Chebyshev–Halley methods for analytic functions

AbstractTwo modifications of the family of Chebyshev–Halley methods are given. The first is to improve the rate of convergence to a multiple zero of an analytic function. The second is to find simultaneously all distinct zeros of a polynomial

A one parameter family of locally quartically convergent zero-finding methods

AbstractA one parameter family of iteration functions for finding simple and multiple zeros of analytic functions is derived. The family includes, as a special case, Traub's quartic square root method and, as limiting cases, the Kiss method of order 4, the Halley and the Newton methods. All the methods of the family are locally quartically convergent for a simple or multiple zero with known multiplicity. The asymptotic error constants for the methods of the family are given. The decreasing ratio at infinity of iteration functions is discussed. The optimum parameter of the family for polynomials is given

Literal resolution of affected equations by Isaac Newton (The study of the history of mathematics 2018)

"The study of the history of mathematics 2018". September 18-21, 2018. edited by Shigeru Jochi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.In 1669 and 1671, Isaac Newton resolved an algebraic equation f(x, y)=0 by expressing y as an infinite series of x . In this paper, we formulate Newton's resolution as a contemporary algorithm along the line of his original text and prove that the series converges asymptotically to the implicit function or one of the branches under certain conditions

Area and moment in De Analysi by Isaac Newton (Study of the History of Mathematics 2020)

"Study of the History of Mathematics 2020". February 1-3, 2021. edited by Naoki Osada. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed.In 1669, Isaac Newton wrote De Analysi to claim the priority of the analysis with infinite series. The method of infinite series requires the antiderivative of a simple curve ax^[m/n] and the derivative of an object to be sought. In the October 1666 tract and De Metodis (1671), Newton expressed the antiderivative using uxional equations, and the derivative by the ratio of the uxions. On the other hand, in De Analysi, Newton represented the antiderivative as the pair of the region described by the ordinate ax^[m/n] and its signed area, and he introduced the term momentum (moment) to represent the differential. In De Analysi, Newton replaced the terms and concepts of the uxional method with those of geometry

An Individual-Based Diploid Model Predicts Limited Conditions Under Which Stochastic Gene Expression Becomes Advantageous

Recent studies suggest the existence of a stochasticity in gene expression (SGE) in many organisms, anditsnon-negligible effecton their phenotype and fitness. To date, however, how SGE affects the key parameters of population genetics are not well understood. SGE can increase the phenotypic variation and act as a load for individuals, if they are at the adaptive optimum in a stable environment. On the other hand, part of the phenotypic variation caused by SGE might become advantageous if individuals at the adaptive optimum become genetically less-adaptive, for example due to an environmental change. Furthermore, SGE of unimportant genes might have little or no fitness consequences. Thus, SGE can be advantageous, disadvantageous, or selectively neutral depending on its context. In addition, there might be a genetic basis that regulates magnitude of SGE, which is often referred to as “modifier genes,” but little is known about the conditions under which such an SGE-modifier gene evolves. In the present study, we conducted individual-based computer simulations to examine these conditions in a diploid model. In the simulations, we considered a single locus that determines organismal fitness for simplicity, and that SGE on the locus creates fitness variation in a stochastic manner. We also considered another locus that modifies the magnitude of SGE. Our results suggested that SGE was always deleterious in stable environments and increased the fixation probability of deleterious mutations in this model. Even under frequently changing environmental conditions, only very strong natural selection made SGE adaptive. These results suggest that the evolution of SGE-modifier genes requires strict balance among the strength of natural selection, magnitude of SGE, and frequency of environmental changes. However, the degree of dominance affected the condition under which SGE become sadvantageous, indicating a better opportunity for the evolution of SGE in different genetic models

A generalized linear model for decomposing cis-regulatory, parent-of-origin, and maternal effects on allele-specific gene expression

Joint quantification of genetic and epigenetic effects on gene expression is important for understanding the establishment of complex gene regulation systems in living organisms. In particular, genomic imprinting and maternal effects play important roles in the developmental process of mammals and flowering plants. However, the influence of these effects on gene expression are difficult to quantify because they act simultaneously with cis-regulatory mutations. Here we propose a simple method to decompose cis-regulatory (i.e., allelic genotype, AG), genomic imprinting (i.e., parent-of-origin, PO), and maternal (i.e., maternal genotype, MG) effects on allele-specific gene expression using RNA-seq data obtained from reciprocal crosses. We evaluated the efficiency of method using a simulated dataset and applied the method to whole-body Drosophila and mouse trophoblast stem cell (TSC) and liver RNA-seq data. Consistent with previous studies, we found little evidence of PO and MG effects in adult Drosophila samples. In contrast, we identified dozens and hundreds of mouse genes with significant PO and MG effects, respectively. Interestingly, a similar number of genes with significant PO effect were detect in mouse TSCs and livers, whereas more genes with significant MG effect were observed in livers. Further application of this method will clarify how these three effects influence gene expression levels in different tissues and developmental stages, and provide novel insight into the evolution of gene expression regulation.Comment: 27 pages, 3 figures, 2 tabl

Molecular cloning, genomic characterization and over-expression of a novel gene, XRRA1, identified from human colorectal cancer cell HCT116(Clone2_XRR )and macaque testis

BACKGROUND: As part of our investigation into the genetic basis of tumor cell radioresponse, we have isolated several clones with a wide range of responses to X-radiation (XR) from an unirradiated human colorectal tumor cell line, HCT116. Using human cDNA microarrays, we recently identified a novel gene that was down-regulated by two-fold in an XR-resistant cell clone, HCT116(Clone2_XRR). We have named this gene as X-ray radiation resistance associated 1 (XRRA1) (GenBank BK000541). Here, we present the first report on the molecular cloning, genomic characterization and over-expression of the XRRA1 gene. RESULTS: We found that XRRA1 was expressed predominantly in testis of both human and macaque. cDNA microarray analysis showed three-fold higher expression of XRRA1 in macaque testis relative to other tissues. We further cloned the macaque XRRA1 cDNA (GenBank AB072776) and a human XRRA1 splice variant from HCT116(Clone2_XRR )(GenBank AY163836). In silico analysis revealed the full-length human XRRA1, mouse, rat and bovine Xrra1 cDNAs. The XRRA1 gene comprises 11 exons and spans 64 kb on chromosome 11q13.3. Human and macaque cDNAs share 96% homology. Human XRRA1 cDNA is 1987 nt long and encodes a protein of 559 aa. XRRA1 protein is highly conserved in human, macaque, mouse, rat, pig, and bovine. GFP-XRRA1 fusion protein was detected in both the nucleus and cytoplasm of HCT116 clones and COS-7 cells. Interestingly, we found evidence that COS-7 cells which over-expressed XRRA1 lacked Ku86 (Ku80, XRCC5), a non-homologous end joining (NHEJ) DNA repair molecule, in the nucleus. RT-PCR analysis showed differential expression of XRRA1 after XR in HCT116 clones manifesting significantly different XR responses. Further, we found that XRRA1 was expressed in most tumor cell types. Surprisingly, mouse Xrra1 was detected in mouse embryonic stem cells R1. CONCLUSIONS: Both XRRA1 cDNA and protein are highly conserved among mammals, suggesting that XRRA1 may have similar functions. Our results also suggest that the genetic modulation of XRRA1 may affect the XR responses of HCT116 clones and that XRRA1 may have a role in the response of human tumor and normal cells to XR. XRRA1 might be correlated with cancer development and might also be an early expressed gene