Macaulay [12, 13] , introducing the notion of inverse systems, proposed duality as a strong combinatorial tool for performing ideal theory investigation. This conference is a survey of the recent combinatorial algorithms stemmed from Macaulay's ideas and the description they offer on the structure of a 0-dimensional ideal.

In this paper, to account for the effect of water stresses in the various growth stages under deficitirrigation, the multiplicative, seasonal and minimal approaches are integrated in the BUDGETmodel. To evaluate the model, the simulated yields for winter wheat (was grown in Sharif Abaddistrict) under various levels of water stress were compared with observed yields. The resultshowed, simulated ...

Abstract. We consider the problem of solving TAP mean field equations by iteration for Ising models with coupling matrices that are drawn at random from general invariant ensembles. We develop an analysis of iterative algorithms using a dynamical functional approach that in the thermodynamic limit yields an effective dynamics of a single variable trajectory. Our main novel contribution is the e...

In Geng, Weiss, and Wol (2011), we pointed to the possibility that a voting mechanism may create or strengthen an entitlement e ect in political-power holders relative to a random-appointment mechanism. This comment documents that such an e ect, if it exists, is not robust.