Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters

[EN] In this paper, we propose a family of optimal eighth order convergent iterative methods for multiple roots with known multiplicity with the introduction of two free parameters and three univariate weight functions. Also numerical experiments have applied to a number of academical test functions and chemical problems for different special schemes from this family that satisfies the conditions given in convergence result.This research was partially supported by Ministerio de Economia y Competitividad MTM2014-52016-C02-2-P and Generalitat Valenciana PROMETEO/2016/089.Zafar, F.; Cordero Barbero, A.; Quratulain, R.; Torregrosa Sánchez, JR. (2018). Optimal iterative methods for finding multiple roots of nonlinear equations using free parameters. Journal of Mathematical Chemistry. 56(7):1884-1901. https://doi.org/10.1007/s10910-017-0813-1S18841901567R. Behl, A. Cordero, S.S. Motsa, J.R. Torregrosa, On developing fourth-order optimal families of methods for multiple roots and their dynamics. Appl. Math. Comput. 265(15), 520–532 (2015)R. Behl, A. Cordero, S.S. Motsa, J.R. Torregrosa, V. Kanwar, An optimal fourth-order family of methods for multiple roots and its dynamics. Numer. Algor. 71(4), 775–796 (2016)R. Behl, A. Cordero, S.S. Motsa, J.R. Torregrosa, An eighth-order family of optimal multiple root finders and its dynamics. Numer. Algor. (2017). doi: 10.1007/s11075-017-0361-6F.I. Chicharro, A. Cordero, J. R. Torregrosa, Drawing dynamical and parameters planes of iterative families and methods. Sci. World J. ID 780153 (2013)A. Constantinides, N. Mostoufi, Numerical Methods for Chemical Engineers with MATLAB Applications (Prentice Hall PTR, New Jersey, 1999)J.M. Douglas, Process Dynamics and Control, vol. 2 (Prentice Hall, Englewood Cliffs, 1972)Y.H. Geum, Y.I. Kim, B. Neta, A class of two-point sixth-order multiple-zero finders of modified double-Newton type and their dynamics. Appl. Math. Comput. 270, 387–400 (2015)Y.H. Geum, Y.I. Kim, B. Neta, A sixth-order family of three-point modified Newton-like multiple-root finders and the dynamics behind their extraneous fixed points. Appl. Math. Comput. 283, 120–140 (2016)J.L. Hueso, E. Martınez, C. Teruel, Determination of multiple roots of nonlinear equations and applications. J. Math. Chem. 53, 880–892 (2015)L.O. Jay, A note on Q-order of convergence. BIT Numer. Math. 41, 422–429 (2001)S. Li, X. Liao, L. Cheng, A new fourth-order iterative method for finding multiple roots of nonlinear equations. Appl. Math. Comput. 215, 1288–1292 (2009)S.G. Li, L.Z. Cheng, B. Neta, Some fourth-order nonlinear solvers with closed formulae for multiple roots. Comput. Math. Appl. 59, 126–135 (2010)B. Liu, X. Zhou, A new family of fourth-order methods for multiple roots of nonlinear equations. Nonlinear Anal. Model. Control 18(2), 143–152 (2013)M. Shacham, Numerical solution of constrained nonlinear algebraic equations. Int. J. Numer. Method Eng. 23, 1455–1481 (1986)M. Sharifi, D.K.R. Babajee, F. Soleymani, Finding the solution of nonlinear equations by a class of optimal methods. Comput. Math. Appl. 63, 764–774 (2012)J.R. Sharma, R. Sharma, Modified Jarratt method for computing multiple roots. Appl. Math. Comput. 217, 878–881 (2010)F. Soleymani, D.K.R. Babajee, T. Lofti, On a numerical technique forfinding multiple zeros and its dynamic. J. Egypt. Math. Soc. 21, 346–353 (2013)F. Soleymani, D.K.R. Babajee, Computing multiple zeros using a class of quartically convergent methods. Alex. Eng. J. 52, 531–541 (2013)R. Thukral, A new family of fourth-order iterative methods for solving nonlinear equations with multiple roots. J. Numer. Math. Stoch. 6(1), 37–44 (2014)R. Thukral, Introduction to higher-order iterative methods for finding multiple roots of nonlinear equations. J. Math. Article ID 404635 (2013)X. Zhou, X. Chen, Y. Song, Constructing higher-order methods for obtaining the muliplte roots of nonlinear equations. J. Comput. Math. Appl. 235, 4199–4206 (2011)X. Zhou, X. Chen, Y. Song, Families of third and fourth order methods for multiple roots of nonlinear equations. Appl. Math. Comput. 219, 6030–6038 (2013

Evolutionary and phenotypic characterization of two spike mutations in European lineage 20E of SARS-CoV-2.

We have detected two mutations in the spike protein of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) at amino acid positions 1163 and 1167 that appeared independently in multiple transmission clusters and different genetic backgrounds. Furthermore, both mutations appeared together in a cluster of 1,627 sequences belonging to clade 20E. This cluster is characterized by 12 additional single nucleotide polymorphisms but no deletions. The available structural information on the S protein in the pre- and postfusion conformations predicts that both mutations confer rigidity, which could potentially decrease viral fitness. Accordingly, we observed reduced infectivity of this spike genotype relative to the ancestral 20E sequence in vitro, and the levels of viral RNA in nasopharyngeal swabs were not significantly higher. Furthermore, the mutations did not impact thermal stability or antibody neutrali- zation by sera from vaccinated individuals but moderately reduce neutralization by convalescent-phase sera from the early stages of the pandemic. Despite multi- ple successful appearances of the two spike mutations during the first year of SARS-CoV-2 evolution, the genotype with both mutations was displaced upon the expansion of the 20I (Alpha) variant. The midterm fate of the genotype investi- gated was consistent with the lack of advantage observed in the clinical and ex- perimental data

Multicopy plasmid integration in Komagataella phaffii mediated by a defective auxotrophic marker

Background: A commonly used approach to improve recombinant protein production is to increase the levels of expression by providing extra-copies of a heterologous gene. In Komagataella phaffii (Pichia pastoris) this is usually accomplished by transforming cells with an expression vector carrying a drug resistance marker following a screening for multicopy clones on plates with increasingly higher concentrations of an antibiotic. Alternatively, defective auxotrophic markers can be used for the same purpose. These markers are generally transcriptionally impaired genes lacking most of the promoter region. Among the defective markers commonly used in Saccharomyces cerevisiae is leu2-d, an allele of LEU2 which is involved in leucine metabolism. Cells transformed with this marker can recover prototrophy when they carry multiple copies of leu2-d in order to compensate the poor transcription from this defective allele. Results: A K. phaffii strain auxotrophic for leucine (M12) was constructed by disrupting endogenous LEU2. The resulting strain was successfully transformed with a vector carrying leu2-d and an EGFP (enhanced green fluorescent protein) reporter gene. Vector copy numbers were determined from selected clones which grew to different colony sizes on transformation plates. A direct correlation was observed between colony size, number of integrated vectors and EGFP production. By using this approach we were able to isolate genetically stable clones bearing as many as 20 integrated copies of the vector and with no significant effects on cell growth. Conclusions: In this work we have successfully developed a genetic system based on a defective auxotrophic which can be applied to improve heterologous protein production in K. phaffii. The system comprises a K. phaffii leu2 strain and an expression vector carrying the defective leu2-d marker which allowed the isolation of multicopy clones after a single transformation step. Because a linear correlation was observed between copy number and heterologous protein production, this system may provide a simple approach to improve recombinant protein productivity in K. phaffii

First-Principles Study of the Electronic and Magnetic Properties of Defects in Carbon Nanostructures

Understanding the magnetic properties of graphenic nanostructures is instrumental in future spintronics applications. These magnetic properties are known to depend crucially on the presence of defects. Here we review our recent theoretical studies using density functional calculations on two types of defects in carbon nanostructures: Substitutional doping with transition metals, and sp$^3$-type defects created by covalent functionalization with organic and inorganic molecules. We focus on such defects because they can be used to create and control magnetism in graphene-based materials. Our main results are summarized as follows: i)Substitutional metal impurities are fully understood using a model based on the hybridization between the $d$ states of the metal atom and the defect levels associated with an unreconstructed D$_{3h}$ carbon vacancy. We identify three different regimes, associated with the occupation of distinct hybridization levels, which determine the magnetic properties obtained with this type of doping; ii) A spin moment of 1.0 $\mu_B$ is always induced by chemical functionalization when a molecule chemisorbs on a graphene layer via a single C-C (or other weakly polar) covalent bond. The magnetic coupling between adsorbates shows a key dependence on the sublattice adsorption site. This effect is similar to that of H adsorption, however, with universal character; iii) The spin moment of substitutional metal impurities can be controlled using strain. In particular, we show that although Ni substitutionals are non-magnetic in flat and unstrained graphene, the magnetism of these defects can be activated by applying either uniaxial strain or curvature to the graphene layer. All these results provide key information about formation and control of defect-induced magnetism in graphene and related materials.Comment: 40 pages, 17 Figures, 62 References; Chapter 2 in Topological Modelling of Nanostructures and Extended Systems (2013) - Springer, edited by A. R. Ashrafi, F. Cataldo, A. Iranmanesh, and O. Or

Large expert-curated database for benchmarking document similarity detection in biomedical literature search

Document recommendation systems for locating relevant literature have mostly relied on methods developed a decade ago. This is largely due to the lack of a large offline gold-standard benchmark of relevant documents that cover a variety of research fields such that newly developed literature search techniques can be compared, improved and translated into practice. To overcome this bottleneck, we have established the RElevant LIterature SearcH consortium consisting of more than 1500 scientists from 84 countries, who have collectively annotated the relevance of over 180 000 PubMed-listed articles with regard to their respective seed (input) article/s. The majority of annotations were contributed by highly experienced, original authors of the seed articles. The collected data cover 76% of all unique PubMed Medical Subject Headings descriptors. No systematic biases were observed across different experience levels, research fields or time spent on annotations. More importantly, annotations of the same document pairs contributed by different scientists were highly concordant. We further show that the three representative baseline methods used to generate recommended articles for evaluation (Okapi Best Matching 25, Term Frequency–Inverse Document Frequency and PubMed Related Articles) had similar overall performances. Additionally, we found that these methods each tend to produce distinct collections of recommended articles, suggesting that a hybrid method may be required to completely capture all relevant articles. The established database server located at https://relishdb.ict.griffith.edu.au is freely available for the downloading of annotation data and the blind testing of new methods. We expect that this benchmark will be useful for stimulating the development of new powerful techniques for title and title/abstract-based search engines for relevant articles in biomedical research

Habitat Fragmentation can Modulate Drought Effects on the Plant-soil-microbial System in Mediterranean Holm Oak (Quercus ilex) Forests

© 2015, Springer Science+Business Media New York. Ecological transformations derived from habitat fragmentation have led to increased threats to above-ground biodiversity. However, the impacts of forest fragmentation on soils and their microbial communities are not well understood. We examined the effects of contrasting fragment sizes on the structure and functioning of soil microbial communities from holm oak forest patches in two bioclimatically different regions of Spain. We used a microcosm approach to simulate the annual summer drought cycle and first autumn rainfall (rewetting), evaluating the functional response of a plant-soil-microbial system. Forest fragment size had a significant effect on physicochemical characteristics and microbial functioning of soils, although the diversity and structure of microbial communities were not affected. The response of our plant-soil-microbial systems to drought was strongly modulated by the bioclimatic conditions and the fragment size from where the soils were obtained. Decreasing fragment size modulated the effects of drought by improving local environmental conditions with higher water and nutrient availability. However, this modulation was stronger for plant-soil-microbial systems built with soils from the northern region (colder and wetter) than for those built with soils from the southern region (warmer and drier) suggesting that the responsiveness of the soil-plant-microbial system to habitat fragmentation was strongly dependent on both the physicochemical characteristics of soils and the historical adaptation of soil microbial communities to specific bioclimatic conditions. This interaction challenges our understanding of future global change scenarios in Mediterranean ecosystems involving drier conditions and increased frequency of forest fragmentation

Constraints on the structure and seasonal variations of Triton’s atmosphere from the 5 October 2017 stellar occultation and previous observations⋆

Context. A stellar occultation by Neptune's main satellite, Triton, was observed on 5 October 2017 from Europe, North Africa, and the USA. We derived 90 light curves from this event, 42 of which yielded a central flash detection. Aims. We aimed at constraining Triton's atmospheric structure and the seasonal variations of its atmospheric pressure since the Voyager 2 epoch (1989). We also derived the shape of the lower atmosphere from central flash analysis. Methods. We used Abel inversions and direct ray-tracing code to provide the density, pressure, and temperature profiles in the altitude range ∼8 km to ∼190 km, corresponding to pressure levels from 9 μbar down to a few nanobars. Results. (i) A pressure of 1.18 ± 0.03 μbar is found at a reference radius of 1400 km (47 km altitude). (ii) A new analysis of the Voyager 2 radio science occultation shows that this is consistent with an extrapolation of pressure down to the surface pressure obtained in 1989. (iii) A survey of occultations obtained between 1989 and 2017 suggests that an enhancement in surface pressure as reported during the 1990s might be real, but debatable, due to very few high S/N light curves and data accessible for reanalysis. The volatile transport model analysed supports a moderate increase in surface pressure, with a maximum value around 2005-2015 no higher than 23 μbar. The pressures observed in 1995-1997 and 2017 appear mutually inconsistent with the volatile transport model presented here. (iv) The central flash structure does not show evidence of an atmospheric distortion. We find an upper limit of 0.0011 for the apparent oblateness of the atmosphere near the 8 km altitude