Rational periodic sequences for the Lyness recurrence

Consider the celebrated Lyness recurrence $x_{n+2}=(a+x_{n+1})/x_{n}$ with $a\in\Q$. First we prove that there exist initial conditions and values of $a$ for which it generates periodic sequences of rational numbers with prime periods $1,2,3,5,6,7,8,9,10$ or $12$ and that these are the only periods that rational sequences $\{x_n\}_n$ can have. It is known that if we restrict our attention to positive rational values of $a$ and positive rational initial conditions the only possible periods are $1,5$ and $9$. Moreover 1-periodic and 5-periodic sequences are easily obtained. We prove that for infinitely many positive values of $a,$ positive 9-period rational sequences occur. This last result is our main contribution and answers an open question left in previous works of Bastien \& Rogalski and Zeeman. We also prove that the level sets of the invariant associated to the Lyness map is a two-parameter family of elliptic curves that is a universal family of the elliptic curves with a point of order $n, n\ge5,$ including $n$ infinity. This fact implies that the Lyness map is a universal normal form for most birrational maps on elliptic curves.

Cardiac motion estimation by joint alignment of tagged MRI sequences

Image registration has been proposed as an automatic method for recovering cardiac displacement fields from Tagged Magnetic Resonance Imaging (tMRI) sequences. Initially performed as a set of pairwise registrations, these techniques have evolved to the use of 3D+t deformation models, requiring metrics of joint image alignment (JA). However, only linear combinations of cost functions defined with respect to the first frame have been used. In this paper, we have applied k-Nearest Neighbors Graphs (kNNG) estimators of the -entropy (H ) to measure the joint similarity between frames, and to combine the information provided by different cardiac views in an unified metric. Experiments performed on six subjects showed a significantly higher accuracy (p < 0.05) with respect to a standard pairwise alignment (PA) approach in terms of mean positional error and variance with respect to manually placed landmarks. The developed method was used to study strains in patients with myocardial infarction, showing a consistency between strain, infarction location, and coronary occlusion. This paper also presentsan interesting clinical application of graph-based metric estimators, showing their value for solving practical problems found in medical imaging.

Indexing strategies for rapid searches of short words in genome sequences.

Searching for matches between large collections of short (14-30 nucleotides) words and sequence databases comprising full genomes or transcriptomes is a common task in biological sequence analysis. We investigated the performance of simple indexing strategies for handling such tasks and developed two programs, fetchGWI and tagger, that index either the database or the query set. Either strategy outperforms megablast for searches with more than 10,000 probes. FetchGWI is shown to be a versatile tool for rapidly searching multiple genomes, whose performance is limited in most cases by the speed of access to the filesystem. We have made publicly available a Web interface for searching the human, mouse, and several other genomes and transcriptomes with oligonucleotide queries.

Study of simple sequence repeat markers from coffee expressed sequences associated to leaf miner resistance

The objective of this work was to identify expressed simple sequence repeats (SSR) markers associated to leaf miner resistance in coffee progenies. Identification of SSR markers was accomplished by directed searches on the Brazilian Coffee Expressed Sequence Tags (EST) database. Sequence analysis of 32 selected SSR loci showed that 65% repeats are of tetra-, 21% of tri- and 14% of dinucleotides. Also, expressed SSR are localized frequently in the 5'-UTR of gene transcript. Moreover, most of the genes containing SSR are associated with defense mechanisms. Polymorphisms were analyzed in progenies segregating for resistance to the leaf miner and corresponding to advanced generations of a Coffea arabica x Coffea racemosa hybrid. Frequency of SSR alleles was 2.1 per locus. However, no polymorphism associated with leaf miner resistance was identified. These results suggest that marker-assisted selection in coffee breeding should be performed on the initial cross, in which genetic variability is still significant.

Bone mineral density in breast cancer patients treated with adjuvant letrozole, tamoxifen, or sequences of letrozole and tamoxifen in the BIG 1-98 study (SAKK 21/07).

BACKGROUND: The risk of osteoporosis and fracture influences the selection of adjuvant endocrine therapy. We analyzed bone mineral density (BMD) in Swiss patients of the Breast International Group (BIG) 1-98 trial [treatment arms: A, tamoxifen (T) for 5 years; B, letrozole (L) for 5 years; C, 2 years of T followed by 3 years of L; D, 2 years of L followed by 3 years of T]. PATIENTS AND METHODS: Dual-energy X-ray absorptiometry (DXA) results were retrospectively collected. Patients without DXA served as control group. Repeated measures models using covariance structures allowing for different times between DXA were used to estimate changes in BMD. Prospectively defined covariates were considered as fixed effects in the multivariable models. RESULTS: Two hundred and sixty-one of 546 patients had one or more DXA with 577 lumbar and 550 hip measurements. Weight, height, prior hormone replacement therapy, and hysterectomy were positively correlated with BMD; the correlation was negative for letrozole arms (B/C/D versus A), known osteoporosis, time on trial, age, chemotherapy, and smoking. Treatment did not influence the occurrence of osteoporosis (T score < -2.5 standard deviation). CONCLUSIONS: All aromatase inhibitor regimens reduced BMD. The sequential schedules were as detrimental for bone density as L monotherapy.

Amplification of 16S rRNA gene sequences to differentiate two highly related bradyrhizobia species

A 16S rRNA gene PCR-based assay was developed aiming at a fast molecular diagnostic method to differentiate the two phylogenetically closely related species Bradyrhizobium japonicum and B. elkanii, isolated from soybean nodules, in order to identify those more competitive and comprising greater nitrogen fixation ability for use in the formulation of commercial inoculants. The assay used was able to discriminate ten reference strains belonging to these two Bradyrhizobium species, as well as to efficiently identify 37 strains isolated from fields cultivated with soybean.

Comparison of 3D segmented gradient-echo and steady-state free precession coronary MRI sequences in patients with coronary artery disease.

OBJECTIVE: Our objective was to compare two state-of-the-art coronary MRI (CMRI) sequences with regard to image quality and diagnostic accuracy for the detection of coronary artery disease (CAD). SUBJECTS AND METHODS: Twenty patients with known CAD were examined with a navigator-gated and corrected free-breathing 3D segmented gradient-echo (turbo field-echo) CMRI sequence and a steady-state free precession sequence (balanced turbo field-echo). CMRI was performed in a transverse plane for the left coronary artery and a double-oblique plane for the right coronary artery system. Subjective image quality (1- to 4-point scale, with 1 indicating excellent quality) and objective image quality parameters were independently determined for both sequences. Sensitivity, specificity, and accuracy for the detection of significant (> or = 50% diameter) coronary artery stenoses were determined as defined in invasive catheter X-ray coronary angiography. RESULTS: Subjective image quality was superior for the balanced turbo field-echo approach (1.8 +/- 0.9 vs 2.3 +/- 1.0 for turbo field-echo; p < 0.001). Vessel sharpness, signal-to-noise ratio, and contrast-to-noise ratio were all superior for the balanced turbo field-echo approach (p < 0.01 for signal-to-noise ratio and contrast-to-noise ratio). Of the 103 segments, 18% of turbo field-echo segments and 9% of balanced turbo field-echo segments had to be excluded from disease evaluation because of insufficient image quality. Sensitivity, specificity, and accuracy for the detection of significant coronary artery stenoses in the evaluated segments were 92%, 67%, 85%, respectively, for turbo field-echo and 82%, 82%, 81%, respectively, for balanced turbo field-echo. CONCLUSION: Balanced turbo field-echo offers improved image quality with significantly fewer nondiagnostic segments when compared with turbo field-echo. For the detection of CAD, both sequences showed comparable accuracy for the visualized segments.

Nuclear localization of mouse fibroblast growth factor 2 requires N-terminal and C-terminal sequences.

In vertebrates, different isoforms of fibroblast growth factor 2 (FGF2) exist, which differ by their N-terminal extension. They show different localization and expression levels and exert distinct biological effects. Nevertheless, genetic inactivation of all FGF2 isoforms in the mouse results in only mild phenotypes. Here, we analyzed mouse FGF2, and show that, as in the human, mouse FGF2 contains CTG-initiated high molecular-weight (HMW) isoforms, which contain a nuclear localization signal, and which mediate localization of this isoform to the nucleus. Using green fluorescent protein-FGF2 fusions, we furthermore observed, that C-terminal deletions disable nuclear localization of the short low-molecular-weight (LMW) 18-kDa isoform. This loss of specific localization is accompanied by a loss in heparin binding. We therefore suggest that, first, localization of mouse FGF2 is comparable to that in other vertebrates and, second, FGF2 contains at least two sequences important for nuclear localization, a nuclear localization sequence at the N terminus which is only contained in the HMW isoform, and another sequence at the C terminus, which is only required for localization of the LMW 18-kDa isoform.

Estimativa da produtividade de café com base em um modelo agrometeorológico-espectral

O objetivo deste trabalho foi avaliar um modelo agrometeorológico-espectral, para estimar a produtividade de cafezais. Utilizaram-se imagens do sensor MODIS e dados agrometeorológicos do modelo regional de previsão do tempo (ETA), para fornecer as variáveis de entrada para o modelo agrometeorológico-espectral da mesorregião geográfica sul/sudoeste do estado de Minas Gerais nos anos-agrícolas de 2003/2004 a 2007/2008. A variável espectral de entrada do modelo agrometeorológico-espectral, índice de área foliar (IAF), usada no cálculo da produtividade máxima, foi estimada com o índice de vegetação por diferença normalizada (NDVI), obtido de imagens MODIS. Outras variáveis de entrada no modelo foram: dados meteorológicos gerados pelo modelo ETA e a capacidade de água disponível no solo. Ao comparar a produtividade média estimada pelo modelo com a fornecida oficialmente pelo IBGE, as diferenças relativas obtidas em escala regional foram de: 0,4, 3,0, 5,3, 1,5 e 8,5% para os anos agrícolas 2003/2004, 2004/2005, 2005/2006, 2006/2007 e 2007/2008, respectivamente. O modelo agrometeorólogico-espectral, que tem como base o modelo de Doorenbos & Kassan, foi tão eficaz para estimar a produtividade dos cafezais quanto o modelo oficial do IBGE. Além disso, foi possível espacializar a quebra de produtividade e prever 80% da produtividade final na primeira quinzena de fevereiro, antes do início da colheita

Molecular phylogenetics and temporal diversification in the genus Aeromonas based on the sequences of five housekeeping genes

Several approaches have been developed to estimate both the relative and absolute rates of speciation and extinction within clades based on molecular phylogenetic reconstructions of evolutionary relationships, according to an underlying model of diversification. However, the macroevolutionary models established for eukaryotes have scarcely been used with prokaryotes. We have investigated the rate and pattern of cladogenesis in the genus Aeromonas (γ-Proteobacteria, Proteobacteria, Bacteria) using the sequences of five housekeeping genes and an uncorrelated relaxed-clock approach. To our knowledge, until now this analysis has never been applied to all the species described in a bacterial genus and thus opens up the possibility of establishing models of speciation from sequence data commonly used in phylogenetic studies of prokaryotes. Our results suggest that the genus Aeromonas began to diverge between 248 and 266 million years ago, exhibiting a constant divergence rate through the Phanerozoic, which could be described as a pure birth process.

T-Coffee: a web server for the multiple sequence alignment of protein and RNA sequences using structural information and homology extension.

This article introduces a new interface for T-Coffee, a consistency-based multiple sequence alignment program. This interface provides an easy and intuitive access to the most popular functionality of the package. These include the default T-Coffee mode for protein and nucleic acid sequences, the M-Coffee mode that allows combining the output of any other aligners, and template-based modes of T-Coffee that deliver high accuracy alignments while using structural or homology derived templates. These three available template modes are Expresso for the alignment of protein with a known 3D-Structure, R-Coffee to align RNA sequences with conserved secondary structures and PSI-Coffee to accurately align distantly related sequences using homology extension. The new server benefits from recent improvements of the T-Coffee algorithm and can align up to 150 sequences as long as 10,000 residues and is available from both http://www.tcoffee.org and its main mirror http://tcoffee.crg.cat.

Molecular dating of caprines using ancient DNA sequences of Myotragus balearicus, an extinct endemic Balearic mammal

Background: Myotragus balearicus was an endemic bovid from the Balearic Islands (Western Mediterranean) that became extinct around 6,000-4,000 years ago. The Myotragus evolutionary lineage became isolated in the islands most probably at the end of the Messinian crisis, when the desiccation of the Mediterranean ended, in a geological date established at 5.35 Mya. Thus, the sequences of Myotragus could be very valuable for calibrating the mammalian mitochondrial DNA clock and, in particular, the tree of the Caprinae subfamily, to which Myotragus belongs. Results: We have retrieved the complete mitochondrial cytochrome b gene (1,143 base pairs), plus fragments of the mitochondrial 12S gene and the nuclear 28S rDNA multi-copy gene from a well preserved Myotragus subfossil bone. The best resolved phylogenetic trees, obtained with the cytochrome b gene, placed Myotragus in a position basal to the Ovis group. Using the calibration provided by the isolation of Balearic Islands, we calculated that the initial radiation of caprines can be dated at 6.2 ± 0.4 Mya. In addition, alpine and southern chamois, considered until recently the same species, split around 1.6 ± 0.3 Mya, indicating that the two chamois species have been separated much longer than previously thought. Conclusion: Since there are almost no extant endemic mammals in Mediterranean islands, the sequence of the extinct Balearic endemic Myotragus has been crucial for allowing us to use the Messinian crisis calibration point for dating the caprines phylogenetic tree.

A note on the degree sequences of graphs with restrictions

Degree sequences of some types of graphs will be studied and characterizedin this paper.

Phylogenetic analysis of plastid and nuclear DNA sequences reveals a rapid late Miocene radiation of the temperate bamboo tribe Arundinarieae (Poaceae, Bambusoideae)

Background: Arundinarieae are a large tribe of temperate woody bamboos for which phylogenetics are poorly understood because of limited taxon sampling and lack of informative characters. Aims: This study assessed phylogenetic relationships, origins and classification of Arundinarieae. Methods: DNA sequences (plastid trnL-F; nuclear ITS) were used for parsimony and Bayesian inference including 41 woody bamboo taxa. Divergence dates were estimated using a relaxed Bayesian clock. Results: Arundinarieae were monophyletic but their molecular divergence was low compared to the tropical Bambuseae. Ancestors of the Arundinarieae lineage were estimated to have diverged from the other bamboos 23 (15-30) million years ago (Mya). However, the Arundinarieae radiation occurred 10 (6-16) Mya compared to 18 (11-25) Mya for the tropical Bambuseae. Some groups could be defined within Arundinarieae, but they do not correspond to recognised subtribes such as Arundinariinae or Shibataeinae. Conclusions: Arundinarieae are a relatively ancient bambusoid lineage that underwent a rapid radiation in the late Miocene. The radiation coincides with the continental collision of the Indo-Australian and Eurasian Plates. Arundinarieae are distributed primarily in East Asia and the Himalayas to northern Southeast Asia. It is unknown whether they were present in Asia long before their radiation, but we believe recent dispersal is a more likely scenario. Keywords: Arundinarieae; Bambuseae; internal transcribed spacer (ITS); molecular clock; phylogenetics; radiation; temperate bamboos; Thamnocalaminae; trnL-F