THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE FINITELY-PUNCTURED SPHERE

Motivated in part by the study of Fadell-Neuwirth short exact sequences, we determine the lower central and derived series for the braid groups of the finitely-punctured sphere. For n >= 1, the class of m-string braid groups B(m)(S(2)\{x(1), ... , x(n)}) of the n-punctured sphere includes the usual Artin braid groups B(m) (for n = 1), those of the annulus, which are Artin groups of type B (for n = 2), and affine Artin groups of type (C) over tilde (for n = 3). We first consider the case n = 1. Motivated by the study of almost periodic solutions of algebraic equations with almost periodic coefficients, Gorin and Lin calculated the commutator subgroup of the Artin braid groups. We extend their results, and show that the lower central series (respectively, derived series) of B(m) is completely determined for all m is an element of N (respectively, for all m not equal 4). In the exceptional case m = 4, we obtain some higher elements of the derived series and its quotients. When n >= 2, we prove that the lower central series (respectively, derived series) of B(m)(S(2)\{x(1), ... , x(n)}) is constant from the commutator subgroup onwards for all m >= 3 (respectively, m >= 5). The case m = 1 is that of the free group of rank n - 1. The case n = 2 is of particular interest notably when m = 2 also. In this case, the commutator subgroup is a free group of infinite rank. We then go on to show that B(2)(S(2)\{x(1), x(2)}) admits various interpretations, as the Baumslag-Solitar group BS(2, 2), or as a one-relator group with non-trivial centre for example. We conclude from this latter fact that B(2)(S(2)\{x(1), x(2)}) is residually nilpotent, and that from the commutator subgroup onwards, its lower central series coincides with that of the free product Z(2) * Z. Further, its lower central series quotients Gamma(i)/Gamma(i+1) are direct sums of copies of Z(2), the number of summands being determined explicitly. In the case m >= 3 and n = 2, we obtain a presentation of the derived subgroup, from which we deduce its Abelianization. Finally, in the case n = 3, we obtain partial results for the derived series, and we prove that the lower central series quotients Gamma(i)/Gamma(i+1) are 2-elementary finitely-generated groups.

The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Naturally acquired inhibitory antibodies to Plasmodium vivax Duffy binding protein are short-lived and allele-specific following a single malaria infection

The Duffy binding protein of Plasmodium vivax (DBP) is a critical adhesion ligand that participates in merozoite invasion of human Duffy-positive erythrocytes. A small outbreak of P. vivax malaria, in a village located in a non-malarious area of Brazil, offered us an opportunity to investigate the DBP immune responses among individuals who had their first and brief exposure to malaria. Thirty-three individuals participated in the five cross-sectional surveys, 15 with confirmed P. vivax infection while residing in the outbreak area (cases) and 18 who had not experienced malaria (non-cases). In the present study, we found that only 20% (three of 15) of the individuals who experienced their first P. vivax infection developed an antibody response to DBP; a secondary boosting can be achieved with a recurrent P. vivax infection. DNA sequences from primary/recurrent P. vivax samples identified a single dbp allele among the samples from the outbreak area. To investigate inhibitory antibodies to the ligand domain of the DBP (cysteine-rich region II, DBP(II)), we performed in vitro assays with mammalian cells expressing DBP(II) sequences which were homologous or not to those from the outbreak isolate. In non-immune individuals, the results of a 12-month follow-up period provided evidence that naturally acquired inhibitory antibodies to DBP(II) are short-lived and biased towards a specific allele.

Unusually short tandem repeats appear to reach chromosome ends of Rhynchosciara americana (Diptera: Sciaridae)

The characterisation of sequences at chromosome ends of Rhynchosciara americana was continued with the screening of a genomic library using as a probe a short repeat identified in a previous report (M-22, 22 bp) which was found to be specific for noncentromeric termini of this species. Simple repeats, complex tandem and apparently dispersed repeats were present in the genomic clones analysed. Repetitive sequences do not define individual chromosome tips as they were found in all noncentromeric ends. A novel and unusually short tandem repeat type for dipteran chromosome ends (named M-16) composed of 16 nucleotides and frequently associated with M-22 arrays was characterised in this work. Islands of M-16 and M-22 tandem repeats were found in all the genomic clones analysed. Individual probes representative of each repetitive element hybridised not only to all noncentromeric ends of R. americana chromosomes but also to inter-telomeric bridges. This contrasted with the other repeat types which displayed sub-telomeric localisation as seen by double detection of hybridised probe and telomeric reverse transcriptase. Some stretches composed of M-16 and M-22 tandem repeats localised in different regions of the analysed genomic clones were either identical or showed sequence similarity that was unexpectedly higher than the mean sequence similarity observed among repeats within each of their tandem arrays. The occurrence of segmental duplications, as deduced by sequence analyses involving the two repeats that appeared to reach chromosome ends, might indicate the involvement of this type of duplication process in the chromosome end maintenance in this species.

Chromosomal studies in four species of genus Chaunus (Bufonidae, Anura): localization of telomeric and ribosomal sequences after fluorescence in situ hybridization (FISH)

Fluorescence in situ hybridization (FISH) using telomeric and ribosomal sequences was performed in four species of toad genus Chaunus: C. ictericus, C. jimi, C. rubescens and C. schneideri. Analyses based on conventional, C-banding and Ag-NOR staining were also carried out. The four species present a 2n = 22 karyotype, composed by metacentric and submetacentric chromosomes, which were indistinguishable either after conventional staining or banding techniques. Constitutive heterochromatin was predominantly located at pericentromeric regions, and telomeric sequences (TTAGGG)(n) were restricted to the end of all chromosomes. Silver staining revealed Ag-NORs located at the short arm of pair 7, and heteromorphism in size of NOR signals was also observed. By contrast, FISH with ribosomal probes clearly demonstrated absence of any heteromorphism in size of rDNA sequences, suggesting that the difference observed after Ag-staining should be attributed to differences in chromosomal condensation and/or gene activity rather than to the number of ribosomal cistrons.

Patterns of diversification in two species of short-tailed bats (Carollia Gray, 1838): the effects of historical fragmentation of Brazilian rainforests

The small-sized frugivorous bat Carollia perspicillata is an understory specialist and occurs in a wide range of lowland habitats, tending to be more common in tropical dry or moist forests of South and Central America. Its sister species, Carollia brevicauda, occurs almost exclusively in the Amazon rainforest. A recent phylogeographic study proposed a hypothesis of origin and subsequent diversification for C. perspicillata along the Atlantic coastal forest of Brazil. Additionally, it also found two allopatric clades for C. brevicauda separated by the Amazon Basin. We used cytochrome b gene sequences and a more extensive sampling to test hypotheses related to the origin and diversification of C. perspicillata plus C. brevicauda clade in South America. The results obtained indicate that there are two sympatric evolutionary lineages within each species. In C. perspicillata, one lineage is limited to the Southern Atlantic Forest, whereas the other is widely distributed. Coalescent analysis points to a simultaneous origin for C. perspicillata and C. brevicauda, although no place for the diversification of each species can be firmly suggested. The phylogeographic pattern shown by C. perspicillata is also congruent with the Pleistocene refugia hypothesis as a likely vicariant phenomenon shaping the present distribution of its intraspecific lineages. (C) 2011 The Linnean Society of London, Biological Journal of the Linnean Society, 2011, 102, 527-539.

Sequence-specific reconstruction from fragmentary databases using seed sequences: implementation and validation on SAGE, proteome and generic sequencing data

Motivation: DNA assembly programs classically perform an all-against-all comparison of reads to identify overlaps, followed by a multiple sequence alignment and generation of a consensus sequence. If the aim is to assemble a particular segment, instead of a whole genome or transcriptome, a target-specific assembly is a more sensible approach. GenSeed is a Perl program that implements a seed-driven recursive assembly consisting of cycles comprising a similarity search, read selection and assembly. The iterative process results in a progressive extension of the original seed sequence. GenSeed was tested and validated on many applications, including the reconstruction of nuclear genes or segments, full-length transcripts, and extrachromosomal genomes. The robustness of the method was confirmed through the use of a variety of DNA and protein seeds, including short sequences derived from SAGE and proteome projects.