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Nestedness is a pattern whereby species-poor assemblages are composed of subsets of the species occurring in richer assemblages. One of the most commonly used measures of the degree of nestedness for presence-absence matrices is the ‘discrepancy’ metric. A hitherto neglected property of that metric is that it may take several values for a given site-by-species matrix in the presence of ties in the marginal totals. This complicates the quantification of nestedness for the observed presence-absence matrix, as well as the assessment of statistical significance, which is typically achieved through Monte Carlo simulations. A solution to the problem is to calculate the minimum discrepancy using a modified algorithm involving permutations of columns with tied totals.

(Z)- and (E)-3,4-dimethyl-hex-3-ene-1,6-diols (1 and 2) have been synthesized in 23% and 68% yields by a three step sequence requiring only one purification at the end. The steps are a) coupling of 2-lithio-1,3-dithiane with (Z)- or (E)-1,4-dibromo-2,3-dimethyl-but-2-ene (3 or 4), b) hydrolysis of the thioketals (8 and 9) with methyl iodide in a mixture of acetonitrile, acetone and water to give the 3,4-dimethyl-hex-3-ene-1,6-diols (10 and 11) and c) reduction with diisobutylaluminum hydride to provide the (Z)- and (E)-diols.

A current-summing digital-to-analog converter can be constructed by combining a switched, binary-weighted resistor network with an operational amplifier. Contributions to total system errors from reference inaccuracies, resistor ratio tolerances, and operational amplifier errors can be held to less than one part in 105 and are normally far outweighed by error contributions from the switches employed. This correspondence describes a technique which reduces the switch error contributions to an insignificant level.

The starting dibromodimethylbutenes (V) are prepared by either cleavage of the anhydride (I), followed by reduction and substitution of OH for bromide, or by bromination of the butadiene (VI).