The calculation of expectations for classes of diffusion processes by Lie symmetry methods

This paper uses Lie symmetry methods to calculate certain expectations for a large class of It\^{o} diffusions. We show that if the problem has sufficient symmetry, then the problem of computing functionals of the form $E_x(e^{-\lambda X_t-\int_0^tg(X_s) ds})$ can be reduced to evaluating a single integral of known functions. Given a drift $f$ we determine the functions $g$ for which the corresponding functional can be calculated by symmetry. Conversely, given $g$, we can determine precisely those drifts $f$ for which the transition density and the functional may be computed by symmetry. Many examples are presented to illustrate the method.Comment: Published in at http://dx.doi.org/10.1214/08-AAP534 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Phylogeny and systematics of the giant rhinoceros beetles (Scarabaeidae: Dynastini)

This report contains the first inclusive phylogenetic analysis and taxonomic structure for the genera presently included within the scarabaeid tribe Dynastini. The study was based upon morphological, biogeographic and molecular data and yielded direct support for the recognition of three subtribes in the Dynastini: Dynastina MacLeay, New Status (Dynastes Kirby, Augosoma Burmeister, Megasoma Kirby, Golofa Hope), Xylotrupina Hope, New Status (Xylotrupes Hope, Allomyrina Arrow, Trypoxylus Minck, Xyloscaptes Prell) and Chalcosomina Rowland and Miller, New Subtribe (Chalcosoma Hope, Haploscapanes Arrow, Beckius Dechambre, Eupatorus Burmeister, Pachyoryctes Arrow). The results provide indirect but significant support for the origin of the tribe Dynastini to be of an age no later than the early Late Cretaceous. Molecular and morphological evidence suggests that Eupatorus as constituted in current taxonomic literature is not monophyletic, and taxonomic alternatives are discussed to address this deficiency. A plausible explanation is also provided for the perplexing use by F. W. Hope of the family-group names Xylotrupidae and Dynastidae

“I’m Here to Do Business. I’m Not Here to Play Games.” Work, Consumption, and Masculinity in \u3ci\u3eStorage Wars\u3c/i\u3e

This essay examines the first season of Storage Wars and suggests the program helps mediate the putative crisis in American masculinity by suggesting that traditional male skills are still essential where knowledge supplants manual labor. We read representations of “men at work” in traditionally “feminine” consumer markets, as a form of masculine recuperation situated within the culture of White male injury. Specifically, Storage Wars appropriates omnivorous consumption, thrift, and collaboration to fit within the masculine repertoire of self-reliance, individualism, and competition. Thus, the program adapts hegemonic masculinity by showcasing male auction bidders adeptly performing feminine consumer practices. Whether the feminine is assimilated into the male body or represented as its Other, we contend that the expressions of masculinity in Storage Wars render women obsolete and subjugated in the marketplaces of the 21st-century economy and contribute to the mediation of the contemporary crisis in masculinity

Lie Symmetry Methods for Multidimensional Linear, Parabolic PDES and Diffusions

In this paper we introduce methods based upon Lie symmetry analysis for the construction of explicit fundamental solutions of multidimensional parabolic PDEs. We give applications to the problem of finding transition probability densities for multidimensional diffusions and to representation theory.Lie symmetry groups; fundamental solutions; transition densities; representation theory

Lie Group Symmetries as Integral Transforms of Fundamental Solutions

We obtain fundamental solutions for PDEs of the form ut = x uxx +f(x)ux ??xru by showing that if the symmetry group of the PDE is nontrivial, it contains a standard integral transform of the fundamental solution. We show that in this case, the problem of finding a fundamental solution can be reduced to inverting a Laplace transform or some other classical transform.lie symmetry groups; fundamental solutions; transition densities; short range models; zero coupon bond pricing

Municipal Property Acquisition Patterns in a Shrinking City: Evidence for the Persistence of an Urban Growth Paradigm in Buffalo, NY

The purpose of this article is to examine municipal property acquisition patterns in shrinking cities. We use data from the City of Buffalo’s municipal property auction records to analyze the spatial distribution of properties offered for sale in its annual tax foreclosure auction. In addition to these data, we examine demolition and building permit records. Our analysis suggests that cities like Buffalo follow strategies based on an urban growth paradigm when responding to abandonment. This paradigm operates under the assumption that growth is a constant and urban development is only limited by fiscal constraints, underdeveloped systems of urban governance, environmental degradation, and resistance by anti-growth coalitions. We recommend that planners in shrinking cities de-emphasize growth based planning and focus on rightsizing strategies. These strategies are based on the assumption that growth is not a constant. Consequently, urban revitalization is concentrated in a smaller urban footprint