The fungal family Clavicipitaceae includes plant symbionts and parasites that produce several psychoactive and bioprotective alkaloids. The family includes grass symbionts in the epichloae clade (Epichloë and Neotyphodium species), which are extraordinarily diverse both in their host interactions and in their alkaloid profiles. Epichloae produce alkaloids of four distinct classes, all of which deter insects, and some—including the infamous ergot alkaloids—have potent effects on mammals. The exceptional chemotypic diversity of the epichloae may relate to their broad range of host interactions, whereby some are pathogenic and contagious, others are mutualistic and vertically transmitted (seed-borne), and still others vary in pathogenic or mutualistic behavior. We profiled the alkaloids and sequenced the genomes of 10 epichloae, three ergot fungi (Claviceps species), a morning-glory symbiont (Periglandula ipomoeae), and a bamboo pathogen (Aciculosporium take), and compared the gene clusters for four classes of alkaloids. Results indicated a strong tendency for alkaloid loci to have conserved cores that specify the skeleton structures and peripheral genes that determine chemical variations that are known to affect their pharmacological specificities. Generally, gene locations in cluster peripheries positioned them near to transposon-derived, AT-rich repeat blocks, which were probably involved in gene losses, duplications, and neofunctionalizations. The alkaloid loci in the epichloae had unusual structures riddled with large, complex, and dynamic repeat blocks. This feature was not reflective of overall differences in repeat contents in the genomes, nor was it characteristic of most other specialized metabolism loci. The organization and dynamics of alkaloid loci and abundant repeat blocks in the epichloae suggested that these fungi are under selection for alkaloid diversification. We suggest that such selection is related to the variable life histories of the epichloae, their protective roles as symbionts, and their associations with the highly speciose and ecologically diverse cool-season grasses.

While the theoretical foundation of optimal camera placement has been studied for decades, its practical implementation has recently attracted significant research interest due to the increasing popularity of visual sensor network. The discrete camera placement problem is NP-hard and many approximate solutions have been independently studied. The goal of this paper is to provide a comprehensive framework in comparing the merits of these techniques. We consider two general classes of camera placement problems and adapt some of the most commonly used approximation techniques in solving them. The accuracy, efficiency and scalability of each technique are analyzed and compared in depth. Extensive experimental results are provided to illustrate the strength and weakness of each method.

We encode the binomials belonging to the toric ideal I A associated with an integral d × n matrix A using a short sum of rational functions as introduced by Barvinok Barvinok (1994); Barvinok and Woods (2003). Under the assumption that d, n are fixed, this representation allows us to compute the Graver basis and the reduced Gröbner basis of the ideal I A , with respect to any term order, in time polynomial in the size of the input. We also derive a polynomial time algorithm for normal form computation which replaces in this new encoding the usual reductions typical of the division algorithm. We describe other applications, such as the computation of Hilbert series of normal semigroup rings, and we indicate further connections to integer programming and statistics.Let A = (a ij ) be an integral d × n-matrix and b ∈ Z d such that the convex polyhedron P = { u ∈ R n : A · u = b and u ≥ 0 } is bounded. Barvinok (1994) ⋆

Due to a production error the article was published with mistakes in the paragraph following Theorem 1. The corrected paragraph appears below.The computation of volumes is one of the most fundamental geometric operations and it has been investigated by several authors from the algorithmic point of view. Although there are a few cases for which the volume can be computed efficiently (e.g., for convex polytopes in fixed dimension), it has been proved that computing the volume of polytopes of varying dimension is #P -hard [9, 17, 26, 30]. Moreover it was proved that even approximating the volume is hard [19]. Clearly, computing Ehrhart polynomials is a harder problem still. To our knowledge there were only two previously known families of varying-dimension polytopes for which there is efficient computation of the volume. These two families are simplices or simple polytopes with a polynomial number of vertices (this follows from Lawrence's volumeThe online version of the original article can be found under

Accurate prediction of complex traits based on whole-genome data is a computational problem of paramount importance, particularly to plant and animal breeders. However, the number of genetic markers is typically orders of magnitude larger than the number of samples (p >> n), amongst other challenges. We assessed the effectiveness of a diverse set of state-of-the-art methods on publicly accessible real data. The most surprising finding was that approaches with feature selection performed better than others on average, in contrast to the expectation in the community that variable selection is mostly ineffective, i.e. that it does not improve accuracy of prediction, in spite of p >> n. We observed superior performance despite a somewhat simplistic approach to variable selection, possibly suggesting an inherent robustness. This bodes well in general since the variable selection methods usually improve interpretability without loss of prediction power. Apart from identifying a set of benchmark data sets (including one simulated data), we also discuss the performance analysis for each data set in terms of the input characteristics.

This paper deals with faces and facets of the family-variable polytope and the characteristic-imset polytope, which are special polytopes used in integer linear programming approaches to statistically learn Bayesian network structure. A common form of linear objectives to be maximized in this area leads to the concept of score equivalence (SE), both for linear objectives and for faces of the family-variable polytope.We characterize the linear space of SE objectives and establish a one-to-one correspondence between SE faces of the family-variable polytope, the faces of the characteristic-imset polytope, and standardized supermodular functions. The characterization of SE facets in terms of extremality of the corresponding supermodular function gives an elegant method to verify whether an inequality is SE-facet-defining for the family-variable polytope.We also show that when maximizing an SE objective one can eliminate linear constraints of the family-variable polytope that correspond to non-SE facets. However, we show that solely considering SE facets is not enough as a counter-example shows; one has to consider the linear inequality constraints that correspond to facets of the characteristic-imset polytope despite the fact that they may not define facets in the family-variable mode.

Tree reconstruction methods are often judged by their accuracy, measured by how close they get to the true tree. Yet, most reconstruction methods like maximum likelihood (ML) do not explicitly maximize this accuracy. To address this problem, we propose a Bayesian solution. Given tree samples, we propose finding the tree estimate that is closest on average to the samples. This "median" tree is known as the Bayes estimator (BE). The BE literally maximizes posterior expected accuracy, measured in terms of closeness (distance) to the true tree. We discuss a unified framework of BE trees, focusing especially on tree distances that are expressible as squared euclidean distances. Notable examples include Robinson-Foulds (RF) distance, quartet distance, and squared path difference. Using both simulated and real data, we show that BEs can be estimated in practice by hill-climbing. In our simulation, we find that BEs tend to be closer to the true tree, compared with ML and neighbor joining. In particular, the BE under squared path difference tends to perform well in terms of both path difference and RF distances.

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