Experiments were conducted in which Ss made classification, recognition, and similarity judgments for 34 schematic faces. A multidimensional scaling (MDS) solution for the faces was derived on the basis of the similarity judgments. This MDS solution was then used in conjunction with an exemplar-similarity model to accurately predict Ss' classification and recognition judgments. Evidence was pro...

We prove the existence of the double scaling limit for unitary invariant ensembles of random matrices with non analytic potentials. The limiting reproducing kernel is expressed in terms of solutions of the Dirac system of differential equations with a potential defined by the Hastings-McLeod solution of the Painleve II equation. Our approach is based on the construction of the perturbation expa...

We examined how two distinct stimulus features, orientation and color, interact as contributions to global stimulus dissimilarity. Five subjects rated dissimilarity between pairs of bars (N = 30) varying in color (four cardinal hues, plus white) and orientation (six angles at 30° intervals). An exploratory analysis with individual-differences multidimensional scaling (MDS) resulted in a 5D solu...

The scaling limit for a class of interacting superprocesses and the associated singular, degenerate stochastic partial differential equation (SDSPDE) are investigated. It is proved that the scaling limit is a coalescing, purely-atomic-measure-valued process which is the unique strong solution of a reconstructed, associated SDSPDE.

One advantage of scaling vectors over a single scaling function is the compatibility of symmetry and orthogonality. This paper investigates the relationship between symmetry, vanishing moments, orthogonality, and support length for a scaling vector Φ. Some general results on scaling vectors and vanishing moments are developed, as well as some necessary conditions for the symbol entries of a sca...

In this paper, we characterize multiresolution analysis(MRA) Parseval frame multiwavelets in L^2(R^d) with matrix dilations of the form (D f )(x) = sqrt{2}f (Ax), where A is an arbitrary expanding dtimes d matrix with integer coefficients, such that |detA| =2. We study a class of generalized low pass matrix filters that allow us to define (and construct) the subclass of MRA tight frame multiwa...