Abelian, amenable operator algebras are similar to C*-algebras

Suppose that H is a complex Hilbert space and that B(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C*-algebra. We do this by showing that if A is an abelian subalgebra of B(H) with the property that given any bounded representation $\varrho: A \to B(H_\varrho)$ of A on a Hilbert space $H_\varrho$, every invariant subspace of $\varrho(A)$ is topologically complemented by another invariant subspace of $\varrho(A)$, then A is similar to an abelian $C^*$-algebra

Large-Scale Integration of Nanoelectromechanical Systems for Gas Sensing Applications

We have developed arrays of nanomechanical systems (NEMS) by large-scale integration, comprising thousands of individual nanoresonators with densities of up to 6 million NEMS per square centimeter. The individual NEMS devices are electrically coupled using a combined series-parallel configuration that is extremely robust with respect to lithographical defects and mechanical or electrostatic-discharge damage. Given the large number of connected nanoresonators, the arrays are able to handle extremely high input powers (>1 W per array, corresponding to <1 mW per nanoresonator) without excessive heating or deterioration of resonance response. We demonstrate the utility of integrated NEMS arrays as high-performance chemical vapor sensors, detecting a part-per-billion concentration of a chemical warfare simulant within only a 2 s exposure period

Withdrawing an explicit request for euthanasia or physician-assisted suicide: a retrospective study on the influence of mental health status and other patient characteristics

BACKGROUND: Mental health status may be closely related to an instability of intentions toward a premature death, but little is known about such instability following an explicit request for euthanasia or physician-assisted suicide (EAS) and patient characteristics associated with a change of mind. METHOD: A questionnaire was sent to 6596 general practitioners in The Netherlands (response rate 60%). Of these, 1681 provided descriptions of the most recent explicit request for EAS they had received in the preceding 18 months. RESULTS: Symptoms of depression and anxiety were related to a change of mind, but no relationship was found with the total score of the NOSGER Mood Dimension. Multinomial regression analysis revealed that patients who changed their mind had more mental health problems and less mental clarity than those who died by EAS. They also had fewer general health problems, had less unbearable and pointless suffering (according to the physician), were less concerned about loss of dignity and alternative treatment options were more frequently available. A further analysis revealed that mental health problems were more prevalent among patients whose requests were refused than among those who changed their mind. The physicians' evaluations of the reasons why a patient requested EAS were similar to a more objective measure of the patient characteristics. CONCLUSIONS: These findings suggest that mental health status must be carefully assessed, and possible instability of desire must be taken into account in the course of a request for EAS. These results require replication, and future studies should adopt a prospective metho

Abelian, amenable operator algebras are similar to C∗ -algebras

Originally published by Duke University PressSuppose that H is a complex Hilbert space and that ℬ(H) denotes the bounded linear operators on H. We show that every abelian, amenable operator algebra is similar to a C∗-algebra. We do this by showing that if ⊆ℬ(H) is an abelian algebra with the property that given any bounded representation ϱ:→ℬ(Hϱ) of on a Hilbert space Hϱ, every invariant subspace of ϱ() is topologically complemented by another invariant subspace of ϱ(), then is similar to an abelian C∗-algebra.Natural Sciences and Engineering Research Council (NSERC

Multi-Armed Bandits for Correlated Markovian Environments with Smoothed Reward Feedback

We study a multi-armed bandit problem in a dynamic environment where arm rewards evolve in a correlated fashion according to a Markov chain. Different than much of the work on related problems, in our formulation a learning algorithm does not have access to either a priori information or observations of the state of the Markov chain and only observes smoothed reward feedback following time intervals we refer to as epochs. We demonstrate that existing methods such as UCB and $\varepsilon$-greedy can suffer linear regret in such an environment. Employing mixing-time bounds on Markov chains, we develop algorithms called EpochUCB and EpochGreedy that draw inspiration from the aforementioned methods, yet which admit sublinear regret guarantees for the problem formulation. Our proposed algorithms proceed in epochs in which an arm is played repeatedly for a number of iterations that grows linearly as a function of the number of times an arm has been played in the past. We analyze these algorithms under two types of smoothed reward feedback at the end of each epoch: a reward that is the discount-average of the discounted rewards within an epoch, and a reward that is the time-average of the rewards within an epoch.Comment: Significant revision of prior version including deeper discussion of related work, gap-independent regret bounds, and regret bounds for discounted reward

On selfadjoint extensions of semigroups of partial isometries

First published in Transactions of the American Mathematical Society in volume 368, 2016, published by the American Mathematical Society. https://doi.org/10.1090/tran/6619Let S be a semigroup of partial isometries acting on a complex, infinite- dimensional, separable Hilbert space. In this paper we seek criteria which will guarantee that the selfadjoint semigroup T generated by S consists of partial isometries as well. Amongst other things, we show that this is the case when the set Q(S) of final projections of elements of S generates an abelian von Neumann algebra of uniform finite multiplicity.Research supported in part by ARRS (Slovenia). Research supported in part by NSERC (Canada)

Apparent diffusion coefficient restriction in the white matter: going beyond acute brain territorial ischemia

BACKGROUND: Reduction of apparent diffusion coefficient (ADC) values in white matter is not always ischaemic in nature. METHODS: We retrospectively analysed our MRI records featuring reduced ADC values in the centrum semiovale without grey matter involvement or significant vasogenic oedema. RESULTS: Several conditions showed the aforementioned MR findings: moose-horn lesions on coronal images in X-linked Charcot-Marie-Tooth disease; small fronto-parietal lesions in Menkes disease; marked signal abnormalities in the myelinised regions in the acute neonatal form of maple syrup urine disease; strip-like involvement of the corpus callosum in glutaric aciduria type 1; persistent periventricular parieto-occipital abnormalities in phenylketonuria; diffuse signal abnormalities with necrotic evolution in global cerebral anoxia or after heroin vapour inhalation; almost completely reversible symmetric fronto-parietal lesions in methotrexate neurotoxicity; chain-like lesions in watershed ischaemia; splenium involvement that normalises in reversible splenial lesions or leads to gliosis in diffuse axonal injury. CONCLUSION: Neuroradiologists must be familiar with these features, thereby preventing misdiagnosis and inappropriate management