On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown.

On the Critical Points of Kyurkchiev’s Method for Solving Algebraic Equations

This paper is dedicated to Prof. Nikolay Kyurkchiev on the occasion of his 70th anniversary This paper gives sufficient conditions for kth approximations of the zeros of polynomial f (x) under which Kyurkchiev’s method fails on the next step. The research is linked with an attack on the global convergence hypothesis of this commonly used in practice method (as correlate hypothesis for Weierstrass–Dochev’s method). Graphical examples are presented.

Divergent selection during speciation of Lake Malawi cichlid fishes inferred from parallel radiations in nuptial coloration

Repeated evolution of the same phenotypic difference during independent episodes of speciation is strong evidence for selection during speciation. More than 1,000 species of cichlids, >10% of the world's freshwater fish species, have arisen within the past million years in Lakes Malawi and Victoria in eastern Africa. Many pairs of closely related sympatric species differ in their nuptial coloration in very similar ways. Nuptial coloration is important in their mate choice, and speciation by sexual selection on genetically or ecologically constrained variation in nuptial coloration had been proposed, which would repeatedly produce similar nuptial types in different populations, a prediction that was difficult to test in the absence of population-level phylogenies. We measured genetic similarity between individuals within and between populations, species, and lake regions by typing 59 individuals at >2,000 polymorphic genetic loci. From these data, we reconstructed, to our knowledge, the first larger species level phylogeny for the most diverse group of Lake Malawi cichlids. We used the genetic and phylogenetic data to test the divergent selection scenario against colonization, character displacement, and hybridization scenarios that could also explain diverse communities. Diversity has arisen by replicated radiations into the same color types, resulting in phenotypically very different, yet closely related, species within and phenotypically highly similar yet unrelated sets of species between regions, which is consistent with divergent selection during speciation and is inconsistent with colonization and character displacement models.

Data compilation on the biological response to ocean acidification: environmental and experimental context of data sets and related literature

The exponential growth of studies on the biological response to ocean acidification over the last few decades has generated a large amount of data. To facilitate data comparison, a data compilation hosted at the data publisher PANGAEA was initiated in 2008 and is updated on a regular basis (doi:10.1594/PANGAEA.149999). By January 2015, a total of 581 data sets (over 4 000 000 data points) from 539 papers had been archived. Here we present the developments of this data compilation five years since its first description by Nisumaa et al. (2010). Most of study sites from which data archived are still in the Northern Hemisphere and the number of archived data from studies from the Southern Hemisphere and polar oceans are still relatively low. Data from 60 studies that investigated the response of a mix of organisms or natural communities were all added after 2010, indicating a welcomed shift from the study of individual organisms to communities and ecosystems. The initial imbalance of considerably more data archived on calcification and primary production than on other processes has improved. There is also a clear tendency towards more data archived from multifactorial studies after 2010. For easier and more effective access to ocean acidification data, the ocean acidification community is strongly encouraged to contribute to the data archiving effort, and help develop standard vocabularies describing the variables and define best practices for archiving ocean acidification data.

Digestive Peptidase Evolution In Holometabolous Insects Led To A Divergent Group Of Enzymes In Lepidoptera.

Trypsins and chymotrypsins are well-studied serine peptidases that cleave peptide bonds at the carboxyl side of basic and hydrophobic l-amino acids, respectively. These enzymes are largely responsible for the digestion of proteins. Three primary processes regulate the activity of these peptidases: secretion, precursor (zymogen) activation and substrate-binding site recognition. Here, we present a detailed phylogenetic analysis of trypsins and chymotrypsins in three orders of holometabolous insects and reveal divergent characteristics of Lepidoptera enzymes in comparison with those of Coleoptera and Diptera. In particular, trypsin subsite S1 was more hydrophilic in Lepidoptera than in Coleoptera and Diptera, whereas subsites S2-S4 were more hydrophobic, suggesting different substrate preferences. Furthermore, Lepidoptera displayed a lineage-specific trypsin group belonging only to the Noctuidae family. Evidence for facilitated trypsin auto-activation events were also observed in all the insect orders studied, with the characteristic zymogen activation motif complementary to the trypsin active site. In contrast, insect chymotrypsins did not seem to have a peculiar evolutionary history with respect to their mammal counterparts. Overall, our findings suggest that the need for fast digestion allowed holometabolous insects to evolve divergent groups of peptidases with high auto-activation rates, and highlight that the evolution of trypsins led to a most diverse group of enzymes in Lepidoptera.

Increased Levels of NOTCH1, NF-kappa B, and Other Interconnected Transcription Factors Characterize Primitive Sets of Hematopoietic Stem Cells

As previously shown, higher levels of NOTCH1 and increased NF-kappa B signaling is a distinctive feature of the more primitive umbilical cord blood (UCB) CD34+ hematopoietic stem cells (HSCs), as compared to bone marrow ( BM). Differences between BM and UCB cell composition also account for this finding. The CD133 marker defines a more primitive cell subset among CD34+ HSC with a proposed hemangioblast potential. To further evaluate the molecular basis related to the more primitive characteristics of UCB and CD133+ HSC, immunomagnetically purified human CD34+ and CD133+ cells from BM and UCB were used on gene expression microarrays studies. UCB CD34+ cells contained a significantly higher proportion of CD133+ cells than BM (70% and 40%, respectively). Cluster analysis showed that BM CD133+ cells grouped with the UCB cells ( CD133+ and CD34+) rather than to BM CD34+ cells. Compared with CD34+ cells, CD133+ had a higher expression of many transcription factors (TFs). Promoter analysis on all these TF genes revealed a significantly higher frequency ( than expected by chance) of NF-kappa B-binding sites (BS), including potentially novel NF-kappa B targets such as RUNX1, GATA3, and USF1. Selected transcripts of TF related to primitive hematopoiesis and self-renewal, such as RUNX1, GATA3, USF1, TAL1, HOXA9, HOXB4, NOTCH1, RELB, and NFKB2 were evaluated by real-time PCR and were all significantly positively correlated. Taken together, our data indicate the existence of an interconnected transcriptional network characterized by higher levels of NOTCH1, NF-kappa B, and other important TFs on more primitive HSC sets.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Genetic potential of a maize population from Southern Brazil for the modified convergent-divergent selection scheme

Maize (Zea mays L.) is a very important cereal to world-wide economy which is also true for Brazil, particularly in the South region. Grain yield and plant height have been chosen as important criteria by breeders and farmers from Santa Catarina State (SC), Brazil. The objective of this work was to estimate genetic-statistic parameters associated with genetic gain for grain yield and plant height, in the first cycle of convergent-divergent half-sib selection in a maize population (MPA1) cultivated by farmers within the municipality of Anchieta (SC). Three experiments were carried out in different small farms at Anchieta using low external agronomic inputs; each experiment represented independent samples of half-sib families, which were evaluated in randomized complete blocks with three replications per location. Significant differences among half-sib families were observed for both variables in all experiments. The expected responses to truncated selection of the 25% better families in each experiment were 5.1, 5.8 and 5.2% for reducing plant height and 3.9, 5.7 and 5.0% for increasing grain yield, respectively. The magnitudes of genetic-statistic parameters estimated evidenced that the composite population MPA1 exhibits enough genetic variability to be used in cyclical process of recurrent selection. There were evidences that the genetic structure of the base population MPA1, as indicated by its genetic variability, may lead to expressive changes in the traits under selection, even under low selection pressure.

The conserved and divergent roles of carbonic anhydrases in the filamentous fungi Aspergillus fumigatus and Aspergillus nidulans

P>Carbon dioxide (CO(2)) and its hydration product bicarbonate (HCO(3)-) are essential molecules in various physiological processes of all living organisms. The reversible interconversion between CO(2) and HCO(3)- is in equilibrium. This reaction is slow without catalyst, but can be rapidly facilitated by Zn2+-metalloenzymes named carbonic anhydrases (CAs). To gain an insight into the function of multiple clades of fungal CA, we chose to investigate the filamentous fungi Aspergillus fumigatus and A. nidulans. We identified four and two CAs in A. fumigatus and A. nidulans, respectively, named cafA-D and canA-B. The cafA and cafB genes are constitutively, strongly expressed whereas cafC and cafD genes are weakly expressed but CO(2)-inducible. Heterologous expression of the A. fumigatus cafB, and A. nidulans canA and canB genes completely rescued the high CO(2)-requiring phenotype of a Saccharomyces cerevisiae Delta nce103 mutant. Only the Delta cafA Delta cafB and Delta canB deletion mutants were unable to grow at 0.033% CO(2), of which growth defects can be restored by high CO(2). Defects in the CAs can affect Aspergilli conidiation. Furthermore, A. fumigatus Delta cafA, Delta cafB, Delta cafC, Delta cafD and Delta cafA Delta cafB mutant strains are fully virulent in a low-dose murine infection.

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

Evolutionary distinctiveness and status of the endangered Lake Eacham rainbowfish (Melanotaenia eachamensis)

The Lake Eacham rainbowfish (Melanotaenia eachamensis) was declared extinct in the wild in the late 1980s after it disappeared from its only known locality, an isolated crater lake in northeast Queensland. Doubts have been raised about whether this taxon is distinct from surrounding populations of the eastern rainbowfish (Melanotaenia splendida splendida). We examined the evolutionary distinctiveness of M. eachamensis, obtained from captive stocks, relative to M. s. splendida through analysis of variation in mtDNA sequences, nuclear microsatellites, and morphometric characters Captive M. eachamensis had mtDNAs that were highly divergent from those in most populations of M. s. splendida. A broader geographic survey using RFLPs revealed some populations initially identified as M. s. splendida, that carried eachamensis mtDNA, whereas some others had mixtures of eachamensis and splendida mtDNA. The presence of eachamensis-like mtDNA in these populations could in principle be due to (1) sorting of ancestral polymorphisms, (2) introgression of M. eachamensis mtDNA into M. s. splendida, or (3) incorrect species boundaries, such that some populations currently assigned to M. s. splendida are M. eachamensis or are mixtures of the two species. These alternatives hypotheses were evaluated through comparisons of four nuclear microsatellite loci and morphometrics and meristics. In analyses of both data sets, populations of M. s. splendida with eachamensis mtDNA were more similar to captive M. eachamensis than to M. s. splendida with splendida mtDNA, supporting hypothesis 3. These results are significant for the management of M. eachamensis in several respects. First the combined molecular and morphological evidence indicates that M. eachamensis is a distinct species and a discrete evolutionarily significant unit worthy of conservation effort. Second it appears that the species boundary between M. eachamensis and M. s. splendida has been misdiagnosed such that there are extant populations on the Atherton Tableland as well as areas where both forms coexist. Accordingly we suggest that M. eachamensis be listed as vulnerable, rather than critical (or extinct in the wild). Third, the discovery of extant but genetically divergent populations of M. eachamensis on the Atherton Tableland broadens the options for future reintroductions to Lake Eacham.

Effect of oral creatine supplementation on near-maximal strength and repeated sets of high-intensity bench press exercise

This study examined the effects of 26 days of oral creatine monohydrate (Cr) supplementation on near-maximal muscular strength, high-intensity bench press performance, and body composition. Eighteen male powerlifters with at least 2 years resistance training experience took part in this 28-day experiment. Pre and postmeasurements (Days 1 and 28) were taken of near-maximal muscular strength, body mass, and % body fat. There were two periods of supplementation Days 2 to 6 and Days 7 to 27. ANOVA and t-tests revealed that Cr supplementation significantly increased body mass and lean body mass with no changes in % body fat. Significant increases in 3-RM strength occurred in both groups, both absolute and relative to body mass; the increases were greater in the Cr group. The change in total repetitions also increased significantly with Cr supplementation both in absolute terms and relative to body mass, while no significant change was seen in the placebo (P) group. Creatine supplementation caused significant changes in the number of BP reps in Sets 1, 4, and 5. No changes occurred in the P group. It appears that 26 days of Cr supplementation significantly improves muscular strength and repeated near-maximal BP performance, and induces changes in body composition.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

Life-history consequences of divergent selection on egg size in Drosophila melanogaster

Life histories are generally assumed to evolve via antagonistic pleiotropy (negative genetic correlations) among traits, and trade-offs between life-history traits are typically studied using either phenotypic manipulations or selection experiments. We investigated the trade-off between egg size and fecundity in Drosophila melanogaster by examining both the phenotypic and genetic relationships between these traits after artificial selection for large and small eggs, relative to female body size. Egg size responded strongly to selection in both directions, increasing in the large-egg selected lines and decreasing in the small-egg selected lines. Phenotypic correlations between egg size and fecundity in the large-egg selected lines were negative, but no relationship between these traits occurred in either the control or small-egg selected lines. There was no negative genetic correlation between egg size and fecundity. Total reproductive allocation decreased in the small-egg selected lines but did not increase in the large-egg lines. Our results have three implications. First, our selection procedure may have forced females selected for large eggs into a physiological trade-off not reflected in a negative genetic correlation between these traits. Second, the lack of a negative genetic correlation between egg size and number suggests that the phenotypic trade-off frequently observed between egg size and number in other organisms may not evolve over the short term via a direct genetic trade-off whereby increases in egg size are automatically accompanied by decreased fecundity. Finally, total reproductive allocation may not evolve independently of egg size as commonly assumed.