rbcL sequences indicate a single evolutionary origin of multinucleate cells in the red algal tribe Callithamnieae.

In the Ceramiaceae, one of the largest families of the red algae, there are from 1 to 4000 nuclei in each vegetative cell, but each tribe is homogeneous with respect to the uninucleate/multinucleate character state, except for the Callithamnieae. The goals of this study were to analyze rbcL gene sequences to clarify the evolution of taxa within the tribe Callithamnieae and to evaluate the potential evolutionary significance of the development of multinucleate cells in certain taxa. The genus Aglaothamnion, segregated from Callithamnion because it is uninucleate, was paraphyletic in all analyses. Callithamnion (including Aristothamnion) was monophyletic although not robustly so, apparently due to variations between taxa in rate of sequence evolution. Morphological synapomorphies were identified at different depths in the tree, supporting the molecular phylogenetic analysis. The uninucleate character state is ancestral in this tribe. The evolution of multinucleate cells has occurred once in the Callithamnieae. Multiple nuclei in each cell may combine the benefits of small C values (rapid cell cycle) with large cells (permitting morphological elaboration) while maintaining a constant ratio of nuclear volume: cytoplasmic volume.

Spectrally bounded operators from von Neumann algebras

We prove that every unital spectrally bounded operator from a properly infinite von Neumann algebra onto a semisimple Banach algebra is a Jordan homomorphism.

Software Release Planning: An Evolutionary and Iterative Approach

Abstract To achieve higher flexibility and to better satisfy actual customer requirements, there is an increasing tendency to develop and deliver software in an incremental fashion. In adopting this process, requirements are delivered in releases and so a decision has to be made on which requirements should be delivered in which release. Three main considerations that need to be taken account of are the technical precedences inherent in the requirements, the typically conflicting priorities as determined by the representative stakeholders, as well as the balance between required and available effort. The technical precedence constraints relate to situations where one requirement cannot be implemented until another is completed or where one requirement is implemented in the same increment as another one. Stakeholder preferences may be based on the perceived value or urgency of delivered requirements to the different stakeholders involved. The technical priorities and individual stakeholder priorities may be in conflict and difficult to reconcile. This paper provides (i) a method for optimally allocating requirements to increments; (ii) a means of assessing and optimizing the degree to which the ordering conflicts with stakeholder priorities within technical precedence constraints; (iii) a means of balancing required and available resources for all increments; and (iv) an overall method called EVOLVE aimed at the continuous planning of incremental software development. The optimization method used is iterative and essentially based on a genetic algorithm. A set of the most promising candidate solutions is generated to support the final decision. The paper evaluates the proposed approach using a sample project.

Entanglement between collective operators in a linear harmonic chain

We investigate entanglement between collective operators of two blocks of oscillators in an infinite linear harmonic chain. These operators are defined as averages over local operators (individual oscillators) in the blocks. On the one hand, this approach of "physical blocks" meets realistic experimental conditions, where measurement apparatuses do not interact with single oscillators but rather with a whole bunch of them, i.e., where in contrast to usually studied "mathematical blocks" not every possible measurement is allowed. On the other, this formalism naturally allows the generalization to blocks which may consist of several noncontiguous regions. We quantify entanglement between the collective operators by a measure based on the Peres-Horodecki criterion and show how it can be extracted and transferred to two qubits. Entanglement between two blocks is found even in the case where none of the oscillators from one block is entangled with an oscillator from the other, showing genuine bipartite entanglement between collective operators. Allowing the blocks to consist of a periodic sequence of subblocks, we verify that entanglement scales at most with the total boundary region. We also apply the approach of collective operators to scalar quantum field theory.