The 'algebra as object' analogy: a view from school

Treating algebraic symbols as objects (eg. “‘a’ means ‘apple’”) is a means of introducing elementary simplification of algebra, but causes problems further on. This current school-based research included an examination of texts still in use in the mathematics department, and interviews with mathematics teachers, year 7 pupils and then year 10 pupils asking them how they would explain, “3a + 2a = 5a” to year 7 pupils. Results included the notion that the ‘algebra as object’ analogy can be found in textbooks in current usage, including those recently published. Teachers knew that they were not ‘supposed’ to use the analogy but not always clear why, nevertheless stating methods of teaching consistent with an‘algebra as object’ approach. Year 7 pupils did not explicitly refer to ‘algebra as object’, although some of their responses could be so interpreted. In the main, year 10 pupils used ‘algebra as object’ to explain simplification of algebra, with some complicated attempts to get round the limitations. Further research would look to establish whether the appearance of ‘algebra as object’ in pupils’ thinking between year 7 and 10 is consistent and, if so, where it arises. Implications also are for on-going teacher training with alternatives to introducing such simplification.

Collision prediction of a moving object within a virtual world

This paper provides a solution for predicting moving/moving and moving/static collisions of objects within a virtual environment. Feasible prediction in real-time virtual worlds can be obtained by encompassing moving objects within a sphere and static objects within a convex polygon. Fast solutions are then attainable by describing the movement of objects parametrically in time as a polynomial.

Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun

A recent paper published in this journal considers the numerical integration of the shallow-water equations using the leapfrog time-stepping scheme [Sun Wen-Yih, Sun Oliver MT. A modified leapfrog scheme for shallow water equations. Comput Fluids 2011;52:69–72]. The authors of that paper propose using the time-averaged height in the numerical calculation of the pressure-gradient force, instead of the instantaneous height at the middle time step. The authors show that this modification doubles the maximum Courant number (and hence the maximum time step) at which the integrations are stable, doubling the computational efficiency. Unfortunately, the pressure-averaging technique proposed by the authors is not original. It was devised and published by Shuman [5] and has been widely used in the atmosphere and ocean modelling community for over 40 years.

Keeping the world at hand: rapid visuomotor processing for hand-object interactions

The existence of hand-centred visual processing has long been established in the macaque premotor cortex. These hand-centred mechanisms have been thought to play some general role in the sensory guidance of movements towards objects, or, more recently, in the sensory guidance of object avoidance movements. We suggest that these hand-centred mechanisms play a specific and prominent role in the rapid selection and control of manual actions following sudden changes in the properties of the objects relevant for hand-object interactions. We discuss recent anatomical and physiological evidence from human and non-human primates, which indicates the existence of rapid processing of visual information for hand-object interactions. This new evidence demonstrates how several stages of the hierarchical visual processing system may be bypassed, feeding the motor system with hand-related visual inputs within just 70 ms following a sudden event. This time window is early enough, and this processing rapid enough, to allow the generation and control of rapid hand-centred avoidance and acquisitive actions, for aversive and desired objects, respectively

Interactions between shallow and deep convection under a finite departure from convective quasi–equilibrium

The present paper presents a simple theory for the transformation of non-precipitating, shallow convection into precipitating, deep convective clouds. In order to make the pertinent point a much idealized system is considered, consisting only of shallow and deep convection without large–scale forcing. The transformation is described by an explicit coupling between these two types of convection. Shallow convection moistens and cools the atmosphere, whereas deep convection dries and warms, leading to destabilization and stabilization respectively. Consequently, in their own stand–alone modes, shallow convection perpetually grows, whereas deep convection simply damps: the former never reaches equilibrium, and the latter is never spontaneously generated. Coupling the modes together is the only way to reconcile these undesirable separate tendencies so that the convective system as a whole can remain in a stable periodic state under this idealized setting. Such coupling is a key missing element in current global atmospheric models. The energy–cycle description as originally formulated by Arakawa and Schubert, and presented herein is suitable for direct implementation into models using a mass–flux parameterization, and would alleviate the current problems with the representation of these two types of convection in numerical models. The present theory also provides a pertinent framework for analyzing large–eddy simulations and cloud–resolving modelling.

Middle and Late Cenomanian anoxia in shallow and deeper shelf environments of western Morocco

The response of shallow-water sequences to oceanic anoxic event 2 and mid-Cenomanian events 1a and 1b was investigated along the west African margin of Morocco north of Agadir (Azazoul) and correlated with the deep-water sequence of the Tarfaya Basin (Mohammed Beach) based on biostratigraphy, mineralogy, phosphorus and stable isotopes. In the deeper Mohammed Beach section results show double peaks in δ13Corg for mid-Cenomanian events 1a and 1b (Rotalipora reicheli biozone, lower CC10a biozone), the characteristic oceanic anoxic event 2 δ13C excursion (Rotalipora cushmani extinction, top of CC10a biozone) and laminated (anoxic) black shale. In the shallow environment north of Agadir, a fluctuating sea-level associated with dysoxic, brackish and mesotrophic conditions prevailed during the middle to late Cenomanian, as indicated by oyster biostromes, nannofossils, planktonic and benthonic foraminiferal assemblages. Anoxic conditions characteristic of oceanic anoxic event 2 (for example, laminated black shales) did not reach into shallow-water environments until the maximum transgression of the early Turonian. Climate conditions decoupled along the western margin of Morocco between mid-Cenomanian event 1b and the Cenomanian–Turonian boundary, as also observed in eastern Tethys. North of Agadir alternating humid and dry seasonal conditions prevailed, whereas in the Tarfaya Basin the climate was dry and seasonal. This climatic decoupling can be attributed to variations in the Intertropical Convergence Zone and in the intensity of the north-east trade winds in tropical areas.

Robust abandoned object detection integrating wide area visual surveillance and social context

This paper presents a video surveillance framework that robustly and efficiently detects abandoned objects in surveillance scenes. The framework is based on a novel threat assessment algorithm which combines the concept of ownership with automatic understanding of social relations in order to infer abandonment of objects. Implementation is achieved through development of a logic-based inference engine based on Prolog. Threat detection performance is conducted by testing against a range of datasets describing realistic situations and demonstrates a reduction in the number of false alarms generated. The proposed system represents the approach employed in the EU SUBITO project (Surveillance of Unattended Baggage and the Identification and Tracking of the Owner).

Desert dust deposition on Mt. Elbrus, Caucasus Mountains, Russia in 2009-2012 as recorded in snow and shallow ice core: high-resolution "provenancing", transport patterns, physical properties and soluble ionic composition

A record of dust deposition events between 2009 and 2012 on Mt. Elbrus, Caucasus Mountains derived from a snow pit and a shallow ice core is presented for the first time for this region. A combination of isotopic analysis, SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived using the HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (cf. 20–100 km) resolution. Seventeen dust deposition events were detected; fourteen occurred in March–June, one in February and two in October. Four events originated in the Sahara, predominantly in north-eastern Libya and eastern Algeria. Thirteen events originated in the Middle East, in the Syrian Desert and northern Mesopotamia, from a mixture of natural and anthropogenic sources. Dust transportation from Sahara was associated with vigorous Saharan depressions, strong surface winds in the source region and mid-tropospheric south-westerly flow with daily winds speeds of 20–30 m s−1 at 700 hPa level and, although these events were less frequent, they resulted in higher dust concentrations in snow. Dust transportation from the Middle East was associated with weaker depressions forming over the source region, high pressure centered over or extending towards the Caspian Sea and a weaker southerly or south-easterly flow towards the Caucasus Mountains with daily wind speeds of 12–18 m s−1 at 700 hPa level. Higher concentrations of nitrates and ammonium characterise dust from the Middle East deposited on Mt. Elbrus in 2009 indicating contribution of anthropogenic sources. The modal values of particle size distributions ranged between 1.98 μm and 4.16 μm. Most samples were characterised by modal values of 2.0–2.8 μm with an average of 2.6 μm and there was no significant difference between dust from the Sahara and the Middle East.

Data assimilation with correlated observation errors: experiments with a 1-D shallow water model

Remote sensing observations often have correlated errors, but the correlations are typically ignored in data assimilation for numerical weather prediction. The assumption of zero correlations is often used with data thinning methods, resulting in a loss of information. As operational centres move towards higher-resolution forecasting, there is a requirement to retain data providing detail on appropriate scales. Thus an alternative approach to dealing with observation error correlations is needed. In this article, we consider several approaches to approximating observation error correlation matrices: diagonal approximations, eigendecomposition approximations and Markov matrices. These approximations are applied in incremental variational assimilation experiments with a 1-D shallow water model using synthetic observations. Our experiments quantify analysis accuracy in comparison with a reference or ‘truth’ trajectory, as well as with analyses using the ‘true’ observation error covariance matrix. We show that it is often better to include an approximate correlation structure in the observation error covariance matrix than to incorrectly assume error independence. Furthermore, by choosing a suitable matrix approximation, it is feasible and computationally cheap to include error correlation structure in a variational data assimilation algorithm.

A Hamiltonian weak-wave model for shallow-water flow

A reduced dynamical model is derived which describes the interaction of weak inertia–gravity waves with nonlinear vortical motion in the context of rotating shallow–water flow. The formal scaling assumptions are (i) that there is a separation in timescales between the vortical motion and the inertia–gravity waves, and (ii) that the divergence is weak compared to the vorticity. The model is Hamiltonian, and possesses conservation laws analogous to those in the shallow–water equations. Unlike the shallow–water equations, the energy invariant is quadratic. Nonlinear stability theorems are derived for this system, and its linear eigenvalue properties are investigated in the context of some simple basic flows.

The energy-cycle analysis of the interactions between shallow and deep atmospheric convection

Interactions between different convection modes can be investigated using an energy–cycle description under a framework of mass–flux parameterization. The present paper systematically investigates this system by taking a limit of two modes: shallow and deep convection. Shallow convection destabilizes itself as well as the other convective modes by moistening and cooling the environment, whereas deep convection stabilizes itself as well as the other modes by drying and warming the environment. As a result, shallow convection leads to a runaway growth process in its stand–alone mode, whereas deep convection simply damps out. Interaction between these two convective modes becomes a rich problem, even when it is limited to the case with no large–scale forcing, because of these opposing tendencies. Only if the two modes are coupled at a proper level can a self–sustaining system arise, exhibiting a periodic cycle. The present study establishes the conditions for self–sustaining periodic solutions. It carefully documents the behaviour of the two mode system in order to facilitate the interpretation of global model behaviours when this energy–cycle is implemented as a closure into a convection parameterization in future.

Dissociating between object affordances and spatial compatibility effects using early response components

Perception and action are tightly linked: objects may be perceived not only in terms of visual features, but also in terms of possibilities for action. Previous studies showed that when a centrally located object has a salient graspable feature (e.g., a handle), it facilitates motor responses corresponding with the feature's position. However, such so-called affordance effects have been criticized as resulting from spatial compatibility effects, due to the visual asymmetry created by the graspable feature, irrespective of any affordances. In order to dissociate between affordance and spatial compatibility effects, we asked participants to perform a simple reaction-time task to typically graspable and non-graspable objects with similar visual features (e.g., lollipop and stop sign). Responses were measured using either electromyography (EMG) on proximal arm muscles during reaching-like movements, or with finger key-presses. In both EMG and button press measurements, participants responded faster when the object was either presented in the same location as the responding hand, or was affordable, resulting in significant and independent spatial compatibility and affordance effects, but no interaction. Furthermore, while the spatial compatibility effect was present from the earliest stages of movement preparation and throughout the different stages of movement execution, the affordance effect was restricted to the early stages of movement execution. Finally, we tested a small group of unilateral arm amputees using EMG, and found residual spatial compatibility but no affordance, suggesting that spatial compatibility effects do not necessarily rely on individuals’ available affordances. Our results show dissociation between affordance and spatial compatibility effects, and suggest that rather than evoking the specific motor action most suitable for interaction with the viewed object, graspable objects prompt the motor system in a general, body-part independent fashion

Unconscious effects of grammatical gender during object categorisation

Does language modulate perception and categorisation of everyday objects? Here, we approach this question from the perspective of grammatical gender in bilinguals. We tested Spanish–English bilinguals and control native speakers of English in a semantic categorisation task on triplets of pictures in an all-in-English context while measuring event-related brain potentials (ERPs). Participants were asked to press a button when the third picture of a triplet belonged to the same semantic category as the first two, and another button when it belonged to a different category. Unbeknownst to them, in half of the trials, the gender of the third picture name in Spanish had the same gender as that of the first two, and the opposite gender in the other half. We found no priming in behavioural results of either semantic relatedness or gender consistency. In contrast, ERPs revealed not only the expected semantic priming effect in both groups, but also a negative modulation by gender inconsistency in Spanish–English bilinguals, exclusively. These results provide evidence for spontaneous and unconscious access to grammatical gender in participants functioning in a context requiring no access to such information, thereby providing support for linguistic relativity effects in the grammatical domain.

Co-eruptive and inter-eruptive surface deformation measured by satellite radar interferometry at Nyamuragira volcano, D.R. Congo, 1996 to 2010.

Interferometric Synthetic Aperture Radar (InSAR) measurements of surface deformation at Nyamuragira Volcano between 1996 and 2010 reveal a variety of co-eruptive and inter-eruptive signals. During 7 of the 8 eruptions in this period deformation was measured that is consistent with the emplacement of shallow near-vertical dykes feeding the eruptive fissures and associated with a NNW-trending fissure zone that traverses the summit caldera. Between eruptions the caldera and the summit part of this fissure zone subsided gradually (b3–5 cm/year). We also find evidence of post-eruption subsidence around the sites of the main vents of some flank eruptions (2002, 2004, 2006, and 2010). In the 6 months prior to the 2010 eruption a10-km wide zone centred on the caldera inflated by 1–2 cm. The low magnitude of this signal suggests that the presumed magma reservoir at 3–8 km depth contains highly compressible magma with little stored elastic strain energy. To the north of the caldera the fissure zone splits into WNW and NE branches around a zone that has a distinct InSAR signal. We interpret this zone to represent an elevated, 'stable' block of basement rocks buried by lavas within the Rift Zone.