The length of unknotting tunnels

We show there exist tunnel number one hyperbolic 3-manifolds with arbitrarily long unknotting tunnel. This provides a negative answer to an old question of Colin Adams.Comment: 20 pages, 6 figures. 20 pages, 6 figures. Daryl Cooper added as author. V2 contains two new sections, including a second proof of the main result, and a proof that the result holds for knots in homology sphere

Komatiitic flows of the pioneer ultramafic complex of the 3.3Ga Weltevreden Formation, Barberton Greenstone Belt, South Africa: stratigraphy, petrology, and geochemistry

The 3.29 Ga Pioneer Ultramafic Complex (WPC) is a 1 km thick east-northeast trending tilted (90° dip) section of layered ultramafic rock in the Weltevreden Formation in the west-northwest region of the Barberton Greenstone Belt (BGB). It was originally interpreted as an intrusive complex with slaty zones that have a linear horizontal fabric produced by shear. However, a recent study identifies these slaty zones as komatiitic tuffs and attributes their horizontal fabric to plane and cross bedding. The present study suggests the non-slaty zones are extrusive komatiitic flows with abundant pyroxene spinifex tops, normal volcanic textures and crystal sizes, and no indication of intrusive cross cutting. A geologic map is presented for WPC komatiites along with a stratigraphic section. The stratigraphic section includes 9 flows or flow sets (numbered WP 1 – 9). WP 1, WP 4, and the lower WP 7 are relatively undifferentiated massive olivine cumulate flows with minor interstitial pyroxenes. WP 2 and 3 are layered komatiitic flows with dunitic to peridotitic bases and increasing pyroxene content and changing pyroxene morphology toward pyroxene spinifex flow tops. Pyroxene spinifex komatiitic basalts are dominant in WP 6 – 8. Each flow type has substantially differing rock and mineral chemistry. Layered komatiitic flows are likely to represent more ponded lavas. WPC komatiites are mineralogically well preserved for Archean komatiites with abundant fresh olivine, orthopyroxene, pigeonite, augite, and chromite. The WPC komatiites are of the Al-undepleted geochemical type with rock and mineral Al2O3/TiO2 very similar to other units of the Weltevreden Formation. This geochemical signature is commonly attributed to the depth of partial melting in plumes, with Al-undepleted komatiites representing shallower partial melting (\u3c450km), and also indicates that WPC komatiites may have a magmatic source related to that of the previously studied Weltevreden Formation komatiites. However, WPC komatiites differ from previously studied Weltevreden Formation komatiites in that they are somewhat less magnesian (maximum olivine Mg# 92.9 vs. 95.6), indicating a lower eruption temperature, but have much more complex and variable lithologic layering

The behavioural need for lying and feeding in the high yielding dairy cow

Experiments were conducted to examine the impact of high milk yields on the behaviour and welfare of dairy cows. A preliminary study determined the social interactions existing within a group of 60 cows from which sub-samples of 20 high and 20 low yielding cows, that were not observed to interact with each other, were identified. These cows were used to examine the behavioural strategies employed by dairy cows coping with increased nutritional demands from milk production. Grazing time significantly increased with milk yield, consequently reducing lying time. A second study measured the appetite of high and low yielding cows for concentrates, using operant conditioning. The high yielding cows demonstrated no greater appetite for concentrates, but post-testing behavioural observations indicated greater appetite for forage, suggesting increased motivation to feed. Subsequent experiments investigated the behavioural effects of lying deprivation on dairy cattle welfare, further examining the feeding-lying conflict. Cows forced to stand had reduced milk yields and demonstrated behavioural signs of fatigue, frustration and stress, which were cumulative. When deprived of lying, a post-deprivation increase in this activity was achieved by reducing feeding time. When deprived of both lying and feeding, a feeding, not lying, post-deprivation increase was observed. However, lying was not reduced to extend feeding time. In conclusion, the motivation to feed was greater in high yielding dairy cows. This resulted in extended grazing and a reduced lying time. Lying can be regarded as an important and highly motivated behaviour and may compromise welfare if reduced. The legitimacy of using individual dairy cows as replicates in the statistical analysis of their behaviour was also investigated. There was no significant difference in the coefficients of variation between cows that were free to interact, and those that were not, for a range of behaviours. Therefore, those cows able to interact did not appear to influence each other's behaviour, supporting the use of individual dairy cows as replicates

The New Jewish Community, New Jewish Schools: Trends and Promises

While representing a small percentage of all private, religious schools, Jewish schools are nonetheless a significant presence on the religious landscape. This article analyzes the rapid growth of Jewish schools over the past three decades and examines possible future directions for Jewish schools

Measuring Galaxy Environments with Deep Redshift Surveys

We study the applicability of several galaxy environment measures (n^th-nearest-neighbor distance, counts in an aperture, and Voronoi volume) within deep redshift surveys. Mock galaxy catalogs are employed to mimic representative photometric and spectroscopic surveys at high redshift (z ~ 1). We investigate the effects of survey edges, redshift precision, redshift-space distortions, and target selection upon each environment measure. We find that even optimistic photometric redshift errors (\sigma_z = 0.02) smear out the line-of-sight galaxy distribution irretrievably on small scales; this significantly limits the application of photometric redshift surveys to environment studies. Edges and holes in a survey field dramatically affect the estimation of environment, with the impact of edge effects depending upon the adopted environment measure. These edge effects considerably limit the usefulness of smaller survey fields (e.g. the GOODS fields) for studies of galaxy environment. In even the poorest groups and clusters, redshift-space distortions limit the effectiveness of each environment statistic; measuring density in projection (e.g. using counts in a cylindrical aperture or a projected n^th-nearest-neighbor distance measure) significantly improves the accuracy of measures in such over-dense environments. For the DEEP2 Galaxy Redshift Survey, we conclude that among the environment estimators tested the projected n^th-nearest-neighbor distance measure provides the most accurate estimate of local galaxy density over a continuous and broad range of scales.Comment: 17 pages including 16 figures, accepted to Ap

Formation of oligopeptides in high yield under simple programmable conditions

Many high-yielding reactions for forming peptide bonds have been developed but these are complex, requiring activated amino-acid precursors and heterogeneous supports. Herein we demonstrate the programmable one-pot dehydration–hydration condensation of amino acids forming oligopeptide chains in around 50% yield. A digital recursive reactor system was developed to investigate this process, performing these reactions with control over parameters such as temperature, number of cycles, cycle duration, initial monomer concentration and initial pH. Glycine oligopeptides up to 20 amino acids long were formed with very high monomer-to-oligomer conversion, and the majority of these products comprised three amino acid residues or more. Having established the formation of glycine homo-oligopeptides, we then demonstrated the co-condensation of glycine with eight other amino acids (Ala, Asp, Glu, His, Lys, Pro, Thr and Val), incorporating a range of side-chain functionality