Dixmier traces and some applications to noncommutative geometry

This is a survey of some recent advances in the theory of singular traces in which the authors have played some part and which were inspired by questions raised by the book of Alain Connes (Noncommutative Geometry, Academic Press 1994). There are some original proofs and ideas but most of the results have appeared elsewhere. Detailed information on the contents is contained in the Introduction.Comment: To appear in Russian Mathematical Surveys (in Russian). New version corrects Latex problems, minor errors and reference

Defining Australian Indigenous wellbeing: do we really want the answer? Implications for policy and practice

ABSTRACT: Indigenous wellbeing is a current priority for the Australian Government. Given this prioritisation one might be tempted to conclude that a readily accessible and consensual definition of Indigenous wellbeing would be available. Such a definition would be important, for example, in the design and delivery of programmes of psychotherapy that aim to improve wellbeing. A literature review was undertaken to locate such a definition. In particular, the relevance of definitions to Indigenous Australians living in remote communities was of interest. While a small number of definitions are frequently cited in the literature, there is not unanimity in their acceptance. It became obvious that the terms “health” and “wellbeing” are often confused. Sometimes health is included as a component of wellbeing, sometimes wellbeing is included as a subset of health, sometimes the terms are used jointly as in “health and wellbeing”, and sometimes persuasive arguments are made that health and wellbeing are different. The politics of wellbeing is a potent theme in the literature. It seems that the indices of wellbeing that are important to the Government may not always be important to Indigenous Australians. Current Australian Government policy could be seen to be more focused on gently steering Indigenous Australians to adopt a Western style of living rather than providing opportunities for them to live lives of personal meaning and value. This tension may well be a fundamental issue in addressing Indigenous wellbeing.&nbsp

Protecting Patient Privacy: Strategies for Regulating Electronic Health Records Exchange

The report offers policymakers 10 recommendations to protect patient privacy as New York state develops a centralized system for sharing electronic medical records. Those recommendations include:Require that the electronic systems employed by HIEs have the capability to sort and segregate medical information in order to comply with guaranteed privacy protections of New York and federal law. Presently, they do not.Offer patients the right to opt-out of the system altogether. Currently, people's records can be uploaded to the system without their consent.Require that patient consent forms offer clear information-sharing options. The forms should give patients three options: to opt-in and allow providers access to their electronic medical records, to opt-out except in the event of a medical emergency, or to opt-out altogether.Prohibit and sanction the misuse of medical information. New York must protect patients from potential bad actors--that small minority of providers who may abuse information out of fear, prejudice or malice.Prohibit the health information-sharing networks from selling data. The State Legislature should pass legislation prohibiting the networks from selling patients' private health information

Spectral flow invariants and twisted cyclic theory from the Haar state on SU_q(2)

In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only non-faithful traces, namely SU_q(2), and also KMS states. Our main results are index theorems (which calculate spectral flow), one using ordinary cyclic cohomology and the other using twisted cyclic cohomology, where the twisting comes from the generator of the modular group of the Haar state. In contrast to the Cuntz algebras studied in [CPR2], the computations are considerably more complex and interesting, because there are nontrivial `eta' contributions to this index.Comment: 25 pages, 1 figur

Quantum Hall Effect and Noncommutative Geometry

We study magnetic Schrodinger operators with random or almost periodic electric potentials on the hyperbolic plane, motivated by the quantum Hall effect in which the hyperbolic geometry provides an effective Hamiltonian. In addition we add some refinements to earlier results. We derive an analogue of the Connes-Kubo formula for the Hall conductance via the quantum adiabatic theorem, identifying it as a geometric invariant associated to an algebra of observables that turns out to be a crossed product algebra. We modify the Fredholm modules defined in [CHMM] in order to prove the integrality of the Hall conductance in this case.Comment: 18 pages, paper rewritte