Derivation of scientific software from mathematical specifications

Often the modification and enhancement of large scientific software systems are severely hampered because many components of the system are written in an implementation dependent fashion, they are inadequately documented, and their functionalities are not precisely known. In this paper we consider how mathematics may be employed to alleviate some of these problems. In particular, we illustrate how the formal specification notation VDM-SL is being used to specify precisely abstract data types for use in the development of scientific software.

A software tool for simulating spatial separation and kinetics in biological membranes

Self-segregation and compartimentalisation are observed experimentally to occur spontaneously on live membranes as well as reconstructed model membranes. It is believed that many of these processes are caused or supported by anomalous diffusive behaviours of biomolecules on membranes due to the complex and heterogeneous nature of these environments. These phenomena are on the one hand of great interest in biology, since they may be an important way for biological systems to selectively localize receptors, regulate signaling or modulate kinetics; and on the other, they provide an inspiration for engineering designs that mimick natural systems. We present an interactive software package we are developing for the purpose of simulating such processes numerically using a fundamental Monte Carlo approach. This program includes the ability to simulate kinetics and mass transport in the presence of either mobile or immobile obstacles and other relevant structures such as liquid-ordered lipid microdomains. We also present preliminary simulation results regarding the selective spatial localization and chemical kinetics modulating power of immobile obstacles on the membrane, obtained using the program.

Objectifying early-number : a visual nomenclature to express mathematical domain knowledge

To address issues of divisive ideologies in the Mathematics Education community and to subsequently advance educational practice, an alternative theoretical framework and operational model is proposed which represents a consilience of constructivist learning theories whilst acknowledging the objective but improvable nature of domain knowledge. Based upon Popper’s three-world model of knowledge, the proposed theory supports the differentiation and explicit modelling of both shared domain knowledge and idiosyncratic personal understanding using a visual nomenclature. The visual nomenclature embodies Piaget’s notion of reflective abstraction and so may support an individual’s experience-based transformation of personal understanding with regards to shared domain knowledge. Using the operational model and visual nomenclature, seminal literature regarding early-number counting and addition was analysed and described. Exemplars of the resultant visual artefacts demonstrate the proposed theory’s viability as a tool with which to characterise the reflective abstraction-based organisation of a domain’s shared knowledge. Utilising such a description of knowledge, future research needs to consider the refinement of the operational model and visual nomenclature to include the analysis, description and scaffolded transformation of personal understanding. A detailed model of knowledge and understanding may then underpin the future development of educational software tools such as computer-mediated teaching and learning environments.

Machine vision toolbox for MATLAB, release 3 [Software]

The Toolbox, combined with MATLAB ® and a modern workstation computer, is a useful and convenient environment for investigation of machine vision algorithms. For modest image sizes the processing rate can be sufficiently ``real-time'' to allow for closed-loop control. Focus of attention methods such as dynamic windowing (not provided) can be used to increase the processing rate. With input from a firewire or web camera (support provided) and output to a robot (not provided) it would be possible to implement a visual servo system entirely in MATLAB. Provides many functions that are useful in machine vision and vision-based control. Useful for photometry, photogrammetry, colorimetry. It includes over 100 functions spanning operations such as image file reading and writing, acquisition, display, filtering, blob, point and line feature extraction, mathematical morphology, homographies, visual Jacobians, camera calibration and color space conversion.

Mathematical modelling of soft callus formation in early murine bone repair

Fracture healing is a complicated coupling of many processes. Yet despite the apparent complexity, fracture repair is usually effective. There is, however, no comprehensive mathematical model addressing the multiple interactions of cells, cytokines and oxygen that includes extra-cellular matrix production and that results in the formation of the early stage soft callus. This thesis develops a one dimensional continuum transport model in the context of early fracture healing. Although fracture healing is a complex interplay of many local factors, critical components are identified and used to construct an hypothesis about regulation of the evolution of early callus formation. Multiple cell lines, cellular differentiation, oxygen levels and cytokine concentrations are examined as factors affecting this model of early bone repair. The model presumes diffusive and chemotactic cell migration mechanisms. It is proposed that the initial signalling regime and oxygen availability arising as consequences of bone fracture, are sufficient to determine the quantity and quality of early soft callus formation. Readily available software and purpose written algorithms have been used to obtain numerical solutions representative of various initial conditions. These numerical distributions of cellular populations reflect available histology obtained from murine osteotomies. The behaviour of the numerical system in response to differing initial conditions can be described by alternative in vivo healing pathways. An experimental basis, as illustrated in murine fracture histology, has been utilised to validate the mathematical model outcomes. The model developed in this thesis has potential for future extension, to incorporate processes leading to woven bone deposition, while maintaining the characteristics that regulate early callus formation.

Mathematical modeling for improved greenhouse gas balances, agro-ecosystems, and policy development: Lessons from the Australian experience

If the land sector is to make significant contributions to mitigating anthropogenic greenhouse gas (GHG) emissions in coming decades, it must do so while concurrently expanding production of food and fiber. In our view, mathematical modeling will be required to provide scientific guidance to meet this challenge. In order to be useful in GHG mitigation policy measures, models must simultaneously meet scientific, software engineering, and human capacity requirements. They can be used to understand GHG fluxes, to evaluate proposed GHG mitigation actions, and to predict and monitor the effects of specific actions; the latter applications require a change in mindset that has parallels with the shift from research modeling to decision support. We compare and contrast 6 agro-ecosystem models (FullCAM, DayCent, DNDC, APSIM, WNMM, and AgMod), chosen because they are used in Australian agriculture and forestry. Underlying structural similarities in the representations of carbon flows though plants and soils in these models are complemented by a diverse range of emphases and approaches to the subprocesses within the agro-ecosystem. None of these agro-ecosystem models handles all land sector GHG fluxes, and considerable model-based uncertainty exists for soil C fluxes and enteric methane emissions. The models also show diverse approaches to the initialisation of model simulations, software implementation, distribution, licensing, and software quality assurance; each of these will differentially affect their usefulness for policy-driven GHG mitigation prediction and monitoring. Specific requirements imposed on the use of models by Australian mitigation policy settings are discussed, and areas for further scientific development of agro-ecosystem models for use in GHG mitigation policy are proposed.

VIP Barcoding: Composition vector-based software for rapid species identification based on DNA barcoding

Species identification based on short sequences of DNA markers, that is, DNA barcoding, has emerged as an integral part of modern taxonomy. However, software for the analysis of large and multilocus barcoding data sets is scarce. The Basic Local Alignment Search Tool (BLAST) is currently the fastest tool capable of handling large databases (e.g. >5000 sequences), but its accuracy is a concern and has been criticized for its local optimization. However, current more accurate software requires sequence alignment or complex calculations, which are time-consuming when dealing with large data sets during data preprocessing or during the search stage. Therefore, it is imperative to develop a practical program for both accurate and scalable species identification for DNA barcoding. In this context, we present VIP Barcoding: a user-friendly software in graphical user interface for rapid DNA barcoding. It adopts a hybrid, two-stage algorithm. First, an alignment-free composition vector (CV) method is utilized to reduce searching space by screening a reference database. The alignment-based K2P distance nearest-neighbour method is then employed to analyse the smaller data set generated in the first stage. In comparison with other software, we demonstrate that VIP Barcoding has (i) higher accuracy than Blastn and several alignment-free methods and (ii) higher scalability than alignment-based distance methods and character-based methods. These results suggest that this platform is able to deal with both large-scale and multilocus barcoding data with accuracy and can contribute to DNA barcoding for modern taxonomy. VIP Barcoding is free and available at http://msl.sls.cuhk.edu.hk/vipbarcoding/.

Mathematical modelling and numerical simulation of phosphine flow during grain fumigation in leaky cylindrical silos

The phosphine distribution in a cylindrical silo containing grain is predicted. A three-dimensional mathematical model, which accounts for multicomponent gas phase transport and the sorption of phosphine into the grain kernel is developed. In addition, a simple model is presented to describe the death of insects within the grain as a function of their exposure to phosphine gas. The proposed model is solved using the commercially available computational fluid dynamics (CFD) software, FLUENT, together with our own C code to customize the solver in order to incorporate the models for sorption and insect extinction. Two types of fumigation delivery are studied, namely, fan- forced from the base of the silo and tablet from the top of the silo. An analysis of the predicted phosphine distribution shows that during fan forced fumigation, the position of the leaky area is very important to the development of the gas flow field and the phosphine distribution in the silo. If the leak is in the lower section of the silo, insects that exist near the top of the silo may not be eradicated. However, the position of a leak does not affect phosphine distribution during tablet fumigation. For such fumigation in a typical silo configuration, phosphine concentrations remain low near the base of the silo. Furthermore, we find that half-life pressure test readings are not an indicator of phosphine distribution during tablet fumigation.

SCARA errobota: mugimendu gaitasunen eta ibilbide sorkuntzaren inplementazioa software grafikoan

[EU]Lan honen gaia SCARA errobot motaren mugimendu gaitasunen analisia egitea da, eta ibilbideen sorkuntzarako metodoekin batera software grafiko batean inplementatzea mugimenduaren simulazioa egin ahal izateko. Errobot serieen zinematikaren oinarrizko ezagutzatik hasita, mota konkretu batetara aplikatu egiten da eta honek aurkezten dituen berezitasunak garatu egiten dira, bi helburutara bideratuta: SCARA errobotaren mugimendu gaitasunak ezagutzea. Ibilbideen sorkuntzarako metodo baten inplementazioa. Hasteko, gaiaren egoera aztertu da, aplikazio nagusien eta ibilbide moten informazioa batzeko. Halaber ibilbideen sorkuntzarako metodoak arakatu dira, erabilera honetarako aproposena aurkitzeko. Jarraian, errobotaren analisia burutu da, ohizko erreminta matematikoak erabiliz, funtsezkoak diren lan eremua eta kokapen singularrak lortzeko. Ostean, software grafikoa garatu da mugimendu gaitasun hauek simulatzeko. Ohiko aplikazioetan oinarritutako ibilbideak sortzeko aukerak gehitu dira. Amaitzeko, oztopoak saihesten dituen ibilbideen sorkuntzarako metodoa inplementatu da, “pick and place” ibilbide motaren barruan.

Mathematical notation in formal specification: Too difficult for the masses? [Correspondence]

The phrase “not much mathematics required” can imply a variety of skill levels. When this phrase is applied to computer scientists, software engineers, and clients in the area of formal specification, the word “much” can be widely misinterpreted with disastrous consequences. A small experiment in reading specifications revealed that students already trained in discrete mathematics and the specification notation performed very poorly; much worse than could reasonably be expected if formal methods proponents are to be believed.

Using mathematical models to predict the development of aircraft cabin fires

Computer based mathematical models describing aircraft fire have a role to play in the design and development of safer aircraft, in the implementation of safer and more rigorous certification criteria and in post mortuum accident investigation. As the cost involved in performing large-scale fire experiments for the next generation 'Ultra High Capacity Aircraft' (UHCA) are expected to be prohibitively high, the development and use of these modelling tools may become essential if these aircraft are to prove a safe and viable reality. By describing the present capabilities and limitations of aircraft fire models, this paper will examine the future development of these models in the areas of large scale applications through parallel computing, combustion modelling and extinguishment modelling.

Demonstration thermo-electric and MHD mathematical models of a 500 kA A1 electrolysis cell

In the present study, a 3D full cell quarter thermo-electric model of a 500kA demonstration cell has been developed and solved. In parallel, a non-linear wave MHD model of the same 500 kA demonstration cell has been developed and solved. A preliminary study of the impact of the interactions between the cell thermo-electric and MHD models will be presented.