We present in this paper an improved estimation of duality gap between binary quadratic program and its Lagrangian dual. More specifically, we obtain this improved estimation using a weighted distance measure between the binary set and certain affine subspace. We show that the optimal weights...

We provide a definition of a diametric magic circle of order n. In this paper, we use techniques in computational algebraic combinatorics and enumerative geometry to construct and to count d-magic circles. We also provide a description of its minimal Hilbert basis and determine the symmetry...

AMS classification: 05C50;

The paper outlines a general framework for statistical legislation. The implications of statistical legislation for the whole statistical system, as well as for centralized versus decentralized statistical systems, are addressed. The general framework is spelled out by identifying "essential"...