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.

On the weak monotonicity of Gini means and other mixture functions

Weak monotonicity was recently proposed as a relaxation of the monotonicity condition for averaging aggregation, and weakly monotone functions were shown to have desirable properties when averaging data corrupted with outliers or noise. We extended the study of weakly monotone averages by analyzing their ϕ-transforms, and we established weak monotonicity of several classes of averaging functions, in particular Gini means and mixture operators. Mixture operators with Gaussian weighting functions were shown to be weakly monotone for a broad range of their parameters. This study assists in identifying averaging functions suitable for data analysis and image processing tasks in the presence of outliers.

Interpolation of Lipschitz functions

This paper describes a new computational approach to multivariate scattered data interpolation. It is assumed that the data is generated by a Lipschitz continuous function f. The proposed approach uses the central interpolation scheme, which produces an optimal interpolant in the worst case scenario. It provides best uniform error bounds on f, and thus translates into reliable learning of f. This paper develops a computationally efficient algorithm for evaluating the interpolant in the multivariate case. We compare the proposed method with the radial basis functions and natural neighbor interpolation, provide the details of the algorithm and illustrate it on numerical experiments. The efficiency of this method surpasses alternative interpolation methods for scattered data.

A comparison of search functions and other navigational tools provided on government websites

This paper reports the outcomes of a study that evaluated the effectiveness of search functions compared to other navigational tools available on government websites. The study used an observation exercise triangulated with a post observation interview. Results suggest that while there wasn't any significant difference in effectiveness between search functions and other navigational tools, the skill with which the search function is implemented and participants' familiarity with the website, are fundamental determinants of users' opinions. Implications of the findings for research and practice are discussed.

The use of analytic hierarchy process to incorporate stakeholder preferences into regional forest planning

Forest management decisions are often characterised by complexity, irreversibility and uncertainty. Much of the complexity arises from the multiple-use nature of forest goods and services, difficulty in monetary valuation of ecological services and the involvement of numerous stakeholders. Under these circumstances, conventional methods such as cost-benefit analysis are ill-suited to evaluate forest decisions. The Analytic Hierarchy Process (AHP), can be useful in regional forest planing as it can accommodate conflictual, multidimensional, incommensurable and incomparable set of objectives. The objective of this paper is to examine the scope and feasibility of the AHP in incorporating stakeholder preferences into regional forest planning. The Australian Regional Forest Agreement Programme is taken as an illustrative case for the analysis. The results show that the AHP can formalize public participation in decision making and increase the transparency and the credibility of the process.

A conditional probability approach to risk assessment for child sexual offenders with different classes of victim

Specific scales were developed for discriminating child sexual offenders with different classes of victim. The project demonstrates a method of individualising scores on actuarial risk assessment measured in a way that makes them more meaningful for those involved in decision-making about individual child sexual offenders. At present, the only quantifiable approach to specific decision-making relies on a general prediction of future behaviour, based on group data. The Bayesian approach is one method that can be used to assist decision-makers to use this information in ways that lead to the more appropriate management of risk. Ultimately, the better management of known child sexual offenders will lead to fewer offences and a reduction in the number of children who lives are profoundly affected by sexual victimisation.

Construction of aggregation functions from data using linear programming

This article examines the construction of aggregation functions from data by minimizing the least absolute deviation criterion. We formulate various instances of such problems as linear programming problems. We consider the cases in which the data are provided as intervals, and the outputs ordering needs to be preserved, and show that linear programming formulation is valid for such cases. This feature is very valuable in practice, since the standard simplex method can be used.

No evidence of expression of two classes of natural antibiotics (cathelicidins and defensins) in a sample of platypus milk

Marsupial neonates are born without a fully functioning immune system, and are known to be protected in part by natural antimicrobial peptides present in their mother's milk. Monotreme neonates hatch at a similar stage in development, and it has been hypothesised that their survival in a non-sterile burrow also relies on the presence of natural antibiotics in their mother's milk. Here we review the field of monotreme lactation and the antimicrobial peptide complement of the platypus (Ornithorhynchus anatinus). Using reverse transcriptasepolymerase chain reaction of milk cell RNA from a sample of platypus milk, we found no evidence for the expression of cathelicidins or defensins in the milk. This was unexpected. We hypothesise that these natural antibiotics may instead be produced by the young platypuses themselves.

Use of aggregation functions in decision making

A key component of many decision making processes is the aggregation step, whereby a set of numbers is summarised with a single representative value. This research showed that aggregation functions can provide a mathematical formalism to deal with issues like vagueness and uncertainty, which arise naturally in various decision contexts.

An analysis of student engagement when taught in classes of different sizes in rural, regional and metropolitan campuses of an Australian university

This study investigates the impact of class size on student engagement and student performance. It is based on an analysis of student university enter scores, student grades and student evaluations in metropolitan, regional and rural campuses of an Australian universityduring trimester 1 of years 2008, 9 & 10. Past literature appears to support the predominant influence of the class size effect on learning, though some findings are mixed and inconclusive. Contrary to the accepted view that higher entry level scores result in higher grades and, conversely, lower entry level scores result in lower grades, the findings suggest that factorsother than entry level scores, contribute to student outcomes and student engagement. The study reveals that student satisfaction of teaching quality is higher in the rural and regional campuses where the cohorts are smaller than at the metropolitan campus. This may be an indication that class size seems to have a predominant influence on student engagement and learning outcomes.

Application of power functions to chromatographic data for the enhancement of signal to noise ratios and separation resolution

Chromatographic detection responses are recorded digitally. A peak is represented ideally by a Guassian distribution. Raising a Guassian distribution to the power ‘n’ increases the height of the peak to that power, but decreases the standard deviation by √n. Hence there is an increasing disparity in detection responses as the signal moves from low level noise, with a corresponding decrease in peak width. This increases the S/N ratio and increases peak to peak resolution. The ramifications of these factors are that poor resolution in complex chromatographic data can be improved, and low signal responses embedded at near noise levels can be enhanced. The application of this data treatment process is potentially very useful in 2D-HPLC where sample dilution occurs between dimension, reducing signal response, and in the application of post-reaction detection methods, where band broadening is increased by virtue of reaction coils. In this work power functions applied to chromatographic data are discussed in the context of (a) complex separation problems, (b) 2D-HPLC separations, and (c) post-column reaction detectors.

A framework for identifying affinity classes of inorganic materials binding peptide sequences

With the rapid development of bionanotechnology, there has been a growing interest recently in identifying the affinity classes of the inorganic materials binding peptide sequences. However, there are some distinct characteristics of inorganic materials binding sequence data that limit the performance of many widely-used classification methods. In this paper, we propose a novel framework to predict the affinity classes of peptide sequences with respect to an associated inorganic material. We first generate a large set of simulated peptide sequences based on our new amino acid transition matrix, and then the probability of test sequences belonging to a specific affinity class is calculated through solving an objective function. In addition, the objective function is solved through iterative propagation of probability estimates among sequences and sequence clusters. Experimental results on a real inorganic material binding sequence dataset show that the proposed framework is highly effective on identifying the affinity classes of inorganic material binding sequences.

Characterisation of RNA in milk and prediction of microRNA functions

 Milk is considered on of the world’s most ‘complete’ food. To characterise milk composition, Amit investigated RNA present of milk form 8 different species ranging from platypus to human. By applying latest RNA sequencing and bioinformatic techniques, his work led to uncover hundreds of novel milk RNAs.