Approximation Simply Characterized

A Well-Characterized Approximation Problem

We consider the following NP optimization problem: Given a set of polynomials Pi(x), i = 1 : : : s of degree at most 2 over GF [p] in n variables, nd a root common to as many as possible of the polynomials Pi(x). We prove that in the case when the polynomials do not contain any squares as monomials, it is always possible to approximate this problem within a factor of p 2 p 1 in polynomial time ...

Simply Presented Tag Modules

A tag module is a generalization, in any abelian category, of a torsion abelian group. The theory of such modules is developed, it is shown that countably generated tag modules are simply presented, and that Ulm's theorem holds for simply presented tag modules. Zippin's theorem is stated and proved for countably generated tag modules. 1. TAG-modules In the theory of torsion abelian groups, a di...

Auxin: simply complicated.

Auxin is a plant hormone involved in an extraordinarily broad variety of biological mechanisms. These range from basic cellular processes, such as endocytosis, cell polarity, and cell cycle control over localized responses such as cell elongation and differential growth, to macroscopic phenomena such as embryogenesis, tissue patterning, and de novo formation of organs. Even though the history o...

Learning from Experience, Simply

There is substantial academic interest in modeling consumer experiential learning. However, (approximately) optimal solutions to forward-looking experiential learning problems are complex, limiting their behavioral plausibility and empirical feasibility. We propose that consumers use cognitively simple heuristic strategies. We explore one viable heuristic – index strategies, and demonstrate tha...

‘Simply my own’