β Scribed by Iiro Honkala; Antoine Lobstein
No coin nor oath required. For personal study only.
Let G=(V, E) be an undirected graph and C a subset of vertices. If the sets B r (v) 5 C, v Β₯ V, are all nonempty and different, where B r (v) denotes the set of all points within distance r from v, we call C an r-identifying code. We give bounds on the best possible density of r-identifying codes in the two-dimensional square lattice.
π SIMILAR VOLUMES
The critical probability for site percolation on the square lattice is not known exactly. Several authors have given rigorous upper and lower bounds. Some recent lower bounds are (each displayed here with the first three digits) 0.503 (Toth [13]), 0.522 (Zuev [15]), and the best lower bound so far,
A cutset in the poset 2 [n] , of subsets of [1, ..., n] ordered by inclusion, is a subset of 2 [n] that intersects every maximal chain. Let 0 : 1 be a real number. Is it possible to find a cutset in 2 [n] that, for each 0 i n, contains at most : ( n i ) subsets of size i ? Let :(n) be the greatest l
Abstroct~Every linear parameter estimation problem gives rise to an overdetermined set of linear equations AX ~ B which is usually solved with the ordinary least squares (LS) method. Often, both A and B are inaccurate. For these cases, a more general fitting technique, called total least squares (TL