Boundary objects and boundary crossing for numeracy teaching

In this paper, we share analysis of an episode of a pre-service teacher’s handling of a map artefact within his practicum teaching of ‘Mathematical Literacy’ in South Africa. Mathematical Literacy, as a post-compulsory phase subject in the South African curriculum, shares many of the aims of numeracy as described in the international literature— including approaches based on the inclusion of real life contexts and a trajectory geared towards work, life and citizenship. Our attention in this paper is focused specifically on artefacts at the boundary of mathematical and contextual activities. We use analysis of the empirical handling of artefacts cast as ‘boundary objects’ to argue the need for ‘boundary crossing’ between mathematical and contextual activities as a critical feature of numeracy teaching. We pay particular attention to the differing conventions and extents of applicability of rules associated with boundary artefacts when working with mathematical or contextual perspectives. Our findings suggest the need to consider boundary objects more seriously within numeracy teacher education, with specific attention to the ways in which they are configured on both sides of the boundary in order to deal effectively with explanations and interactions in classrooms aiming to promote numeracy

New MR sequences in daily practice: susceptibility weighted imaging. A pictorial essay

Background Susceptibility-weighted imaging (SWI) is a relatively new magnetic resonance (MR) technique that exploits the magnetic susceptibility differences of various tissues, such as blood, iron and calcification, as a new source of contrast enhancement. This pictorial review is aimed at illustrating and discussing its main clinical applications. Methods SWI is based on high-resolution, threedimensional (3D), fully velocity-compensated gradientecho sequences using both magnitude and phase images. A phase mask obtained from the MR phase images is multiplied with magnitude images in order to increase the visualisation of the smaller veins and other sources of susceptibility effects, which are displayed at best after postprocessing of the 3D dataset with the minimal intensity projection (minIP) algorithm. Results SWI is very useful in detecting cerebral microbleeds in ageing and occult low-flow vascular malformations, in characterising brain tumours and degenerative diseases of the brain, and in recognizing calcifications in various pathological conditions. The phase images are especially useful in differentiating between paramagnetic susceptibility effects of blood and diamagnetic effects of calcium. SWI can also be used to evaluate changes in iron content in different neurodegenerative disorders. Conclusion SWI is useful in differentiating and characterising diverse brain disorders

Graphene on hexagonal boron nitride as a tunable hyperbolic metamaterial

Hexagonal boron nitride (h-BN) is a natural hyperbolic material1, in which the dielectric constants are the same in the basal plane (ε[superscript t] ≡ ε[superscript x] = ε[superscript y]) but have opposite signs (ε[superscript t] ε[superscript z ]< 0) in the normal plane (ε[superscript z]). Owing to this property, finite-thickness slabs of h-BN act as multimode waveguides for the propagation of hyperbolic phonon polaritons—collective modes that originate from the coupling between photons and electric dipoles in phonons. However, control of these hyperbolic phonon polaritons modes has remained challenging, mostly because their electrodynamic properties are dictated by the crystal lattice of h-BN. Here we show, by direct nano-infrared imaging, that these hyperbolic polaritons can be effectively modulated in a van der Waals heterostructure composed of monolayer graphene on h-BN. Tunability originates from the hybridization of surface plasmon polaritons in graphene with hyperbolic phonon polaritons in h-BN so that the eigenmodes of the graphene/h-BN heterostructure are hyperbolic plasmon–phonon polaritons. The hyperbolic plasmon–phonon polaritons in graphene/h-BN suffer little from ohmic losses, making their propagation length 1.5–2.0 times greater than that of hyperbolic phonon polaritons in h-BN. The hyperbolic plasmon–phonon polaritons possess the combined virtues of surface plasmon polaritons in graphene and hyperbolic phonon polaritons in h-BN. Therefore, graphene/h-BN can be classified as an electromagnetic metamaterial as the resulting properties of these devices are not present in its constituent elements alone

Calculation of molecular thermochemical data and their availability in databases

Thermodynamic properties of molecules can be obtained by experiment, by statistical mechanics in conjunction with electronic structure theory and by empirical rules like group additivity. The latter two methods are briefly re-viewed in this chapter. The overview of electronic structure methods is intended for readers less experienced in electronic structure theory and focuses on concepts without going into mathematical details. This is followed by a brief description of group additivity schemes; finally, an overview of databases listing reliable thermochemical data is given

Reflections on the entrepreneurial state, innovation and social justice

The state and its role in technological innovation and social justice have become, once again, fashionable topics of political and economic debate. A number of innovation theorists argue that never more than today, it is necessary to rethink the state’s entrepreneurial role in society and welfare. Their argument provides justification for the existence of the state, going beyond classical political theory and especially contractarian accounts of legitimacy and obligation. It emphasises the ability and willingness of the state to take risks and reduce uncertainty of economic agents for the sake of innovation that can make everyone better off. This paper insists that although the risk-taking argument of innovation theorists deserves further attention and analysis, it should not be abstracted from a holistic politico-theoretical approach to the state. Such an approach is necessary for a critical understanding of the complex set of predominantly political institutions which compose the state and which have been historically developed to guarantee social evolution. Any risk-taking for innovative enterprise and mission-oriented investment ought to be justified and legitimised on the grounds of principled democratic procedures. This implies that innovation itself is a value-laden political process, requiring participation in the decision-making and standards of fairness

Catching-up in the global factory: analysis and policy implications

MNEs shape the location of activities in the world economy, linking diverse regions in what has been called the global factory. This study portrays the evolution of incomes and employment in the global factory using a quantitative input–output approach. We find emerging economies forging ahead relative to advanced economies in income derived from fabrication activities, handling the physical transformation process of goods. In contrast, convergence in income derived from knowledge-intensive activities carried out in pre- and post-fabrication stages is much slower. We discuss possible barriers to catching-up and policy implications for emerging economies in developing innovation capabilities, stressing the pivotal role of MNEs

Arrival Directions of Cosmic Rays above 32 EeV from Phase One of the Pierre Auger Observatory

A promising energy range to look for angular correlations between cosmic rays of extragalactic origin and their sources is at the highest energies, above a few tens of EeV (1 EeV equivalent to 10^(18) eV). Despite the flux of these particles being extremely low, the area of similar to 3000 km^(2) covered at the Pierre Auger Observatory, and the 17 yr data-taking period of the Phase 1 of its operations, have enabled us to measure the arrival directions of more than 2600 ultra-high-energy cosmic rays above 32 EeV. We publish this data set, the largest available at such energies from an integrated exposure of 122,000 km^(2) sr yr, and search it for anisotropies over the 3.4 pi steradians covered with the Observatory. Evidence for a deviation in excess of isotropy at intermediate angular scales, with similar to 15 degrees Gaussian spread or similar to 25 degrees top-hat radius, is obtained at the 4 sigma significance level for cosmic-ray energies above similar to 40 EeV

Search for Ultra-high-energy Photons from Gravitational Wave Sources with the Pierre Auger Observatory

A search for time-directional coincidences of ultra-high-energy (UHE) photons above 10 EeV with gravitational wave (GW) events from the LIGO/Virgo runs O1 to O3 is conducted with the Pierre Auger Observatory. Due to the distinctive properties of photon interactions and to the background expected from hadronic showers, a subset of the most interesting GW events is selected based on their localization quality and distance. Time periods of 1000 s around and 1 day after the GW events are analyzed. No coincidences are observed. Upper limits on the UHE photon fluence from a GW event are derived that are typically at &amp; SIM;7 MeV cm(-2) (time period 1000 s) and &amp; SIM;35 MeV cm(-2) (time period 1 day). Due to the proximity of the binary neutron star merger GW170817, the energy of the source transferred into UHE photons above 40 EeV is constrained to be less than 20% of its total GW energy. These are the first limits on UHE photons from GW sources

Searches for Ultra-High-Energy Photons at the Pierre Auger Observatory

The Pierre Auger Observatory, which is the largest air-shower experiment in the world, offers unprecedented exposure to neutral particles at the highest energies. Since the start of data collection more than 18 years ago, various searches for ultra-high-energy (UHE, E greater than or similar to 10^(17) eV) photons have been performed, either for a diffuse flux of UHE photons, for point sources of UHE photons or for UHE photons associated with transient events such as gravitational wave events. In the present paper, we summarize these searches and review the current results obtained using the wealth of data collected by the Pierre Auger Observatory