Erratum: Betweenness Centralization for Bipartite Graphs

We address two related issues. First, we analyze the effects of risk preferences on cooperation in social dilemmas. Second, we compare social dilemmas in which outcomes represent gains with dilemmas where outcomes represent losses. We show that predictions on gain‐loss asymmetries with respect to conditions for cooperation crucially depend on assumptions concerning risk preferences. Under the assumption of risk aversion for gains as well as losses together with an assumption of decreasing absolute risk aversion, conditions for cooperation are less restrictive if outcomes represent losses than if outcomes represent gains. Conversely ‐ and counterintuitively ‐ under the assumption of S‐shaped utility, conditions for cooperation are more restrictive if outcomes represent losses than if outcomes represent gains. We provide an experimental test of such predictions. Only a minority of subjects behaves consistent with the assumption of S‐shaped utility. Furthermore, we find no empirical evidence for a general difference between cooperation in social dilemmas in which outcomes represent gains and dilemmas where outcomes represent losses. We do find evidence that risk preferences affect cooperation rates.     

Number concepts with Number Worlds : thickening understandings

This study focuses on the nature of preservice elementary school teachers’ understandings of several concepts in elementary number theory that are evoked by a computer-based microworld called Number Worlds. In particular, the focus is on the concepts of factor, multiple and prime number. The notion of ‘thickness’ is examined with respect to understanding mathematical concepts and alludes to various attributes of Number Worlds that may be responsible for provoking different layers and depths of understanding, termed ‘thick understanding’.     

Assessment of the fatigue crack closure phenomenon in damage-tolerant aluminium alloy by in-situ high-resolution synchrotron X-ray microtomography

Synchrotron X-ray microtomography has been utilized for the in-situ observation of steady-state plane-strain fatigue crack growth. A high-resolution experimental configuration and phase contrast imaging technique have enabled the reconstruction of crack images with an isotropic voxel with a 0.7 µm edge. The details of a crack are readily observed, together with evidence of the incidence and mechanical influence of closure. After preliminary investigations of the achievable accuracy and reproducibility, a variety of measurement methods are used to quantify crack-opening displacement (COD) and closure from the tomography data. Utilization of the physical displacements of microstructural features is proposed to obtain detailed COD data, and its feasibility is confirmed. Loss of fracture surface contact occurs gradually up to the maximum load. This is significantly different from tendencies reported where a single definable opening level is essentially assumed to exist. The closure behaviour is found to be attributable mainly to pronounced generation of mode III displacement which may be caused by local crack topology. Many small points of closure still remain near the crack tip, suggesting that the near-tip contact induces crack growth resistance. The effects of overloading are also discussed.     

Crystallization behaviour of ALD-Ta2O5 thin films: the application of in-situ TEM

The microstructure of Ta₂O₅ thin films, deposited onto Si substrates by atomic layer deposition (ALD), was investigated, using in situ transmission electron microscopy (TEM). As-deposited amorphous films crystallize as the orthorhombic phase L-Ta₂O₅ upon heating at 750°C. Two dominant crystallographic orientations are found, one with (0?0?1) and (1?11?0) planes perpendicular to the substrate, while the other has (0?0?1) planes parallel to the substrate. The grains consist of subgrains which are rotated a few degrees with respect to each other. The kinetics of the crystallization were studied by in-situ TEM heating experiments carried out at nominal temperatures of 790°C, 820°C and 850°C. They reveal that the growth and crystallization activation energies are about 4.2?eV and 6.3?eV, respectively. Tilted subgrains keep forming during growth until they come in contact with neighbouring grains. The crystallization behaviour can be approximated by the Kolmogorov–Johnson–Mehl–Avrami (KJMA or Avrami) equation, giving mode parameters of 2.5, 1.9, and 1.7 at 790°C, 820°C and 850°C, respectively. A small value of mode parameters is attributed to decreasing growth and nucleation rates with time.     

To be or to become: how dynamic geometry changes discourse

In this article, we investigate the impact of the introduction of a dynamic geometry environment on mathematical thinking by identifying changes in discourse engendered by its introduction in a high school geometry class. Our focus is on the teacher, and we find significant differences between static and dynamic geometry in terms of the ways in which the teacher talks about geometric objects, makes use of visual artifacts and models geometric reasoning. Even though these changes have major implications for the geometry being studied, they are made only very implicitly in the classroom.     

Lee–Yang Theorems and the Complexity of Computing Averages

We study the complexity of computing average quantities related to spin systems, such as the mean magnetization and susceptibility in the ferromagnetic Ising model, and the average dimer count (or average size of a matching) in the monomer-dimer model. By establishing connections between the complexity of computing these averages and the location of the complex zeros of the partition function, we show that these averages are #P-hard to compute, and hence, under standard assumptions, computationally intractable. In the case of the Ising model, our approach requires us to prove an extension of the famous Lee–Yang Theorem from the 1950s.     

An alternative approach for measuring the scattered acoustic pressure field of immersed single and multiple cylinders

The form function of an elastic target can be obtained from the scattered signal through a deconvolution process. The deconvolution process uses the signal measured from an acoustically hard target (reference signal) to compensate for the impulse response of the measurement system. In this paper, it is shown that this approach limits the usable frequency range of the signal and leads to inaccuracies in the final results. An alternative approach is proposed in which the reference signal is replaced by the specular echo. A procedure is described for extracting the specular echo from the measured signal even in cases where it is not completely isolated from the resonant components. Modifications are made to the existing deconvolution formulation and it is further extended to be applicable to multiple scattering measurements. Experimental results show that the new approach provides improved accuracy and wider usable frequency range in both single and multiple scattering experiments.     

Perturbations of nuclear <Emphasis Type="Italic">C</Emphasis>*-algebras

Kadison and Kastler introduced a natural metric on the collection of all C*-subalgebras of the bounded operators on a separable Hilbert space. They conjectured that sufficiently close algebras are unitarily conjugate. We establish this conjecture when one algebra is separable and nuclear. We also consider one-sided versions of these notions, and we obtain embeddings from certain near inclusions involving separable nuclear C*-algebras. At the end of the paper we demonstrate how our methods lead to improved characterisations of some of the types of algebras that are of current interest in the classification programme.     

Calibrated and decalibrated approximations of nonlinear dynamic systems

Nonlinear Dynamics - The motion of a physical system can generally be described by multiple coordinate representations, which obey nonlinear equations of motion and are related by nonlinear...     

EELS characterisation of bulk CaCu3Ti4O12 ceramics

CaCu3Ti4O12 (CCTO) is a cubic perovskite phase and sintered ceramics exhibit high permittivity at room temperature. Electron energy-loss spectroscopy (EELS) and energy dispersive X-ray spectrometry (EDS) data have been collected from samples of CCTO to relate the observed electrical properties to the microstructure and chemistry on the nanoscale. CCTO ceramics were sintered for 24h at 1115 degrees C in air, giving a grain size of 50-300 microm. Ti L(2,3)-, Cu L(2,3)- and O K-edge EEL data were collected for bulk CCTO (within grain) and compared with well characterised Ti-oxides, CaTiO3 and BaTiO3 perovskites. The bulk metal L(2,3)-edge data for CCTO suggest that Cu is divalent and Ti is present as Ti4+. The O K-edge of CCTO shows increased near-edge structure (NES) compared to those of the simple perovskites.