Evolution of the probability distribution function of galaxies in redshift-space

We present a new analytic calculation for the redshift-space evolution of the 1-point galaxy Probability Distribution Function (PDF). The nonlinear evolution of the matter density field is treated by second-order Eulerian perturbation theory and transformed to the galaxy density field via a second-order local biasing scheme. We then transform the galaxy density field to redshift space, again to second order. Our method uses an exact statistical treatment based on the Chapman-Kolmogorov equation to propagate the probability distribution of the initial mass field to the final redshifted galaxy density field. We derive the moment generating function of the PDF and use it to find a new, closed-form expression for the skewness of the redshifted galaxy distribution. We show that our formalism is general enough to allow a non-deterministic (or stochastic) biasing prescription. We demonstrate the dependence of the redshift space PDF on cosmological and biasing parameters. Our results are compared with existing models for the PDF in redshift space and with the results of biased N-body simulations. We find that our PDF accurately models the redshift space evolution and the nonlinear biasing.Comment: 15 pages, 7 figures, submitted to MNRA

Evolution of the cosmological density distribution function

We present a new calculation for the evolution of the 1-point Probability Distribution Function (PDF) of the cosmological density field based on an exact statistical treatment. Using the Chapman-Kolmogorov equation and second-order Eulerian perturbation theory we propagate the initial density distribution into the nonlinear regime. Our calculations yield the moment generating function, allowing a straightforward derivation of the skewness of the PDF to second order. We find a new dependency on the initial perturbation spectrum. We compare our results with other approximations to the 1-pt PDF, and with N-body simulations. We find that our distribution accurately models the evolution of the 1-pt PDF of dark matter.Comment: 7 pages, 7 figures, accepted for publication in MNRA

Cartan Calculus on Quantum Lie Algebras

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum spaces we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra, the ``Cartan Calculus''. (This is an extended version of a talk presented by P. Schupp at the XXII$^{th}$ International Conference on Differential Geometric Methods in Theoretical Physics, Ixtapa, Mexico, September 1993)Comment: 15 pages in LaTeX, LBL-34833 and UCB-PTH-93/3

Cartan Calculus for Hopf Algebras and Quantum Groups

A generalization of the differential geometry of forms and vector fields to the case of quantum Lie algebras is given. In an abstract formulation that incorporates many existing examples of differential geometry on quantum groups, we combine an exterior derivative, inner derivations, Lie derivatives, forms and functions all into one big algebra. In particular we find a generalized Cartan identity that holds on the whole quantum universal enveloping algebra of the left-invariant vector fields and implicit commutation relations for a left-invariant basis of 1-forms.Comment: 15 pages (submitted to Comm. Math. Phys.

Illness as ethical practice: Truth & subjectivity, governmentality & freedom in HIV/AIDS discourse

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This thesis aims to understand the connexions between the ethical practices associated with suffering a chronic illness and possibilities of truth, subjectivity, governmentality and freedom. This is attempted via an analysis of the specific case of HIV/AIDS. In the 1980s there emerged a variety of competing ways to construct the truth of HIV/AIDS. By the early 1990s, however, one particular way of thinking about and problematizing the syndrome - an account which reflected less the repressive intentions and perspectives of recently ascendant neo-liberal governments than the efforts and world-views of grass-roots community activism - had achieved ascendancy. This approach to HIV/AIDS remains today the authoritative one, and that from which expertise on the subject is derived. The emergence to pre-eminence of this way of thinking about HIV/AIDS is mapped, and three of its principal manifestations are examined in detail, using techniques of textual analysis. It is argued that within these texts, through the use of various forms of textual management, ethical subject relations of the sort discussed by Foucault are constructed, which delimit the possibilities of being for those who are touched by the disease, and which comprise elements of an ethico-panoptic regulatory technology. The parallels and differences between the technologies of government articulated via these 'community' based discourses and those of recent neo-liberal discourses are explored, with consideration being given to their implications for the practising of resistance and of freedom by people infected or affected by HIV or AIDS. Engagement with the field in this fashion is uncommon within sociology of HIV/AIDS, and to do so raises a variety of conceptual and methodological issues. Hence, within this thesis the task of interrogating HIV/AIDS discourse is radically linked to the construction of a distinct form of sociology, derived from the Foucauldian project of the 'history of the present'