Diagonalization and Jordan Normal Form – motivation through Maple

Following an introduction to the diagonalization of matrices, one of the more difficult topics for students to grasp in linear algebra is the concept of Jordan normal form. In this note, we show how the important notions of diagonalization and Jordan normal form can be introduced and developed through the use of the computer algebra package Maple®.

The roles of olfaction and vision in host-plant finding by the diamondback moth, Plutella xylostella

The relative roles of olfaction and vision in the crepuscular host-finding process of a major lepidopteran pest of cruciferous crops, the diamondback moth Plutella xylostella are investigated in a series of laboratory and semi-field experiments. Flying female moths use volatile plant chemical cues to locate and to promote landing on their host, even in complex mixed-crop environments in large cages. Multiple regression analysis shows that both the plant position (front, middle or back rows) and the type of plant (host plant, nonhost plant) are needed to explain the distribution of insects in such a mixed-crop situation. This strong plant position effect indicates that, when host plants are present in a mixture, foraging P. xylostella are more likely to alight on the first row of the plants. The findings are discussed with regard to current theories of host-plant location by phytophagous insects and the possible implications for integrated pest management.

Enhancing the selenium content of bovine milk through alteration of the form and concentration of selenium in the diet of the dairy cow

Since estimated dietary selenium intake in the UK has declined steadily from around 60 mug day(-1) in 1975 to 34 mug day(-1) in 1997, there is a need to increase selenium intake from staple foods such as milk and milk products. An experiment was therefore done to investigate the relationship between dietary source and concentration of selenium and the selenium content of bovine milk. In a 3 x 3 factorial design, 90 mid-lactation Holstein dairy cows were supplemented over 8 weeks with either sodium selenite (S), a chelated selenium product (Selenium Metasolate(TM)) (C) or a selenium yeast (Sel-plex(TM)) (Y) at three different dietary inclusion levels of 0.38 (L), 0.76 (M) and 1.14 (H) mg kg(-1) dry matter (DM). Significant increases in milk selenium concentration were observed for all three sources with increasing inclusion level in the diet, but Y gave a much greater response (up to +65 mug l(-1)) than the other two sources of selenium (S and C up to +4 and +6 mug l(-1) respectively). The Y source also resulted in a substantially higher apparent efficiency of transfer of selenium from diet to milk than S or C. Feeding Y at the lowest dietary concentration, and thus within the maximum level permitted under EU regulations, resulted in milk with a selenium concentration of 28 mug l(-1). If the selenium concentration of milk in the UK was increased to this value, it would, at current consumption rates, provide an extra 8.7 mug selenium day(-1), or 11 and 14% of daily recommended national intake for men and women respectively. (C) 2004 Society of Chemical Industry.

Crystal structure of a monomeric form of SARS-CoV endonuclease nsp15 suggests a role for hexamerization as an allosteric switch

Mature nonstructural protein-15 (nsp15) from the severe acute respiratory syndrome coronavirus (SARS-CoV) contains a novel uridylate-specific Mn2+-dependent endoribonuclease (NendoU). Structure studies of the full-length form of the obligate hexameric enzyme from two CoVs, SARS-CoV and murine hepatitis virus, and its monomeric homologue, XendoU from Xenopus laevis, combined with mutagenesis studies have implicated several residues in enzymatic activity and the N-terminal domain as the major determinant of hexamerization. However, the tight link between hexamerization and enzyme activity in NendoUs has remained an enigma. Here, we report the structure of a trimmed, monomeric form of SARS-CoV nsp15 (residues 28 to 335) determined to a resolution of 2.9 A. The catalytic loop (residues 234 to 249) with its two reactive histidines (His 234 and His 249) is dramatically flipped by approximately 120 degrees into the active site cleft. Furthermore, the catalytic nucleophile Lys 289 points in a diametrically opposite direction, a consequence of an outward displacement of the supporting loop (residues 276 to 295). In the full-length hexameric forms, these two loops are packed against each other and are stabilized by intimate intersubunit interactions. Our results support the hypothesis that absence of an adjacent monomer due to deletion of the hexamerization domain is the most likely cause for disruption of the active site, offering a structural basis for why only the hexameric form of this enzyme is active.

The component polypeptide chains of bovine insulin nucleate or inhibit aggregation of the parent protein in a conformation-dependent manner

Amyloid fibrils are typically rigid, unbrariched structures with diameters of similar to 10 nm and lengths up to several micrometres, and are associated with more than 20 diseases including Alzheimer's disease and type II diabetes. Insulin is a small, predominantly alpha-helical protein consisting of 51 residues in two disulfide-linked polypeptide chains that readily assembles into amyloid fibrils under conditions of low PH and elevated temperature. We demonstrate here that both the A-chain and the B-chain of insulin are capable of forming amyloid fibrils in isolation under similar conditions, with fibrillar morphologies that differ from those composed of intact insulin. Both the A-chain and B-chain fibrils were found to be able to cross-seed the fibrillization of the parent protein, although these reactions were substantially less efficient than self-seeding with fibrils composed of full-length insulin. In both cases, the cross-seeded fibrils were morphologically distinct from the seeding, material, but shared common characteristics with typical insulin fibrils, including a very similar helical repeat. The broader distribution of heights of the cross-seeded fibrils compared to typical insulin fibrils, however, indicates that their underling protofilament hierarchy may be subtly different. In addition, and remarkably in view of this seeding behavior, the soluble forms of the A-chain and B-chain peptides were found to be capable of inhibiting insulin fibril formation. Studies using mass spectrometry suggest that this behavior might be attributable to complex formation between insulin and the A-chain and B-chain peptides. The finding that the same chemical form of a polypeptide chain in different physical states can either stimulate or inhibit the conversion of a protein into amyloid fibrils sheds new light on the mechanisms underlying fibril formation, fibril strain propagation and amyloid disease initiation and progression. (c) 2006 Elsevier Ltd. All rights reserved.

Discovery of three polymorphs of 7-fluoroisatin reveals challenges in using computational crystal structure prediction as a complement to experimental screening

A combined computational and experimental polymorph search was undertaken to establish the crystal forms of 7-fluoroisatin, a simple molecule with no reported crystal structures, to evaluate the value of crystal structure prediction studies as an aid to solid form discovery. Three polymorphs were found in a manual crystallisation screen, as well as two solvates. Form I ( P2(1)/c, Z0 1), found from the majority of solvent evaporation experiments, corresponded to the most stable form in the computational search of Z0 1 structures. Form III ( P21/ a, Z0 2) is probably a metastable form, which was only found concomitantly with form I, and has the same dimeric R2 2( 8) hydrogen bonding motif as form I and the majority of the computed low energy structures. However, the most thermodynamically stable polymorph, form II ( P1 , Z0 2), has an expanded four molecule R 4 4( 18) hydrogen bonding motif, which could not have been found within the routine computational study. The computed relative energies of the three forms are not in accord with experimental results. Thus, the experimental finding of three crystalline polymorphs of 7- fluoroisatin illustrates the many challenges for computational screening to be a tool for the experimental crystal engineer, in contrast to the results for an analogous investigation of 5- fluoroisatin.

Architect and user interaction: The spoken representation of form and functional meaning

The paper is an investigation of the exchange of ideas and information between an architect and building users in the early stages of the building design process before the design brief or any drawings have been produced. The purpose of the research is to gain insight into the type of information users exchange with architects in early design conversations and to better understand the influence the format of design interactions and interactional behaviours have on the exchange of information. We report an empirical study of pre-briefing conversations in which the overwhelming majority of the exchanges were about the functional or structural attributes of space, discussion that touched on the phenomenological, perceptual and the symbolic meanings of space were rare. We explore the contextual features of meetings and the conversational strategies taken by the architect to prompt the users for information and the influence these had on the information provided. Recommendations are made on the format and structure of pre-briefing conversations and on designers' strategies for raising the level of information provided by the user beyond the functional or structural attributes of space.

Responsiveness to change by standard-form contract drafters: A case study of the FIDIC White Book

Purpose – The purpose of this paper is to focus on the Fédération Internationale des Ingénieurs-Conseils (FIDIC) White Book standard form of building contract. It tracks the changes to this contract over its four editions, and seeks to identify their underlying causes. Design/methodology/approach – The changes made to the White Book are quantified using a specific type of quantitative content analysis. The amended clauses are then examined to understand the nature of the changes made. Findings – The length of the contract increased by 34 per cent between 1990 and 2006. A large proportion of the overall increase can be attributed to the clauses dealing with “conflict of interest/corruption” and “dispute resolution”. In both instances, the FIDIC drafting committees have responded to international developments to discourage corruption, and to encourage the use of alternative dispute resolution. Between 1998 and 2006, the average length of the sentences increased slightly, raising the question of whether long sentences are easily understood by users of contracts. Research limitations/implications – Quantification of text appears to be particularly useful for the analysis of documents which are regularly updated because changes can be clearly identified and the length of sentences can be determined, leading to conclusions about the readability of the text. However, caution is needed because changes of great relevance can be made to contract clauses without actually affecting their length. Practical implications – The paper will be instructive for contract drafters and informative for users of FIDIC's White Book. Originality/value – Quantifying text has been rarely used regarding standard-form contracts in the field of construction.

Recovery of norbixin from a raw extraction solution of annatto pigments using colloidal gas aphrons (CGAs)

Annatto dyes are widely used in food and are finding increasing interest also for their application in the pharmaceutical and cosmetics industry. Bixin is the main pigment extracted from annatto seeds and accounts for 80% of the carotenoids in the outer coat of the seeds; norbixin being the water-soluble form of the bixin. Typically annatto dyes are extracted from the seeds by mechanical means or solutions of alkali, edible oil or organic solvents, or a combination of the two depending on the desired final product. In this work CGAs are investigated as an alternative separation method for the recovery of norbixin from a raw extraction solution of annatto pigments in KOH. A volume of CGAs generated from a cationic surfactant (CTAB) solution is mixed with a volume of annatto solution and when the mixture is allowed to settle it separates into the top aphron phase and the bottom liquid phase. Potassium norbixinate presented in the annatto solution will interact with the surfactant in the aphron phase, which results in the effective separation of norbixin. Recovery= 94% was achieved at a CTAB to norbixin molar ratio of 3.3. In addition a mechanism of separation is proposed here based on the separation results with the cationic surfactant and an anionic surfactant (bis-2-ethyl hexyl sulfosuccinate, AOT) and measurements of surfactant to norbixin ratio in the aphron phase; electrostatic interactions between the surfactant and norbixin molecules result in the fort-nation of a coloured complex and effective separation of norbixin. (c) 2005 Elsevier B.V. All rights reserved.

Treatment response in child anxiety is differentially related to the form of maternal anxiety disorder

An examination was made of the extent to which maternal anxiety predicted response to treatment of children presenting with an anxiety disorder. In a sample of 55 children referred to a local NHS CAMH service for treatment of an anxiety disorder, systematic mental state interview assessment was made of both mothers and children, and both completed self-report questionnaires to assess aspects of anxiety, both immediately before the children received treatment and following treatment. Children of mothers with anxiety disorder overall responded less well to treatment than children of mothers with no anxiety disorder. There was some diagnostic specificity in this in that children of mothers with GAD did as well in treatment as children whose mothers had no anxiety, whereas children of mothers with social phobia did poorly. The outcome for children with anxiety appears to be related to the presence and nature of maternal anxiety. It would seem prudent that treatment of children with anxiety involves assessment of maternal anxiety. It is important to establish in systematic investigation whether treatment of maternal anxiety improves the outcome for child anxiety.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.