2008 NOV 24 - (VerticalNews.com) -- "It is proved that any pseudo-Boolean function f can be represented as f(x) equivalent to z + phi(x,(x) over bar), where z is the minimum of f and phi is a polynomial with positive coefficients in the original variables x(i) and in their complements (x) over bar (i)," scientists in Rome, Italy report.

  "A non-constructivc proof and a constructive one are given," wrote B. Simeone and colleagues, La Sapienza University ...read more

  2008 NOV 24 - (VerticalNews.com) -- "We propose a generic model for the ''weighted voting'' aggregation step performed by several methods in Supervised classification," scientists writing in the journal Discrete Applied Mathematics report.

  "Further, we construct an algorithm to enumerate the number of distinct aggregate classifiers that arise in this model," wrote J. Adem and colleagues.

  The researchers concluded: "When there are only two classes in the classification problem, we show that a class of functions that arises from aggregate classifiers coincides with the class of self-dual positive threshold Boolean functions. ...read more

  2008 NOV 24 - (VerticalNews.com) -- According to recent research from Lausanne, Switzerland, "This paper is motivated by a method used for DNA sequencing by hybridization presented in [Jacek Blazewicz, Marta Kasprzak, Computational complexity of isothernnic DNA sequencing by hybridization, Discrete Appl. Math. 154 (5) (2006) 718-7291. This paper presents a class of digraphs: the quasi-adjoint graphs."

  "This class includes the ones used in the paper cited above. A polynomial recognition algorithm in O(n(3)), as well as a polynomial algorithm in O(n(2) + m(2)) for finding a Hamiltonian circuit in these graphs are given," wrote J. Blazewicz and colleagues ...read more