Analysis of Agglomerative Clustering

The diameter $k$-clustering problem is the problem of partitioning a finite subset of $\mathbb{R}^d$ into $k$ subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem (for all values of $k$) is the agglomerative clustering algorithm with the complete linkage strategy. For decades, this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper, we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension $d$ is a constant, we show that for any $k$ the solution computed by this algorithm is an $O(\log k)$-approximation to the diameter $k$-clustering problem. Our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm. Furthermore, we analyze the closely related $k$-center and discrete $k$-center problem. For the corresponding agglomerative algorithms, we deduce an approximation factor of $O(\log k)$ as well.Comment: A preliminary version of this article appeared in Proceedings of the 28th International Symposium on Theoretical Aspects of Computer Science (STACS '11), March 2011, pp. 308-319. This article also appeared in Algorithmica. The final publication is available at http://link.springer.com/article/10.1007/s00453-012-9717-

Building an Assessment Use Argument for sign language: the BSL Nonsense Sign Repetition Test

In this article, we adapt a concept designed to structure language testing more effectively, the Assessment Use Argument (AUA), as a framework for the development and/or use of sign language assessments for deaf children who are taught in a sign bilingual education setting. By drawing on data from a recent investigation of deaf children's nonsense sign repetition skills in British Sign Language, we demonstrate the steps of implementing the AUA in practical test design, development and use. This approach provides us with a framework which clearly states the competing values and which stakeholders hold these values. As such, it offers a useful foundation for test-designers, as well as for practitioners in sign bilingual education, for the interpretation of test scores and the consequences of their use

The genera Melanothamnus Bornet & Falkenberg and Vertebrata S.F. Gray constitute well-defined clades of the red algal tribe Polysiphonieae (Rhodomelaceae, Ceramiales).

Polysiphonia is the largest genus of red algae, and several schemes subdividing it into smaller taxa have been proposed since its original description. Most of these proposals were not generally accepted, and currently the tribe Polysiphonieae consists of the large genus Polysiphonia (190 species), the segregate genus Neosiphonia (43 species), and 13 smaller genera (< 10 species each). In this paper, phylogenetic relationships of the tribe Polysiphonieae are analysed, with particular emphasis on the genera Carradoriella, Fernandosiphonia, Melanothamnus, Neosiphonia, Polysiphonia sensu stricto, Streblocladia and Vertebrata. We evaluated the consistency of 14 selected morphological characters in the identified clades. Based on molecular phylogenetic (rbcL and 18S genes) and morphological evidence, two speciose genera are recognized: Vertebrata (including the type species of the genera Ctenosiphonia, Enelittosiphonia, Boergeseniella and Brongniartella) and Melanothamnus (including the type species of the genera Fernandosiphonia and Neosiphonia). Both genera are distinguished from other members of the Polysiphonieae by synapomorphic characters, the emergence of which could have provided evolutionarily selective advantages for these two lineages. In Vertebrata trichoblast cells are multinucleate, possibly associated with the development of extraordinarily long, photoprotective, trichoblasts. Melanothamnus has 3-celled carpogonial branches and plastids lying exclusively on radial walls of the pericentral cells, which similarly may improve resistance to damage caused by excessive light. Other relevant characters that are constant in each genus are also shared with other clades. The evolutionary origin of the genera Melanothamnus and Vertebrata is estimated as 75.7-95.78 and 90.7-138.66 Ma, respectively. Despite arising in the Cretaceous, before the closure of the Tethys Seaway, Melanothamnus is a predominantly Indo-Pacific genus and its near-absence from the northeastern Atlantic is enigmatic. The nomenclatural implications of this work are that 46 species are here transferred to Melanothamnus, six species are transferred to Vertebrata and 13 names are resurrected for Vertebrata

Phylogenetic Analysis of Seven WRKY Genes across the Palm Subtribe Attaleinae (Arecaceae) Identifies Syagrus as Sister Group of the Coconut

BACKGROUND:The Cocoseae is one of 13 tribes of Arecaceae subfam. Arecoideae, and contains a number of palms with significant economic importance, including the monotypic and pantropical Cocos nucifera L., the coconut, the origins of which have been one of the "abominable mysteries" of palm systematics for decades. Previous studies with predominantly plastid genes weakly supported American ancestry for the coconut but ambiguous sister relationships. In this paper, we use multiple single copy nuclear loci to address the phylogeny of the Cocoseae subtribe Attaleinae, and resolve the closest extant relative of the coconut. METHODOLOGY/PRINCIPAL FINDINGS:We present the results of combined analysis of DNA sequences of seven WRKY transcription factor loci across 72 samples of Arecaceae tribe Cocoseae subtribe Attaleinae, representing all genera classified within the subtribe, and three outgroup taxa with maximum parsimony, maximum likelihood, and Bayesian approaches, producing highly congruent and well-resolved trees that robustly identify the genus Syagrus as sister to Cocos and resolve novel and well-supported relationships among the other genera of the Attaleinae. We also address incongruence among the gene trees with gene tree reconciliation analysis, and assign estimated ages to the nodes of our tree. CONCLUSIONS/SIGNIFICANCE:This study represents the as yet most extensive phylogenetic analyses of Cocoseae subtribe Attaleinae. We present a well-resolved and supported phylogeny of the subtribe that robustly indicates a sister relationship between Cocos and Syagrus. This is not only of biogeographic interest, but will also open fruitful avenues of inquiry regarding evolution of functional genes useful for crop improvement. Establishment of two major clades of American Attaleinae occurred in the Oligocene (ca. 37 MYBP) in Eastern Brazil. The divergence of Cocos from Syagrus is estimated at 35 MYBP. The biogeographic and morphological congruence that we see for clades resolved in the Attaleinae suggests that WRKY loci are informative markers for investigating the phylogenetic relationships of the palm family

The Genetics and Genomics of Virus Resistance in Maize

Viruses cause significant diseases on maize worldwide. Intensive agronomic practices, changes in vector distribution, and the introduction of vectors and viruses into new areas can result in emerging disease problems. Because deployment of resistant hybrids and cultivars is considered to be both economically viable and environmentally sustainable, genes and quantitative trait loci for most economically important virus diseases have been identified. Examination of multiple studies indicates the importance of regions of maize chromosomes 2, 3, 6, and 10 in virus resistance. An understanding of the molecular basis of virus resistance in maize is beginning to emerge, and two genes conferring resistance to sugarcane mosaic virus, Scmv1 and Scmv2, have been cloned and characterized. Recent studies provide hints of other pathways and genes critical to virus resistance in maize, but further work is required to determine the roles of these in virus susceptibility and resistance. This research will be facilitated by rapidly advancing technologies for functional analysis of genes in maize

Summary and Recommendations from Working Group 1: model uncertainty representations in convection-permitting / shorter lead-time / limited-area ensembles

WG3 discussed both the pros and cons of existing schemes as Working group 1 considered the treatment of model uncertainty (MU) in high-resolution ensembles, at grid spacings of order 1-5 km. These systems are often run for regional weather forecasting, perhaps over a single country, and for lead times of up to 5 days. Looking ahead, ECMWF’s strategy seeks to deliver global medium-range ensemble forecasts with 3-4 km grid spacings by 2030. It is questionable for what grid spacing we should dispense with a deep convection parameterization, but it will be either switched off or damped in these systems, such that deep convection can be assumed to be dominated by explicit motions. One of the problems with limited-area ensemble systems at this scale is that spread depends not only on the modelling system itself but also on the variability inherited from the large-scale boundary conditions. There is often thought to be a lack of spread in our high-resolution EPS (ensemble prediction systems), but this could reflect a lack of diversity on larger scales. The relative importance of lateral-boundary diversity and the model uncertainty mechanisms is regime dependent. The lateral boundaries will generally be more important in midlatitude winter but less so for summertime convection in relatively weak synoptic flow