Surgery and the spinorial tau-invariant

We associate to a compact spin manifold M a real-valued invariant \tau(M) by taking the supremum over all conformal classes over the infimum inside each conformal class of the first positive Dirac eigenvalue, normalized to volume 1. This invariant is a spinorial analogue of Schoen's $\sigma$-constant, also known as the smooth Yamabe number. We prove that if N is obtained from M by surgery of codimension at least 2, then $\tau(N) \geq \min\{\tau(M),\Lambda_n\}$ with $\Lambda_n>0$. Various topological conclusions can be drawn, in particular that \tau is a spin-bordism invariant below $\Lambda_n$. Below $\Lambda_n$, the values of $\tau$ cannot accumulate from above when varied over all manifolds of a fixed dimension.Comment: to appear in CPD

The Cauchy problems for Einstein metrics and parallel spinors

We show that in the analytic category, given a Riemannian metric $g$ on a hypersurface $M\subset \Z$ and a symmetric tensor $W$ on $M$, the metric $g$ can be locally extended to a Riemannian Einstein metric on $Z$ with second fundamental form $W$, provided that $g$ and $W$ satisfy the constraints on $M$ imposed by the contracted Codazzi equations. We use this fact to study the Cauchy problem for metrics with parallel spinors in the real analytic category and give an affirmative answer to a question raised in B\"ar, Gauduchon, Moroianu (2005). We also answer negatively the corresponding questions in the smooth category.Comment: 28 pages; final versio

A spinorial energy functional: critical points and gradient flow

On the universal bundle of unit spinors we study a natural energy functional whose critical points, if dim M \geq 3, are precisely the pairs (g, {\phi}) consisting of a Ricci-flat Riemannian metric g together with a parallel g-spinor {\phi}. We investigate the basic properties of this functional and study its negative gradient flow, the so-called spinor flow. In particular, we prove short-time existence and uniqueness for this flow.Comment: Small changes, final versio

Timed Implementation Relations for the Distributed Test Architecture

In order to test systems that have physically distributed interfaces, called ports, we might use a distributed approach in which there is a separate tester at each port. If the testers do not synchronise during testing then we cannot always determine the relative order of events observed at different ports and this leads to new notions of correctness that have been described using corresponding implementation relations. We study the situation in which each tester has a local clock and timestamps its observations. If we know nothing about how the local clocks relate then this does not affect the implementation relation while if the local clocks agree exactly then we can reconstruct the sequence of observations made. In practice, however, we are likely to be between these extremes: the local clocks will not agree exactly but we have some information regarding how they can differ. We start by assuming that a local tester interacts synchronously with the corresponding port of the system under test and then extend this to the case where communications can be asynchronous, considering both the first-in-first-out (FIFO) case and the non-FIFO case. The new implementation relations are stronger than implementation relations for distributed testing that do not use timestamps but still reflect the distributed nature of observations. This paper explores these alternatives and derives corresponding implementation relations

Using schedulers to test probabilistic distributed systems

This is the author's accepted manuscript. The final publication is available at Springer via http://dx.doi.org/10.1007/s00165-012-0244-5. Copyright © 2012, British Computer Society.Formal methods are one of the most important approaches to increasing the confidence in the correctness of software systems. A formal specification can be used as an oracle in testing since one can determine whether an observed behaviour is allowed by the specification. This is an important feature of formal testing: behaviours of the system observed in testing are compared with the specification and ideally this comparison is automated. In this paper we study a formal testing framework to deal with systems that interact with their environment at physically distributed interfaces, called ports, and where choices between different possibilities are probabilistically quantified. Building on previous work, we introduce two families of schedulers to resolve nondeterministic choices among different actions of the system. The first type of schedulers, which we call global schedulers, resolves nondeterministic choices by representing the environment as a single global scheduler. The second type, which we call localised schedulers, models the environment as a set of schedulers with there being one scheduler for each port. We formally define the application of schedulers to systems and provide and study different implementation relations in this setting

The reductive activation of CO2 across a Ti═Ti double bond: synthetic, structural, and mechanistic studies

[Image: see text] The reactivity of the bis(pentalene)dititanium double-sandwich compound Ti(2)Pn(†)(2) (1) (Pn(†) = 1,4-{Si(i)Pr(3)}(2)C(8)H(4)) with CO(2) is investigated in detail using spectroscopic, X-ray crystallographic, and computational studies. When the CO(2) reaction is performed at −78 °C, the 1:1 adduct 4 is formed, and low-temperature spectroscopic measurements are consistent with a CO(2) molecule bound symmetrically to the two Ti centers in a μ:η(2),η(2) binding mode, a structure also indicated by theory. Upon warming to room temperature the coordinated CO(2) is quantitatively reduced over a period of minutes to give the bis(oxo)-bridged dimer 2 and the dicarbonyl complex 3. In situ NMR studies indicated that this decomposition proceeds in a stepwise process via monooxo (5) and monocarbonyl (7) double-sandwich complexes, which have been independently synthesized and structurally characterized. 5 is thermally unstable with respect to a μ-O dimer in which the Ti–Ti bond has been cleaved and one pentalene ligand binds in an η(8) fashion to each of the formally Ti(III) centers. The molecular structure of 7 shows a “side-on” bound carbonyl ligand. Bonding of the double-sandwich species Ti(2)Pn(2) (Pn = C(8)H(6)) to other fragments has been investigated by density functional theory calculations and fragment analysis, providing insight into the CO(2) reaction pathway consistent with the experimentally observed intermediates. A key step in the proposed mechanism is disproportionation of a mono(oxo) di-Ti(III) species to yield di-Ti(II) and di-Ti(IV) products. 1 forms a structurally characterized, thermally stable CS(2) adduct 8 that shows symmetrical binding to the Ti(2) unit and supports the formulation of 4. The reaction of 1 with COS forms a thermally unstable complex 9 that undergoes scission to give mono(μ-S) mono(CO) species 10. Ph(3)PS is an effective sulfur transfer agent for 1, enabling the synthesis of mono(μ-S) complex 11 with a double-sandwich structure and bis(μ-S) dimer 12 in which the Ti–Ti bond has been cleaved

Mitochondrial phylogeography and demographic history of the Vicuña: implications for conservation

The vicuña (Vicugna vicugna; Miller, 1924) is a conservation success story, having recovered from near extinction in the 1960s to current population levels estimated at 275 000. However, lack of information about its demographic history and genetic diversity has limited both our understanding of its recovery and the development of science-based conservation measures. To examine the evolution and recent demographic history of the vicuña across its current range and to assess its genetic variation and population structure, we sequenced mitochondrial DNA from the control region (CR) for 261 individuals from 29 populations across Peru, Chile and Argentina. Our results suggest that populations currently designated as Vicugna vicugna vicugna and Vicugna vicugna mensalis comprise separate mitochondrial lineages. The current population distribution appears to be the result of a recent demographic expansion associated with the last major glacial event of the Pleistocene in the northern (18 to 22°S) dry Andes 14–12 000 years ago and the establishment of an extremely arid belt known as the 'Dry Diagonal' to 29°S. Within the Dry Diagonal, small populations of V. v. vicugna appear to have survived showing the genetic signature of demographic isolation, whereas to the north V. v. mensalis populations underwent a rapid demographic expansion before recent anthropogenic impacts

Decoherence, einselection, and the quantum origins of the classical

Decoherence is caused by the interaction with the environment. Environment monitors certain observables of the system, destroying interference between the pointer states corresponding to their eigenvalues. This leads to environment-induced superselection or einselection, a quantum process associated with selective loss of information. Einselected pointer states are stable. They can retain correlations with the rest of the Universe in spite of the environment. Einselection enforces classicality by imposing an effective ban on the vast majority of the Hilbert space, eliminating especially the flagrantly non-local "Schr\"odinger cat" states. Classical structure of phase space emerges from the quantum Hilbert space in the appropriate macroscopic limit: Combination of einselection with dynamics leads to the idealizations of a point and of a classical trajectory. In measurements, einselection replaces quantum entanglement between the apparatus and the measured system with the classical correlation.Comment: Final version of the review, with brutally compressed figures. Apart from the changes introduced in the editorial process the text is identical with that in the Rev. Mod. Phys. July issue. Also available from http://www.vjquantuminfo.or

Updated Systematic Review and Meta-Analysis of the Performance of Risk Prediction Rules in Children and Young People with Febrile Neutropenia

Introduction: Febrile neutropenia is a common and potentially life-threatening complication of treatment for childhood cancer, which has increasingly been subject to targeted treatment based on clinical risk stratification. Our previous meta-analysis demonstrated 16 rules had been described and 2 of them subject to validation in more than one study. We aimed to advance our knowledge of evidence on the discriminatory ability and predictive accuracy of such risk stratification clinical decision rules (CDR) for children and young people with cancer by updating our systematic review. Methods: The review was conducted in accordance with Centre for Reviews and Dissemination methods, searching multiple electronic databases, using two independent reviewers, formal critical appraisal with QUADAS and meta-analysis with random effects models where appropriate. It was registered with PROSPERO: CRD42011001685. Results: We found 9 new publications describing a further 7 new CDR, and validations of 7 rules. Six CDR have now been subject to testing across more than two data sets. Most validations demonstrated the rule to be less efficient than when initially proposed; geographical differences appeared to be one explanation for this. Conclusion: The use of clinical decision rules will require local validation before widespread use. Considerable uncertainty remains over the most effective rule to use in each population, and an ongoing individual-patient-data meta-analysis should develop and test a more reliable CDR to improve stratification and optimise therapy. Despite current challenges, we believe it will be possible to define an internationally effective CDR to harmonise the treatment of children with febrile neutropenia