Mixed partitions of sets of triples into small planes

We continue our study of partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. We develop further necessary conditions for the existence of partitions of such sets into copies of PG(2, 2) and copies of AG(2, 3), and deal with the cases v = 13, 14, 15 and 17. These partitions, together with those already known for v = 12, 16 and 18, then become starters for recursive constructions of further infinite families of partitions. (C) 2004 Elsevier B.V. All rights reserved.

Subcycling first- and second-order generalizations of the trapezoidal rule

Subcycling algorithms which employ multiple timesteps have been previously proposed for explicit direct integration of first- and second-order systems of equations arising in finite element analysis, as well as for integration using explicit/implicit partitions of a model. The author has recently extended this work to implicit/implicit multi-timestep partitions of both first- and second-order systems. In this paper, improved algorithms for multi-timestep implicit integration are introduced, that overcome some weaknesses of those proposed previously. In particular, in the second-order case, improved stability is obtained. Some of the energy conservation properties of the Newmark family of algorithms are shown to be preserved in the new multi-timestep extensions of the Newmark method. In the first-order case, the generalized trapezoidal rule is extended to multiple timesteps, in a simple way that permits an implicit/implicit partition. Explicit special cases of the present algorithms exist. These are compared to algorithms proposed previously. (C) 1998 John Wiley & Sons, Ltd.

A total-evidence phylogeny of ticks provides insights into the evolution of life cycles and biogeography

We inferred the phylogeny of 33 species of ticks from the subfamilies Rhipicephalinae and Hyalomminae from analyses of nuclear and mitochondrial DNA and morphology. We used nucleotide sequences from 12S rRNA, cytochrome c oxidase I, internal transcribed spacer 2 of the nuclear rRNA, and 18S rRNA. Nucleotide sequences and morphology were analyzed separately and together in a total-evidence analysis. Analyses of the five partitions together (3303 characters) gave the best-resolved and the best-supported hypothesis so far for the phylogeny of ticks in the Rhipicephalinae and Hyalomminae, despite the fact that some partitions did not have data for some taxa. However, most of the hidden conflict (lower support in the total-evidence analyses compared to that in the individual analyses) was found in those partitions that had taxa without data. The partitions with complete taxonomic sampling had more hidden support (higher support in the total-evidence analyses compared to that in the separate-partition analyses) than hidden conflict. Mapping of geographic origins of ticks onto our phylogeny indicates an African origin for the Rhipicephalinae sensu lato (i.e., including Hyalomma spp.), the Rhipicephalus-Boophilus lineage, the Dermacentor-Anocentor lineage, and the Rhipicephalus-Booophilus-Nosomma-Hyalomma-Rhipicentor lineage. The Nosomma-Hyalomma lineage appears to have evolved in Asia. Our total-evidence phylogeny indicates that (i) the genus Rhipicephalus is paraphyletic with respect to the genus Boophilus, (ii) the genus Dermacentor is paraphyletic with respect to the genus Anocentor, and (iii) some subgenera of the genera Hyalomma and Rhipicephalus are paraphyletic with respect to other subgenera in these genera. Study of the Rhipicephalinae and Hyalomminae over the last 7 years has shown that analyses of individual datasets (e.g., one gene or morphology) seldom resolve many phylogenetic relationships, but analyses of more than one dataset can generate well-resolved phylogenies for these ticks. (C) 2001 Academic Press.

Phylogenetic revision of Agapophytinae subf.n. (Diptera : Therevidae) based on molecular and morphological evidence

Agapophytinae subf.n. is a highly diverse lineage of Australasian Therevidae, comprising eight described and two new genera: Agapophytus Guerin-Meneville, Acupalpa Krober, Acraspisa Krober, Belonalys Krober, Bonjeania Irwin & Lyneborg, Parapsilocephala Krober, Acatopygia Krober, Laxotela Winterton & Irwin, Pipinnipons gen.n. and Patanothrix gen.n. A genus-level cladistic analysis of the subfamily was undertaken using sixty-eight adult morphological characters and c. 1000 base pairs of the elongation factor-1 alpha (EF-1 alpha) protein coding gene. The morphological data partition produced three most parsimonious cladograms, whereas the molecular data partition gave a single most parsimonious cladogram, which did not match any of the cladograms found in the morphological analysis. The level of congruence between the data partitions was determined using the partition homogeneity test (HTF) and Wilcoxon signed ranks rest. Despite being significantly incongruent in at least one of the incongruence tests, the partitions were combined in a simultaneous analysis. The combined data yielded a single cladogram that was better supported than that of the individual partitions analysed separately. The relative contributions of the data partitions to support for individual nodes on the combined cladogram were investigated using Partitioned Bremer Support. The level of support for many nodes on the combined cladogram was non-additive and often greater than the sum of support for the respective nodes on individual partitions. This synergistic interaction between incongruent data partitions indicates a common phylogenetic signal in both partitions. It also suggests that criteria for partition combination based solely on incongruence may be misleading. The phylogenetic relationships of the genera are discussed using the combined data. A key to genera of Agapophytinae is presented, with genera diagnosed and figured. Two new genera are described: Patanothrix with a new species (Pat. skevingtoni) and Pat. wilsoni (Mann) transferred from Parapsilocephala, and Pipinnipons with a new species (Pip. kroeberi). Pipinnipons fascipennis (Krober) is transferred from Squamopygin Krober and Pip. imitans (Mann) is transferred from Agapophytus. Agapophytus bicolor (Krober) is transferred from Parapsilocephala. Agapophytus varipennis Mann is synonymised with Aga, queenslandi Krober and Aga. flavicornis Mann is synonymised with Aga. pallidicornis (Krober).

Overlarge sets of 2-(11, 5, 2) designs and related configurations

We consider the construction of several configurations, including: • overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs; • an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12 × 12 square with interesting row and column properties; • a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square; • bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

Explicit/implicit partitioning and a new explicit form of the generalized alpha method

Most finite element packages use the Newmark algorithm for time integration of structural dynamics. Various algorithms have been proposed to better optimize the high frequency dissipation of this algorithm. Hulbert and Chung proposed both implicit and explicit forms of the generalized alpha method. The algorithms optimize high frequency dissipation effectively, and despite recent work on algorithms that possess momentum conserving/energy dissipative properties in a non-linear context, the generalized alpha method remains an efficient way to solve many problems, especially with adaptive timestep control. However, the implicit and explicit algorithms use incompatible parameter sets and cannot be used together in a spatial partition, whereas this can be done for the Newmark algorithm, as Hughes and Liu demonstrated, and for the HHT-alpha algorithm developed from it. The present paper shows that the explicit generalized alpha method can be rewritten so that it becomes compatible with the implicit form. All four algorithmic parameters can be matched between the explicit and implicit forms. An element interface between implicit and explicit partitions can then be used, analogous to that devised by Hughes and Liu to extend the Newmark method. The stability of the explicit/implicit algorithm is examined in a linear context and found to exceed that of the explicit partition. The element partition is significantly less dissipative of intermediate frequencies than one using the HHT-alpha method. The explicit algorithm can also be rewritten so that the discrete equation of motion evaluates forces from displacements and velocities found at the predicted mid-point of a cycle. Copyright (C) 2003 John Wiley Sons, Ltd.

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).