A modified DEA model to estimate the importance of objectives with an application to agricultural economics

This paper demonstrates a connection between data envelopment analysis (DEA) and a non-interactive elicitation method to estimate the weights of objectives for decision-makers in a multiple attribute approach. This connection gives rise to a modified DEA model that allows us to estimate not only efficiency measures but also preference weights by radially projecting each unit onto a linear combination of the elements of the payoff matrix (which is obtained by standard multicriteria methods). For users of multiple attribute decision analysis the basic contribution of this paper is a new interpretation in terms of efficiency of the non-interactive methodology employed to estimate weights in a multicriteria approach. We also propose a modified procedure to calculate an efficient payoff matrix and a procedure to estimate weights through a radial projection rather than a distance minimization. For DEA users, we provide a modified DEA procedure to calculate preference weights and efficiency measures that does not depend on any observations in the dataset. This methodology has been applied to an agricultural case study in Spain.

Generalized isotropic Lipkin-Meshkov-Glick models: ground state entanglement and quantum entropies

We introduce a new class of generalized isotropic Lipkin–Meshkov–Glick models with su(m+1) spin and long-range non-constant interactions, whose non-degenerate ground state is a Dicke state of su(m+1) type. We evaluate in closed form the reduced density matrix of a block of Lspins when the whole system is in its ground state, and study the corresponding von Neumann and Rényi entanglement entropies in the thermodynamic limit. We show that both of these entropies scale as a log L when L tends to infinity, where the coefficient a is equal to (m  −  k)/2 in the ground state phase with k vanishing magnon densities. In particular, our results show that none of these generalized Lipkin–Meshkov–Glick models are critical, since when L-->∞ their Rényi entropy R_q becomes independent of the parameter q. We have also computed the Tsallis entanglement entropy of the ground state of these generalized su(m+1) Lipkin–Meshkov–Glick models, finding that it can be made extensive by an appropriate choice of its parameter only when m-k≥3. Finally, in the su(3) case we construct in detail the phase diagram of the ground state in parameter space, showing that it is determined in a simple way by the weights of the fundamental representation of su(3). This is also true in the su(m+1) case; for instance, we prove that the region for which all the magnon densities are non-vanishing is an (m  +  1)-simplex in R^m whose vertices are the weights of the fundamental representation of su(m+1).