the fictional dead as matter unfettered by genre, consistently signifying beyond their own inanimate silences, revealing suppressed and unpalatable themes of racial and sexual violence, child abuse and cannibalistic consumerism. Along with Walker’s story, this study considers these ideas through new readings of Stephen King’s novella The Body, Raymond Carver’s story “So Much Water So Close to Home,” and The Road by Cormac McCarthy. While these writers may form an unlikely grouping in terms of style, each uses pastoral remains as significant material, deploying the dead as Gothic entities that force the reader to confront America’s darkest social and historical matters

RCAF Identity in Bomber Command: Squadron Names and Sponsors

Royal Canadian Air Force bomber squadrons which served overseas during the Second World War were not only identified on the Commonwealth air forces order of battle by the customary squadron number but by a title or nickname as well. Additionally, Canadian squadrons received formal sponsorship and support, generally from Canadian communities or other organizations. In one instance the sponsor was a major Hollywood film studio which also mobilized its roster of movie stars to the cause. Needless to say, these practices were something of a departure from the general orthodoxy within the parent RAF, where the normal practice was to identify squadrons by a unit number only. Nor were they much observed within the other Dominion air forces. But for Canada they played a part in fostering the identity and esprit of the RCAF, publicizing the contributions of Canadian bomber crews and serving the policy of Canadianization

Twistor Topology of the Fermat Cubic

We describe topologically the discriminant locus of a smooth cubic surface in the complex projective space ${\mathbb{CP}}^3$ that contains 5 fibres of the projection ${\mathbb{CP}}^3 \longrightarrow S^4$

Stochastic filtering via L2 projection on mixture manifolds with computer algorithms and numerical examples

We examine some differential geometric approaches to finding approximate solutions to the continuous time nonlinear filtering problem. Our primary focus is a new projection method for the optimal filter infinite dimensional Stochastic Partial Differential Equation (SPDE), based on the direct L2 metric and on a family of normal mixtures. We compare this method to earlier projection methods based on the Hellinger distance/Fisher metric and exponential families, and we compare the L2 mixture projection filter with a particle method with the same number of parameters, using the Levy metric. We prove that for a simple choice of the mixture manifold the L2 mixture projection filter coincides with a Galerkin method, whereas for more general mixture manifolds the equivalence does not hold and the L2 mixture filter is more general. We study particular systems that may illustrate the advantages of this new filter over other algorithms when comparing outputs with the optimal filter. We finally consider a specific software design that is suited for a numerically efficient implementation of this filter and provide numerical examples.Comment: Updated and expanded version published in the Journal reference below. Preprint updates: January 2016 (v3) added projection of Zakai Equation and difference with projection of Kushner-Stratonovich (section 4.1). August 2014 (v2) added Galerkin equivalence proof (Section 5) to the March 2013 (v1) versio