We show that if the number I of incidences between m points and n planes in R is sufficiently large, then the incidence graph (that connects points to their incident planes) contains a large complete bipartite subgraph involving r points and s planes, so that rs ≥ I2 mn−a(m+n), for some constant a > 0. This is shown to be almost tight in the worst case because there are examples of arbitrarily ...

Fuzzy incidence graphs can be used as models for nondeterministic interconnection networks having extra node-edgerelationships. For example, ramps in a highway system may be modeled as a fuzzy incidence graph so that unexpectedflow between cities and highways can be effectively studied and controlled. Like node and edge connectivity in graphs,node connectivity and arc connectivity in fuzzy inci...

AIMS Conventional definitions of obesity, e.g. body mass index (BMI) ≥ 30 kg/m² or waist circumference cut-points of 102 cm (men) and 88 cm (women), may underestimate metabolic risk in non-Europeans. We prospectively identified equivalent ethnicity-specific obesity cut-points for the estimation of diabetes risk in British South Asians, African-Caribbeans and Europeans. METHODS We studied a po...

Transmission X-ray mirrors have been fabricated from 300-400 nm-thick low-stress silicon nitride windows of size 0.6 mm x 85 mm. The windows act as a high-pass energy filter at grazing incidence in an X-ray beam for the beam transmitted through the window. The energy cut-off can be selected by adjusting the incidence angle of the transmission mirror, because the energy cut-off is a function of ...

The cut polytope P,(G) of a graph G is the convex hull of the incidence vectors of all cuts of G; the cut cone C(G) of G is the cone generated by the incidence vectors of all cuts of G. We introduce the operation of collapsing an inequality valid over the cut cone C(K,) of the complete graph with n vertices: it consists of identifying vertices and adding the weights of the corresponding inciden...

We have previously reported that the majority of sudden cardiac death (SCD) events were associated with postprandial hyperlipidemia in Japanese subjects. In this investigation, we have compared LDL-cholesterol (LDL-C) and remnant-like lipoprotein particles (RLP) as cardiovascular risk factors in SCD cases, especially in Pokkuri death syndrome (PDS) cases who had nearly normal coronary arteries....

Deza, M. and M. Laurent, The even and odd cut polytopes, Discrete Mathematics 119 (1993) 49966. The cut polytope P, is the convex hull of the incidence vectors of all cuts of the complete graph K, on n nodes. An even cut is a cut of even cardinality. For n odd, all cuts are even. For n even, we consider the even cut polytope EvP,, defined as the convex hull of the incidence vectors of all even ...