On the pivot structure for the weighing matrix W(12,11)

In the present article we concentrate our study on the growth problem for the weighing matrix W(12,11) and show that the unique W(12,11) has three pivot structures. An improved algorithm for extending a k × k (0,+,-) matrix to a W(n,n-1), if possible, has been developed to simplify the proof. For the implementation of the algorithm special emphasis is given to the notions of data structures and parallel processing.     

Reducing structural changes in van Emde Boas' data structure to the lower bound for the dynamic predecessor problem

We consider the problem of maintaining a dynamic ordered set of n integers in a universe U under the operations of insertion, deletion and predecessor queries. The computation model used is a unit-cost RAM, with a word length of w bits, and the universe size is |U|=2^w. We present a data structure that uses O(|U|/log|U|+n) space, performs all the operations in O(loglog|U|) time and needs O(loglog|U|/logloglog|U|) structural changes per update operation. The data structure is a simplified version of the van Emde Boas' tree introducing, in its construction and functioning, new concepts, which help to keep the important information for searching along the path of the tree, in a more compact and organized way.     

On path lengths modulo three

We show that between any two nodes of a cubic, planar, three-connected graph there are three paths whose lengths are 0, 1, and 2 modulo 3, respectively. The proof is by a rather extensive case analysis. Counterexamples show that all three hypotheses (i.e., planarity, degree-three, and three-connectivity) are necessary.     

Development of an epi-fluorescence assay for monitoring yeast viability and pretreatment hydrolysate toxicity in the presence of lignocellulosic solids

Applied Biochemistry and Biotechnology -     

Comparative 11A structure of two molluscan hemocyanins from 3D cryo-electron microscopy

Hemocyanins are giant extracellular proteins that transport oxygen in the hemolymph of many molluscs. Molluscan hemocyanins are cylindrical decamers or didecamers of a 350-400 kDa subunit that contains seven or eight different covalently linked globular functional units (FUs), arranged in a linear manner. Each FU carries a single copper active site and reversibly binds one dioxygen molecule. As a consequence, the decamer can carry up to 70 or 80 O(2) molecules. Although complete sequence information is now available from several molluscan hemocyanins, many details of the quaternary structure are still unclear, including the topology of the 10 subunits within the decamer. Here we show 3D reconstructions from cryo-electron micrographs of the hemocyanin decamer of Nautilus pompilius (Cephalopoda) and Haliotis tuberculata (Gastropoda) at a resolution of 11A (FSC(1/2-bit) criterion). The wall structure of both hemocyanins is very similar and shows, as in previous reconstructions, three tiers with 20 functional units each that encircle the cylinder wall, and the 10 oblique minor and major wall grooves. However, the six types of wall FUs of the polypeptide subunit, termed a-b-c-d-e-f, are now for the first time individually discernable by their specific orientation, shape, and connections. Also, the internal collar complex of the decamers shows superior resolution which, in this case, reveals striking differences between the two hemocyanins. The five arcs (FU-g pairs) of the central collar (in both hemocyanins) and the five slabs (FU-h pairs) of the peripheral collar (only present in Haliotis hemocyanin), as well as their connections to the wall and to each other are now more clearly defined. The arc is attached to the wall through a feature termed the anchor, a previously undescribed structural element of the hemocyanin wall.