Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Single-Particle Green Functions in Exactly Solvable Models of Bose and Fermi Liquids

Based on a class of exactly solvable models of interacting bose and fermi liquids, we compute the single-particle propagators of these systems exactly for all wavelengths and energies and in any number of spatial dimensions. The field operators are expressed in terms of bose fields that correspond to displacements of the condensate in the bose case and displacements of the fermi sea in the fermi case. Unlike some of the previous attempts, the present attempt reduces the answer for the spectral function in any dimension in both fermi and bose systems to quadratures. It is shown that when only the lowest order sea-displacement terms are included, the random phase approximation in its many guises is recovered in the fermi case, and Bogoliubov's theory in the bose case. The momentum distribution is evaluated using two different approaches, exact diagonalisation and the equation of motion approach. The novelty being of course, the exact computation of single-particle properties including short wavelength behaviour.Comment: Latest version to be published in Phys. Rev. B. enlarged to around 40 page

How payment for research participation can be coercive

The idea that payment for research participation can be coercive appears widespread among research ethics committee members, researchers, and regulatory bodies. Yet analysis of the concept of coercion by philosophers and bioethicists has mostly concluded that payment does not coerce, because coercion necessarily involves threats, not offers. In this article we aim to resolve this disagreement by distinguishing between two distinct but overlapping concepts of coercion. Consent- undermining coercion marks out certain actions as impermissible and certain agreements as unenforceable. By contrast, coercion as subjection indicates a way in which someone’s interests can be partially set back in virtue of being subject to another’s foreign will. While offers of payment do not normally constitute consent-undermining coercion, they do sometimes constitute coercion as subjection. We offer an analysis of coercion as subjection and propose three possible practical responses to worries about the coerciveness of payment

“Members of the Same Club”: Challenges and Decisions Faced by US IRBs in Identifying and Managing Conflicts of Interest

Conflicts of interest (COIs) in research have received increasing attention, but many questions arise about how Institutional Review Boards (IRBs) view and approach these. Methods: I conducted in-depth interviews of 2 hours each with 46 US IRB chairs, administrators, and members, exploring COI and other issues related to research integrity. I contacted leaders of 60 IRBs (every fourth one among the top 240 institutions by NIH funding), and interviewed IRB leaders from 34 of these institutions (response rate = 55%). Data were analyzed using standard qualitative methods, informed by Grounded Theory. Results: IRBs confront financial and non-financial COIs of PIs, institutions, and IRBs themselves. IRB members may seek to help, or compete with, principal investigators (PIs). Non-financial COI also often appear to be “indirect financial” conflicts based on gain (or loss) not to oneself, but to one's colleagues or larger institution. IRBs faced challenges identifying and managing these COI, and often felt that they could be more effective. IRBs' management of their own potential COI vary, and conflicted members may observe, participate, and/or vote in discussions. Individual IRB members frequently judge for themselves whether to recuse themselves. Challenges arise in addressing these issues, since institutions and PIs need funding, financial information is considered confidential, and COI can be unconscious. Conclusions: This study, the first to explore qualitatively how IRBs confront COIs and probe how IRBs confront non-financial COIs, suggests that IRBs face several types of financial and non-financial COIs, involving themselves, PIs, and institutions, and respond varyingly. These data have critical implications for practice and policy. Disclosure of indirect and non-financial COIs to subjects may not be feasible, partly since IRBs, not PIs, are conflicted. Needs exist to consider guidelines and clarifications concerning when and how, in protocol reviews, IRB members should recuse themselves from participating, observing, and/or voting

Universality of the break-up profile for the KdV equation in the small dispersion limit using the Riemann-Hilbert approach

We obtain an asymptotic expansion for the solution of the Cauchy problem for the Korteweg-de Vries (KdV) equation in the small dispersion limit near the point of gradient catastrophe (x_c,t_c) for the solution of the dispersionless equation. The sub-leading term in this expansion is described by the smooth solution of a fourth order ODE, which is a higher order analogue to the Painleve I equation. This is in accordance with a conjecture of Dubrovin, suggesting that this is a universal phenomenon for any Hamiltonian perturbation of a hyperbolic equation. Using the Deift/Zhou steepest descent method applied on the Riemann-Hilbert problem for the KdV equation, we are able to prove the asymptotic expansion rigorously in a double scaling limit.Comment: 30 page

On critical behaviour in systems of Hamiltonian partial differential equations

We study the critical behaviour of solutions to weakly dispersive Hamiltonian systems considered as perturbations of elliptic and hyperbolic systems of hydrodynamic type with two components. We argue that near the critical point of gradient catastrophe of the dispersionless system, the solutions to a suitable initial value problem for the perturbed equations are approximately described by particular solutions to the Painlev\ue9-I (PI) equation or its fourth-order analogue P2I. As concrete examples, we discuss nonlinear Schr\uf6dinger equations in the semiclassical limit. A numerical study of these cases provides strong evidence in support of the conjecture