Mathematics, programming, and STEM

Learning mathematics is a complex and dynamic process. In this paper, the authors adopt a semiotic framework (Yeh & Nason, 2004) and highlight programming as one of the main aspects of the semiosis or meaning-making for the learning of mathematics. During a 10-week teaching experiment, mathematical meaning-making was enriched when primary students wrote Logo programs to create 3D virtual worlds. The analysis of results found deep learning in mathematics, as well as in technology and engineering areas. This prompted a rethinking about the nature of learning mathematics and a need to employ and examine a more holistic learning approach for the learning in science, technology, engineering, and mathematics (STEM) areas.

Application of Mathematical Programming to the Plywood Design and Manufacturing Problem

Plywood manufacture includes two fundamental stages. The first is to peel or separate logs into veneer sheets of different thicknesses. The second is to assemble veneer sheets into finished plywood products. At the first stage a decision must be made as to the number of different veneer thicknesses to be peeled and what these thicknesses should be. At the second stage, choices must be made as to how these veneers will be assembled into final products to meet certain constraints while minimizing wood loss. These decisions present a fundamental management dilemma. Costs of peeling, drying, storage, handling, etc. can be reduced by decreasing the number of veneer thicknesses peeled. However, a reduced set of thickness options may make it infeasible to produce the variety of products demanded by the market or increase wood loss by requiring less efficient selection of thicknesses for assembly. In this paper the joint problem of veneer choice and plywood construction is formulated as a nonlinear integer programming problem. A relatively simple optimal solution procedure is developed that exploits special problem structure. This procedure is examined on data from a British Columbia plywood mill. Restricted to the existing set of veneer thicknesses and plywood designs used by that mill, the procedure generated a solution that reduced wood loss by 79 percent, thereby increasing net revenue by 6.86 percent. Additional experiments were performed that examined the consequences of changing the number of veneer thicknesses used. Extensions are discussed that permit the consideration of more than one wood species.

Functional programming systems revisited

Functional Programming (FP) systems are modified and extended to form Nondeterministic Functional Programming (NFP) systems in which nondeterministic programs can be specified and both deterministic and nondeterministic programs can be verified essentially within the system. It is shown that the algebra of NFP programs has simpler laws in comparison with the algebra of FP programs. "Regular" forms are introduced to put forward a disciplined way of reasoning about programs. Finally, an alternative definition of "linear" forms is proposed for reasoning about recursively defined programs. This definition, when used to test the linearity of forms, results in simpler verification conditions than those generated by the original definition of linear forms.

DFL: A Data Flow Language

Many novel computer architectures like array and multiprocessors which achieve high performance through the use of concurrency exploit variations of the von Neumann model of computation. The effective utilization of the machines makes special demands on programmers and their programming languages, such as the structuring of data into vectors or the partitioning of programs into concurrent processes. In comparison, the data flow model of computation demands only that the principle of structured programming be followed. A data flow program, often represented as a data flow graph, is a program that expresses a computation by indicating the data dependencies among operators. A data flow computer is a machine designed to take advantage of concurrency in data flow graphs by executing data independent operations in parallel. In this paper, we discuss the design of a high level language (DFL: Data Flow Language) suitable for data flow computers. Some sample procedures in DFL are presented. The implementation aspects have not been discussed in detail since there are no new problems encountered. The language DFL embodies the concepts of functional programming, but in appearance closely resembles Pascal. The language is a better vehicle than the data flow graph for expressing a parallel algorithm. The compiler has been implemented on a DEC 1090 system in Pascal.

Feasibility of a stepped wedge cluster RCT and concurrent observational sub-study to evaluate the effects of modified ward night lighting on inpatient fall rates and sleep quality: A protocol for a pilot trial

Background: Falls among hospitalised patients impose a considerable burden on health systems globally and prevention is a priority. Some patient-level interventions have been effective in reducing falls, but others have not. An alternative and promising approach to reducing inpatient falls is through the modification of the hospital physical environment and the night lighting of hospital wards is a leading candidate for investigation. In this pilot trial, we will determine the feasibility of conducting a main trial to evaluate the effects of modified night lighting on inpatient ward level fall rates. We will test also the feasibility of collecting novel forms of patient level data through a concurrent observational sub-study. Methods/design: A stepped wedge, cluster randomised controlled trial will be conducted in six inpatient wards over 14 months in a metropolitan teaching hospital in Brisbane (Australia). The intervention will consist of supplementary night lighting installed across all patient rooms within study wards. The planned placement of luminaires, configurations and spectral characteristics are based on prior published research and pre-trial testing and modification. We will collect data on rates of falls on study wards (falls per 1000 patient days), the proportion of patients who fall once or more, and average length of stay. We will recruit two patients per ward per month to a concurrent observational sub-study aimed at understanding potential impacts on a range of patient sleep and mobility behaviour. The effect on the environment will be monitored with sensors to detect variation in light levels and night-time room activity. We will also collect data on possible patient-level confounders including demographics, pre-admission sleep quality, reported vision, hearing impairment and functional status. Discussion: This pragmatic pilot trial will assess the feasibility of conducting a main trial to investigate the effects of modified night lighting on inpatient fall rates using several new methods previously untested in the context of environmental modifications and patient safety. Pilot data collected through both parts of the trial will be utilised to inform sample size calculations, trial design and final data collection methods for a subsequent main trial.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

Optimal Interconnections in the Design of Microprocessors and Digital Systems

This paper recasts the multiple data path assignment problem solved by Torng and Wilhelm by the dynamic programming method [1] into a minimal covering problem following a switching theoretic approach. The concept of bus compatibility for the data transfers is used to obtain the various ways of interconnecting the circuit modules with the minimum number of buses that allow concurrent data transfers. These have been called the feasible solutions of the problem. The minimal cost solutions are obtained by assigning weights to the bus-compatible sets present in the feasible solutions. Minimization of the cost of the solution by increasing the number of buses is also discussed.

A dynamic programming model for optimising feeding and slaughter decisions regarding fattening pigs

Costs of purchasing new piglets and of feeding them until slaughter are the main variable expenditures in pig fattening. They both depend on slaughter intensity, the nature of feeding patterns and the technological constraints of pig fattening, such as genotype. Therefore, it is of interest to examine the effect of production technology and changes in input and output prices on feeding and slaughter decisions. This study examines the problem by using a dynamic programming model that links genetic characteristics of a pig to feeding decisions and the timing of slaughter and takes into account how these jointly affect the quality-adjusted value of a carcass. The model simulates the growth mechanism of a pig under optional feeding and slaughter patterns and then solves the optimal feeding and slaughter decisions recursively. The state of nature and the genotype of a pig are known in the analysis. The main contribution of this study is the dynamic approach that explicitly takes into account carcass quality while simultaneously optimising feeding and slaughter decisions. The method maximises the internal rate of return to the capacity unit. Hence, the results can have vital impact on competitiveness of pig production, which is known to be quite capital-intensive. The results suggest that producer can significantly benefit from improvements in the pig's genotype, because they improve efficiency of pig production. The annual benefits from obtaining pigs of improved genotype can be more than €20 per capacity unit. The annual net benefits of animal breeding to pig farms can also be considerable. Animals of improved genotype can reach optimal slaughter maturity quicker and produce leaner meat than animals of poor genotype. In order to fully utilise the benefits of animal breeding, the producer must adjust feeding and slaughter patterns on the basis of genotype. The results suggest that the producer can benefit from flexible feeding technology. The flexible feeding technology segregates pigs into groups according to their weight, carcass leanness, genotype and sex and thereafter optimises feeding and slaughter decisions separately for these groups. Typically, such a technology provides incentives to feed piglets with protein-rich feed such that the genetic potential to produce leaner meat is fully utilised. When the pig approaches slaughter maturity, the share of protein-rich feed in the diet gradually decreases and the amount of energy-rich feed increases. Generally, the optimal slaughter weight is within the weight range that pays the highest price per kilogram of pig meat. The optimal feeding pattern and the optimal timing of slaughter depend on price ratios. Particularly, an increase in the price of pig meat provides incentives to increase the growth rates up to the pig's biological maximum by increasing the amount of energy in the feed. Price changes and changes in slaughter premium can also have large income effects. Key words: barley, carcass composition, dynamic programming, feeding, genotypes, lean, pig fattening, precision agriculture, productivity, slaughter weight, soybeans

On the bottleneck linear programming problem

In this paper, the results on primal methods for Bottleneck Linear Programming (BLP) problem are briefly surveyed, the primal method is presented and the degenerate case related to Bottleneck Transportation Problem (BTP) is explicitly considered. The algorithm is based on the idea of using auxiliary coefficients as is done by Garfinkel and Rao [6]. The modification presented for the BTP rectifies the defect in Hammer's method in the case of degenerate basic feasible solution. Illustrative numerical examples are also given.

Conclaves and concurrent expert evidence: A positive development in Australian legal practice?

Many Australian courts now prefer pre-hearing meetings of experts (conclaves) being convened to prepare joint reports to identify areas of agreement and disagreement, followed by concurrent expert evidence at trial. This contrasts to the traditional approach where experts did not meet before trial and did not give evidence together. Most judges, lawyers and expert witnesses favour this as a positive development in Australian legal practice, at least for civil disputes. This new approach impacts medical practitioners who are called upon to give expert evidence, or who are parties to disputes before the courts. Arguably, it is too soon to tell whether the relative lack of transparency at the conclave stage will give rise to difficulties in the coronial, disciplinary and criminal arenas.

Programming rumen bacterial communities in newborn Merino lambs

Establishment of the rumen microbiome can be affected by both early-life dietary measures and rumen microbial inoculation. This study used a 2 × 3 factorial design to evaluate the effects of inclusion of dietary fat type and the effects of rumen inoculum from different sources on ruminal bacterial communities present in early stages of the lambs’ life. Two different diets were fed ad libitum to 36 pregnant ewes (and their lambs) from 1 month pre-lambing until weaning. Diets consisted of chaffed lucerne and cereal hay and 4% molasses, with either 4% distilled coconut oil (CO) provided as a source of rumen-active fat or 4% Megalac® provided as a source of rumen-protected fat (PF). One of three inoculums was introduced orally to all lambs, being either (1) rumen fluid from donor ewes fed the PF diet; (2) rumen fluid from donor ewes fed CO; or (3) a control treatment of MilliQ-water. After weaning at 3 months of age, each of the six lamb treatment groups were grazed in spatially separated paddocks. Rumen bacterial populations of ewes and lambs were characterised using 454 amplicon pyrosequencing of the V3/V4 regions of the 16S rRNA gene. Species richness and biodiversity of the bacterial communities were found to be affected by the diet in ewes and lambs and by inoculation treatment of the lambs. Principal coordinate analysis and analysis of similarity (ANOSIM) showed between diet differences in bacterial community groups existed in ewes and differential bacterial clusters occurred in lambs due to both diet and neonatal inoculation. Diet and rumen inoculation acted together to clearly differentiate the bacterial communities through to weaning, however the microbiome effects of these initial early life interventions diminished with time so that rumen bacterial communities showed greater similarity 2 months after weaning. These results demonstrate that ruminal bacterial communities of newborn lambs can be altered by modifying the diet of their mothers. Moreover, the rumen microbiome of lambs can be changed by diet while they are suckling or by inoculating their rumen, and resulting changes in the rumen bacterial microbiome can persist beyond weaning.

Middleware for Mobile Sensing Applications in Urban Environments

Sensor networks represent an attractive tool to observe the physical world. Networks of tiny sensors can be used to detect a fire in a forest, to monitor the level of pollution in a river, or to check on the structural integrity of a bridge. Application-specific deployments of static-sensor networks have been widely investigated. Commonly, these networks involve a centralized data-collection point and no sharing of data outside the organization that owns it. Although this approach can accommodate many application scenarios, it significantly deviates from the pervasive computing vision of ubiquitous sensing where user applications seamlessly access anytime, anywhere data produced by sensors embedded in the surroundings. With the ubiquity and ever-increasing capabilities of mobile devices, urban environments can help give substance to the ubiquitous sensing vision through Urbanets, spontaneously created urban networks. Urbanets consist of mobile multi-sensor devices, such as smart phones and vehicular systems, public sensor networks deployed by municipalities, and individual sensors incorporated in buildings, roads, or daily artifacts. My thesis is that "multi-sensor mobile devices can be successfully programmed to become the underpinning elements of an open, infrastructure-less, distributed sensing platform that can bring sensor data out of their traditional close-loop networks into everyday urban applications". Urbanets can support a variety of services ranging from emergency and surveillance to tourist guidance and entertainment. For instance, cars can be used to provide traffic information services to alert drivers to upcoming traffic jams, and phones to provide shopping recommender services to inform users of special offers at the mall. Urbanets cannot be programmed using traditional distributed computing models, which assume underlying networks with functionally homogeneous nodes, stable configurations, and known delays. Conversely, Urbanets have functionally heterogeneous nodes, volatile configurations, and unknown delays. Instead, solutions developed for sensor networks and mobile ad hoc networks can be leveraged to provide novel architectures that address Urbanet-specific requirements, while providing useful abstractions that hide the network complexity from the programmer. This dissertation presents two middleware architectures that can support mobile sensing applications in Urbanets. Contory offers a declarative programming model that views Urbanets as a distributed sensor database and exposes an SQL-like interface to developers. Context-aware Migratory Services provides a client-server paradigm, where services are capable of migrating to different nodes in the network in order to maintain a continuous and semantically correct interaction with clients. Compared to previous approaches to supporting mobile sensing urban applications, our architectures are entirely distributed and do not assume constant availability of Internet connectivity. In addition, they allow on-demand collection of sensor data with the accuracy and at the frequency required by every application. These architectures have been implemented in Java and tested on smart phones. They have proved successful in supporting several prototype applications and experimental results obtained in ad hoc networks of phones have demonstrated their feasibility with reasonable performance in terms of latency, memory, and energy consumption.

Finite field computation technique for exact solution of systems of linear equations and interval linear programming problems

An error-free computational approach is employed for finding the integer solution to a system of linear equations, using finite-field arithmetic. This approach is also extended to find the optimum solution for linear inequalities such as those arising in interval linear programming probloms.