Brunnian links are determined by their complements

If L_1 and L_2 are two Brunnian links with all pairwise linking numbers 0, then we show that L_1 and L_2 are equivalent if and only if they have homeomorphic complements. In particular, this holds for all Brunnian links with at least three components. If L_1 is a Brunnian link with all pairwise linking numbers 0, and the complement of L_2 is homeomorphic to the complement of L_1, then we show that L_2 may be obtained from L_1 by a sequence of twists around unknotted components. Finally, we show that for any positive integer n, an algorithm for detecting an n-component unlink leads immediately to an algorithm for detecting an unlink of any number of components. This algorithmic generalization is conceptually simple, but probably computationally impractical.Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol1/agt-1-7.abs.htm

MUSTANG 3.3 Millimeter Continuum Observations of Class 0 Protostars

We present observations of six Class 0 protostars at 3.3 mm (90 GHz) using the 64-pixel MUSTANG bolometer camera on the 100-m Green Bank Telescope. The 3.3 mm photometry is analyzed along with shorter wavelength observations to derive spectral indices (S_nu ~ nu^alpha) of the measured emission. We utilize previously published dust continuum radiative transfer models to estimate the characteristic dust temperature within the central beam of our observations. We present constraints on the millimeter dust opacity index, beta, between 0.862 mm, 1.25 mm, and 3.3 mm. Beta_mm typically ranges from 1.0 to 2.4 for Class 0 sources. The relative contributions from disk emission and envelope emission are estimated at 3.3 mm. L483 is found to have negligible disk emission at 3.3 mm while L1527 is dominated by disk emission within the central beam. The beta_mm^disk <= 0.8 - 1.4 for L1527 indicates that grain growth is likely occurring in the disk. The photometry presented in this paper may be combined with future interferometric observations of Class 0 envelopes and disks.Comment: 19 pages, 3 figures, AJ accepted, in pres

Finishing the euchromatic sequence of the human genome

The sequence of the human genome encodes the genetic instructions for human physiology, as well as rich information about human evolution. In 2001, the International Human Genome Sequencing Consortium reported a draft sequence of the euchromatic portion of the human genome. Since then, the international collaboration has worked to convert this draft into a genome sequence with high accuracy and nearly complete coverage. Here, we report the result of this finishing process. The current genome sequence (Build 35) contains 2.85 billion nucleotides interrupted by only 341 gaps. It covers ∼99% of the euchromatic genome and is accurate to an error rate of ∼1 event per 100,000 bases. Many of the remaining euchromatic gaps are associated with segmental duplications and will require focused work with new methods. The near-complete sequence, the first for a vertebrate, greatly improves the precision of biological analyses of the human genome including studies of gene number, birth and death. Notably, the human enome seems to encode only 20,000-25,000 protein-coding genes. The genome sequence reported here should serve as a firm foundation for biomedical research in the decades ahead

Understanding crystallization pathways leading to manganese oxide polymorph formation.

Hydrothermal synthesis is challenging in metal oxide systems with diverse polymorphism, as reaction products are often sensitive to subtle variations in synthesis parameters. This sensitivity is rooted in the non-equilibrium nature of low-temperature crystallization, where competition between different metastable phases can lead to complex multistage crystallization pathways. Here, we propose an ab initio framework to predict how particle size and solution composition influence polymorph stability during nucleation and growth. We validate this framework using in situ X-ray scattering, by monitoring how the hydrothermal synthesis of MnO2 proceeds through different crystallization pathways under varying solution potassium ion concentrations ([K+] = 0, 0.2, and 0.33 M). We find that our computed size-dependent phase diagrams qualitatively capture which metastable polymorphs appear, the order of their appearance, and their relative lifetimes. Our combined computational and experimental approach offers a rational and systematic paradigm for the aqueous synthesis of target metal oxides