Twisted conjugacy classes in nilpotent groups

A group is said to have the R(infinity) property if every automorphism has an infinite number of twisted conjugacy classes. We study the question whether G has the R(infinity) property when G is a finitely generated torsion-free nilpotent group. As a consequence, we show that for every positive integer n >= 5, there is a compact nilmanifold of dimension n on which every homeomorphism is isotopic to a fixed point free homeomorphism. As a by-product, we give a purely group theoretic proof that the free group on two generators has the R(infinity) property. The R(infinity) property for virtually abelian and for C-nilpotent groups are also discussed.

TWISTED CONJUGACY CLASSES IN R. THOMPSON`S GROUP F

In this article, we prove that any automorphism of R. Thompson`s group F has infinitely many twisted conjugacy classes. The result follows from the work of Brin, together with standard facts about R. Thompson`s group F, and elementary properties of the Reidemeister numbers.

SIGMA THEORY AND TWISTED CONJUGACY CLASSES

Using Sigma theory we show that for large classes of groups G there is a subgroup H of finite index in Aut(G) such that for phi is an element of H the Reidemeister number R(phi) is infinite. This includes all finitely generated nonpolycyclic groups G that fall into one of the following classes: nilpotent-by-abelian groups of type FP(infinity); groups G/G `` of finite Prufer rank; groups G of type FP(2) without free nonabelian subgroups and with nonpolycyclic maximal metabelian quotient; some direct products of groups; or the pure symmetric automorphism group. Using a different argument we show that the result also holds for 1-ended nonabelian nonsurface limit groups. In some cases, such as with the generalized Thompson`s groups F(n,0) and their finite direct products, H = Aut(G).

Twisted conjugacy classes in symplectic groups, mapping class groups and braid groups (with an appendix written jointly with Francois Dahmani)

We prove that the symplectic group Sp(2n, Z) and the mapping class group Mod(S) of a compact surface S satisfy the R(infinity) property. We also show that B(n)(S), the full braid group on n-strings of a surface S, satisfies the R(infinity) property in the cases where S is either the compact disk D, or the sphere S(2). This means that for any automorphism phi of G, where G is one of the above groups, the number of twisted phi-conjugacy classes is infinite.

Equivariant Nielsen root theory for G-maps

Let X be a compact Hausdorff space, Y be a connected topological manifold, f : X -> Y be a map between closed manifolds and a is an element of Y. The vanishing of the Nielsen root number N(f; a) implies that f is homotopic to a root free map h, i.e., h similar to f and h(-1) (a) = empty set. In this paper, we prove an equivariant analog of this result for G-maps between G-spaces where G is a finite group. (C) 2010 Elsevier B.V. All rights reserved.

Tooth Abnormalities of Number and Position in the Permanent Dentition of Patients With Complete Bilateral Cleft Lip and Palate

Objective: To radiographically evaluate the prevalence of tooth abnormalities of number and position in the permanent dentition of individuals with complete bilateral cleft lip and palate. Design: Cross-sectional retrospective. Setting: Hospital for Rehabilitation of Craniofacial Anomalies, University of Sao Paulo, Bauru, Brazil. Patients: Two hundred five individuals with complete bilateral cleft lip and palate. Interventions: Analysis of patient records and panoramic radiographs. Main outcome measures: Evaluation of hypodontia and supernumerary teeth and analysis of the position of the permanent maxillary lateral incisor in relation to the alveolar cleft. Results: Hypodontia was observed in 144 patients (70.2%), and the highest prevalence was observed for the maxillary lateral incisor. When both lateral incisors were present (43%), they were primarily located on the distal side of the cleft (25%). Supernumerary teeth were observed in 11.7% of individuals. Conclusion: Patients with cleft lip and palate presented high prevalence of hypodontia and supernumerary teeth. The prevailing characteristics of their location may suggest the presence of a similar genetic component for the occurrence of hypodontia and cleft.

Dental anomalies of number in the permanent dentition of patients with bilateral cleft lip: Radiographic study

Objective: To radiographically evaluate the prevalence of dental anomalies in patients with complete and incomplete bilateral cleft lip, comparing the prevalence of anomalies between genders and cleft types. Setting: Hospital for Rehabilitation of Craniofacial Anomalies, University of Sao Paulo (HRAC/USP), Bauru, Sao Paulo, Brazil. Participants: 150 randomly selected panoramic radiographs of individuals with complete or incomplete bilateral cleft lip; patient age 12 to 25 years (mean age 13.8 years). Results: Data were statistically analyzed to compare the possible association between presence of hypodontia and supernumerary teeth, according to gender and cleft type. Among the 150 patients evaluated, 80 (53.3%) were male and 70 (46.6%) were female. Since no statistically significant difference was found in hypodontia between genders, data were grouped for analysis, revealing prevalence of 31.6% for complete clefts and 26.8% for incomplete clefts. Concerning supernumerary teeth, the prevalence for the male patients was 28.2% for complete cleft lip and 29.2% for incomplete cleft lip. For female patients, the prevalence was significantly (p = .006) lower for complete cleft lip (17.5%) than for incomplete cleft lip (46.6%). Conclusions: The present results suggest that the prevalence of hypodontia was higher in patients with complete cleft lip, and the prevalence of supernumerary teeth was higher in patients with incomplete cleft lip, in agreement with previous studies.

The Tnt1 family member Retrosol copy number and structure disclose retrotransposon diversification in different Solanum species

Eukaryotic genome expansion/retraction caused by LTR-retrotransposon activity is dependent on the expression of full length copies to trigger efficient transposition and recombination-driven events. The Tnt1 family of retrotransposons has served as a model to evaluate the diversity among closely related elements within Solanaceae species and found that members of the family vary mainly in their U3 region of the long terminal repeats (LTRs). Recovery of a full length genomic copy of Retrosol was performed through a PCR-based approach from wild potato, Solanum oplocense. Further characterization focusing on both LTR sequences of the amplified copy allowed estimating an approximate insertion time at 2 million years ago thus supporting the occurrence of transposition cycles after genus divergence. Copy number of Tnt1-like elements in Solanum species were determined through genomic quantitative PCR whereby results sustain that Retrosol in Solanum species is a low copy number retrotransposon (1-4 copies) while Retrolyc1 has an intermediate copy number (38 copies) in S. peruvianum. Comparative analysis of retrotransposon content revealed no correlation between genome size or ploidy level and Retrosol copy number. The tetraploid cultivated potato with a cellular genome size of 1,715 Mbp harbours similar copy number per monoploid genome than other diploid Solanum species (613-884 Mbp). Conversely, S. peruvianum genome (1,125 Mbp) has a higher copy number. These results point towards a lineage specific dynamic flux regarding the history of amplification/activity of Tnt1-like elements in the genome of Solanum species.

Copy number variants on the X chromosome in women with primary ovarian insufficiency

Objective: To investigate whether submicroscopic copy number variants (CNVs) on the X chromosome can be identified in women with primary ovarian insufficiency (POI), defined as spontaneous secondary amenorrhea before 40 years of age accompanied by follicle-stimulating hormone levels above 40 IU/L on at least two occasions. Design: Analysis of intensity data of single nucleotide polymorphism (SNP) probes generated by genomewide Illumina 370k CNV BeadChips, followed by the validation of identified loci using a custom designed ultra-high-density comparative genomic hybridization array containing 48,325 probes evenly distributed over the X chromosome. Setting: Multicenter genetic cohort study in the Netherlands. Patient(s): 108 Dutch Caucasian women with POI, 97 of whom passed quality control, who had a normal karyogram and absent fragile X premutation, and 235 healthy Dutch Caucasian women as controls. Intervention(s): None. Main Outcome Measure(s): Amount and locus of X chromosomal microdeletions or duplications. Result(s): Intensity differences between SNP probes identify microdeletions and duplications. The initial analysis identified an overrepresentation of deletions in POI patients. Moreover, CNVs in two genes on the Xq21.3 locus (i.e., PCDH11X and TGIF2LX) were statistically significantly associated with the POI phenotype. Mean size of identified CNVs was 262 kb. However, in the validation study the identified putative Xq21.3 deletions samples did not show deviations in intensities in consecutive probes. Conclusion(s): X chromosomal submicroscopic CNVs do not play a major role in Caucasian POI patients. We provide guidelines on how submicroscopic cytogenetic POI research should be conducted. (Fertil Steril (R) 2011;95:1584-8. (C) 2011 by American Society for Reproductive Medicine.)

Chromosome homologies of the highly rearranged karyotypes of four Akodon species (Rodentia, Cricetidae) resolved by reciprocal chromosome painting: the evolution of the lowest diploid number in rodents

Traditionally comparative cytogenetic studies are based mainly on banding patterns. Nevertheless, when dealing with species with highly rearranged genomes, as in Akodon species, or with other highly divergent species, cytogenetic comparisons of banding patterns prove inadequate. Hence, comparative chromosome painting has become the method of choice for genome comparisons at the cytogenetic level since it allows complete chromosome probes of a species to be hybridized in situ onto chromosomes of other species, detecting homologous genomic regions between them. In the present study, we have explored the highly rearranged complements of the Akodon species using reciprocal chromosome painting through species-specific chromosome probes obtained by chromosome sorting. The results revealed complete homology among the complements of Akodon sp. n. (ASP), 2n = 10; Akodon cursor (ACU), 2n = 15; Akodon montensis (AMO), 2n = 24; and Akodon paranaensis (APA), 2n = 44, and extensive chromosome rearrangements have been detected within the species with high precision. Robertsonian and tandem rearrangements, pericentric inversions and/or centromere repositioning, paracentric inversion, translocations, insertions, and breakpoints, where chromosomal rearrangements, seen to be favorable, were observed. Chromosome painting using the APA set of 21 autosomes plus X and Y revealed eight syntenic segments that are shared with A. montensis, A. cursor, and ASP, and one syntenic segment shared by A. montensis and A. cursor plus five exclusive chromosome associations for A. cursor and six for ASP chromosome X, except for the heterochromatin region of ASP X, and even chromosome Y shared complete homology among the species. These data indicate that all those closely related species have experienced a recent extensive process of autosomal rearrangement in which, except for ASP, there is still complete conservation of sex chromosomes homologies.

Influence of organic fertilization on the number of culturable diazotrophic endophytic bacteria isolated from sugarcane

The numbers of culturable diazotrophic endophytic bacteria (CDEB) from roots stems and leaves of sugarcane submitted to organic inorganic or no fertilization were compared In order to determine the size of the N(2) fixing populations the Most Probable Number technique (MPN) was used The quantification of diazotrophic bacteria by using the acetylene reduction assay (ARA) was more accurate than observing the bacterial growth in the vials to confirm N(2) fixing capability the detection of gene nifH was performed on a sample of 105 Isolated bacteria The production of extracellular enzymes involved in the penetration of the plants by the bacteria was also studied The results showed that organic fertilization enhances the number of CDEB when compared with conventional fertilization used throughout the growing season The maximum number of bacteria was detected in the roots Roots and stems presented the greatest number of CDEB in the middle of the cropping season and in leaves numbers varied according to the treatment Using two pairs of primers and two different methods the nifH gene was found in 104 of the 105 tested isolates Larger amounts of pectinase were released by isolates from sugarcane treated with conventional fertilizers (66%) whereas larger amounts of cellulase were released by strains isolated from sugarcane treated with organic fertilizers (80%) (C) 2010 Elsevier Masson SAS All rights reserved

Using non-homogeneous Poisson models with multiple change-points to estimate the number of ozone exceedances in Mexico City

In this paper, we consider some non-homogeneous Poisson models to estimate the probability that an air quality standard is exceeded a given number of times in a time interval of interest. We assume that the number of exceedances occurs according to a non-homogeneous Poisson process (NHPP). This Poisson process has rate function lambda(t), t >= 0, which depends on some parameters that must be estimated. We take into account two cases of rate functions: the Weibull and the Goel-Okumoto. We consider models with and without change-points. When the presence of change-points is assumed, we may have the presence of either one, two or three change-points, depending of the data set. The parameters of the rate functions are estimated using a Gibbs sampling algorithm. Results are applied to ozone data provided by the Mexico City monitoring network. In a first instance, we assume that there are no change-points present. Depending on the adjustment of the model, we assume the presence of either one, two or three change-points. Copyright (C) 2009 John Wiley & Sons, Ltd.

Estimating the number of ozone peaks in Mexico City using a non-homogeneous Poisson model

In this paper, we consider the problem of estimating the number of times an air quality standard is exceeded in a given period of time. A non-homogeneous Poisson model is proposed to analyse this issue. The rate at which the Poisson events occur is given by a rate function lambda(t), t >= 0. This rate function also depends on some parameters that need to be estimated. Two forms of lambda(t), t >= 0 are considered. One of them is of the Weibull form and the other is of the exponentiated-Weibull form. The parameters estimation is made using a Bayesian formulation based on the Gibbs sampling algorithm. The assignation of the prior distributions for the parameters is made in two stages. In the first stage, non-informative prior distributions are considered. Using the information provided by the first stage, more informative prior distributions are used in the second one. The theoretical development is applied to data provided by the monitoring network of Mexico City. The rate function that best fit the data varies according to the region of the city and/or threshold that is considered. In some cases the best fit is the Weibull form and in other cases the best option is the exponentiated-Weibull. Copyright (C) 2007 John Wiley & Sons, Ltd.

Mixed multiplicities and the minimal number of generator of modules

Let (R, m) be a d-dimensional Noetherian local ring. In this work we prove that the mixed Buchsbaum-Rim multiplicity for a finite family of R-submodules of R(p) of finite colength coincides with the Buchsbaum-Rim multiplicity of the module generated by a suitable superficial sequence, that is, we generalize for modules the well-known Risler-Teissier theorem. As a consequence, we give a new proof of a generalization for modules of the fundamental Rees` mixed Multiplicity theorem, which was first proved by Kirby and Rees in (1994, [8]). We use the above result to give an upper bound for the minimal number of generators of a finite colength R-submodule of R(p) in terms of mixed multiplicities for modules, which generalize a similar bound obtained by Cruz and Verma in (2000, [5]) for m-primary ideals. (C) 2009 Elsevier B.V. All rights reserved.

REIDEMEISTER TORSION AND ANALYTIC TORSION OF SPHERES

We provide a simple topological derivation of a formula for the Reidemeister and the analytic torsion of spheres.