Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, if any element of the critical set is deleted, the remaining set can be embedded in more than one latin square of order n. In this paper we find smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

Somatotopic organization and cortical projections of the ventrobasal complex of the flying fox: an "inverted" wing representation in the thalamus

The present study investigates the somatotopic representation in the somatosensory thalamus of a megachiropteran bat. Using standard microelectrode mapping techniques, representational maps were generated for the ventrobasal (Vb) and posterior (Po) thalamic complexes of the Grey-headed flying fox. Anatomical tracing from neocortical injections provided additional data confirming the somatotopy found physiologically. A full representation of the body surface innervated by the trigeminal and spinal nerves was found. However, in contrast with other mammals, the representations of the forelimb and adjacent thoracic trunk within the thalamus were inverted. This means that the distal portions of the wing membrane and the tips of the digits were represented dorsally in Vb, and the thoracic trunk was represented ventrally In Po the digit tips were represented in the ventral most portion and the thoracic trunk in the dorsal portion of the nucleus. These results are discussed in relation to similarities of megachiropteran somatosensory thalamic nuclei to those of other mammalian species and in relation to the formation of thalamic somatotopic maps and fiber sorting.

Thermal characterization of copolymers obtained by radiation grafting of styrene onto poly(tetrafluoroethyleneperfluoropropylvinylether) substrates: thermal decomposition, melting behavior and low-temperature transitions

Differential scanning calorimetric (DSC) and thermogravimetric analysis (TGA) have been used to study the thermal decomposition, the melting behavior and low-temperature transitions of copolymers obtained by radiation-induced grafting of styrene onto poly (tetrafluoroethylene- perfluoropropylvinylether) (PFA) substrates. PFA with different contents of perfluoropropylvinylether (PPVE) as a comonomer have been investigated. A two step degradation pattern was observed from TGA thermograms of all the grafted copolymers, which was attributed to degradation of PSTY followed by the degradation of the PFA backbone at higher temperature. One broad melting peak can be identified for all copolymers, which has two components in the samples with higher PPVE content. The melting peak, crystal-crystal transition and the degree of crystallinity of the grafted copolymers increases with radiation grafting up to 50 kGy, followed by a decrease at higher doses. No such decrease was observed in the ungrafted PFA samples after irradiation. This indicated that the changes in the heats of transitions and crystallinity at low doses are due to the radiation effects on the microstructure of PFA (chain scission), whereas at higher doses the grafted PSTY is the driving force behind these changes. (C) 2001 Elsevier Science Ltd. All rights reserved.

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.

Development and reorganization of corticospinal projections in EphA4 deficient mice

The Eph family of receptor tyrosine kinases and their ligands, the ephrins, are important regulators of axon guidance and cell migration in the developing nervous system. Inactivation of the EphA4 gene results in axon guidance defects of the corticospinal tract, a major descending motor pathway that originates in the cortex and terminates at all levels of the spinal cord. In this investigation, we report that although the initial development of the corticospinal projection is normal through the cortex, internal capsule, cerebral peduncle, and medulla in the brain of EphA4 deficient animals, corticospinal axons exhibit gross abnormalities when they enter the gray matter of the spinal cord. Notably, many corticospinal axons fail to remain confined to one side of the spinal cord during development and instead, aberrantly project across the midline, terminating ipsilateral to their cells of origin. Given the possible repulsive interactions between EphA4 and one of its ligands, ephrinB3, this defect could be consistent with a loss of responsiveness by corticospinal axons to ephrinB3 that is expressed at the spinal cord midline. Furthermore, we show that EphA4 deficient animals exhibit ventral displacement of the mature corticospinal termination pattern, suggesting that developing corticospinal axons, which may also express ephrinB3, fail to be repelled from areas of high EphA4 expression in the intermediate zone of the normal spinal cord. Taken together, these results suggest that the dual expression of EphA4 on corticospinal axons and also within the surrounding gray matter is very important for the correct development and termination of the corticospinal projection within the spinal cord. J. Comp. Neurol. 436: 248-262, 2001. (C) 2001 Wiley-Liss, Inc.

Factors affecting the establishment and dispersal of nymphs of Pristhesancus plagipennis Walker (Hemiptera : Reduviidae) when released onto soybean, cotton and sunflower crops

A problem with augmenting predatory bugs through mass release is the logistical difficulty of delivering nymphs onto the foliage of field crops. In this paper we examine postrelease establishment and dispersal of the nymphs of the predatory bug Pristhesancus plagipennis on soybean, cotton and sunflower in an effort to devise an appropriate strategy for field release. The effects of predator stadia and release rates on field establishment and within-crop-canopy dispersal after hand release were recorded in soybean, cotton and sunflower. Field establishment improved with the release of more-developed nymphs, with third instars providing the most appropriate compromise between field hardiness and rearing cost. Increased nymphal density at the point of release had little effect on nymphal dispersal throughout the crop canopy. The patterns of nymphal dispersal observed on the three crops suggest that crop-canopy architecture may have an effect on the ability of nymphs to spread out postrelease, as nymphs dispersed poorly in cotton and sunflower compared to soybean. To overcome poor dispersal of nymphs after release, a mechanical release method, where nymphs were mixed with vermiculite and delivered onto a target crop through a spinning disk fertiliser spreader, was tested, and provided similar nymph establishment rates and dispersal patterns as releasing nymphs individually by hand. The implications of nymph dispersal and field hardiness in regard to inundative field release techniques are discussed.

Copolymers obtained by the radiation-induced grafting of styrene onto poly(tetrafluoroethylene-co-perfluoropropylvinyl ether) substrates. 1. Preparation and structural investigation

A study has been made to investigate the radiation grafting of styrene onto poly(tetrafluoroethylene-co-perfluoropropylvinyl ether) (PFA) substrates, using the simultaneous irradiation method. Two PFA polymers of different comonomer perfluoropropyl vinyl ether (PPVE) content and degree of crystallinity were used. Effects of grafting conditions such as monomer concentrations, type of solvent, dose rate, and irradiation dose on the grafting yield were investigated. Of the six different solvents used, the most efficient in terms of increasing grafting yield were dichloromethane, benzene, and methanol. The degree of grafting increased with increasing radiation dose up to 500 kGy, stabilizing above this dose. However, the grafting yield decreased with an increase in the dose rate. The grafting of styrene onto the PFA substrates was confirmed by FTIR-ATR and micro-Raman spectroscopy, The increase in the overall grafting yield was accompanied by a proportional increase in the penetration depth of the grafts into the substrate.

Spectroscopic study of the penetration depth of grafted polystyrene onto poly (tetrafluoroethylene-co-perfluoropropylvinylether) substrates. 1. Effect of grafting conditions

This study concerns the radiation grafting of styrene onto poly(tetrafluoroethylene-co-perfluoropropylvinylether) (PFA) substrates and the penetration depth of the graft. Grafting was obtained by the simultaneous irradiation method, and the spectroscopic analysis was made with the micro-Raman technique. Effects of grafting conditions such as the type of solvent, dose rate, and irradiation dose on the grafting yield were investigated. Of the different solvents used, the most efficient in terms of increasing grafting yield were dichloromethane, benzene, and methanol, respectively. A mixture of methanol and dichloromethane used as a solvent for styrene achieved a higher degree of grafting and concentration of grafted polystyrene onto the surface of PFA substrates than solutions of the monomer in the separate solvents. The degree of grafting increased with increasing radiation dose up to 500 kGy, stabilizing above this dose. However, the grafting yield decreased with an increase in the dose rate. The increase in the overall grafting yield was accompanied by a proportional increase in the penetration depth of the grafts into the substrate. (C) 2002 Wiley Periodicals, Inc.

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

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.