Orthogonal weighted linear L1 and L∞ approximation and applications

AbstractLet S={s1,s2,...,sn} be a set of sites in Ed, where every site si has a positive real weight ωi. This paper gives algorithms to find weighted orthogonal L∞ and L1 approximating hyperplanes for S. The algorithm for the weighted orthogonal L1 approximation is shown to require O(nd) worst-case time and O(n) space for d ≥ 2. The algorithm for the weighted orthogonal L∞ approximation is shown to require O(n log n) worst-case time and O(n) space for d = 2, and O(n⌊dl2 + 1⌋) worst-case time and O(n⌊(d+1)/2⌋) space for d > 2. In the latter case, the expected time complexity may be reduced to O(n⌊(d+1)/2⌋). The L∞ approximation algorithm can be modified to solve the problem of finding the width of a set of n points in Ed, and the problem of finding a stabbing hyperplane for a set of n hyperspheres in Ed with varying radii. The time and space complexities of the width and stabbing algorithms are seen to be the same as those of the L∞ approximation algorithm

Balancing Graph Voronoi Diagrams

Abstract—Many facility location problems are concerned with minimizing operation and transportation costs by par-titioning territory into regions of similar size, each of which is served by a facility. For many optimization problems, the overall cost can be reduced by means of a partitioning into balanced subsets, especially in those cases where the cost associated with a subset is superlinear in its size. In this paper, we consider the problem of generating a Voronoi partition of a discrete graph so as to achieve balance conditions on the region sizes. Through experimentation, we first establish that the region sizes of randomly-generated graph Voronoi diagrams vary greatly in practice. We then show how to achieve a balanced partition of a graph via Voronoi site resampling. For bounded-degree graphs, where each of the n nodes has degree at most d, and for an initial randomly-chosen set of s Voronoi nodes, we prove that, by extending the set of Voronoi nodes using an algorithm by Thorup and Zwick, each Voronoi region has size at most 4dn/s+1 nodes, and that the expected size of the extended set of Voronoi nodes is at most 2s logn. Keywords-graph Voronoi diagram; balancing; facility loca-tion; territorial design I

Image Retrieval with Reciprocal and shared Nearest Neighbors

International audienceContent-based image retrieval systems typically rely on a similarity measure between image vector representations, such as in bag-of-words, to rank the database images in decreasing order of expected relevance to the query. However, the inherent asymmetry of k-nearest neighborhoods is not properly accounted for by traditional similarity measures, possibly leading to a loss of retrieval accuracy. This paper addresses this issue by proposing similarity measures that use neighborhood information to assess the relationship between images. First, we extend previous work on k-reciprocal nearest neighbors to produce new measures that improve over the original primary metric. Second, we propose measures defined on sets of shared nearest neighbors for re-ranking the shortlist. Both these methods are simple, yet they significantly improve the accuracy of image search engines on standard benchmark datasets

Deleterious Mutation Burden and Its Association with Complex Traits in Sorghum (Sorghum bicolor)

Sorghum (Sorghum bicolor L.) is a major food cereal for millions of people worldwide. The sorghum genome, like other species, accumulates deleterious mutations, likely impacting its fitness. The lack of recombination, drift, and the coupling with favorable loci impede the removal of deleterious mutations from the genome by selection. To study how deleterious variants impact phenotypes, we identified putative deleterious mutations among ∼5.5 M segregating variants of 229 diverse biomass sorghum lines. We provide the whole-genome estimate of the deleterious burden in sorghum, showing that ∼33% of nonsynonymous substitutions are putatively deleterious. The pattern of mutation burden varies appreciably among racial groups. Across racial groups, the mutation burden correlated negatively with biomass, plant height, specific leaf area (SLA), and tissue starch content (TSC), suggesting that deleterious burden decreases trait fitness. Putatively deleterious variants explain roughly one-half of the genetic variance. However, there is only moderate improvement in total heritable variance explained for biomass (7.6%) and plant height (average of 3.1% across all stages). There is no advantage in total heritable variance for SLA and TSC. The contribution of putatively deleterious variants to phenotypic diversity therefore appears to be dependent on the genetic architecture of traits. Overall, these results suggest that incorporating putatively deleterious variants into genomic models slightly improves prediction accuracy because of extensive linkage. Knowledge of deleterious variants could be leveraged for sorghum breeding through either genome editing and/or conventional breeding that focuses on the selection of progeny with fewer deleterious alleles

Survivability Is More Fundamental Than Evolvability

For a lineage to survive over long time periods, it must sometimes change. This has given rise to the term evolvability, meaning the tendency to produce adaptive variation. One lineage may be superior to another in terms of its current standing variation, or it may tend to produce more adaptive variation. However, evolutionary outcomes depend on more than standing variation and produced adaptive variation: deleterious variation also matters. Evolvability, as most commonly interpreted, is not predictive of evolutionary outcomes. Here, we define a predictive measure of the evolutionary success of a lineage that we call the k-survivability, defined as the probability that the lineage avoids extinction for k generations. We estimate the k-survivability using multiple experimental replicates. Because we measure evolutionary outcomes, the initial standing variation, the full spectrum of generated variation, and the heritability of that variation are all incorporated. Survivability also accounts for the decreased joint likelihood of extinction of sub-lineages when they 1) disperse in space, or 2) diversify in lifestyle. We illustrate measurement of survivability with in silico models, and suggest that it may also be measured in vivo using multiple longitudinal replicates. The k-survivability is a metric that enables the quantitative study of, for example, the evolution of 1) mutation rates, 2) dispersal mechanisms, 3) the genotype-phenotype map, and 4) sexual reproduction, in temporally and spatially fluctuating environments. Although these disparate phenomena evolve by well-understood microevolutionary rules, they are also subject to the macroevolutionary constraint of long-term survivability

Deficiency of Huntingtin Has Pleiotropic Effects in the Social Amoeba Dictyostelium discoideum

Huntingtin is a large HEAT repeat protein first identified in humans, where a polyglutamine tract expansion near the amino terminus causes a gain-of-function mechanism that leads to selective neuronal loss in Huntington's disease (HD). Genetic evidence in humans and knock-in mouse models suggests that this gain-of-function involves an increase or deregulation of some aspect of huntingtin's normal function(s), which remains poorly understood. As huntingtin shows evolutionary conservation, a powerful approach to discovering its normal biochemical role(s) is to study the effects caused by its deficiency in a model organism with a short life-cycle that comprises both cellular and multicellular developmental stages. To facilitate studies aimed at detailed knowledge of huntingtin's normal function(s), we generated a null mutant of hd, the HD ortholog in Dictyostelium discoideum. Dictyostelium cells lacking endogenous huntingtin were viable but during development did not exhibit the typical polarized morphology of Dictyostelium cells, streamed poorly to form aggregates by accretion rather than chemotaxis, showed disorganized F-actin staining, exhibited extreme sensitivity to hypoosmotic stress, and failed to form EDTA-resistant cell–cell contacts. Surprisingly, chemotactic streaming could be rescued in the presence of the bivalent cations Ca2+ or Mg2+ but not pulses of cAMP. Although hd− cells completed development, it was delayed and proceeded asynchronously, producing small fruiting bodies with round, defective spores that germinated spontaneously within a glassy sorus. When developed as chimeras with wild-type cells, hd− cells failed to populate the pre-spore region of the slug. In Dictyostelium, huntingtin deficiency is compatible with survival of the organism but renders cells sensitive to low osmolarity, which produces pleiotropic cell autonomous defects that affect cAMP signaling and as a consequence development. Thus, Dictyostelium provides a novel haploid organism model for genetic, cell biological, and biochemical studies to delineate the functions of the HD protein

Gut Microbial Gene Expression in Mother-Fed and Formula-Fed Piglets

Effects of diet on the structure and function of gut microbial communities in newborn infants are poorly understood. High-resolution molecular studies are needed to definitively ascertain whether gut microbial communities are distinct in milk-fed and formula-fed infants.Pyrosequencing-based whole transcriptome shotgun sequencing (RNA-seq) was used to evaluate community wide gut microbial gene expression in 21 day old neonatal piglets fed either with sow's milk (mother fed, MF; n = 4) or with artificial formula (formula fed, FF; n = 4). Microbial DNA and RNA were harvested from cecal contents for each animal. cDNA libraries and 16S rDNA amplicons were sequenced on the Roche 454 GS-FLX Titanium system. Communities were similar at the level of phylum but were dissimilar at the level of genus; Prevotella was the dominant genus within MF samples and Bacteroides was most abundant within FF samples. Screened cDNA sequences were assigned functional annotations by the MG-RAST annotation pipeline and based upon best-BLASTX-hits to the NCBI COG database. Patterns of gene expression were very similar in MF and FF animals. All samples were enriched with transcripts encoding enzymes for carbohydrate and protein metabolism, as well as proteins involved in stress response, binding to host epithelium, and lipopolysaccharide metabolism. Carbohydrate utilization transcripts were generally similar in both groups. The abundance of enzymes involved in several pathways related to amino acid metabolism (e.g., arginine metabolism) and oxidative stress response differed in MF and FF animals.Abundant transcripts identified in this study likely contribute to a core microbial metatranscriptome in the distal intestine. Although microbial community gene expression was generally similar in the cecal contents of MF and FF neonatal piglets, several differentially abundant gene clusters were identified. Further investigations of gut microbial gene expression will contribute to a better understanding of normal and abnormal enteric microbiology in animals and humans

Mate choice for genetic quality when environments vary: suggestions for empirical progress

Mate choice for good-genes remains one of the most controversial evolutionary processes ever proposed. This is partly because strong directional choice should theoretically deplete the genetic variation that explains the evolution of this type of female mating preferences (the so-called lek paradox). Moreover, good-genes benefits are generally assumed to be too small to outweigh opposing direct selection on females. Here, we review recent progress in the study of mate choice for genetic quality, focussing particularly on the potential for genotype by environment interactions (GEIs) to rescue additive genetic variation for quality, and thereby resolve the lek paradox. We raise five questions that we think will stimulate empirical progress in this field, and suggest directions for research in each area: 1) How is condition-dependence affected by environmental variation? 2) How important are GEIs for maintaining additive genetic variance in condition? 3) How much do GEIs reduce the signalling value of male condition? 4) How does GEI affect the multivariate version of the lek paradox? 5) Have mating biases for high-condition males evolved because of indirect benefits