RESUMEN
We propose a new model to approximate spatiotemporal noise covariance for use in neural electromagnetic source analysis, which better captures temporal variability in background activity. As with other existing formalisms, our model employs a Kronecker product of matrices representing temporal and spatial covariance. In our model, spatial components are allowed to have differing temporal covariances. Variability is represented as a series of Kronecker products of spatial component covariances and corresponding temporal covariances. Unlike previous attempts to model covariance through a sum of Kronecker products, our model is designed to have a computationally manageable inverse. Despite increased descriptive power, inversion of the model is fast, making it useful in source analysis. We have explored two versions of the model. One is estimated based on the assumption that spatial components of background noise have uncorrelated time courses. Another version, which gives closer approximation, is based on the assumption that time courses are statistically independent. The accuracy of the structural approximation is compared to an existing model, based on a single Kronecker product, using both Frobenius norm of the difference between spatiotemporal sample covariance and a model, and scatter plots. Performance of ours and previous models is compared in source analysis of a large number of single dipole problems with simulated time courses and with background from authentic magnetoencephalography data.
Asunto(s)
Electroencefalografía/métodos , Magnetoencefalografía/métodos , Procesamiento de Señales Asistido por Computador , Algoritmos , Animales , Mapeo Encefálico/métodos , Corteza Cerebral/patología , Estimulación Eléctrica , Potenciales Evocados , Humanos , Modelos Estadísticos , Distribución Normal , Reproducibilidad de los Resultados , Factores de TiempoRESUMEN
A fruitful way to build upon French-language research on development of analogical and propositional processes in logical reasoning tasks is to use dynamic systems tools to describe and analyze relevant developmental pathways. Issues to address include (1) the characteristics of developmental transitions, such as hysteresis; (2) the nature of growth processes, such as hierarchical development or predator-prey interactions; and (3) the construction of effective scales for measuring change in logical reasoning.