The block numerical range of analytic operator functions

We introduce the block numerical range Wn(L) of an operator function L with respect to a decomposition H = H1⊕. . .⊕Hn of the underlying Hilbert space. Our main results include the spectral inclusion property and estimates of the norm of the resolvent for analytic L . They generalise, and improve, the corresponding results for the numerical range (which is the case n = 1) since the block numerical range is contained in, and may be much smaller than, the usual numerical range. We show that refinements of the decomposition entail inclusions between the corresponding block numerical ranges and that the block numerical range of the operator matrix function L contains those of its principal subminors. For the special case of operator polynomials, we investigate the boundedness of Wn(L) and we prove a Perron-Frobenius type result for the block numerical radius of monic operator polynomials with coefficients that are positive in Hilbert lattice sense.

Measuring the mechanical properties of plant cells by combining micro-indentation with osmotic treatments

Growth in plants results from the interaction between genetic and signalling networks and the mechanical properties of cells and tissues. There has been a recent resurgence in research directed at understanding the mechanical aspects of growth, and their feedback on genetic regulation. This has been driven in part by the development of new micro-indentation techniques to measure the mechanical properties of plant cells in vivo. However, the interpretation of indentation experiments remains a challenge, since the force measures results from a combination of turgor pressure, cell wall stiffness, and cell and indenter geometry. In order to interpret the measurements, an accurate mechanical model of the experiment is required. Here, we used a plant cell system with a simple geometry, Nicotiana tabacum Bright Yellow-2 (BY-2) cells, to examine the sensitivity of micro-indentation to a variety of mechanical and experimental parameters. Using a finite-element mechanical model, we found that, for indentations of a few microns on turgid cells, the measurements were mostly sensitive to turgor pressure and the radius of the cell, and not to the exact indenter shape or elastic properties of the cell wall. By complementing indentation experiments with osmotic experiments to measure the elastic strain in turgid cells, we could fit the model to both turgor pressure and cell wall elasticity. This allowed us to interpret apparent stiffness values in terms of meaningful physical parameters that are relevant for morphogenesis.

Consensus on the Need for a Hierarchical List of Patient-reported Pain Outcomes for Metaanalyses of Knee Osteoarthritis Trials: An OMERACT Objective.

OBJECTIVE Although protocol registration for systematic reviews is still not mandatory, reviewers should be strongly encouraged to register the protocol to identify the methodological approach, including all outcomes of interest. This will minimize the likelihood of biased decisions in reviews, such as selective outcome reporting. A group of international experts convened to address issues regarding the need to develop hierarchical lists of outcome measurement instruments for a particular outcome for metaanalyses. METHODS Multiple outcome measurement instruments exist to measure the same outcome. Metaanalysis of knee osteoarthritis (OA) trials, and the assessment of pain as an outcome, was used as an exemplar to assess how Outcome Measures in Rheumatology (OMERACT), the Cochrane Collaboration, and other international initiatives might contribute in this area. The meeting began with formal presentations of background topics, empirical evidence from the literature, and a brief introduction to 2 existing hierarchical lists of pain outcome measurement instruments recommended for metaanalyses of knee OA trials. RESULTS After discussions, most participants agreed that there is a need to develop a methodology for generation of hierarchical lists of outcome measurement instruments to guide metaanalyses. Tools that could be used to steer development of such a prioritized list are the COSMIN checklist (Consensus-based Standards for the selection of health status Measurement Instruments) and the OMERACT Filter 2.0. CONCLUSION We list meta-epidemiological research agenda items that address the frequency of reported outcomes in trials, as well as methodologies to assess the best measurement properties (i.e., truth, discrimination, and feasibility).

Thermal and collisional history of Tishomingo iron meteorite: More evidence for early disruption of differentiated planetesimals

Tishomingo is a chemically and structurally unique iron with 32.5 wt.% Ni that contains 20% residual taenite and 80% martensite plates, which formed on cooling to between -75 and -200 °C, probably the lowest temperature recorded by any meteorite. Our studies using transmission (TEM) and scanning electron microscopy (SEM), X-ray microanalysis (AEM) and electron backscatter diffraction (EBSD) show that martensite plates in Tishomingo formed in a single crystal of taenite and decomposed during reheating forming 10-100 nm taenite particles with ∼50 wt.% Ni, kamacite with ∼4 wt.%Ni, along with martensite or taenite with 32 wt.% Ni. EBSD data and experimental constraints show that Tishomingo was reheated to 320-400 °C for about a year transforming some martensite to kamacite and to taenite particles and some martensite directly to taenite without composition change. Fizzy-textured intergrowths of troilite, kamacite with 2.7 wt.% Ni and 2.6 wt.% Co, and taenite with 56 wt.% Ni and 0.15 wt.% Co formed by localized shock melting. A single impact probably melted the sub-mm sulfides, formed stishovite, and reheated and decomposed the martensite plates. Tishomingo and its near-twin Willow Grove, which has 28 wt.% Ni, differ from IAB-related irons like Santa Catharina and San Cristobal that contain 25-36 wt.% Ni, as they are highly depleted in moderately volatile siderophiles and enriched in Ir and other refractory elements. Tishomingo and Willow Grove therefore resemble IVB irons but are chemically distinct. The absence of cloudy taenite in these two irons shows that they cooled through 250 °C abnormally fast at >0.01 °C/yr. Thus this grouplet, like the IVA and IVB irons, suffered an early impact that disrupted their parent body when it was still hot. Our noble gas data show that Tishomingo was excavated from its parent body about 100 to 200 Myr ago and exposed to cosmic rays as a meteoroid with a radius of ∼50-85 cm.

Quantum Nondemolition Measurement Enables Macroscopic Leggett-Garg Tests

We show how a test of macroscopic realism based on Leggett-Garg inequalities (LGIs) can be performed in a macroscopic system. Using a continuous-variable approach, we consider quantum nondemolition (QND) measurements applied to atomic ensembles undergoing magnetically driven coherent oscillation. We identify measurement schemes requiring only Gaussian states as inputs and giving a significant LGI violation with realistic experimental parameters and imperfections. The predicted violation is shown to be due to true quantum effects rather than to a classical invasivity of the measurement. Using QND measurements to tighten the “clumsiness loophole” forces the stubborn macrorealist to recreate quantum backaction in his or her account of measurement.

Pollen and charcoal in lake sediments compared with historically documented forest fires in southern Switzerland since AD 1920

Charcoal in unlaminated sediments dated by 210Pb was analysed by the pollen-slide and thin-section methods. The results were compared with the number and area of forest fires on different spatial scales in the area around Lago di Origlio as listed in the wildfire database of southern Switzerland since AD 1920. The influx of the number of charcoal particles > 75 µm2 in pollen slides correlates well with the number of annual forest fires recorded within a distance of 20-50 km from the coring site. Hence a size-class distinction or an area measurement by image analysis may not be absolutely necessary for the reconstruction of regional fire history. A regression equation was computed and tested against an independent data set. Its use makes it possible to estimate the charcoal area influx (or concentration) from the particle number influx (or concentration). Local fires within a radius of 2 km around the coring site correlate well with the area influx of charcoal particles estimated by the thin-section method measuring the area of charcoal particles larger than 20 000 µm2 or longer than 50 µm. Pollen percentages and influx values suggest that intensive agriculture and Castanea sativa cultivation were reduced 30-40 years ago, followed by an increase of forest area and a development to more natural woodlands. The traditional Castanea sativa cultivation was characterized by a complete use of the biomass produced, so abandonment of chestnut led to an increasing accumulation of dead biomass, thereby raising the fire risk. On the other hand, the pollen record of the regional vegetation does not show any clear response to the increase of fire frequency during the last three decades in this area.