The application of total positivity to computer aided curve and surface design

technical reportOf particular importance in an interactive curve and surface design system is the interface to the user. The mathematical model employed in the system must be sufficiently flexible for interaction between designer and machine to converge to a satisfactory result. The mathematical theory of Total Positivity is combined with the interactive techniques of Bezier and Riesenfeld in developing new methods of shape representation which retain the valuable variation-diminishing and convex hull properties of Bernstein and B-spline approximation, while providing improvements in the interactive interface to the user. Specifically, extending the Bezier notion of using a polygon to describe a smooth curve, methods of assigning a weight to each vertex which will control the amount of local fit to the polygon or polygonal net are provided. Thus, the designer can cause "cusps" and "flats" easily by manipulating the "tension" at each vertex. Further, the generalization from curves to surfaces can be done with rectilinear data or triangular data. Illustrations are provided from an experimental implementation of the newly constructed models as a demonstration of their feasibility and utility in computer aided curve and surface design

PhylOTU: a high-throughput procedure quantifies microbial community diversity and resolves novel taxa from metagenomic data.

Microbial diversity is typically characterized by clustering ribosomal RNA (SSU-rRNA) sequences into operational taxonomic units (OTUs). Targeted sequencing of environmental SSU-rRNA markers via PCR may fail to detect OTUs due to biases in priming and amplification. Analysis of shotgun sequenced environmental DNA, known as metagenomics, avoids amplification bias but generates fragmentary, non-overlapping sequence reads that cannot be clustered by existing OTU-finding methods. To circumvent these limitations, we developed PhylOTU, a computational workflow that identifies OTUs from metagenomic SSU-rRNA sequence data through the use of phylogenetic principles and probabilistic sequence profiles. Using simulated metagenomic data, we quantified the accuracy with which PhylOTU clusters reads into OTUs. Comparisons of PCR and shotgun sequenced SSU-rRNA markers derived from the global open ocean revealed that while PCR libraries identify more OTUs per sequenced residue, metagenomic libraries recover a greater taxonomic diversity of OTUs. In addition, we discover novel species, genera and families in the metagenomic libraries, including OTUs from phyla missed by analysis of PCR sequences. Taken together, these results suggest that PhylOTU enables characterization of part of the biosphere currently hidden from PCR-based surveys of diversity

Sorting and Selection in Posets

Classical problems of sorting and searching assume an underlying linear ordering of the objects being compared. In this paper, we study these problems in the context of partially ordered sets, in which some pairs of objects are incomparable. This generalization is interesting from a combinatorial perspective, and it has immediate applications in ranking scenarios where there is no underlying linear ordering, e.g., conference submissions. It also has applications in reconstructing certain types of networks, including biological networks. Our results represent significant progress over previous results from two decades ago by Faigle and Turán. In particular, we present the first algorithm that sorts a width-w poset of size n with query complexity O(n(w+\log n)) and prove that this query complexity is asymptotically optimal. We also describe a variant of Mergesort with query complexity O(wn log n/w) and total complexity O(w2n log n/w); an algorithm with the same query complexity was given by Faigle and Turán, but no efficient implementation of that algorithm is known. Both our sorting algorithms can be applied with negligible overhead to the more general problem of reconstructing transitive relations. We also consider two related problems: finding the minimal elements, and its generalization to finding the bottom k “levels,” called the k-selection problem. We give efficient deterministic and randomized algorithms for finding the minimal elements with query complexity and total complexity O(wn). We provide matching lower bounds for the query complexity up to a factor of 2 and generalize the results to the k-selection problem. Finally, we present efficient algorithms for computing a linear extension of a poset and computing the heights of all elements

GATA4 controls regionalization of tissue immunity and commensal-driven immunopathology

There is growing recognition that regionalization of bacterial colonization and immunity along the intestinal tract has an important role in health and disease. Yet, the mechanisms underlying intestinal regionalization and its dysregulation in disease are not well understood. This study found that regional epithelial expression of the transcription factor GATA4 controls bacterial colonization and inflammatory tissue immunity in the proximal small intestine by regulating retinol metabolism and luminal IgA. Furthermore, in mice without jejunal GATA4 expression, the commensal segmented filamentous bacteria promoted pathogenic inflammatory immune responses that disrupted barrier function and increased mortality upon Citrobacter rodentium infection. In celiac disease patients, low GATA4 expression was associated with metabolic alterations, mucosal Actinobacillus, and increased IL-17 immunity. Taken together, these results reveal broad impacts of GATA4-regulated intestinal regionalization on bacterial colonization and tissue immunity, highlighting an elaborate interdependence of intestinal metabolism, immunity, and microbiota in homeostasis and disease.</p

Antibiotic resistance: a physicist’s view

The problem of antibiotic resistance poses challenges across many disciplines. One such challenge is to understand the fundamental science of how antibiotics work, and how resistance to them can emerge. This is an area where physicists can make important contributions. Here, we highlight cases where this is already happening, and suggest directions for further physics involvement in antimicrobial research.Comment: 7 pages, 1 figur

Gene prediction in metagenomic fragments: A large scale machine learning approach

<p>Abstract</p> <p>Background</p> <p>Metagenomics is an approach to the characterization of microbial genomes via the direct isolation of genomic sequences from the environment without prior cultivation. The amount of metagenomic sequence data is growing fast while computational methods for metagenome analysis are still in their infancy. In contrast to genomic sequences of single species, which can usually be assembled and analyzed by many available methods, a large proportion of metagenome data remains as unassembled anonymous sequencing reads. One of the aims of all metagenomic sequencing projects is the identification of novel genes. Short length, for example, Sanger sequencing yields on average 700 bp fragments, and unknown phylogenetic origin of most fragments require approaches to gene prediction that are different from the currently available methods for genomes of single species. In particular, the large size of metagenomic samples requires fast and accurate methods with small numbers of false positive predictions.</p> <p>Results</p> <p>We introduce a novel gene prediction algorithm for metagenomic fragments based on a two-stage machine learning approach. In the first stage, we use linear discriminants for monocodon usage, dicodon usage and translation initiation sites to extract features from DNA sequences. In the second stage, an artificial neural network combines these features with open reading frame length and fragment GC-content to compute the probability that this open reading frame encodes a protein. This probability is used for the classification and scoring of gene candidates. With large scale training, our method provides fast single fragment predictions with good sensitivity and specificity on artificially fragmented genomic DNA. Additionally, this method is able to predict translation initiation sites accurately and distinguishes complete from incomplete genes with high reliability.</p> <p>Conclusion</p> <p>Large scale machine learning methods are well-suited for gene prediction in metagenomic DNA fragments. In particular, the combination of linear discriminants and neural networks is promising and should be considered for integration into metagenomic analysis pipelines. The data sets can be downloaded from the URL provided (see Availability and requirements section).</p

Predicting Prokaryotic Ecological Niches Using Genome Sequence Analysis

Automated DNA sequencing technology is so rapid that analysis has become the rate-limiting step. Hundreds of prokaryotic genome sequences are publicly available, with new genomes uploaded at the rate of approximately 20 per month. As a result, this growing body of genome sequences will include microorganisms not previously identified, isolated, or observed. We hypothesize that evolutionary pressure exerted by an ecological niche selects for a similar genetic repertoire in those prokaryotes that occupy the same niche, and that this is due to both vertical and horizontal transmission. To test this, we have developed a novel method to classify prokaryotes, by calculating their Pfam protein domain distributions and clustering them with all other sequenced prokaryotic species. Clusters of organisms are visualized in two dimensions as ‘mountains’ on a topological map. When compared to a phylogenetic map constructed using 16S rRNA, this map more accurately clusters prokaryotes according to functional and environmental attributes. We demonstrate the ability of this map, which we term a “niche map”, to cluster according to ecological niche both quantitatively and qualitatively, and propose that this method be used to associate uncharacterized prokaryotes with their ecological niche as a means of predicting their functional role directly from their genome sequence