The non-linear equations of motion describing the laminar, isothermal and incompressible flow in a rectangular domain bounded by two weakly permeable, moving porous walls, which enable the fluid to enter or exit during successive expansions or contractions, are considered. We apply Lie-group method for determining symmetry reductions of partial differential equations. Lie-group method starts out with a general infinitesimal group of transformations under which given partial differential equations are invariant, then, the determining equations are derived. The determining equations are a set of linear differential equations, the solution of which gives the infinitesimals of the dependent and independent variables. After the group has been determined, a solution to the given partial differential equation may be found from the invariant surface condition such that its solution leads to similarity variables that reduce the number of independent variables in the system. Effect of the permeation Reynolds number R e and the dimensionless wall dilation rate a on self-axial velocity have been studied both analytically and numerically and the results are plotted.

Minicolumnar changes that generalize throughout a significant portion of the cortex have macroscopic structural correlates that may be visualized with modern structural neuroimaging techniques. In magnetic resonance images (MRIs) of fourteen autistic patients and 28 controls, the present study found macroscopic morphological correlates to recent neuropathological findings suggesting a minicolumnopathy in autism. Autistic patients manifested a significant reduction in NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author Manuscript the aperture for afferent/efferent cortical connections, i.e., gyral window. Furthermore, the size of the gyral window directly correlated to the size of the corpus callosum. A reduced gyral window constrains the possible size of projection fibers and biases connectivity towards shorter corticocortical fibers at the expense of longer association/commisural fibers. The findings may help explain abnormalities in motor skill development, differences in postnatal brain growth, and the regression of acquired functions observed in some autistic patients.

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Abstract. A new 3D segmentation method based on the level set technique is proposed. The main contribution is a robust evolutionary model which requires no fine tuning of parameters. A closed 3D surface propagates from an initial position towards the desired region boundaries through an iterative evolution of a specific 4D implicit function. Information about the regions is involved by estimating, at each iteration, parameters of probability density functions. The method can be applied to different kinds of data, e.g for segmenting anatomical structures in 3D magnetic resonance images and angiography. Experimental results of these two types of data are discussed.

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