Representing geometrical knowledge

This paper introduces perspex algebra which is being developed as a common representation of geometrical knowledge. A perspex can currently be interpreted in one of four ways. First, the algebraic perspex is a generalization of matrices, it provides the most general representation for all of the interpretations of a perspex. The algebraic perspex can be used to describe arbitrary sets of coordinates. The remaining three interpretations of the perspex are all related to square matrices and operate in a Euclidean model of projective space-time, called perspex space. Perspex space differs from the usual Euclidean model of projective space in that it contains the point at nullity. It is argued that the point at nullity is necessary for a consistent account of perspective in top-down vision. Second, the geometric perspex is a simplex in perspex space. It can be used as a primitive building block for shapes, or as a way of recording landmarks on shapes. Third, the transformational perspex describes linear transformations in perspex space that provide the affine and perspective transformations in space-time. It can be used to match a prototype shape to an image, even in so called 'accidental' views where the depth of an object disappears from view, or an object stays in the same place across time. Fourth, the parametric perspex describes the geometric and transformational perspexes in terms of parameters that are related to everyday English descriptions. The parametric perspex can be used to obtain both continuous and categorical perception of objects. The paper ends with a discussion of issues related to using a perspex to describe logic.

Changing standards revisited: children’s awareness and knowledge of features of written standard English at ages 10-11

This paper reports the findings of a small-scale research project which investigated the levels of awareness and knowledge of written standard English of 10 and 11 year old children in two English primary schools. The project involved repeating in 2010 a written questionnaire previously used with children in the same schools in three separate surveys in 1999, 2002 and 2005. Data from the latest survey are compared to those from the previous three. The analysis seeks to identify any changes over time in children’s ability to recognise non-standard forms and supply standard English alternatives, as well as their ability to use technical terms related to language variation. Differences between the performance of boys and girls and that of the two schools are also analysed. The paper concludes that the socio-economic context of the schools may be a more important factor than gender in variations over time identified in the data.

Measuring the effects of manipulating stimulus presentation time on sensorimotor alpha and low beta reactivity during hand movement observation

The present study addresses three methodological questions that have been ignored in previous research on EEG indices of the human mirror neuron system (hMNS), particularly in regard to autistic individuals. The first question regards how to elicit the EEG indexed hMNS during movement observation: Is hMNS activation best elicited using long stimulus presentations or multiple short repetitions? The second question regards what EEG sensorimotor frequency bands reflect sensorimotor reactivity during hand movement observation? The third question regards how widespread is the EEG reactivity over the sensorimotor cortex during movement observation? The present study explored sensorimotor alpha and low beta reactivity during hand movement versus static hand or bouncing balls observation and compared two experimental protocols (long exposure vs. multiple repetitions) in the same participants. Results using the multiple repetitions protocol indicated a greater low beta desynchronisation over the sensorimotor cortex during hand movement compared to static hand and bouncing balls observation. This result was not achieved using the long exposure protocol. Therefore, the present study suggests that the multiple repetitions protocol is a more robust protocol to use when exploring the sensorimotor reactivity induced by hand action observation. In addition, sensorimotor low beta desynchronisation was differently modulated during hand movement, static hand and bouncing balls observation (non-biological motion) while it was not the case for sensorimotor alpha and that suggest that low beta may be a more sensitive index of hMNS activation during biological motion observation. In conclusion the present study indicates that sensorimotor reactivity of low beta during hand movement observation was found to be more widespread over the sensorimotor cortex than previously thought.

A characterization of the food industries

Consistent conjectures applied to the food industries are investigated. This is a homogeneous-product, quantity-setting model with identical firms. When firm numbers are fixed, the consistent conjecture is monopolistic. When variable, consistency requires firm output to expand with exit and contract with entry, but no conjecture exists that is consistent with equilibrium.

Femtosecond pulse shaping using differential evolutionary algorithm and wavelet operators

Evolutionary meta-algorithms for pulse shaping of broadband femtosecond duration laser pulses are proposed. The genetic algorithm searching the evolutionary landscape for desired pulse shapes consists of a population of waveforms (genes), each made from two concatenated vectors, specifying phases and magnitudes, respectively, over a range of frequencies. Frequency domain operators such as mutation, two-point crossover average crossover, polynomial phase mutation, creep and three-point smoothing as well as a time-domain crossover are combined to produce fitter offsprings at each iteration step. The algorithm applies roulette wheel selection; elitists and linear fitness scaling to the gene population. A differential evolution (DE) operator that provides a source of directed mutation and new wavelet operators are proposed. Using properly tuned parameters for DE, the meta-algorithm is used to solve a waveform matching problem. Tuning allows either a greedy directed search near the best known solution or a robust search across the entire parameter space.