Narrow Results

We propose a two-step algorithm that efficiently constructs a schedule of minimum makespan for the precedence multiprocessor constrained scheduling problem in the presence of hierarchical communications and task duplication. We consider the case where all the tasks of the precedence graph have unit execution times, and the multiprocessor is composed by an unbounded number of clusters with two identical processors each. The communication delay for transferring the data between a predecessor-task and a successor-task executed on processors of different clusters take a unit of time, while this cost becomes null whenever these tasks are executed on the same processor or on different processors of the same cluster. The first step of the algorithm computes for each task an earliest starting time of any of its copies and constructs a critical graph whereas the second step uses the obtained critical graph and task duplication to build up an earliest optimal schedule.

In software product line engineering (SPLE), many studies have been conducted on commonality- and variability-based feature extraction methods and on the reasoning and refinement of feature models (FMs), aiming to enhance the appropriateness and reusability of the constructed FMs in compliance with feature-oriented development. The existing methods, however, failed to assure the developed applications that contain ambiguities between the features generated in FMs by analyzers' intuitions, and hindered the reuse of such applications. Moreover, the accuracy measurements of models based on mathematics-based theoretical verification methods are difficult to apply in practice. Therefore, a refinement technique is demanded to enhance the FM accuracy.

This paper aims to identify abnormal feature duplications and collisions based on the feature attributes to address the potential ambiguities between the features in an FM generated for a target domain, and to construct more precise FMs by presenting a technique for eliminating such abnormalities. For this purpose, the profiles of the formalized attributes were first defined based on MDR. Based on the semantics and relationships between the attributes, the duplications and collisions were identified using an analysis matrix, and were generalized to formulate rules by level. Such rules were evaluated to remove the duplications and collisions. In addition, using a supporting analyzer, the features in the initial FM were registered on a repository and were analyzed for feature duplications and collisions based on the saved attribute data.

The refinements of the ambiguities between such features are likely to enable the construction of more precise application FMs and the generation of common features with higher reusability. Further, the environments using support tools are expected to provide convenience in the similarity analysis and reuse of features.

We introduce two groups of duplication processes that extend the well known Cayley–Dickson process. The first one allows to embed every $4$-dimensional (4D) real unital algebra ${𝒜}$ into an 8D real unital algebra denoted by $\mathrm{\text{FD}}({𝒜}).$ We also find the conditions on ${𝒜}$ under which $\mathrm{\text{FD}}({𝒜})$ is a division algebra. This covers the most classes of known $4$D real division algebras. The second process allows us to embed particular classes of $4$D RDAs into $8$D RDAs. Besides, both duplication processes give an infinite family of non-isomorphic $8$D real division algebras whose derivation algebras contain $\mathrm{\text{su}}(2)$.

The rice (Oryza sativa L.) genome has become the reference genome to which others are compared. Part of the reason for this is that rice has the lowest DNA content of the common cereals and its gene content and gene order are found in other grass species used for food. Having the genome sequence of rice, both japonica and indica, allows comparisons with regard to genomic structure, gene constitution, and gene expression. Map locations for single-copy genes, families of genes, and quantitative trait loci (QTLs) are often compared among species, usually with rice as the reference. Specialized databases have been developed to facilitate cross-species homology relationships relative to genome and EST sequencing, protein structure, gene function, and other useful aspects. The evolutionary relationship of rice and several other cereals such as maize (Zea mays L.) and sorghum is clearly observed when highlighting syntenic regions. The colinearity of rice and American wildrice (Zizania palustris) has been exploited to develop a molecular genetic map and to locate QTLs in wildrice. The goal of this paper is to illustrate the value of rice for comparative genome referencing.