Mathematical Modelling and Computer Simulations in Undergraduate Biology Education

A course in computational biology that introduces undergraduate biology students to mathematical modelling and computer simulations is described. Spreadsheets offer the perfect environment to introduce our biology students to computational thinking and the increasing role that computer simulations are playing in biology research. Here, we detail the spreadsheet modelling of some of the simulations covered in the course; the Lotka-Volterra predator-prey model, a cellular automaton model of tumor growth, and a model of an infectious disease outbreak. The experience of implementing computational biology simulations in a spreadsheet environment encourages and enables our biology students to use computer simulations and spreadsheets more in their future research, and makes our students more comfortable when interpreting scientific literature that pertains to computational biology research. These are important skills that our biology students will need in their future careers as researchers and scientists

Conceptual modelling: Towards detecting modelling errors in engineering applications

Rapid advancements of modern technologies put high demands on mathematical modelling of engineering systems. Typically, systems are no longer “simple” objects, but rather coupled systems involving multiphysics phenomena, the modelling of which involves coupling of models that describe different phenomena. After constructing a mathematical model, it is essential to analyse the correctness of the coupled models and to detect modelling errors compromising the final modelling result. Broadly, there are two classes of modelling errors: (a) errors related to abstract modelling, eg, conceptual errors concerning the coherence of a model as a whole and (b) errors related to concrete modelling or instance modelling, eg, questions of approximation quality and implementation. Instance modelling errors, on the one hand, are relatively well understood. Abstract modelling errors, on the other, are not appropriately addressed by modern modelling methodologies. The aim of this paper is to initiate a discussion on abstract approaches and their usability for mathematical modelling of engineering systems with the goal of making it possible to catch conceptual modelling errors early and automatically by computer assistant tools. To that end, we argue that it is necessary to identify and employ suitable mathematical abstractions to capture an accurate conceptual description of the process of modelling engineering systems

Modelling of mathematical programs: An analysis of strategy and an outline description of a computer assisted system

The salient components of the mathematical programming modeling activity are first analysed. Earlier generation systems such as program generators and procedural (modelling) languages are briefly discussed. A proposal for a computer assisted modelling scheme is then put forward. The proposed system contrasts with the earlier approaches in that no computer programming expertise is required on the part of the modeller. A mathematical programming model is usually constructed by progressive definition of dimensions, data tables, model variables, model constraints and the matrix coefficients which connect the last two entities. The philosophy and design of the experimental system supports this approach to model description. This aspect is illustrated by a few examples. The introduction of computer assistance in structuring of the data and the resulting model is novel and is in line with recent developments in friendly and flexible user interface

Computer assisted mathematical programming

A Computer Assisted Mathematical Programming (Modelling) System (CAMPS) is described in this paper. The system uses program generator techniques for model creation and contrasts with earlier approaches which use a special purpose language to construct models. Thus no programming skill is required to formulate a model. In designing the system we have first analysed the salient components of the mathematical programming activity. A mathematical programming model is usually constructed by progressive definition of dimensions, data tables, model variables, model constraints and the matrix coefficients which connect the last two entities. Computer assistance is provided to structure the data and the resulting model in the above sequence. In addition to this novel feature and the automatic documentation facility, the system is in line with recent developments, and incorporates a friendly and flexible user interface

Teaching mathematical modelling: a research based approach

A collaborative, research based laboratory experiment in mathematical modelling was included in a bioprocess engineering laboratory module, taught as part of an interdisciplinary program in biotechnology. The class was divided into six groups of three students and given the task of investigating a novel diafiltration process that is currently the focus of international research. Different aspects of the problem were assigned to each group and inter-group communication via email was required to ensure that there was a coherent set of objectives for each group and for the class as a whole. The software package, Berkeley Madonna, was used for all calculations. As well as giving the students an introduction to mathematical modelling and computer programming, this approach helped to illustrate the importance of research in bioprocess engineering. In general, the experiment was well received by the students and the fact that they were discovering new knowledge generated a degree of enthusiasm. However, many students were consumed by the technical demands of computer programming, especially the attention to detail required. Thus, they did not think too deeply about the physical aspects of the system they were modelling. In future years, therefore, consideration will be given to giving the student prior instruction in the use of the software

Computer simulations, mathematics and economics

Economists lise different kinds of computer simulation. However, there is little attention on the theory of simulation, which is considered either a technology or an extension of mathematical theory or, else, a way of modelling that is alternative to verbal description and mathematical models. The paper suggests a systematisation of the relationship between simulations, mathematics and economics. In particular, it traces the evolution of simulation techniques, comments some of the contributions that deal with their nature, and, finally, illustrates with some examples their influence on economie theory. Keywords: Computer simulation, economie methodology, multi-agent programming techniques.

Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

A framework and simulation engine for studying artificial life

The area of computer-generated artificial life-forms is a relatively recent field of inter-disciplinary study that involves mathematical modelling, physical intuition and ideas from chemistry and biology and computational science. Although the attribution of “life” to non biological systems is still controversial, several groups agree that certain emergent properties can be ascribed to computer simulated systems that can be constructed to “live” in a simulated environment. In this paper we discuss some of the issues and infrastructure necessary to construct a simulation laboratory for the study of computer generated artificial life-forms. We review possible technologies and present some preliminary studies based around simple models

Некоторые математические аспекты преподавания курса «Трехмерное моделирование» для художественных специальностей

Teaching of a training course «Three-dimensional modelling» in modern conditions assumes presence of mathematical base of the description of curves of the second and third order. Squarelow and cubic B-splines, surfaces Bezier, NURBS-surfaces is simultaneously elements of mathematics and toolkit computer graphics. One of most important points of preparation of experts is a transfer of three-dimensional modelling and computer graphics from «a category of entertainments» in high-quality scientific discipline with a fundamental mathematical basi