THE LOWER CENTRAL AND DERIVED SERIES OF THE BRAID GROUPS OF THE SPHERE

In this paper, we determine the lower central and derived series for the braid groups of the sphere. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is important in its own right. The braid groups of the 2-sphere S(2) were studied by Fadell, Van Buskirk and Gillette during the 1960s, and are of particular interest due to the fact that they have torsion elements (which were characterised by Murasugi). We first prove that for all n epsilon N, the lower central series of the n-string braid group B(n)(S(2)) is constant from the commutator subgroup onwards. We obtain a presentation of Gamma(2)(Bn(S(2))), from which we observe that Gamma(2)(B(4)(S(2))) is a semi-direct product of the quaternion group Q(8) of order 8 by a free group F(2) of rank 2. As for the derived series of Bn(S(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group Bn(S(2)) being finite and soluble for n <= 3, the critical case is n = 4 for which the derived subgroup is the above semi-direct product Q(8) (sic) F(2). By proving a general result concerning the structure of the derived subgroup of a semi-direct product, we are able to determine completely the derived series of B(4)(S(2)) which from (B(4)(S(2)))(4) onwards coincides with that of the free group of rank 2, as well as its successive derived series quotients.

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.

The classification and the conjugacy classes of the finite subgroups of the sphere braid groups

Let n >= 3. We classify the finite groups which are realised as subgroups of the sphere braid group B(n)(S(2)). Such groups must be of cohomological period 2 or 4. Depending on the value of n, we show that the following are the maximal finite subgroups of B(n)(S(2)): Z(2(n-1)); the dicyclic groups of order 4n and 4(n - 2); the binary tetrahedral group T*; the binary octahedral group O*; and the binary icosahedral group I(*). We give geometric as well as some explicit algebraic constructions of these groups in B(n)(S(2)) and determine the number of conjugacy classes of such finite subgroups. We also reprove Murasugi`s classification of the torsion elements of B(n)(S(2)) and explain how the finite subgroups of B(n)(S(2)) are related to this classification, as well as to the lower central and derived series of B(n)(S(2)).

Sr-Nd isotopic evidence for crustal contamination in the Niquelandia complex, Goias, Central Brazil

The Niquelandia complex is a Neoproterozoic mafic-ultramafic intrusion resulting from fractional crystallization of primary picritic basalt intrusions. It consists of two layered sequences: a lower and larger one (LS), where four stratigraphic units exhibit an upward decrease of ultramafic layers and increase of gabbroic layers; an upper, smaller sequence (US), separated from LS by a high-temperature shear zone and consisting of two stratigraphic units (gabbros + anorthosites and amphibolites). Nd and Sr isotopic analyses and rare earth element (REE) profiles provide evidence that the complex suffered important crustal contamination. The LS isotopic array trends from a DM region with positive epsilon Nd and moderately positive epsilon Sr towards a field occupied by crustal xenoliths, especially abundant in the upper LS (negative epsilon Nd and large, positive E:Sr). Each LS stratigraphic unit is distinct from the next underlying unit, showing lower epsilon Nd and higher epsilon Sr, suggesting inputs of fresh magma and mixing with the contaminated, residual magma. The US is characterised by a relatively high variation of epsilon Nd and constant epsilon Sr. REE patterns vary within each unit from LREE depleted to LREE enriched in the samples having lower epsilon Nd and higher epsilon Sr. The contamination process has been modelled by using the EC-AFC algorithms from [Spera, F.J., Bohrson, W.A., 2001. Energy-constrained open-system magmatic processes 1: general model and energy-constrained assimilation and fractional crystallization (EC-AFC) formulation. J. Petrology 42, 999-1018]. The differences between the LS and US isotopic arrays are consistent with contamination by the same crustal component, provided that its melting degree was higher in LS than in US. The different degrees of anatexis are explained by the heat budget released from the magma, higher in LS (because of its larger mass) than in US. Comparison of the correlations between isotopes and incompatible trace element ratios of the models and of the gabbros shows some differences, which are demonstrably related with the variable amount of cumulus phases and trapped melt in the gabbros. (c) 2007 Elsevier Ltd. All rights reserved.

Timing and sequence of primary tooth eruption in children with cleft lip and palate

OBJECTIVE: To determine the timing and sequence of eruption of primary teeth in children with complete bilateral cleft lip and palate. MATERIAL AND METHODS: This cross-sectional study was conducted at the Hospital for Rehabilitation of Craniofacial Anomalies of the University of São Paulo, Bauru, SP, Brazil, with a sample of 395 children (128 girls and 267 boys) aged 0 to 48 months, with complete bilateral cleft lip and palate. RESULTS: Children with complete bilateral clefts presented a higher mean age of eruption of all primary teeth for both arches and both genders, compared to children without clefts. This difference was statistically signifcant for all teeth, except for the maxillary first molar. Mean age of eruption of most teeth was lower for girls compared to boys. The greatest delay was found for the maxillary lateral incisor, which was the eighth tooth of children with clefts of both genders. Analyzing by gender, the maxillary lateral incisor was the eighth tooth to erupt in girls and the last in boys. CONCLUSION: The results suggest an interference of the cleft on the timing and sequence of eruption of primary teeth.

Gait kinematic analysis in patients with a mild form of central cord syndrome

Background: Central cord syndrome (CCS) is considered the most common incomplete spinal cord injury (SCI). Independent ambulation was achieved in 87-97% in young patients with CCS but no gait analysis studies have been reported before in such pathology. The aim of this study was to analyze the gait characteristics of subjects with CCS and to compare the findings with a healthy age, sex and anthropomorphically matched control group (CG), walking both at a self-selected speed and at the same speed. Methods: Twelve CCS patients and a CG of twenty subjects were analyzed. Kinematic data were obtained using a three-dimensional motion analysis system with two scanner units. The CG were asked to walk at two different speeds, at a self-selected speed and at a slower one, similar to the mean gait speed previously registered in the CCS patient group. Temporal, spatial variables and kinematic variables (maximum and minimum lower limb joint angles throughout the gait cycle in each plane, along with the gait cycle instants of occurrence and the joint range of motion ROM) were compared between the two groups walking at similar speeds. Results: The kinematic parameters were compared when both groups walked at a similar speed, given that there was a significant difference in the self-selected speeds (p < 0.05). Hip abduction and knee flexion at initial contact, as well as minimal knee flexion at stance, were larger in the CCS group (p < 0.05). However, the range of knee and ankle motion in the sagittal plane was greater in the CG group (p < 0.05). The maximal ankle plantar-flexion values in stance phase and at toe off were larger in the CG (p < 0.05). Conclusions: The gait pattern of CCS patients showed a decrease of knee and ankle sagittal ROM during level walking and an increase in hip abduction to increase base of support. The findings of this study help to improve the understanding how CCS affects gait changes in the lower limbs.

Changes in cardiac heparan sulfate proteoglycan expression and streptozotocin-induced diastolic dysfunction in rats

Background: Changes in the proteoglycans glypican and syndecan-4 have been reported in several pathological conditions, but little is known about their expression in the heart during diabetes. The aim of this study was to investigate in vivo heart function changes and alterations in mRNA expression and protein levels of glypican-1 and syndecan-4 in cardiac and skeletal muscles during streptozotocin (STZ)-induced diabetes. Methods: Diabetes was induced in male Wistar rats by STZ administration. The rats were assigned to one of the following groups: control (sham injection), after 24 hours, 10 days, or 30 days of STZ administration. Echocardiography was performed in the control and STZ 10-day groups. Western and Northern blots were used to quantify protein and mRNA levels in all groups. Immunohistochemistry was performed in the control and 30-day groups to correlate the observed mRNA changes to the protein expression. Results: In vivo cardiac functional analysis performed using echocardiography in the 10-day group showed diastolic dysfunction with alterations in the peak velocity of early (E) diastolic filling and isovolumic relaxation time (IVRT) indices. These functional alterations observed in the STZ 10-day group correlated with the concomitant increase in syndecan-4 and glypican-1 protein expression. Cardiac glypican-1 mRNA and skeletal syndecan-4 mRNA and protein levels increased in the STZ 30-day group. On the other hand, the amount of glypican in skeletal muscle was lower than that in the control group. The same results were obtained from immunohistochemistry analysis. Conclusion: Our data suggest that membrane proteoglycans participate in the sequence of events triggered by diabetes and inflicted on cardiac and skeletal muscles.

A comparison of lower limb EMG and ground reaction forces between barefoot and shod gait in participants with diabetic neuropathic and healthy controls

Background: It is known that when barefoot, gait biomechanics of diabetic neuropathic patients differ from nondiabetic individuals. However, it is still unknown whether these biomechanical changes are also present during shod gait which is clinically advised for these patients. This study investigated the effect of the participants own shoes on gait biomechanics in diabetic neuropathic individuals compared to barefoot gait patterns and healthy controls. Methods: Ground reaction forces and lower limb EMG activities were analyzed in 21 non-diabetic adults (50.9 +/- 7.3 yr, 24.3 +/- 2.6 kg/m(2)) and 24 diabetic neuropathic participants (55.2 +/- 7.9 yr, 27.0 +/- 4.4 kg/m(2)). EMG patterns of vastus lateralis, lateral gastrocnemius and tibialis anterior, along with the vertical and antero-posterior ground reaction forces were studied during shod and barefoot gait. Results: Regardless of the disease, walking with shoes promoted an increase in the first peak vertical force and the peak horizontal propulsive force. Diabetic individuals had a delay in the lateral gastrocnemius EMG activity with no delay in the vastus lateralis. They also demonstrated a higher peak horizontal braking force walking with shoes compared to barefoot. Diabetic participants also had a smaller second peak vertical force in shod gait and a delay in the vastus lateralis EMG activity in barefoot gait compared to controls. Conclusions: The change in plantar sensory information that occurs when wearing shoes revealed a different motor strategy in diabetic individuals. Walking with shoes did not attenuate vertical forces in either group. Though changes in motor strategy were apparent, the biomechanical did not support the argument that the use of shoes contributes to altered motor responses during gait.

A score system for quality evaluation of RNA sequence tags: an improvement for gene expression profiling

Background: High-throughput molecular approaches for gene expression profiling, such as Serial Analysis of Gene Expression (SAGE), Massively Parallel Signature Sequencing (MPSS) or Sequencing-by-Synthesis (SBS) represent powerful techniques that provide global transcription profiles of different cell types through sequencing of short fragments of transcripts, denominated sequence tags. These techniques have improved our understanding about the relationships between these expression profiles and cellular phenotypes. Despite this, more reliable datasets are still necessary. In this work, we present a web-based tool named S3T: Score System for Sequence Tags, to index sequenced tags in accordance with their reliability. This is made through a series of evaluations based on a defined rule set. S3T allows the identification/selection of tags, considered more reliable for further gene expression analysis. Results: This methodology was applied to a public SAGE dataset. In order to compare data before and after filtering, a hierarchical clustering analysis was performed in samples from the same type of tissue, in distinct biological conditions, using these two datasets. Our results provide evidences suggesting that it is possible to find more congruous clusters after using S3T scoring system. Conclusion: These results substantiate the proposed application to generate more reliable data. This is a significant contribution for determination of global gene expression profiles. The library analysis with S3T is freely available at http://gdm.fmrp.usp.br/s3t/.S3T source code and datasets can also be downloaded from the aforementioned website.

Molecular and geographic analyses of vampire bat-transmitted cattle rabies in central Brazil

Background: Vampire bats are important rabies virus vectors, causing critical problems in both the livestock industry and public health sector in Latin America. In order to assess the epidemiological characteristics of vampire bat-transmitted rabies, the authors conducted phylogenetic and geographical analyses using sequence data of a large number of cattle rabies isolates collected from a wide geographical area in Brazil. Methods: Partial nucleoprotein genes of rabies viruses isolated from 666 cattle and 18 vampire bats between 1987 and 2006 were sequenced and used for phylogenetic analysis. The genetic variants were plotted on topographical maps of Brazil. Results: In this study, 593 samples consisting of 24 genetic variants were analyzed. Regional localization of variants was observed, with the distribution of several variants found to be delimited by mountain ranges which served as geographic boundaries. The geographical distributions of vampire-bat and cattle isolates that were classified as the identical phylogenetic group were found to overlap with high certainty. Most of the samples analyzed in this study were isolated from adjacent areas linked by rivers. Conclusion: This study revealed the existence of several dozen regional variants associated with vampire bats in Brazil, with the distribution patterns of these variants found to be affected by mountain ranges and rivers. These results suggest that epidemiological characteristics of vampire bat-related rabies appear to be associated with the topographical and geographical characteristics of areas where cattle are maintained, and the factors affecting vampire bat ecology.

Leishmania-Specific Surface Antigens Show Sub-Genus Sequence Variation and Immune Recognition

Background: A family of hydrophilic acylated surface (HASP) proteins, containing extensive and variant amino acid repeats, is expressed at the plasma membrane in infective extracellular (metacyclic) and intracellular (amastigote) stages of Old World Leishmania species. While HASPs are antigenic in the host and can induce protective immune responses, the biological functions of these Leishmania-specific proteins remain unresolved. Previous genome analysis has suggested that parasites of the sub-genus Leishmania (Viannia) have lost HASP genes from their genomes. Methods/Principal Findings: We have used molecular and cellular methods to analyse HASP expression in New World Leishmania mexicana complex species and show that, unlike in L. major, these proteins are expressed predominantly following differentiation into amastigotes within macrophages. Further genome analysis has revealed that the L. (Viannia) species, L. (V.) braziliensis, does express HASP-like proteins of low amino acid similarity but with similar biochemical characteristics, from genes present on a region of chromosome 23 that is syntenic with the HASP/SHERP locus in Old World Leishmania species and the L. (L.) mexicana complex. A related gene is also present in Leptomonas seymouri and this may represent the ancestral copy of these Leishmania-genus specific sequences. The L. braziliensis HASP-like proteins (named the orthologous (o) HASPs) are predominantly expressed on the plasma membrane in amastigotes and are recognised by immune sera taken from 4 out of 6 leishmaniasis patients tested in an endemic region of Brazil. Analysis of the repetitive domains of the oHASPs has shown considerable genetic variation in parasite isolates taken from the same patients, suggesting that antigenic change may play a role in immune recognition of this protein family. Conclusions/Significance: These findings confirm that antigenic hydrophilic acylated proteins are expressed from genes in the same chromosomal region in species across the genus Leishmania. These proteins are surface-exposed on amastigotes (although L. (L.) major parasites also express HASPB on the metacyclic plasma membrane). The central repetitive domains of the HASPs are highly variant in their amino acid sequences, both within and between species, consistent with a role in immune recognition in the host.

Sexual maturity and egg production in an unexploited population of the red squat lobster Pleuroncodes monodon (Decapoda, Galatheidae) from Central America

The squat lobster Pleuroncodes monodon is one of the most common and abundant galatheid species in the deepwater fishery of Pacific coast of America. In contrast with Peru and Chile, the red squat lobster is not commercially exploited in Costa Rica. Here we estimated the size of sexual maturity and analysed egg production in P. monodon from the Pacific of Costa Rica; the results might be important for an adequate management strategy when initiating a sustainable fishery of this resource in Costa Rica. Analyses of allometric growth revealed that females and males reached their morphological sexual maturity at 26.9 and 30.4 mm CL. respectively. The percentage of immature females captured in the present study (54%) suggests that almost half of females are able to reproduce before they are caught. Egg production was positively correlated with body size; females that measured between 24.1 and 29.0 mm CL contributed roughly 90% to the offspring production of the population. Females from Costa Rica had a considerably lower average egg volume (0.039 mm(3)) and higher fecundity (9810) than females from Chile. In comparison to other American galatheids P. monodon from Costa Rica produces numerous but small eggs, a typical strategy of species with a prolonged larval development. An analysis between our results and information published about P. monodon from Chile also revealed differences in the size-frequency distribution shape of both populations. The non-exploited character of the Costa Rican P. monodon population and a latitudinal (temperature-related) cline in body size might be associated with these differences. (C) 2010 Elsevier B.V. All rights reserved.

Quantifying subclinical central nervous lesions in primary antiphospholipid syndrome: The role of magnetization transfer imaging

Purpose: To define the role of magnetization transfer imaging (MTI) in detecting subclinical central nervous system (CNS) lesions in primary antiphospholipid syndrome (PAPS). Materials and Methods: Ten non-CNS PAPS patients were compared to 10 CNS PAPS patients and 10 age- and sex-matched controls. All PAPS patients met Sapporo criteria. All Subjects underwent conventional MRI and complementary MTI analysis to compose histograms. CNS viability was determined according to the magnetization transfer ratio (MTR) by mean pixel intensity (MPI) and the mean peak height (MPH). Volumetric cerebral measurements were assessed by brain parenchyma factor (BPF) and total/cerebral volume. Results: MTR histograms analysis revealed that MPI was significantly different among groups (P < 0.0001). Non-CNS PAPS had a higher MPI than CNS PAPS, (30.5 +/- 1.01 vs. 25.1 +/- 3.17 percent unit (pu); P < 0.05) although lower than controls (30.5 +/- 1.01 vs. 31.20 < 0.50 pu; P < 0.05). MPH in non-CNS PAPS (5.57 +/- 0.20% (1/pu)} was similar to controls (5.63 +/- 0.20% (1/pu), P > 0.05) and higher than CNS PAPS (4.71 +/- 0.30% (1/pu), P < 0.05). A higher peak location (PL) was also observed in the CNS PAPS group in comparison with the other groups (P < 0.0001). In addition, a lower BPF was found in non-CNS PAPS compared to controls (0.80 +/- 0.03 vs. 0.84 +/- 0.02 units; P < 0.05) but similar to CNS PAPS (0.80 +/- 0.03 vs. 0.79 +/- 0.05 units; P > 0.05). Conclusion: Our findings suggest that non-CNS PAPS patients have subclinical cerebral damage. The long-term-clinical relevance of MTI analysis in these patients needs to be defined by prospective studies.

INTENSITY-MODULATED AND 3D-CONFORMAL RADIOTHERAPY FOR WHOLE-VENTRICULAR IRRADIATION AS COMPARED WITH CONVENTIONAL WHOLE-BRAIN IRRADIATION IN THE MANAGEMENT OF LOCALIZED CENTRAL NERVOUS SYSTEM GERM CELL TUMORS

Purpose: To compare the sparing potential of cerebral hemispheres with intensity-modulated radiotherapy (IMRT) and three-dimensional conformal radiotherapy (3D-CRT) for whole-ventricular irradiation (WVI) and conventional whole-brain irradiation (WBI) in the management of localized central nervous system germ cell tumors (CNSGCTs). Methods and Materials: Ten cases of patients with localized CNSGCTs and submitted to WVI by use of IMRT with or without a ""boost"" to the primary lesion were selected. For comparison purposes, similar treatment plans were produced by use of 3D-CRT (WVI with or without boost) and WBI (opposed lateral fields with or without boost), and cerebral hemisphere sparing was evaluated at dose levels ranging from 2 Gy to 40 Gy. Results: The median prescription dose for WVI was 30.6 Gy (range, 25.2-37.5 Gy), and that for the boost was 16.5 Gy (range, 0-23.4 Gy). Mean irradiated cerebral hemisphere volumes were lower for WVI with IMRT than for 3D-CRT and were lower for WVI with 3D-CRT than for WBI. Intensity-modulated radiotherapy was associated with the lowest irradiated volumes, with reductions of 7.5%, 12.2%, and 9.0% at dose levels., compared with 3D-CRT. Intensity-modulated radiotherapy provided of 20, 30, and 40 Gy, respectively statistically significant reductions of median irradiated volumes at all dose levels (p = 0.002 or less). However, estimated radiation doses to peripheral areas of the body were 1.9 times higher with IMRT than with 3D-CRT. Conclusions: Although IMRT is associated with increased radiation doses to peripheral areas of the body, its use can spare a significant amount of normal central nervous system tissue compared with 3D-CRT or WBI in the setting of CNSGCT treatment. (C) 2010 Elsevier Inc.