Bernoulli free-boundary problems in strip-like domains and a property of permanent waves on water of finite depth

We study weak solutions for a class of free-boundary problems which includes as a special case the classical problem of travelling gravity waves on water of finite depth. We show that such problems are equivalent to problems in fixed domains and study the regularity of their solutions. We also prove that in very general situations the free boundary is necessarily the graph of a function.

Constancy in the perception of speech when the level of room-reflections varies

A speech message played several metres from the listener in a room is usually heard to have much the same phonetic content as it does when played nearby, even though the different amounts of reflected sound make the temporal envelopes of these signals very different. To study this ‘constancy’ effect, listeners heard speech messages and speech-like sounds comprising 8 auditory-filter shaped noise-bands that had temporal envelopes corresponding to those in these filters when the speech message is played. The ‘contexts’ were “next you’ll get _to click on”, into which a “sir” or “stir” test word was inserted. These test words were from an 11-step continuum, formed by amplitude modulation. Listeners identified the test words appropriately, even in the 8-band conditions where the speech had a ‘robotic’ quality. Constancy was assessed by comparing the influence of room reflections on the test word across conditions where the context had either the same level of room reflections (i.e. from the same, far distance), or where it had a much lower level (i.e. from nearby). Constancy effects were obtained with both the natural- and the 8-band speech. Results are considered in terms of the degree of ‘matching’ between the context’s and test-word’s bands.

Speech perception and phonological short-term memory capacity in language impairment: preliminary evidence from adolescents with specific language impairment (SLI) and autism spectrum disorders (ASD)

Background: The cognitive bases of language impairment in specific language impairment (SLI) and autism spectrum disorders (ASD) were investigated in a novel non-word comparison task which manipulated phonological short-term memory (PSTM) and speech perception, both implicated in poor non-word repetition. Aims: This study aimed to investigate the contributions of PSTM and speech perception in non-word processing and whether individuals with SLI and ASD plus language impairment (ALI) show similar or different patterns of deficit in these cognitive processes. Method & Procedures: Three groups of adolescents (aged 14–17 years), 14 with SLI, 16 with ALI, and 17 age and non-verbal IQ matched typically developing (TD) controls, made speeded discriminations between non-word pairs. Stimuli varied in PSTM load (two- or four-syllables) and speech perception load (mismatches on a word-initial or word-medial segment). Outcomes & Results: Reaction times showed effects of both non-word length and mismatch position and these factors interacted: four-syllable and word-initial mismatch stimuli resulted in the slowest decisions. Individuals with language impairment showed the same pattern of performance as those with typical development in the reaction time data. A marginal interaction between group and item length was driven by the SLI and ALI groups being less accurate with long items than short ones, a difference not found in the TD group. Conclusions & Implications: Non-word discrimination suggests that there are similarities and differences between adolescents with SLI and ALI and their TD peers. Reaction times appear to be affected by increasing PSTM and speech perception loads in a similar way. However, there was some, albeit weaker, evidence that adolescents with SLI and ALI are less accurate than TD individuals, with both showing an effect of PSTM load. This may indicate, at some level, the processing substrate supporting both PSTM and speech perception is intact in adolescents with SLI and ALI, but also in both there may be impaired access to PSTM resources.

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.