We study the I-ultrafilters on ω, where I is a a collection of subsets of a set X , usually R or ω1. The I-ultrafilters usually contain the P -points, often as a small proper subset. We study relations between I-ultrafilters for various I, and closure of I-ultrafilters under ultrafilter sums. We consider, but do not settle, the question whether I-ultrafilters always exist.

The clique vector c(G) of a graph G is the sequence (c1, c2, . . . , cd) in N, where ci is the number of cliques in G with i vertices and d is the largest cardinality of a clique in G. In this note, we use tools from commutative algebra to characterize all possible clique vectors of k-connected chordal graphs.

For every pattern P , consisting of a finite set of points in the plane, S′ P (n) is defined as the largest number of similar copies of P among sets of n points in the plane without 3 points on a line. A general construction, based on iterated Minkovski sums, is used to obtain new lower bounds for S′ P (n) when P is an arbitrary pattern. Improved bounds are obtained when P is a triangle or a re...

When adjusting the contrast setting on a television set, we experience a perceptual change in the global image contrast. But how is that statistic computed? We addressed this using a contrast-matching task for checkerboard configurations of micro-patterns in which the contrasts and spatial spreads of two interdigitated components were controlled independently. When the patterns differed greatly...

let $r$ be a right artinian ring or a perfect commutative‎‎ring‎. ‎let $m$ be a noncosingular self-generator $sum$-lifting‎‎module‎. ‎then $m$ has a direct decomposition $m=oplus_{iin i} m_i$‎,‎where each $m_i$ is noetherian quasi-projective and each‎‎endomorphism ring $end(m_i)$ is local‎.

We develop a new analysis of the lateral geniculate nucleus (LGN) input to a cortical simple cell, demonstrating that this input is the sum of two terms, a linear term and a nonlinear term. In response to a drifting grating, the linear term represents the temporal modulation of input, and the nonlinear term represents the mean input. The nonlinear term, which grows with stimulus contrast, has b...