Models of adding relations to an organization structure of a complete K-ary tree

This paper proposes three models of adding relations to an organization structure which is a complete K-ary tree of height H: (i) a model of adding an edge between two nodes with the same depth N, (ii) a model of adding edges between every pair of nodes with the same depth N and (iii) a model of adding edges between every pair of siblings with the same depth N. For each of the three models, an optimal depth N* is obtained by maximizing the total shortening path length which is the sum of shortening lengths of shortest paths between every pair of all nodes. (c) 2005 Elsevier B.V. All rights reserved.

Decompositions of complete tripartite graphs into triangles with an edge attached

Let K(r, s, t) denote the complete tripartite graph with partite sets of size r, s and t, where r less than or equal to s less than or equal to t. Let D be the graph consisting of a triangle with an edge attached. We show that K(r, s, t) may be decomposed into copies of D if and only if 4 divides rs + st + rt and t less than or equal to 3rs/(r + s).

Common multiples of complete graphs and a 4-cycle

A graph G is a common multiple of two graphs H-1 and H-2 if there exists a decomposition of G into edge-disjoint copies of H-1 and also a decomposition of G into edge-disjoint copies of H-2. In this paper, we consider the case where H-1 is the 4-cycle C-4 and H-2 is the complete graph with n vertices K-n. We determine, for all positive integers n, the set of integers q for which there exists a common multiple of C-4 and K-n having precisely q edges. (C) 2003 Elsevier B.V. All rights reserved.

Cube factorizations of complete graphs

A cube factorization of the complete graph on n vertices, K-n, is a 3-factorization of & in which the components of each factor are cubes. We show that there exists a cube factorization of & if and only if n equivalent to 16 (mod 24), thus providing a new family of uniform 3 -factorizations as well as a partial solution to an open problem posed by Kotzig in 1979. (C) 2004 Wiley Periodicals, Inc.

The extended metamorphosis of a complete bipartite design into a cycle system

A K-t,K-t-design of order n is an edge-disjoint decomposition of K-n into copies of K-t,K-t. When t is odd, an extended metamorphosis of a K-t,K-t-design of order n into a 2t-cycle system of order n is obtained by taking (t - 1)/2 edge-disjoint cycles of length 2t from each K-t,K-t block, and rearranging all the remaining 1-factors in each K-t,K-t block into further 2t-cycles. The 'extended' refers to the fact that as many subgraphs isomorphic to a 2t-cycle as possible are removed from each K-t,K-t block, rather than merely one subgraph. In this paper an extended metamorphosis of a K-t,K-t-design of order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is given for all odd t > 3. A metamorphosis of a 2-fold K-t,K-t-design of any order congruent to 1 (mod 4t(2)) into a 2t-cycle system of the same order is also given, for all odd t > 3. (The case t = 3 appeared in Ars Combin. 64 (2002) 65-80.) When t is even, the graph K-t,K-t is easily seen to contain t/2 edge-disjoint cycles of length 2t, and so the metamorphosis in that case is straightforward. (C) 2004 Elsevier B.V. All rights reserved.

Cytochrome c(551) from Starkeya novella - Characterization, spectroscopic properties, and phylogeny of a diheme protein of the SoxAX family

Cytochromes from the SoxAX family have a major role in thiosulfate oxidation via the thiosulfate-oxidizing multi-enzyme system (TOMES). Previously characterized SoxAX proteins from Rhodovulum sulficlophilum and Paracoccus pantotrophus contain three heme c groups, two of which are located on the SoxA subunit. In contrast, the SoxAX protein purified from Starkeya novella was found to contain only two heme groups. Mass spectrometry showed that a disulfide bond replaced the second heme group found in the diheme SoxA subunits. Apparent molecular masses of 27,229 +/- 10.3 Da and 20,258.6 +/- 1 Da were determined for SoxA and SoxX with an overall mass of 49.7 kDa, indicating a heterodimeric structure. Optical redox potentiometry found that the two heme cofactors are reduced at similar potentials (versus NHE) that are as follows: + 133 mV (pH 6.0); + 104 mV (pH 7.0); +49 (pH 7.9) and +10 mV (pH 8.7). EPR spectroscopy revealed that both ferric heme groups are in the low spin state, and the spectra were consistent with one heme having a His/Cys axial ligation and the other having a His/Met axial ligation. The His/Cys ligated heme is present in different conformational states and gives rise to three distinct signals. Amino acid sequencing was used to unambiguously assign the protein to the encoding genes, soxAX, which are part of a complete sox gene cluster found in S. novella. Phylogenetic analysis of soxA- and soxX-related gene sequences indicates a parallel development of SoxA and SoxY, with the diheme and monoheme SoxA sequences located on clearly separated branches of a phylogenetic tree.

Alpha-cellulose δ13C variation in mangrove tree rings correlates well with annual sea level trend between 1982 and 1999

A pilot study of tree rings in a modern mangrove tree (Rhizophora apiculata) from Leizhou Peninsula, northern South China Sea shows that ( 1) the tree-rings are annual; ( 2) the ring widths decrease; and ( 3) their alpha-cellulose delta(13)C values increase from 1982 to 1999 AD, consistent with the trends of annual sea level, salinity and sea surface temperatures in the same period. We propose that such changes were caused by increasingly longer duration of waterlogging in response to sea-level rise. If this is the case, alpha-cellulose delta(13)C in mangrove tree rings can be used as a potential indicator of past sea level fluctuations.

Some equitably 3-colourable cycle decompositions of complete equipartite graphs

Let G be a graph in which each vertex has been coloured using one of k colours, say c(1), c(2),.. , c(k). If an m-cycle C in G has n(i) vertices coloured c(i), i = 1, 2,..., k, and vertical bar n(i) - n(j)vertical bar <= 1 for any i, j is an element of {1, 2,..., k}, then C is said to be equitably k-coloured. An m-cycle decomposition C of a graph G is equitably k-colourable if the vertices of G can be coloured so that every m-cycle in W is equitably k-coloured. For m = 3, 4 and 5 we completely settle the existence question for equitably 3-colourable m-cycle decompositions of complete equipartite graphs. (c) 2005 Elsevier B.V. All rights reserved.

Copper sensitivity of cueO mutants of Escherichia coli K-12 and the biochemical suppression of this phenotype

The cueO gene of Escherichia coli encodes a multi-copper oxidase, which contributes to copper tolerance in this bacterium. It was observed that a cueO mutant was highly sensitive to killing by copper ions when cells were grown on defined minimal media. Copper sensitivity was correlated with accumulation of copper in the mutant strain. Growth of the cueO mutant in the presence of copper could be restored by addition of divalent zinc and manganese ions or ferrous iron but not by other first row transition metal ions or magnesium ions. Copper toxicity towards a cueO mutant Could also be suppressed by addition of the superoxide quencher 1,2-dihydroxybenzene-3,5-disulfonic acid (tiron), suggesting that a primary cause of copper toxicity is the copper-catalyzed production of superoxide anions in the cytoplasm. (C) 2005 Elsevier Inc. All rights reserved.

BM+-tree: A hyperplane-based index method for high-dimensional metric spaces

In this paper, we propose a novel high-dimensional index method, the BM+-tree, to support efficient processing of similarity search queries in high-dimensional spaces. The main idea of the proposed index is to improve data partitioning efficiency in a high-dimensional space by using a rotary binary hyperplane, which further partitions a subspace and can also take advantage of the twin node concept used in the M+-tree. Compared with the key dimension concept in the M+-tree, the binary hyperplane is more effective in data filtering. High space utilization is achieved by dynamically performing data reallocation between twin nodes. In addition, a post processing step is used after index building to ensure effective filtration. Experimental results using two types of real data sets illustrate a significantly improved filtering efficiency.

Efficient spatial clustering algorithm using binary tree

In this paper we present an efficient k-Means clustering algorithm for two dimensional data. The proposed algorithm re-organizes dataset into a form of nested binary tree*. Data items are compared at each node with only two nearest means with respect to each dimension and assigned to the one that has the closer mean. The main intuition of our research is as follows: We build the nested binary tree. Then we scan the data in raster order by in-order traversal of the tree. Lastly we compare data item at each node to the only two nearest means to assign the value to the intendant cluster. In this way we are able to save the computational cost significantly by reducing the number of comparisons with means and also by the least use to Euclidian distance formula. Our results showed that our method can perform clustering operation much faster than the classical ones. © Springer-Verlag Berlin Heidelberg 2005