Connecting the Dots: Finding Continuity Across Visuospatial Tasks and Development

Discrete Dynamics of Dynamic Neural Fields

Large and small cortexes of the brain are known to contain vast amounts of neurons that interact with one another. They thus form a continuum of active neural networks whose dynamics are yet to be fully understood. One way to model these activities is to use dynamic neural fields which are mathematical models that approximately describe the behavior of these congregations of neurons. These models have been used in neuroinformatics, neuroscience, robotics, and network analysis to understand not only brain functions or brain diseases, but also learning and brain plasticity. In their theoretical forms, they are given as ordinary or partial differential equations with or without diffusion. Many of their mathematical properties are still under-studied. In this paper, we propose to analyze discrete versions dynamic neural fields based on nearly exact discretization schemes techniques. In particular, we will discuss conditions for the stability of nontrivial solutions of these models, based on various types of kernels and corresponding parameters. Monte Carlo simulations are given for illustration.

A Dynamical Reconceptualization of Executive-Function Development

Executive function plays a foundational role in everyday behaviors across the life span. The theoretical understanding of executive-function development, however, is still a work in progress. Doebel proposed that executive-function development reflects skills using control in the service of behavior-using mental content such as knowledge and beliefs to guide behavior in a context-specific fashion. This liberating view contrasts with modular views of executive function. This new view resembles some older dynamic-systems concepts that long ago proposed that behavior reflects the assembly of multiple pieces in context. We dig into this resemblance and evaluate what else dynamic-systems theory adds to the understanding of executive-function development. We describe core dynamic-systems concepts and apply them to executive function-as conceptualized by Doebel-and through this lens explain the multilevel nature of goal-directed behavior and how a capacity to behave in a goal-directed fashion across contexts emerges over development. We then describe a dynamic systems model of goal-directed behavior during childhood and, finally, address broader theoretical implications of dynamic-systems theory and propose new translational implications for fostering children's capacity to behave in a goal-directed fashion across everyday contexts.