We study the maximum possible sign rank of N×N sign matrices with a given VC dimension d. For d = 1, this maximum is 3. For d = 2, this maximum is Θ̃(N1/2). Similar (slightly less accurate) statements hold for d > 2 as well. We discuss the tightness of our methods, and describe connections to combinatorics, communication complexity and learning theory. We also provide explicit examples of matric...

Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for th...

| Methods for matrix decomposition have found numerous applications in image processing, in particular for the problem of template decomposition. Since existing matrix decomposition techniques are mainly concerned with the linear domain, we consider it timely to investigate matrix decomposition techniques in the nonlinear domain with applications in image processing. The mathematical basis for ...

The minimum rank of a simple graph G is the smallest possible rank over all symmetric real matrices A whose nonzero off-diagonal entries correspond to the edges of G. Using the zero forcing number, we prove that the minimum rank of the r-th butterfly network is 1 9 [ (3r + 1)2r+1 − 2(−1)r ] and that this is equal to the rank of its adjacency matrix.