Three types of monotonicity of averaging functions

Monotonicity with respect to all arguments is fundamental to the definition of aggregation functions, which are one of the basic tools in knowledge-based systems. The functions known as means (or averages) are idempotent and typically are monotone, however there are many important classes of means that are non-monotone. Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging functions. In this paper we discuss the concepts of directional and cone monotonicity, and monotonicity with respect to majority of inputs and coalitions of inputs. We establish the relations between various kinds of monotonicity, and illustrate it on various examples. We also provide a construction method for cone monotone functions.

Fast algorithm for the cutting angle method of global optimization

The cutting angle method for global optimization was proposed in 1999 by Andramonov et al. (Appl. Math. Lett. 12 (1999) 95). Computer implementation of the resulting algorithm indicates that running time could be improved with appropriate modifications to the underlying mathematical description. In this article, we describe the initial algorithm and introduce a new one which we prove is significantly faster at each stage. Results of numerical experiments performed on a Pentium III 750 Mhz processor are presented.

Validation of a food-frequency questionnaire assessment of carotenoid and vitamin E intake using weighed food records and plasma biomarkers: the method of triads model.

Background: Reliability or validity studies are important for the evaluation of measurement error in dietary assessment methods. An approach to validation known as the method of triads uses triangulation techniques to calculate the validity coefficient of a food-frequency questionnaire (FFQ).

Objective: To assess the validity of an FFQ estimates of carotenoid and vitamin E intake against serum biomarker measurements and weighed food records (WFRs), by applying the method of triads. Design: The study population was a sub-sample of adult participants in a randomised controlled trial of b-carotene and sunscreen in the prevention of skin cancer. Dietary intake was assessed by a self-administered FFQ and a WFR. Nonfasting blood samples were collected and plasma analysed for five carotenoids (a-carotene, b-carotene, b-cryptoxanthin, lutein, lycopene) and vitamin E. Correlation coefficients were calculated between each of the dietary methods and the validity coefficient was calculated using
the method of triads. The 95% confidence intervals for the validity coefficients were estimated using bootstrap sampling.

Results: The validity coefficients of the FFQ were highest for a-carotene (0.85) and lycopene (0.62), followed by b-carotene (0.55) and total carotenoids (0.55), while the lowest validity coefficient was for lutein (0.19). The method of triads could not be used for b-cryptoxanthin and vitamin E, as one of the three underlying correlations was negative.

Conclusions: Results were similar to other studies of validity using biomarkers and the method of triads. For many dietary factors, the upper limit of the validity coefficients was less than 0.5 and therefore only strong relationships between dietary exposure and disease will be detected.

Easy, cheap and true : the case for promoting the Curwen method of teaching choral singing in developing countries

The Curwen method (Tonic Sol-fa) was developed by the Rev. John Cunven in England from the 1840s originally as a means of teaching music reading from staff notation. However, in the 1872 Standard Course, staff notation was dispensed with altogether in favour of Tonic Sol-fa "letter" notation. By the end of the century, Tonic Sol-fa had spread from Britain to many overseas countries. Although aspects were later incorporated into staff-based teaching
systems such as the Kodaly approach and the "New Curwen Method", Tonic Sol-fa in its late nineteenth century ' form has been "extinct" in Britain for several decades. Nevertheless, it is "alive and well", indeed flourishing, in certain African, Asian and Pacific countries. This paper analyses the Tonic Sol-fa system in terms of contemporary pedagogical practice and notational theory. The paper also reports on the use of Tonic Sol-fa in two countries - South Africa and Fiji - where it is now the mainstay of community choral music. It is argued that, particularly for developing countries, the Curwen method and its letter notation should be seriously considered as an alternative to staff notation methods as a highly effective means of promoting school and community choral singing.

Parallelization of the discrete gradient method of non-smooth optimization and its applications

We investigate parallelization and performance of the discrete gradient method of nonsmooth optimization. This derivative free method is shown to be an effective optimization tool, able to skip many shallow local minima of nonconvex nondifferentiable objective functions. Although this is a sequential iterative method, we were able to parallelize critical steps of the algorithm, and this lead to a significant improvement in performance on multiprocessor computer clusters. We applied this method to a difficult polyatomic clusters problem in computational chemistry, and found this method to outperform other algorithms.

A new method of evaluating the fineness and residual gum content of hemp fibres

The demand for eco-friendly apparel and technical textiles has led to a resurgence of interests in bast fibres such as hemp. The lack of fast and objective evaluation of the quality attributes of bast fibres has been a major barrier to the advancement of the bast fibre industry. One of the most important quality attributes of a fibre is its fineness. For bast fibres, the fibre fineness measurement can also reflect the degree of fibre separation during retting or degumming. The traditional method of evaluating the fineness and residual gum content of bast fibres is a very tedious process. In this paper, degummed hemp fibres have been measured for fineness on an Optical Fibre Diameter Analyser (OFDA), and the results have been co-related with the residual gum content in the fibre samples. Since hemp fibres do not have a circular cross section, it is the width of the fibre that gets measured by the OFDA instrument, and this width has been used as an indication of the fibre fineness in this paper. The findings from this study suggest that the optical method can provide a fast and objective way of evaluating the fineness of hemp fibres, and that there is a good correlation between the fibre „width‟ measurement and the residual gum content.

A novel method of tube manufacture for vehicle crashworthiness utilising the QUICKSTEP™ Process.

A novel method of composite tube manufacture was developed for potential use in automotive crash structures. Tubes were crushed axially under quasi-static conditions and highly repeatable behaviour was observed with an average specific energy absorption of -85kJ/kg. DMTA results indicated that the tubes were fully cured, even when the cycle was reduced to 7 minutes, giving this process huge potential for high-volume production.

Extended cutting angle method of global optimization

Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.

Effectiveness of recording in primary science : a study of the ability of junior primary school pupils to use drawing as an effective method of communication in science lessons

Drawing as a means of recording is a very common practice in junior primary science lessons. This is largely due to the availability of necessary materials. Also, most youg children have some degree of drawing skill and enjoy drawing activities. Since 1956 the science curriculum to be implemented in primary classrooms in Victoria has changed from one that was based largely on nature study (biological) to one that includes physical and technological aspects. Further, there have been changes in the teaching methodologies advocated for use in science lessons. A modified Interactive Teaching Approach was used for the studies. Drawing was the main means by which the children recorded information. The topic of 'shells' was used to enable collection of data about the children's enjoyment of the activity and satisfaction with their achievement. This study was replicated using the topic 'rocks'; again data were collected concerning satisfaction and enjoyment. During a series of lessons on 'snails' data were collected concerning the achievement of 'process' and 'objective' purposes that teachers might have in mind when setting a drawing activity. In addition to providing data about purposes the study stimulated some questions regarding the techniques the children had used in their drawings. Accordingly, data concerning the use of graphic techniques by the children were collected during a series of lessons on 'oils'. The data collected and analysed in the various studies highlighted the value of drawing in junior primary school science lessons. It also validated strategies developed by the author and designed to help teachers and children use drawing effectively in science activities.

Is phase-specific, community-oriented treatment of early psychosis- an economically viable method of improving outcome?

Objective: The Early Psychosis Prevention and Intervention Centre (EPPIC) provides a comprehensive 'real-world' model of early intervention to young people experiencing an emerging psychotic disorder. A prospective study has already provided evidence of improved clinical outcome at 12 months after entry. The present study examined whether the service was also cost-effective.

Method: A cost-effectiveness analysis compared EPPIC with its immediate precursor service, from the perspective of the government funding agency. Only direct costs were included.

Results: EPPIC proved to be more cost-effective. The weighted average cost per patient for the first 12 months was cheaper (by äD 7110 per patient), while treatment outcomes were superior. The savings were due to the marked reduction in in-patient costs outweighing substantial increases in the costs of community care.

Conclusion: These results, while encouraging in terms of the further development of integrated, phase-specific intervention programmes for early psychosis, are not conclusive, and further research is required.

A construction method of Atanassov’s intuitionistic fuzzy sets for image processing

In this work we introduce a new construction method of Atanassov's intuitionistic fuzzy sets (A-IFSs) from fuzzy sets. We use A-IFSs in image processing. We propose a new image magnification algorithm using A-IFSs. This algorithm is characterized by its simplicity and its efficiency.

METHOD OF MANUFACTURE

A process for producing boron nitride nanotubes and nanotube films, which process comprises heating a liquid composition comprising boron particles and a metal compound, wherein heating takes place at a temperature of from 800-1300 DEG C in a gaseous atmosphere containing nitrogen that causes boron nitride nanotubes to grow, and wherein the boron particles have an average particle size of less than 100 nm, and wherein the metal compound is selected such that it promotes the growth of boron nitride nanotubes during heating.