Monotone matrix functions of successive orders

This paper extends a result obtained by Wigner and von Neumann. We prove that a non-constant real-valued function, f(x), in C^3(I) where I is an interval of the real line, is a monotone matrix function of order n+1 on I if and only if a related, modified function gx0 (x) is a monotone matrix function of order n for every value of x0 in I, assuming that f' is strictly positive on I

DISCOV: A Neural Model of Colour Vision, with Applications to Image Processing and Classification

The DISCOV (Dimensionless Shunting Colour Vision) system models a cascade of primate colour vision cells: retinal ganglion, thalamic single opponent, and two classes of cortical double opponents. A unified model fotmalism derived from psychophysical axioms produces transparent network dynamics and principled parameter settings. DISCOV fits an array of physiological data for each cell type, and makes testable experimental predictions. Properties of DISCOV model cells are compared with properties of conesponding components in the alternative Neural Fusion model. A benchmark testbed demonstrates the marginal computational utility of each model cell type on a recognition task derived from orthophoto imagery.Air Force Office of Scientific Research (F49620-01-1-0423); National Geospatial-Intelligence Agency (NMA 201-01-1-2016); National Science Foundation (SBE-035437, DGE-0221680); Office of Naval Research (N00014-01-1-0624

Algebraic and Geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups coincides with the geometric intersection number for the sphere complex of the connected sum of copies of $S^2\times S^1$.Comment: 7 page