Face Representation in Cortex: Studies Using a Simple and Not So Special Model

The face inversion effect has been widely documented as an effect of the uniqueness of face processing. Using a computational model, we show that the face inversion effect is a byproduct of expertise with respect to the face object class. In simulations using HMAX, a hierarchical, shape based model, we show that the magnitude of the inversion effect is a function of the specificity of the representation. Using many, sharply tuned units, an ``expert'' has a large inversion effect. On the other hand, if fewer, broadly tuned units are used, the expertise is lost, and this ``novice'' has a small inversion effect. As the size of the inversion effect is a product of the representation, not the object class, given the right training we can create experts and novices in any object class. Using the same representations as with faces, we create experts and novices for cars. We also measure the feasibility of a view-based model for recognition of rotated objects using HMAX. Using faces, we show that transfer of learning to novel views is possible. Given only one training view, the view-based model can recognize a face at a new orientation via interpolation from the views to which it had been tuned. Although the model can generalize well to upright faces, inverted faces yield poor performance because the features change differently under rotation

Nodal bases for the serendipity family of finite elements

Using the notion of multivariate lower set interpolation, we construct nodal basis functions for the serendipity family of finite elements, of any order and any dimension. For the purpose of computation, we also show how to express these functions as linear combinations of tensor-product polynomials.Comment: Pre-print of version that will appear in Foundations of Computational Mathematic