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)).

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.

A reliable measure of similarity based on dependency for short time series: an application to gene expression networks

Background: Microarray techniques have become an important tool to the investigation of genetic relationships and the assignment of different phenotypes. Since microarrays are still very expensive, most of the experiments are performed with small samples. This paper introduces a method to quantify dependency between data series composed of few sample points. The method is used to construct gene co-expression subnetworks of highly significant edges. Results: The results shown here are for an adapted subset of a Saccharomyces cerevisiae gene expression data set with low temporal resolution and poor statistics. The method reveals common transcription factors with a high confidence level and allows the construction of subnetworks with high biological relevance that reveals characteristic features of the processes driving the organism adaptations to specific environmental conditions. Conclusion: Our method allows a reliable and sophisticated analysis of microarray data even under severe constraints. The utilization of systems biology improves the biologists ability to elucidate the mechanisms underlying celular processes and to formulate new hypotheses.

Relationship of autonomic imbalance and circadian disruption with obesity and type 2 diabetes in resistant hypertensive patients

Background: Hypertension, diabetes and obesity are not isolated findings, but a series of interacting interactive physiologic derangements. Taking into account genetic background and lifestyle behavior, AI (autonomic imbalance) could be a common root for RHTN (resistant hypertension) or RHTN plus type 2 diabetes (T2D) comorbidity development. Moreover, circadian disruption can lead to metabolic and vasomotor impairments such as obesity, insulin resistance and resistant hypertension. In order to better understand the triggered emergence of obesity and T2D comorbidity in resistant hypertension, we investigated the pattern of autonomic activity in the circadian rhythm in RHTN with and without type 2 diabetes (T2D), and its relationship with serum adiponectin concentration. Methods: Twenty five RHTN patients (15 non-T2D and 10 T2D, 15 males, 10 females; age range 34 to 70 years) were evaluated using the following parameters: BMI (body mass index), biochemical analysis, serum adiponectinemia, echocardiogram and ambulatory electrocardiograph heart rate variability (HRV) in time and frequency domains stratified into three periods: 24 hour, day time and night time. Results: Both groups demonstrated similar characteristics despite of the laboratory analysis concerning T2D like fasting glucose, HbA1c levels and hypertriglyceridemia. Both groups also revealed disruption of the circadian rhythm: inverted sympathetic and parasympathetic tones during day (parasympathetic > sympathetic tone) and night periods (sympathetic > parasympathetic tone). T2D group had increased BMI and serum triglyceride levels (mean 33.7 +/- 4.0 vs 26.6 +/- 3.7 kg/m(2) - p = 0.00; 254.8 +/- 226.4 vs 108.6 +/- 48.7 mg/dL - p = 0.04), lower levels of adiponectin (6729.7 +/- 3381.5 vs 10911.5 +/- 5554.0 ng/mL - p = 0.04) and greater autonomic imbalance evaluated by HRV parameters in time domain compared to non-T2D RHTN patients. Total patients had HRV correlated positively with serum adiponectin (r = 0.37 [95% CI - 0.04 - 1.00] p = 0.03), negatively with HbA1c levels (r = -0.58 [95% CI -1.00 - -0.3] p = 0.00) and also adiponectin correlated negatively with HbA1c levels (r = -0.40 [95% CI -1.00 - -0.07] p = 0.02). Conclusion: Type 2 diabetes comorbidity is associated with greater autonomic imbalance, lower adiponectin levels and greater BMI in RHTN patients. Similar circadian disruption was also found in both groups indicating the importance of lifestyle behavior in the genesis of RHTN.

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.

Polar organic marker compounds in atmospheric aerosols during the LBA-SMOCC 2002 biomass burning experiment in Rondonia, Brazil: sources and source processes, time series, diel variations and size distributions

Measurements of polar organic marker compounds were performed on aerosols that were collected at a pasture site in the Amazon basin (Rondonia, Brazil) using a high-volume dichotomous sampler (HVDS) and a Micro-Orifice Uniform Deposit Impactor (MOUDI) within the framework of the 2002 LBA-SMOCC (Large-Scale Biosphere Atmosphere Experiment in Amazonia - Smoke Aerosols, Clouds, Rainfall, and Climate: Aerosols From Biomass Burning Perturb Global and Regional Climate) campaign. The campaign spanned the late dry season (biomass burning), a transition period, and the onset of the wet season (clean conditions). In the present study a more detailed discussion is presented compared to previous reports on the behavior of selected polar marker compounds, including levoglucosan, malic acid, isoprene secondary organic aerosol (SOA) tracers and tracers for fungal spores. The tracer data are discussed taking into account new insights that recently became available into their stability and/or aerosol formation processes. During all three periods, levoglucosan was the most dominant identified organic species in the PM(2.5) size fraction of the HVDS samples. In the dry period levoglucosan reached concentrations of up to 7.5 mu g m(-3) and exhibited diel variations with a nighttime prevalence. It was closely associated with the PM mass in the size-segregated samples and was mainly present in the fine mode, except during the wet period where it peaked in the coarse mode. Isoprene SOA tracers showed an average concentration of 250 ng m(-3) during the dry period versus 157 ng m(-3) during the transition period and 52 ng m(-3) during the wet period. Malic acid and the 2-methyltetrols exhibited a different size distribution pattern, which is consistent with different aerosol formation processes (i.e., gas-to-particle partitioning in the case of malic acid and heterogeneous formation from gas-phase precursors in the case of the 2-methyltetrols). The 2-methyltetrols were mainly associated with the fine mode during all periods, while malic acid was prevalent in the fine mode only during the dry and transition periods, and dominant in the coarse mode during the wet period. The sum of the fungal spore tracers arabitol, mannitol, and erythritol in the PM(2.5) fraction of the HVDS samples during the dry, transition, and wet periods was, on average, 54 ng m(-3), 34 ng m(-3), and 27 ng m(-3), respectively, and revealed minor day/night variation. The mass size distributions of arabitol and mannitol during all periods showed similar patterns and an association with the coarse mode, consistent with their primary origin. The results show that even under the heavy smoke conditions of the dry period a natural background with contributions from bioaerosols and isoprene SOA can be revealed. The enhancement in isoprene SOA in the dry season is mainly attributed to an increased acidity of the aerosols, increased NO(x) concentrations and a decreased wet deposition.

Inference of gene regulatory networks from time series by Tsallis entropy

Background: The inference of gene regulatory networks (GRNs) from large-scale expression profiles is one of the most challenging problems of Systems Biology nowadays. Many techniques and models have been proposed for this task. However, it is not generally possible to recover the original topology with great accuracy, mainly due to the short time series data in face of the high complexity of the networks and the intrinsic noise of the expression measurements. In order to improve the accuracy of GRNs inference methods based on entropy (mutual information), a new criterion function is here proposed. Results: In this paper we introduce the use of generalized entropy proposed by Tsallis, for the inference of GRNs from time series expression profiles. The inference process is based on a feature selection approach and the conditional entropy is applied as criterion function. In order to assess the proposed methodology, the algorithm is applied to recover the network topology from temporal expressions generated by an artificial gene network (AGN) model as well as from the DREAM challenge. The adopted AGN is based on theoretical models of complex networks and its gene transference function is obtained from random drawing on the set of possible Boolean functions, thus creating its dynamics. On the other hand, DREAM time series data presents variation of network size and its topologies are based on real networks. The dynamics are generated by continuous differential equations with noise and perturbation. By adopting both data sources, it is possible to estimate the average quality of the inference with respect to different network topologies, transfer functions and network sizes. Conclusions: A remarkable improvement of accuracy was observed in the experimental results by reducing the number of false connections in the inferred topology by the non-Shannon entropy. The obtained best free parameter of the Tsallis entropy was on average in the range 2.5 <= q <= 3.5 (hence, subextensive entropy), which opens new perspectives for GRNs inference methods based on information theory and for investigation of the nonextensivity of such networks. The inference algorithm and criterion function proposed here were implemented and included in the DimReduction software, which is freely available at http://sourceforge.net/projects/dimreduction and http://code.google.com/p/dimreduction/.

Forecasting fuel ethanol consumption in Brazil by time series models: 2006-2012

This article analysed scenarios for Brazilian consumption of ethanol for the period 2006 to 2012. The results show that if the country`s GDP sustains a 4.6% a year growth, domestic consumption of fuel ethanol could increase to 25.16 billion liters in this period, which is a volume relatively close to the forecasted gasoline consumption of 31 billion liters. At a lower GDP growth of 1.22% a year, gasoline consumption would be reduced and domestic ethanol consumption in Brazil would be no higher than 18.32 billion liters. Contrary to the current situation, forecasts indicated that hydrated ethanol consumption could become much higher than anhydrous consumption in Brazil. The former is being consumed in cars moved exclusively by ethanol and flex-fuel cars, successfully introduced in the country at 2003. Flex cars allow Brazilian consumers to choose between gasoline and hydrated ethanol and immediately switch to whichever fuel presents the most favourable relative price.

Synthesis, antichagasic in vitro evaluation, cytotoxicity assays, molecular modeling and SAR/QSAR studies of a 2-phenyl-3-(1-phenyl-1H-pyrazol-4-yl)-acrylic acid benzylidene-carbohydrazide series

Chagas disease (American trypanosomiasis) is one of the most important parasitic diseases with serious social and economic impacts mainly on Latin America. This work reports the synthesis, in vitro trypanocidal evaluation, cytotoxicity assays, and molecular modeling and SAR/QSAR studies of a new series of N-phenylpyrazole benzylidene-carbohydrazides. The results pointed 6k (X = H, Y = p-NO(2), pIC(50) = 4.55 M) and 6l (X = F, Y = p-CN, pIC(50) = 4.27 M) as the most potent derivatives compared to crystal violet (pIC(50) = 3.77 M). The halogen-benzylidene-carbohydrazide presented the lowest potency whereas 6l showed the most promising pro. le with low toxicity (0% of cell death). The best equation from the 4D-QSAR analysis (Model 1) was able to explain 85% of the activity variability. The QSAR graphical representation revealed that bulky X-substituents decreased the potency whereas hydrophobic and hydrogen bond acceptor Y-substituents increased it. (C) 2008 Elsevier Ltd. All rights reserved.

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.

Tessier No. 4 Facial Cleft: Evolution of Surgical Treatment in a Large Series of Patients

Background: Tessier no. 4 facial cleft is a rare, complex, and challenging craniofacial malformation. The present article aims to describe different clinical features evidenced in 21 cases of this malformation, discussing a 20-year experience with and evolution of its surgical treatment. Methods: Some demographic data, clinical features, and reconstructive results were evaluated retrospectively. These patients have been evaluated and treated in three specialized Brazilian craniofacial centers. Nineteen were already operated on, with a mean follow-up of 3.5 years (range, 1 to 20 years). Results: Sex distribution showed a male prevalence (2: 1). The average age of initial treatment was 5.4 years. Four cases were affected on the right side of the face, seven on the left, and 10 bilaterally. Six patients had other rare associated facial clefts, including nos. 5 (three patients), 7, 9, and 10. Cleft upper lip was evidenced in all patients, and maxillary hypoplasia was present in five and maxilla cleft in eight. Lower eyelid coloboma was seen in almost every case (19 patients); 10 of these had medial canthus dystopia. Four patients had amniotic bands in the limbs. Surgical repair was individualized to each patient. Surgical experience gained with these patients allowed the authors to develop some technical modifications, which have improved aesthetic results, camouflaging scars into natural folds and anatomical units, without compromising functional outcomes. Conclusions: The great majority of Tessier no. 4 facial clefts can be appropriately treated using local flaps. Classic techniques are extremely useful, but long-term results could be improved if the technical modifications described were adopted. (Plast. Reconstr. Surg. 122: 1505, 2008.)

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.