A new genus and new species of fan worms (Polychaeta: Sabellidae) from Atlantic and Pacific Oceans-the formal treatment of taxon names as explanatory hypotheses

Members of Parasabella minuta Treadwell, 1941, subsequently moved to Perkinsiana, were collected during a survey of rocky intertidal polychaetes along the state of Sao Paulo, Brazil. Additional specimens, which are referred to two new species, were also found in similar habitats from the Bocas del Toro Archipelago, Caribbean Panama, and Oahu Island, Hawaii. A phylogenetic analysis of Sabellinae, including members of P. minuta and the two new species, provided justification for establishing a new generic hypothesis, Sabellomma gen. nov., for these individuals. Formal definitions are also provided for Sabellomma minuta gen. nov., comb. nov., S. collinae gen. nov., spec. nov., and S. harrisae gen. nov., spec. nov., along with descriptions of individuals to which these hypotheses apply. The generic name Aracia nom. nov., is provided to replace Kirkia Nogueira, Lopez and Rossi, 2004, pre-occupied by a mollusk.

Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.