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Applications of the pickup and delivery problem with time windows and last-in-first-out (LIFO) loading (PDPTWL) constraints can be found in the transportation of animals, heavyweight goods, and hazardous materials, where unloading vehicles requires more time and special handling. Examples include carrying livestock, cars, and chemical containers. Research on exact methods to solve the pickup and delivery problem with time windows (PDPTW) and its variants has mainly focused on branch-and-price-and-cut algorithms. In this paper, we propose a novel exact approach based on fragments—a series of pickup and delivery requests starting and ending with an empty vehicle. We use fragments to formulate a relaxed network flow model with side constraints. Lazy constraints are used to cut off any illegal solution that may occur while solving the integer program. Extensive computational experiments show that the proposed approach is superior to the current state-of-the-art method.

In many large first year undergraduate courses in the health sciences, students participate in practical sessions (pracs) in which they are taught about and provided with opportunities to practice basic skills and techniques for measuring biophysical and psychological variables. We have successfully developed and implemented an Online Student Laboratory Data Repository in an introductory health science course which provides rich opportunities for using a large, student centric dataset in lecture components of the course to explore and evaluate underlying principles, models and theories within the discipline or profession. In future work we will examine its effectiveness in improving collaboration between undergraduate students from different health science programs.

Epidemiology is the study of the distribution of disease in human populations. This means that authentically teaching primary data collection in epidemiology is difficult as students cannot easily access suitable human populations. Using an action research methodology, this paper studied the use of a virtual human population (called The Island) to enable students to experience many features of authentic primary data collection in epidemiological research. The Island was used in a course introducing epidemiology and biostatistics for students in non-quantitative disciplines. This paper discusses how The Island was introduced into the course, and then evaluates the change. Students were highly engaged, and students and teaching staff responded favourably to the use of The Island, with 70% of students agreeing or strongly agreeing that The Island was easy to use, and 64% agreeing or strongly agreeing that the use of a virtual population was beneficial to their understanding of epidemiology.

We report here on a practitioner study of a first year undergraduate service course that aligns a webbased, student-lecturer communication system with the mathematical curriculum. The report presents and analyses data from students and from the lecturer and outlines the nature of the technical interface. We indicate how communication of the students’ affective learning needs had a positive influence on the professional development of the lecturer himself. Furthermore, we claim that success of mathematics/statistics teaching that integrates emotional responses from learners is intimately related to the knowledge, skills, beliefs and values of the lecturer.

Statistical skills and statistical literacy have emerged as important areas in education. While it has a rich mathematical basis, successful understanding and application of statistics incorporates other types of knowledge. In a similar way, beliefs about statistics can be described using the same framework as beliefs about mathematics, but statistical beliefs bring other aspects as well. This article describes a project for investigating student beliefs in statistics through the creation of pictures of understanding. It presents a classification of statistical concepts and attitudes which are motivated by research in statistical literacy and then shows how these can be refined to be more reliably applied in practice.

A large number of models have been derived from the two-parameter Weibull distribution and are referred to as Weibull models. They exhibit a wide range of shapes for the density and hazard functions, which makes them suitable for modelling complex failure data sets. The WPP and IWPP plot allows one to determine in a systematic manner if one or more of these models are suitable for modelling a given data set. This paper deals with this topic.

Fleeming Jenkin's swamping argument (1867) is re-examined in relation to subsequent criticisms of its assumptions. Jenkin's original argument purported to show that, under blending inheritance, natural selection could not operate on ‘sports’ or ‘single variations’. A serious flaw in Jenkin's model was exposed in a forgotten paper in 1871. Darwin accepted Jenkin's ‘flawed’ conclusion, though he did not fully understand the argument. Both Jenkin and Darwin regarded the swamping argument as a barrier to evolution within a single lineage. A completely different interpretation of the phrase ‘swamping argument’, first put forward by Romanes in 1886, identified it with the problem of the role of free intercrossing in preventing speciation. The latter problem also underlies current debate about the possibility of sympatric speciation and is as serious under particulate as under blending inheritance. Jenkin's argument depended on the assumption of blending inheritance; when modified to remove the ‘flaw’ in his model, it ceased to present a barrier to the operation of natural selection within a lineage, provided that the mutation rate was high enough to maintain adequate genetic variability under blending.

Flying insects constantly face the challenge of choosing efficient, safe and collision-free routes while navigating through dense foliage. We examined the route-choice behavior of foraging honeybees when they encountered a barrier which could be traversed by flying through one of two apertures, positioned side by side. When the bees’ choice behavior was averaged over the entire tested population, the two apertures were chosen with equal frequency when they were equally wide. When the apertures were of different width, the bees, on average, showed a preference for the wider aperture, which increased sharply with the difference between the aperture widths. Thus, bees are able to discriminate the widths of oncoming gaps and choose the passage which is presumably safer and quicker to transit. Examination of the behavior of individual bees revealed that, when the two apertures were equally wide, ca. 55% of the bees displayed no side bias in their choices. However, the remaining 45% showed varying degrees of bias, with one half of them preferring the left-hand aperture, and the other half the right-hand aperture. The existence of distinct individual biases was confirmed by measuring the times required by biased bees to transit various aperture configurations: The transit time was longer if a bee’s intrinsic bias forced it to engage with the narrower aperture. Our results show that, at the population level, bees do not exhibit ‘handedness’ in choosing routes; however, individual bees display an idiosyncratic bias that can range from a strong left bias, through zero bias, to a strong right bias. In honeybees, previous studies of olfactory and visual learning have demonstrated clear biases at the population level. To our knowledge, our study is the first to uncover the existence of individually distinct biases in honeybees. We also show how a distribution of biases among individual honeybees can be advantageous in facilitating rapid transit of a group of bees through a cluttered environment, without any centralized decision-making or control.

Galton greeted Darwin's theory of pangenesis with enthusiasm, and tried to test the assumption that the heredity particles circulate in the blood by transfusion experiments on rabbits. The failure of these experiments led him to reject this assumption, and in the 1870s he developed an alternative theory of heredity, which incorporated those parts of Darwin's theory that did not involve the transportation of hereditary particles throughout the system. He supposed that the fertilized ovum contains a large number of hereditary elements, which he collectively called the "stirp," a few of which are patent, developing into particular cell types, while the rest remain latent; the latent elements can be transmitted to the next generation, while the patent elements, with rare exceptions, cannot since they have developed into cells. The problem with this theory is that it does not explain the similarity between parent and child unless there is a high correlation between latent and patent elements. Galton probably came to realize this problem during his subsequent statistical work on heredity, and he quietly dropped the idea that patent elements are not transmitted in Natural Inheritance (1889). Galton thought that brothers and sisters had identical stirps, and he attributed differences between them to variability in the choice of patent elements from the stirp, that is to say to developmental variability. He attributed the likeness of monozygotic twins to the similarity of their developmental environment. Galton's twin method was to track the life history changes of twins to see whether twins who were similar at birth diverged in dissimilar environments or whether twins who were dissimilar at birth converged in similar environments. It is quite different from the modern twin method of comparing the similarities between monozygotic and dizygotic twins, on the assumption that monozygotic twins are genetically identical whereas dizygotic twins are not. It has been argued that Galton foreshadowed Weismann's theory in the continuity of the germ-plasm, but this is only true in a weak sense. They both believed that the inheritance of acquired characters was either rare or impossible, but Galton did not forestall the essential part of Weismann's theory, that the germ-plasm of the zygote is doubled, with one part being reserved for the formation of the germ-cells.

Galton's ancestral law states that the two parent contribute between them on average one-half of the total heritage of the offspring, the four grandparents one-quarter, and so on. He interpreted this law both as a representation of the separate contributions of each ancestor to the heritage of the offspring and as a multiple regression formula for predicting the value of a trait from ancestral values. Logical reconstruction of the law is presented based on formalizing Galton's model of heredity outlined in Natural Inheritance (Galton, 1889). The resulting law has a free parameter to be empirically estimated which represents the frequency of latent hereditary elements that are not expressed in a particular individual but are capable of transmission to the next generation. The equation representing ancestral contributions to the heritage of the offspring differs from the multiple regression equation for predicting the value of a trait from ancestral values. The former equation reduces to Galton's ancestral law when the proportion of latent elements is 0.5, the latter when this proportion 0.6. Galton's rather different derivations of the law in 1885 and 1897 are described, and their shortcomings are discussed in the light of these results (Galton, 1885, 1897).

Course projects have been argued to help develop students’ statistical thinking, but implementing authentic and realistic course projects still presents major challenges. This paper evaluated students’ experiences and perceptions of using an online simulated virtual environment, known as the Island, for implementing major course projects within an online masters level introductory statistics course. The use of the Island aimed to overcome significant practical and ethical constraints imposed on project-based work in online courses. The project required students to answer a self-posed research question by gathering and analysing data using methods covered in the course. The project was divided into two parts, a mid-semester proposal and an end of semester online presentation. Following completion of the projects, forty-two students responded to a questionnaire which rated their level of agreement to three aspects of using the Island: engagement, ease of use and contributes to understanding. Students were also asked to provide qualitative comments and five students participated in semi-structured interviews. Qualitative feedback was analysed to help explain the results from the quantitative questionnaire. In conclusion, perceptions of the use of the Island for project-based assessment were very positive. Qualitative feedback provided insight into how the Island-based projects may help to develop students’ statistical thinking.

We develop a generalised polynomial formalism which captures the concept of an algebra of piece-wise defined polynomials. The formalism is based on the Boolean power construction of universal algebra. A generalisation of the theory of substitution homomorphisms is developed. The abstract operation of composition of generalised polynomials in one variable is defined and shown to correspond to function composition. On one level, a polynomial may be viewed as an algorithm, giving a sequence of operations to be performed on a finite set of elements of an algebra. We consider an extension of this notion which also captures the important algorithmic notion of branching. The emphasis is entirely algebraic, and the role of substitution is as significant as for standard polynomials. We refer the reader to Lausch and Nobauer [1] for the background theory of generalised polynomials for single sorted universal algebras. We build on the many sorted case, although the basic concepts are essentially the same. The

It is important for students learning statistical reasoning to see data in context. One of the best ways of achieving this is to involve students in data production and so in the past ten years we have had first-year students undertake real experiments of their own choosing as part of our introductory statistics course. However in practice students are limited in what they can do. Many want to conduct experiments involving human subjects, requiring ethics approval, while even those not wanting to use humans may have general health and safety issues. Epidemiological studies have really not been possible at all. We present an open-ended virtual environment, the Island, to help overcome these limitations while still engaging students with study design and data collection. Students work with a population of virtual humans living on the Island and are able to conduct a wide variety of experiments with them as subjects. The Islanders also live in villages, have ancestors and die from a range of diseases, allowing students to study the epidemiology of the island as well. In this paper we will give an overview of this Island and its design, highlighting some of the features and the issues, and sharing our experiences of using the Island in teaching and learning.

It has been shown previously that the synonymous substitution rate between Escherichia coli and Salmonella typhimurium is lower in highly than in weakly expressed genes, and it has been suggested that this is due to stronger selection for translational efficiency in highly expressed genes as reflected in their greater codon usage bias. This hypothesis is tested here by comparing the substitution rate in codon families with different patterns of synonymous codon use. It is shown that the decline in the substitution rate across expression levels is as great for codon families that do not appear to be subject to selection for translational efficiency as for those that are. This implies that selection on translational efficiency is not responsible for the decline in the substitution rate across genes. It is argued that the most likely explanation for this decline is a decrease in the mutation rate. It is also shown that a simple evolutionary model in which synonymous codon use is determined by a balance between mutation, selection for an optimal codon, and genetic drift predicts that selection should have little effect on the substitution rate in the present case.

Over 30 lines from the v = 3-0, 4-1, 7-3 and 8-4 vibrational series of the hydrogen molecule have been observed from λ = 7600-8800 A in the reflection nebula NGC 2023, originating from levels up to 41000 K above ground. This is the first time that H 2 has been observed in the optical CCD regime and these are the highest excitation lines from the ground electronic state that have yet been detected. The spectrum shows the characteristics expected of UV fluorescence, although in detail there are some differences from model predictions

It is argued that the bias in synonymous codon usage observed in unicellular organisms is due to a balance between the forces of selection and mutation in a finite population, with greater bias in highly expressed genes reflecting stronger selection for efficiency of translation. A population genetic model is developed taking into account population size and selective differences between synonymous codons. A biochemical model is then developed to predict the magnitude of selective differences between synonymous codons in unicellular organisms in which growth rate (or possibly growth yield) can be equated with fitness. Selection can arise from differences in either the speed or the accuracy of translation. A model for the effect of speed of translation on fitness is considered in detail, a similar model for accuracy more briefly. The model is successful in predicting a difference in the degree of bias at the beginning than in the rest of the gene under some circumstances, as observed in Escherichia coli, but grossly overestimates the amount of bias expected. Possible reasons for this discrepancy are discussed.

It has been suggested that there may be inequalities in the types of substitution on the two DNA strands (in particular, in the frequencies of transversions from R to Y and from Y to R) due to a higher error rate on the lagging than the leading strand during replication. Reexamination of 11 kb of the beta-globin region sequenced in six primates fails to confirm this suggestion. Examination of the 73-kb beta-globin region sequenced in humans shows that the frequency of pyrimidines in different parts of this region is more variable than expected in a random sequence, but the pattern is more consistent with nonrandomness generated by DNA turnover mechanisms than with strand asymmetry due to a higher error rate on the lagging strand.

We present methods for estimating the parameters of inheritance and selection that appear in a quantitative genetic model for the evolution growth trajectories and other "infinite-dimensional" traits that we recently introduced. Two methods for estimating the additive genetic covariance function are developed, a "full" model that fully fits the data and a "reduced" model that generates a smoothed estimate consistent with the sampling errors in the data. By decomposing the covariance function into its eigenvalues and eigenfunctions, it is possible to identify potential evolutionary changes in the population's mean growth trajectory for which there is (and those for which there is not) genetic variation. Algorithms for estimating these quantities, their confidence intervals, and for testing hypotheses about them are developed. These techniques are illustrated by an analysis of early growth in mice. Compatible methods for estimating the selection gradient function acting on growth trajectories in natural or domesticated populations are presented. We show how the estimates for the additive genetic covariance function and the selection gradient function can be used to predict the evolutionary change in a population's mean growth trajectory.

The effect of neighbouring bases on the usage of synonymous codons in genes with low codon usage bias in yeast and E. coli is examined. The codon adaptation index is employed to identify a group of genes in each organism with low codon usage bias, which are likely to be weakly expressed. A similar pattern is found in complementary sequences with respect to synonymous usage of A vs G or of U vs C. It is suggested that this may reflect an effect of context on mutation rates in weakly expressed genes.

A course in epidemiology and biostatistics, taken by students in health promotion and other public health disciplines, is evaluated and assessed in light of a recent university directive to incorporate blended learning, and the projected increase of online students into the course. A formal curriculum evaluation was informed by qualitative data from academic staff teaching into the course and students enrolled in the course. Five areas of challenge are identified: the volume of content; the authenticity of content; the course scheduling; the disconnection between the two course components; and the authenticity of the assessment. Some potential solutions have been identified, and the use of a virtual human population proposed as an avenue for introducing these solutions in a blended learning context. The process of conducting a formal curriculum evaluation in the context of introducing blended learning may prove useful in higher education courses looking to introduce blended learning, especially in disciplines that require students to interact with people.

For many products (for example, automobiles), failures failures depend on age and usage and, in this case, failures are random points in a two-dimensional plane with the two axes representing age and usage. In contrast to the one-dimensional case (where failures are random points along the time axis) the modeling of two-dimensional failures has received very little attention. In this chapter we discuss various issues (such as modeling process, parameter estimation, model analysis) for the two-dimensional case and compare it with the one-dimensional case.

Summary Wallace's 1858 paper ‘On the tendency of varieties to depart indefinitely from the original type’ is often thought to present a theory of natural selection identical with that of Darwin. Examination of Wallace's argument shows that it is different from Darwin's because Wallace thought that an inferior variety could coexist with a superior variety until environmental deterioration forced the extinction of the inferior one. Other interpretations of Wallace's argument are re-examined in the light of this finding.

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined., 9 pages, 3 figures, accepted for publication in PASA

This paper analyzes the impact of corruption in a stylized timber industry representative of many South-East Asian nations, where corruption is common and market driven logging is the leading contributor to deforestation. Corruption is analyzed using a three-player open-loop difference game consisting of a commercial logging contractor, a central government, and a regional government intermediary responsible for enforcing the government’s forest property rights. The intermediary, however, is assumed to either cooperate fully with the contract logger or the central government. The game is piecewise non-linear in both the control and state variables making analytical solutions hard to derive. A genetic algorithm approach is therefore used to solve the model numerically. The results indicate that corruption may negatively impact on an economy due to mis-management of forest resources.

Proof by refutation of a geometry theorem that is not universally true produces a Grobner basis whose elements, called side polynomials, may be used to give inequations that can be added to the hypotheses to give a valid theorem. We show that (in a certain sense) all possible subsidiary conditions are implied by those obtained from the basis; that what we call the kind of truth of the theorem may be derived from the basis; and that the side polynomials may be classified in a useful way. We analyse the relationship between side polynomials and kinds of truth, and we give a unified algorithmic treatment of side polynomials, with examples generated by an implementation.

We use complex vectors in geometrical reasoning, specifically automated theorem proving. The calculations are embedded in Clifford algebras, but commutative polynomial techniques can be used. Using the Grobner basis package in the computer algebra package Maple, this approach is shown to have efficiency benefits in situations where distance and angle relations amongst geometrical entities predominate.

We present a procedure for generating inductive theories from systems of equational data. An analysis of the consistency of the resulting conjectures is used to generate experiments and to select between competing theories. An application to a blocks world is given.

It has been shown previously that the synonymous substitution rate between Escherichia coli and Salmonella typhimurium is lower in highly than in weakly expressed genes, and it has been suggested that this is due to stronger selection for translational efficiency in highly expressed genes as reflected in their greater codon usage bias. This hypothesis is tested here by comparing the substitution rate in codon families with different patterns of synonymous codon use. It is shown that the decline in the substitution rate across expression levels is as great for codon families that do not appear to be subject to selection for translational efficiency as for those that are. This implies that selection on translational efficiency is not responsible for the decline in the substitution rate across genes. It is argued that the most likely explanation for this decline is a decrease in the mutation rate. It is also shown that a simple evolutionary model in which synonymous codon use is determined by a balance between mutation, selection for an optimal codon, and genetic drift predicts that selection should have little effect on the substitution rate in the present case.

The frequency of use of the three alternative translation termination codons has been examined in 165 Escherichia coli, 52 Bacillus subtilis and 106 Saccharomyces cerevisiae genes. Genes were first categorised according to their degree of bias in sense codon usage. In each species there is a very strong bias in favour of UAA (over UAG and UGA) in genes where sense codon usage is highly biased. This bias declines, principally with an increase in the use of UGA, in genes with lower sense codon bias. It appears that selection operating during translation may maintain the bias in stop codon usage. Such selection could result from the greater availability of UAA-cognate release factor(s), or from a lower frequency of translational readthrough at UAA.

Strongly biased codon usage is common in unicellular organisms, particularly in highly expressed genes. The bias is most simply explained as a balance between selection and mutation, with selection favouring those codons which are more efficiently translated. In a review Ikemura (1985) has proposed four rules for predicting which codons will be preferred, based on the properties of the transfer RNAs responsible for translating messenger RNA into protein. In this paper codon usage in E. coli and yeast is re-examined using the recent compilation of Maruyama et al. (1986). The codon adaptation index of Sharp and Li (1986a) is used as a measure of gene expression to investigate the importance of this factor. It is found that Ikemura's rules successfully predict preferred codons for yeast, but that two of them work less well for E. coli, and it is suggested that some of the apparent bias in weakly expressed genes of E. coli may be due to contextual effects on mutation rates.

Data are presented on the frequency of close inbreeding and on inbreeding depression in a Great Tit population in Wytham Wood near Oxford. A theoretical distribution is fitted to data on the dispersal of young birds, and a model is constructed to predict the amount of inbreeding expected in a large, uniform habitat in terms of the dispersal distribution and of the breeding structure of the population.

SUMMARYThe results of a previous paper on the effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci have been extended to include the possibility that, in addition to selection for an optimal value, there may be independent selection in favour of heterozygotes; it is assumed for simplicity that at each locus the heterozygote has the same advantage,s, over each of the homozygotes. Under selection alone there is a stable equilibrium ifs>ca2, wherecis a measure of the intensity of the optimizing selection andais the effect of a gene substitution. Under the additional forces exerted by mutation and by drift due to finite population size each locus behaves independently of the other loci as if it had a heterozygous advantage equal to (s−ca2).

If a metric character is determined by an effectively infinite number of loci, selection cannot cause any permanent change in the genetic variance but will cause a temporary change which is rapidly reversed when selection ceases. This change is due entirely to the correlation between pairs of loci which is induced by selection; the correlation is negative, leading to a reduction in the genetic variance under stabilizing or directional selection, and is positive, leading to an increase in the variance under disruptive selection. When selection ceases, the correlation rapidly disappears as joint equilibrium at pairs of loci is reestablished, and the variance returns to its original value. An expression is derived for the predicted amount of change in the genetic variance due to disequilibrium in the absence of linkage. The change is likely to be small under selection intensities found under natural conditions, but it may be appreciable under intense artificial selection. This limiting result shows that the ...

SUMMARYThe effect of optimizing selection, mutation and drift on a metric character determined by a large number of loci with equal effects without dominance was investigated theoretically. Conditions for a stable equilibrium under selection and mutation, in the absence of drift, have been obtained, and hence the amount of genetic variability which can be maintained by mutation has been determined. An approximate expression for the average amount of genetic variability to be expected in the presence of drift in a population of finite size has also been obtained and evaluated.