On a Theorem by Van Vleck Regarding Sturm Sequences

In 1900 E. B. Van Vleck proposed a very efficient method to compute the Sturm sequence of a polynomial p (x) ∈ Z[x] by triangularizing one of Sylvester’s matrices of p (x) and its derivative p′(x). That method works fine only for the case of complete sequences provided no pivots take place. In 1917, A. J. Pell and R. L. Gordon pointed out this “weakness” in Van Vleck’s theorem, rectified it but did not extend his method, so that it also works in the cases of: (a) complete Sturm sequences with pivot, and (b) incomplete Sturm sequences. Despite its importance, the Pell-Gordon Theorem for polynomials in Q[x] has been totally forgotten and, to our knowledge, it is referenced by us for the first time in the literature. In this paper we go over Van Vleck’s theorem and method, modify slightly the formula of the Pell-Gordon Theorem and present a general triangularization method, called the VanVleck-Pell-Gordon method, that correctly computes in Z[x] polynomial Sturm sequences, both complete and incomplete.

On the Remainders Obtained in Finding the Greatest Common Divisor of Two Polynomials

In 1917 Pell (1) and Gordon used sylvester2, Sylvester’s little known and hardly ever used matrix of 1853, to compute(2) the coefficients of a Sturmian remainder — obtained in applying in Q[x], Sturm’s algorithm on two polynomials f, g ∈ Z[x] of degree n — in terms of the determinants (3) of the corresponding submatrices of sylvester2. Thus, they solved a problem that had eluded both J. J. Sylvester, in 1853, and E. B. Van Vleck, in 1900. (4) In this paper we extend the work by Pell and Gordon and show how to compute (2) the coefficients of an Euclidean remainder — obtained in finding in Q[x], the greatest common divisor of f, g ∈ Z[x] of degree n — in terms of the determinants (5) of the corresponding submatrices of sylvester1, Sylvester’s widely known and used matrix of 1840. (1) See the link http://en.wikipedia.org/wiki/Anna_Johnson_Pell_Wheeler for her biography (2) Both for complete and incomplete sequences, as defined in the sequel. (3) Also known as modified subresultants. (4) Using determinants Sylvester and Van Vleck were able to compute the coefficients of Sturmian remainders only for the case of complete sequences. (5) Also known as (proper) subresultants.

[Diagnosis and treatment of oculomotor deficits in Möbius sequence]

This article reviews the spectrum of possible motility disorders and ocular misalignment in patients with Möbius sequence. The various options for strabismus surgery are discussed and a stepwise algorithm is presented.

[Non-oculomotor eye involvement in Moebius sequence]

Moebius sequence is a congenital disorder that not only affects the oculomotor system but also the eyes themselves. Ocular involvement might be sight-threatening and needs regular follow-up by an ophthalmologist.

Stable isotope response to lake eutrophication: Calibration of a high-resolution lacustrine sequence from Baldeggersee, Switzerland

Stable isotope analyses of discrete seasonal layers from a 108-yr annually laminated freeze-core from Baldeg-gersee, a small, eutrophic lake in central Switzerland, provide information on the climatological and environmental factors, including lake eutrophication, that control oxygen and carbon isotopic composition of epilimnic biologically induced calcite precipitate. During the last 100 yr, Baldeggersee has undergone major increases in productivity and eutrophication in response to nutrient loading from agriculture and industrialization in the lake's watershed. Calibration of the isotopic signal in Baldeggersee to historical limnological data quantitatively links evidence of isotopic depletion in the sedimented calcite to trophic state of the lake. δ18O values from the spring/summer “light” sediment layers steadily diverged to more depleted values in response to historical eutrophication: measured δ18O values were up to 21.5‰ more negative than calculated equilibrium δ18O values. Evidence for 13C depletion in the calcite, relative to equilibrium values, is more difficult to ascertain because of an overall dominance of isotopic enrichment in the dissolved inorganic pool as productivity in Baldeggersee increases. A positive association exists between the degree of oxygen-18 depletion and the calcite crystal size. Thus, large amorphous calcite grains can be used as a proxy for recognizing apparent isotopic nonequilibrium in sediment sequences from highly productive lacustrine environments from all geologic time scales. In contrast to the light layers, the oxygen isotopic composition of the calcite in the late summer/fall “dark” sediment layers is unaffected by the apparent isotope nonequilibrium. Oxygen and carbon isotope values from the dark laminae in the Baldeggersee sediment therefore provide environmental and climatological proxies that can be calibrated with known environmental and regional climate data for the last century.

Genome Sequence Of Streptomyces Wadayamensis Strain A23, An Endophytic Actinobacterium From Citrus Reticulata.

The actinobacterium Streptomyces wadayamensis A23 is an endophyte of Citrus reticulata that produces the antimycin and mannopeptimycin antibiotics, among others. The strain has the capability to inhibit Xylella fastidiosa growth. The draft genome of S. wadayamensis A23 has ~7.0 Mb and 6,006 protein-coding sequences, with a 73.5% G+C content.

Genome Sequence Of Bacillus Safensis Cfa06, Isolated From Biodegraded Petroleum In Brazil.

Bacillus safensis is a microorganism recognized for its biotechnological and industrial potential due to its interesting enzymatic portfolio. Here, as a means of gathering information about the importance of this species in oil biodegradation, we report a draft genome sequence of a strain isolated from petroleum.

Overlapped Sequence Types (sts) And Serogroups Of Avian Pathogenic (apec) And Human Extra-intestinal Pathogenic (expec) Escherichia Coli Isolated In Brazil.

Avian pathogenic Escherichia coli (APEC) strains belong to a category that is associated with colibacillosis, a serious illness in the poultry industry worldwide. Additionally, some APEC groups have recently been described as potential zoonotic agents. In this work, we compared APEC strains with extraintestinal pathogenic E. coli (ExPEC) strains isolated from clinical cases of humans with extra-intestinal diseases such as urinary tract infections (UTI) and bacteremia. PCR results showed that genes usually found in the ColV plasmid (tsh, iucA, iss, and hlyF) were associated with APEC strains while fyuA, irp-2, fepC sitDchrom, fimH, crl, csgA, afa, iha, sat, hlyA, hra, cnf1, kpsMTII, clpVSakai and malX were associated with human ExPEC. Both categories shared nine serogroups (O2, O6, O7, O8, O11, O19, O25, O73 and O153) and seven sequence types (ST10, ST88, ST93, ST117, ST131, ST155, ST359, ST648 and ST1011). Interestingly, ST95, which is associated with the zoonotic potential of APEC and is spread in avian E. coli of North America and Europe, was not detected among 76 APEC strains. When the strains were clustered based on the presence of virulence genes, most ExPEC strains (71.7%) were contained in one cluster while most APEC strains (63.2%) segregated to another. In general, the strains showed distinct genetic and fingerprint patterns, but avian and human strains of ST359, or ST23 clonal complex (CC), presented more than 70% of similarity by PFGE. The results demonstrate that some zoonotic-related STs (ST117, ST131, ST10CC, ST23CC) are present in Brazil. Also, the presence of moderate fingerprint similarities between ST359 E. coli of avian and human origin indicates that strains of this ST are candidates for having zoonotic potential.

Draft Genome Sequence Of Ft9, A Novel Bacillus Cereus Strain Isolated From A Brazilian Thermal Spring.

A Bacillus cereus strain, FT9, isolated from a hot spring in the midwest region of Brazil, had its entire genome sequenced.

Phtx-ii A Basic Myotoxic Phospholipase A2 From Porthidium Hyoprora Snake Venom, Pharmacological Characterization And Amino Acid Sequence By Mass Spectrometry.

A monomeric basic PLA2 (PhTX-II) of 14149.08 Da molecular weight was purified to homogeneity from Porthidium hyoprora venom. Amino acid sequence by in tandem mass spectrometry revealed that PhTX-II belongs to Asp49 PLA2 enzyme class and displays conserved domains as the catalytic network, Ca2+-binding loop and the hydrophobic channel of access to the catalytic site, reflected in the high catalytic activity displayed by the enzyme. Moreover, PhTX-II PLA2 showed an allosteric behavior and its enzymatic activity was dependent on Ca2+. Examination of PhTX-II PLA2 by CD spectroscopy indicated a high content of alpha-helical structures, similar to the known structure of secreted phospholipase IIA group suggesting a similar folding. PhTX-II PLA2 causes neuromuscular blockade in avian neuromuscular preparations with a significant direct action on skeletal muscle function, as well as, induced local edema and myotoxicity, in mice. The treatment of PhTX-II by BPB resulted in complete loss of their catalytic activity that was accompanied by loss of their edematogenic effect. On the other hand, enzymatic activity of PhTX-II contributes to this neuromuscular blockade and local myotoxicity is dependent not only on enzymatic activity. These results show that PhTX-II is a myotoxic Asp49 PLA2 that contributes with toxic actions caused by P. hyoprora venom.

The Putative Leishmania Telomerase Rna (leishter) Undergoes Trans-splicing And Contains A Conserved Template Sequence.

Telomerase RNAs (TERs) are highly divergent between species, varying in size and sequence composition. Here, we identify a candidate for the telomerase RNA component of Leishmania genus, which includes species that cause leishmaniasis, a neglected tropical disease. Merging a thorough computational screening combined with RNA-seq evidence, we mapped a non-coding RNA gene localized in a syntenic locus on chromosome 25 of five Leishmania species that shares partial synteny with both Trypanosoma brucei TER locus and a putative TER candidate-containing locus of Crithidia fasciculata. Using target-driven molecular biology approaches, we detected a ∼2,100 nt transcript (LeishTER) that contains a 5' spliced leader (SL) cap, a putative 3' polyA tail and a predicted C/D box snoRNA domain. LeishTER is expressed at similar levels in the logarithmic and stationary growth phases of promastigote forms. A 5'SL capped LeishTER co-immunoprecipitated and co-localized with the telomerase protein component (TERT) in a cell cycle-dependent manner. Prediction of its secondary structure strongly suggests the existence of a bona fide single-stranded template sequence and a conserved C[U/C]GUCA motif-containing helix II, representing the template boundary element. This study paves the way for further investigations on the biogenesis of parasite TERT ribonucleoproteins (RNPs) and its role in parasite telomere biology.

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.

The mitochondrial genome of the stingless bee Melipona bicolor (Hymenoptera, Apidae, Meliponini): sequence, gene organization and a unique tRNA translocation event conserved across the tribe Meliponini

At present a complete mtDNA sequence has been reported for only two hymenopterans, the Old World honey bee, Apis mellifera and the sawfly Perga condei. Among the bee group, the tribe Meliponini (stingless bees) has some distinction due to its Pantropical distribution, great number of species and large importance as main pollinators in several ecosystems, including the Brazilian rain forest. However few molecular studies have been conducted on this group of bees and few sequence data from mitochondrial genomes have been described. In this project, we PCR amplified and sequenced 78% of the mitochondrial genome of the stingless bee Melipona bicolor (Apidae, Meliponini). The sequenced region contains all of the 13 mitochondrial protein-coding genes, 18 of 22 tRNA genes, and both rRNA genes (one of them was partially sequenced). We also report the genome organization (gene content and order), gene translation, genetic code, and other molecular features, such as base frequencies, codon usage, gene initiation and termination. We compare these characteristics of M. bicolor to those of the mitochondrial genome of A. mellifera and other insects. A highly biased A+T content is a typical characteristic of the A. mellifera mitochondrial genome and it was even more extreme in that of M. bicolor. Length and compositional differences between M. bicolor and A. mellifera genes were detected and the gene order was compared. Eleven tRNA gene translocations were observed between these two species. This latter finding was surprising, considering the taxonomic proximity of these two bee tribes. The tRNA Lys gene translocation was investigated within Meliponini and showed high conservation across the Pantropical range of the tribe.

In silico analysis of Simple Sequence Repeats from chloroplast genomes of Solanaceae species

The availaibilty of chloroplast genome (cpDNA) sequences of Atropa belladonna, Nicotiana sylvestris, N tabacum, N tomentosiformis, Solanum bulbocastanum, S lycopersicum and S tuberosum, which are Solanaceae species, allowed us to analyze the organization of cpSSRs in their genic and intergenic regions In general, the number of cpSSRs in cpDNA ranged from 161 in S tuberosum to 226 in N tabacum, and the number of intergenic cpSSRs was higher than genic cpSSRs The mononucleotide repeats were the most frequent in studied species, but we also identified di-, tri-, tetra-, penta- and hexanucleotide repeats Multiple alignments of all cpSSRs sequence from Solanaceae species made the identification of nucleotide variability possible and the phylogeny was estimated by maximum parsimony Our study showed that the plastome database can be exploited for phylogenetic analyses and biotechnological approaches

Phylogenetic relationships in Solanaceae and related species based on cpDNA sequence from plastid trnE-trnT region

Intergenic spacers of chloroplast DNA (cpDNA) are very useful in phylogenetic and population genetic studies of plant species, to study their potential integration in phylogenetic analysis. The non-coding trnE-trnT intergenic spacer of cpDNA was analyzed to assess the nucleotide sequence polymorphism of 16 Solanaceae species and to estimate its ability to contribute to the resolution of phylogenetic studies of this group. Multiple alignments of DNA sequences of trnE-trnT intergenic spacer made the identification of nucleotide variability in this region possible and the phylogeny was estimated by maximum parsimony and rooted with Convolvulaceae Ipomoea batalas, the most closely related family. Besides, this intergenic spacer was tested for the phylogenetic ability to differentiate taxonomic levels. For this purpose, species from four other families were analyzed and compared with Solanaceae species. Results confirmed polymorphism in the trnE-trnT region at different taxonomic levels.