On Waring's problem: two squares and three biquadrates

We investigate sums of mixed powers involving two squares and three biquadrates. In particular, subject to the truth of the Generalised Riemann Hypothesis and the Elliott-Halberstam Conjecture, we show that all large natural numbers n with 8 not dividing n, n not congruent to 2 modulo 3, and n not congruent to 14 modulo 16, are the sum of 2 squares and 3 biquadrates.Comment: to appear in Mathematik

Ventilation of animal shelters

Caption title.Digitized 2006 AES MoU

Buildings for the dairy enterprise

Cover title.Includes bibliographical references

The durability of fence posts

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Advances in biodiversity: metagenomics and the unveiling of biological dark matter

BACKGROUND: Efforts to harmonize genomic data standards used by the biodiversity and metagenomic research communities have shown that prokaryotic data cannot be understood or represented in a traditional, classical biological context for conceptual reasons, not technical ones. RESULTS: Biology, like physics, has a fundamental duality—the classical macroscale eukaryotic realm vs. the quantum microscale microbial realm—with the two realms differing profoundly, and counter-intuitively, from one another. Just as classical physics is emergent from and cannot explain the microscale realm of quantum physics, so classical biology is emergent from and cannot explain the microscale realm of prokaryotic life. Classical biology describes the familiar, macroscale realm of multi-cellular eukaryotic organisms, which constitute a highly derived and constrained evolutionary subset of the biosphere, unrepresentative of the vast, mostly unseen, microbial world of prokaryotic life that comprises at least half of the planet’s biomass and most of its genetic diversity. The two realms occupy fundamentally different mega-niches: eukaryotes interact primarily mechanically with the environment, prokaryotes primarily physiologically. Further, many foundational tenets of classical biology simply do not apply to prokaryotic biology. CONCLUSION: Classical genetics one held that genes, arranged on chromosomes like beads on a string, were the fundamental units of mutation, recombination, and heredity. Then, molecular analysis showed that there were no fundamental units, no beads, no string. Similarly, classical biology asserts that individual organisms and species are fundamental units of ecology, evolution, and biodiversity, composing an evolutionary history of objectively real, lineage-defined groups in a single-rooted tree of life. Now, metagenomic tools are forcing a recognition that there are no completely objective individuals, no unique lineages, and no one true tree. The newly revealed biosphere of microbial dark matter cannot be understood merely by extending the concepts and methods of eukaryotic macrobiology. The unveiling of biological dark matter is allowing us to see, for the first time, the diversity of the entire biosphere and, to paraphrase Darwin, is providing a new view of life. Advancing and understanding that view will require major revisions to some of the most fundamental concepts and theories in biology

A Primer on Metagenomics

Metagenomics is a discipline that enables the genomic study of uncultured microorganisms. Faster, cheaper sequencing technologies and the ability to sequence uncultured microbes sampled directly from their habitats are expanding and transforming our view of the microbial world. Distilling meaningful information from the millions of new genomic sequences presents a serious challenge to bioinformaticians. In cultured microbes, the genomic data come from a single clone, making sequence assembly and annotation tractable. In metagenomics, the data come from heterogeneous microbial communities, sometimes containing more than 10,000 species, with the sequence data being noisy and partial. From sampling, to assembly, to gene calling and function prediction, bioinformatics faces new demands in interpreting voluminous, noisy, and often partial sequence data. Although metagenomics is a relative newcomer to science, the past few years have seen an explosion in computational methods applied to metagenomic-based research. It is therefore not within the scope of this article to provide an exhaustive review. Rather, we provide here a concise yet comprehensive introduction to the current computational requirements presented by metagenomics, and review the recent progress made. We also note whether there is software that implements any of the methods presented here, and briefly review its utility. Nevertheless, it would be useful if readers of this article would avail themselves of the comment section provided by this journal, and relate their own experiences. Finally, the last section of this article provides a few representative studies illustrating different facets of recent scientific discoveries made using metagenomics

The control of gullies

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The draft of farm wagons as affected by height of wheel and width of tire

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TOPSAN: a collaborative annotation environment for structural genomics

<p>Abstract</p> <p>Background</p> <p>Many protein structures determined in high-throughput structural genomics centers, despite their significant novelty and importance, are available only as PDB depositions and are not accompanied by a peer-reviewed manuscript. Because of this they are not accessible by the standard tools of literature searches, remaining underutilized by the broad biological community.</p> <p>Results</p> <p>To address this issue we have developed TOPSAN, The Open Protein Structure Annotation Network, a web-based platform that combines the openness of the wiki model with the quality control of scientific communication. TOPSAN enables research collaborations and scientific dialogue among globally distributed participants, the results of which are reviewed by experts and eventually validated by peer review. The immediate goal of TOPSAN is to harness the combined experience, knowledge, and data from such collaborations in order to enhance the impact of the astonishing number and diversity of structures being determined by structural genomics centers and high-throughput structural biology.</p> <p>Conclusions</p> <p>TOPSAN combines features of automated annotation databases and formal, peer-reviewed scientific research literature, providing an ideal vehicle to bridge a gap between rapidly accumulating data from high-throughput technologies and a much slower pace for its analysis and integration with other, relevant research.</p