Representations of Hermitian Commutative *-Algebras by Unbounded Operators

We give a spectral theorem for unital representations of Hermitian commutative unital *-algebras by possibly unbounded operators in a pre-Hilbert space. A more general result is known for the case in which the *-algebra is countably generated

Sustaining Indigenous futures? Welfare reform and responsibility for the other

Debates about the provision of welfare over the past decade have been founded upon an increasing concern with the responsibilities of welfare recipients. In Australia, as elsewhere, the emphasis has been on recipients’ responsibility to rise above their circumstances (no matter how constraining) in order to ‘give something back’ to society. This practice of ‘responsibilisation’ has recently been extended to parents and residents of certain remote Northern Territory and Far North Queensland communities, in response to an inquiry into the protection of Aboriginal children from sexual abuse (Northern Territory Government 2007). Parents and community members have an enforceable obligation to control and civilise their own conduct as well as that of their children (see Yeend & Dow 2007). The approach to welfare reform in Indigenous communities introduced by the former Howard Government is punitive and paternalistic. Aboriginal parents and community members are subject to a new income management regime in cases of child neglect or by reason of geographical location. Indeed, in seventy-three designated Northern Territory communities the reforms are obligatory and indiscriminately applied to all residents (Altman 2007, p. 311). Income management diverts all or part of a person’s hitherto inalienable benefit payments to a special account for the provision of priority needs. Worryingly, specific details about the circumstances that trigger subjection to income management—for those who do not inhabit prescribed NT communities—and the precise meaning of priority needs are not spelt out in legislation. The bill also eschews the principle of antidiscrimination (Yeend & Dow 2007, pp. 7, 4). Influential Indigenous leader Noel Pearson (2000) has long supported this kind of intervention as part of a broader solution to community dysfunction, child abuse and neglect. Indeed, the legislation implements Cape York welfare reform trials that extend income management and other measures to specified Far North Queensland communities based on recommendations put forward by Pearson and the Cape York Institute (2007). Pearson’s support for welfare reform is, however, grounded in albeit a contested positive alternative vision of reciprocal responsibility, economic development and selfdetermination. Broadly bipartisan support indicates that the latest welfare reform measures are likely to have a significant effect on the future of Indigenous citizenship. While the Howard Government has recently been replaced by a more progressive Labor government, the new government remains committed to the changes in their current form until a review scheduled for mid-2008. The review, as well as the more collaborative approach of the current government, renders careful critical analysis and public scrutiny of Indigenous welfare reform an urgent and productive task. Drawing on the work of Emmanuel Levinas (1969), this paper questions the normative assumptions underpinning these changes. Negatively, I question two frameworks for thinking about responsibility that inform Indigenous welfare reform; namely, protection and mutual obligation. Positively, I argue for an alternative approach to welfare reform that both foregrounds a sense of responsibility for the other and sustains alterity

Group Frames with Few Distinct Inner Products and Low Coherence

Frame theory has been a popular subject in the design of structured signals and codes in recent years, with applications ranging from the design of measurement matrices in compressive sensing, to spherical codes for data compression and data transmission, to spacetime codes for MIMO communications, and to measurement operators in quantum sensing. High-performance codes usually arise from designing frames whose elements have mutually low coherence. Building off the original "group frame" design of Slepian which has since been elaborated in the works of Vale and Waldron, we present several new frame constructions based on cyclic and generalized dihedral groups. Slepian's original construction was based on the premise that group structure allows one to reduce the number of distinct inner pairwise inner products in a frame with $n$ elements from $\frac{n(n-1)}{2}$ to $n-1$. All of our constructions further utilize the group structure to produce tight frames with even fewer distinct inner product values between the frame elements. When $n$ is prime, for example, we use cyclic groups to construct $m$-dimensional frame vectors with at most $\frac{n-1}{m}$ distinct inner products. We use this behavior to bound the coherence of our frames via arguments based on the frame potential, and derive even tighter bounds from combinatorial and algebraic arguments using the group structure alone. In certain cases, we recover well-known Welch bound achieving frames. In cases where the Welch bound has not been achieved, and is not known to be achievable, we obtain frames with close to Welch bound performance

An intersection in population control: Welfare reform and indigenous people with a partial capacity to work in the Australian Northern Territory

In Australia, in the last decade, there have been significant policy changes to income support payments for people with a disability and Indigenous people. These policy reforms intersect in the experience of Indigenous people with a partial capacity to work in the Northern Territory who are subject to compulsory income management if classified as long-term welfare payment recipients. This intersection is overlooked in existing research and government policy. In this article, we apply intersectionality and Southern disability theory as frameworks to analyse how Indigenous people with a partial capacity to work (PCW) in the Northern Territory are governed under compulsory income management. Whilst the program is theoretically race and ability neutral, in practice it targets specific categories of people because it fails to address the structural and cultural barriers experienced by Indigenous people with a disability and reinscribes disabling and colonising technologies of population control

Theory of the critical state of low-dimensional spin glass

We analyse the critical region of finite-($d$)-dimensional Ising spin glass, in particular the limit of $d$ closely above the lower critical dimension $d_\ell$. At criticality the thermally active degrees of freedom are surfaces (of width zero) enclosing clusters of spins that may reverse with respect to their environment. The surfaces are organised in finite interacting structures. These may be called {\em protodroplets}\/, since in the off-critical limit they reduce to the Fisher and Huse droplets. This picture provides an explanation for the phenomenon of critical chaos discovered earlier. It also implies that the spin-spin and energy-energy correlation functions are multifractal and we present scaling laws that describe them. Several of our results should be verifiable in Monte Carlo studies at finite temperature in $d=3$.Comment: RevTeX, 33 pages + 1 PostScript figure (uuencoded). Uses german.sty and an input file def.tex, joined. Three additional figures may be requested from the author