Relationships between various characterisations of wave tails

One can define several properties of wave equations that correspond to the absence of tails in their solutions, the most common one by far being Huygens' principle. Not all of these definitions are equivalent, although they are sometimes assumed to be. We analyse this issue in detail for linear scalar waves, establishing some relationships between the various properties. Huygens' principle is almost always equivalent to the characteristic propagation property, and in two spacetime dimensions the latter is equivalent to the zeroth order progressing wave propagation property. Higher order progressing waves in general do have tails, and do not seem to admit a simple physical characterisation, but they are nevertheless useful because of their close association with exactly solvable two-dimensional equations.Comment: Plain TeX, 26 page

Coordinated optimization of visual cortical maps (II) Numerical studies

It is an attractive hypothesis that the spatial structure of visual cortical architecture can be explained by the coordinated optimization of multiple visual cortical maps representing orientation preference (OP), ocular dominance (OD), spatial frequency, or direction preference. In part (I) of this study we defined a class of analytically tractable coordinated optimization models and solved representative examples in which a spatially complex organization of the orientation preference map is induced by inter-map interactions. We found that attractor solutions near symmetry breaking threshold predict a highly ordered map layout and require a substantial OD bias for OP pinwheel stabilization. Here we examine in numerical simulations whether such models exhibit biologically more realistic spatially irregular solutions at a finite distance from threshold and when transients towards attractor states are considered. We also examine whether model behavior qualitatively changes when the spatial periodicities of the two maps are detuned and when considering more than 2 feature dimensions. Our numerical results support the view that neither minimal energy states nor intermediate transient states of our coordinated optimization models successfully explain the spatially irregular architecture of the visual cortex. We discuss several alternative scenarios and additional factors that may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with arXiv:1102.335

A Multi-Stage Model for Fundamental Functional Properties in Primary Visual Cortex

Many neurons in mammalian primary visual cortex have properties such as sharp tuning for contour orientation, strong selectivity for motion direction, and insensitivity to stimulus polarity, that are not shared with their sub-cortical counterparts. Successful models have been developed for a number of these properties but in one case, direction selectivity, there is no consensus about underlying mechanisms. We here define a model that accounts for many of the empirical observations concerning direction selectivity. The model describes a single column of cat primary visual cortex and comprises a series of processing stages. Each neuron in the first cortical stage receives input from a small number of on-centre and off-centre relay cells in the lateral geniculate nucleus. Consistent with recent physiological evidence, the off-centre inputs to cortex precede the on-centre inputs by a small (∼4 ms) interval, and it is this difference that confers direction selectivity on model neurons. We show that the resulting model successfully matches the following empirical data: the proportion of cells that are direction selective; tilted spatiotemporal receptive fields; phase advance in the response to a stationary contrast-reversing grating stepped across the receptive field. The model also accounts for several other fundamental properties. Receptive fields have elongated subregions, orientation selectivity is strong, and the distribution of orientation tuning bandwidth across neurons is similar to that seen in the laboratory. Finally, neurons in the first stage have properties corresponding to simple cells, and more complex-like cells emerge in later stages. The results therefore show that a simple feed-forward model can account for a number of the fundamental properties of primary visual cortex

Belongingness in early secondary school: Key factors that primary and secondary schools need to consider

© 2015 Vaz et al. It is unknown if, and how, students redefine their sense of school belongingness after negotiating the transition to secondary school. The current study used longitudinal data from 266 students with, and without, disabilities who negotiated the transition from 52 primary schools to 152 secondary schools. The study presents the 13 most significant personal student and contextual factors associated with belongingness in the first year of secondary school. Student perception of school belongingness was found to be stable across the transition. No variability in school belongingness due to gender, disability or household-socio-economic status (SES) was noted. Primary school belongingness accounted for 22% of the variability in secondary school belongingness. Several personal student factors (competence, coping skills) and school factors (low-level classroom task-goal orientation), which influenced belongingness in primary school, continued to influence belongingness in secondary school. In secondary school, effort-goal orientation of the student and perception of their school's tolerance to disability were each associated with perception of school belongingness. Family factors did not influence belongingness in secondary school. Findings of the current study highlight the need for primary schools to foster belongingness among their students at an early age, and transfer students' belongingness profiles as part of the handover documentation. Most of the factors that influenced school belongingness before and after the transition to secondary are amenable to change

On the Origin of the Functional Architecture of the Cortex

The basic structure of receptive fields and functional maps in primary visual cortex is established without exposure to normal sensory experience and before the onset of the critical period. How the brain wires these circuits in the early stages of development remains unknown. Possible explanations include activity-dependent mechanisms driven by spontaneous activity in the retina and thalamus, and molecular guidance orchestrating thalamo-cortical connections on a fine spatial scale. Here I propose an alternative hypothesis: the blueprint for receptive fields, feature maps, and their inter-relationships may reside in the layout of the retinal ganglion cell mosaics along with a simple statistical connectivity scheme dictating the wiring between thalamus and cortex. The model is shown to account for a number of experimental findings, including the relationship between retinotopy, orientation maps, spatial frequency maps and cytochrome oxidase patches. The theory's simplicity, explanatory and predictive power makes it a serious candidate for the origin of the functional architecture of primary visual cortex

The personal and contextual contributors to school belongingness among primary school students

School belongingness has gained currency among educators and school health professionals as an important determinant of adolescent health. The current cross-sectional study presents the 15 most significant personal and contextual factors that collectively explain 66.4% (two-thirds) of the variability in 12-year old students' perceptions of belongingness in primary school. The study is part of a larger longitudinal study investigating the factors associated with student adjustment in the transition from primary to secondary school. The study found that girls and students with disabilities had higher school belongingness scores than boys, and their typically developing counterparts respectively; and explained 2.5% of the variability in school belongingness. The majority (47.1% out of 66.4%) of the variability in school belongingness was explained by student personal factors, such as social acceptance, physical appearance competence, coping skills, and social affiliation motivation; followed by parental expectations (3% out of 66.4%), and school-based factors (13.9% out of 66.4%) such as, classroom involvement, task-goal structure, autonomy provision, cultural pluralism, and absence of bullying. Each of the identified contributors of primary school belongingness can be shaped through interventions, system changes, or policy reforms