Specific impairments in cognitive development: a dynamical systems approach

Neuropsychologists have frequently proposed that domain-specific deficits can be observed in developmental disorders (e.g., phonology in dyslexia, theory of mind in autism, grammar in specific language impairment, face recognition in prosopagnosia, mathematics in dyscalculia). These deficits appeal to a modular cognitive architecture. However, specific developmental deficits are at odds with theories that posit a high degree of interactivity between cognitive abilities across development. If there are early deficits, why do these not spread across the cognitive system during development? Or experience compensatory help from other initially intact components? We address these questions within a dynamical systems framework (van der Maas et al., 2006). We explore the conditions for deficit spread and compensation for a range of possible cognitive architectures, from modular to fully distributed. While preliminary, the results point to the importance of specifying precisely the normal developmental architecture of a system prior to characterizing patterns of impairment that might emerge from it

Modelling individual variability in cognitive development

Investigating variability in reasoning tasks can provide insights into key issues in the study of cognitive development. These include the mechanisms that underlie developmental transitions, and the distinction between individual differences and developmental disorders. We explored the mechanistic basis of variability in two connectionist models of cognitive development, a model of the Piagetian balance scale task (McClelland, 1989) and a model of the Piagetian conservation task (Shultz, 1998). For the balance scale task, we began with a simple feed-forward connectionist model and training patterns based on McClelland (1989). We investigated computational parameters, problem encodings, and training environments that contributed to variability in development, both across groups and within individuals. We report on the parameters that affect the complexity of reasoning and the nature of ‘rule’ transitions exhibited by networks learning to reason about balance scale problems. For the conservation task, we took the task structure and problem encoding of Shultz (1998) as our base model. We examined the computational parameters, problem encodings, and training environments that contributed to variability in development, in particular examining the parameters that affected the emergence of abstraction. We relate the findings to existing cognitive theories on the causes of individual differences in development

Application of Hertz Vector Diffraction Theory to the Diffraction of Focused Gaussian Beams and Calculations of Focal Parameters

Hertz vector diffraction theory is applied to a focused TEM00 Gaussian light field passing through a circular aperture. The resulting theoretical vector field model reproduces plane-wave diffractive behavior for severely clipped beams, expected Gaussian beam behavior for unperturbed focused Gaussian beams as well as unique diffracted-Gaussian behavior between the two regimes. The maximum intensity obtainable and the width of the beam in the focal plane are investigated as a function of the clipping ratio between the aperture radius and the beam width in the aperture plane