We propose two algorithms for constructing and training compact feedforward networks of linear threshold units. The SHIFT procedure constructs networks with a single hidden layer while the PTI… (More)

Let C be the clutter of odd circuits of a signed graph ðG;SÞ: For nonnegative integral edge-weights w; we are interested in the linear program minðwtx: xðCÞ51; for C 2 C; and x50Þ; which we denote by… (More)

We give an “excluded minor” and a “structural” characterization of digraphs that have the property that for every subdigraph of , the maximum number of disjoint circuits in is equal to the minimum… (More)

A binary clutter is the family of odd circuits of a binary mat roid, that is, the family of circuits that intersect with odd cardinality a fixed given subset of elemen ts. LetA denote the0;1 matrix… (More)

A pair of square0, 1 matricesA, B such thatAB = E + kI (whereE is the n × n matrix of all 1s andk is a positive integer) are called Lehman matrices . These matrices figure prominently in Lehman’s… (More)

Seymour proved that the set of odd circuits of a signed binar y matroid(M; ) has the Max-Flow Min-Cut property if and only if it does not contain a minor isomorphic to(M(K4); E(K4)). We give a… (More)

Several of the finest unclaimed prizes in directed graph theory involve the packing of directed joins. One difficulty in claiming these prizes is that the broad conjecture posed by Edmonds and Giles,… (More)