Analyzing Domain of Convergence for Broyden’s Method

Broyden’s method is a quasi-Newton iterative method used to find roots of non-linear systems of equations. Research has shown and improved the rate of convergence for special cases and specific applications of the method. However, there is limited literature regarding the well-posedness of the method. In practice, a numerical method must reliably converge to the appropriate root. This paper will discuss the domain of attraction for the roots of a system found by using Broyden’s method. A method of approximating the radius of convergence of a root will be described which considers the largest disk centered at the root such that all values within the disk converge to the root. Literature on Broyden’s method has conflicting claims about the initial approximation of the Jacobian. Plots will demonstrate the effect of the initial guess of the Jacobian for the iterative scheme. In this paper, the importance of using a finite difference approximation for the initial guess of the Jacobian will be shown through examples of 2 × 2 systems of equations

Service Learning and Assessment: A Field Guide for Teachers

Recent advances in understanding the human brain, intelligence, and how we learn1 indicate that successful schools need to provide • rich, safe learning environments that address multiple realms of intelligence; • opportunities for experiential learning to promote construction of knowledge and understanding; • opportunities to develop both intelligence and skills through mediated learning; • opportunities to transfer learning through reflection; and • balanced assessment measures that include portfolios and performance assessments as well as more conventional standardized tests

Genetics meets Pathology - an increasingly important relationship.

The analytical power of modern methods for DNA analysis has outstripped our capability to interpret and understand the data generated. To make good use of this genomic data in a biomedical setting (whether for research or diagnosis), it is vital that we understand the mechanisms through which mutations affect biochemical pathways and physiological systems. This lies at the centre of what genetics is all about, and it is the reason why genetics and genomics should go hand in hand whenever possible. In this Annual Review Issue of the Journal of Pathology, we have assembled a collection of 16 expert reviews covering a wide range of topics. Through these, we illustrate the power of genetic analysis to improve our understanding of normal physiology and disease pathology, and thereby to think in rational ways about clinical management

Lack of involvement of known DNA methyltransferases in familial hydatidiform mole implies the involvement of other factors in establishment of imprinting in the human female germline

BACKGROUND: Differential methylation of the two alleles is a hallmark of imprinted genes. Correspondingly, loss of DNA methyltransferase function results in aberrant imprinting and abnormal post-fertilization development. In the mouse, mutations of the oocyte-specific isoform of the DNA methyltransferase Dnmt1 (Dnmt1o) and of the methyltransferase-like Dnmt3L gene result in specific failures of imprint establishment or maintenance, at multiple loci. We have previously shown in humans that an analogous inherited failure to establish imprinting at multiple loci in the female germline underlies a rare phenotype of recurrent hydatidiform mole. RESULTS: We have identified a human homologue of the murine Dnmt1o and assessed its pattern of expression. Human DNMT1o mRNA is detectable in mature oocytes and early fertilized embryos but not in any somatic tissues analysed. The somatic isoform of DNMT1 mRNA, in contrast, is not detectable in human oocytes. In the previously-described family with multi-locus imprinting failure, mutation of DNMT1o and of the other known members of this gene family has been excluded. CONCLUSIONS: Mutation of the known DNMT genes does not underlie familial hydatidiform mole, at least in the family under study. This suggests that trans-acting factors other than the known methyltransferases are required for imprint establishment in humans, a concept that has indirect support from recent biochemical studies of DNMT3L

Molecular basis of essential fructosuria: molecular cloning and mutational analysis of human ketohexokinase (fructokinase)

Essential fructosuria is one of the oldest known inborn errors of metabolism. It is a benign condition which is believed to result from deficiency of hepatic fructokinase (ketohexokinase, KHK, E.C.2.7.1.3). This enzyme catalyses the first step of metabolism of dietary fructose, conversion of fructose to fructose-1-phosphate. Despite the early recognition of this disorder, the primary structure of human KHK and the molecular basis of essential fructosuria have not been previously defined. In this report, the isolation and sequencing of full-length cDNA clones encoding human ketohexokinase are described. Alternative mRNA species and alternative KHK isozymes are produced by alternative polyadenylation and splicing of the KHK gene. The KHK proteins show a high level of sequence conservation relative to rat KHK. Direct evidence that mutation of the KHK structural gene is the cause of essential fructosuria was also obtained. In a well-characterized family, in which three of eight siblings have fructosurla, all affected individuals are compound heterozygotes for two mutations Gly40Arg and Ala43Thr. Both mutations result from G→A transitions, and each alters the same conserved region of the KHK protein. Neither mutation was seen in a sample of 52 unrelated control individuals. An additional conservative amino acid change (Val49lle) was present on the KHK allele bearing Ala43Th