We show how to compute for n-vertex planar graphs in O(n11/6 polylog(n)) expected time the diameter and the sum of the pairwise distances. The algorithms work for directed graphs with real weights and no negative cycles. In O(n15/8 polylog(n)) expected time we can also compute the number of pairs of vertices at distance smaller than a given threshold. These are the first algorithms for these pr...

This study analyses the physical stature of runaway apprentices and military deserters based on advertisements collected from 18-century newspapers, in order to explore the biological welfare of colonial and early-national Americans. The results indicate that heights declined somewhat at mid-century, but increased substantially thereafter. The findings are generally in keeping with trends in mo...

Bollobás, Erdős, and Szemerédi (1975) [1] investigated a tripartite generalization of the Zarankiewicz problem: what minimum degree forces graph with n vertices in each part to contain an octahedral K3(2)? They proved that n+2−1/2n3/4 suffices suggested it could be weakened n+cn1/2 for some constant c>0. In this note we show their method only gives n+(1+o(1))n11/12 provide many constructions if...

This study analyses the physical stature of runaway apprentices and military deserters based on advertisements collected from 18-century newspapers, in order to explore the biological welfare of colonial and early-national Americans. The results indicate that heights declined somewhat at mid-century, but increased substantially thereafter. The findings are generally in keeping with trends in mo...

Supergravities are usually presented in a so-called 1.5 order formulation. Here we present a general scheme to derive pure 1 st order formulations of supergravities from the 1.5 order ones. The example of N4 = 1 supergravity will be rederived and new results for N4 = 2 and N11 = 1 will be presented. It seems that beyond four dimensions the auxiliary fields introduced to obtain first order formu...

We present efficient algorithms for broadcasting multiple messages. We assume n processors, one of which contains m packets that it must broadcast to each of the remaining n 1 processors. The processors communicate in rounds. In one round each processor is able to send one packet to any other processor and receive one packet from any other processor. We give a broadcasting algorithm which requi...