Mathematical modelling for the digital society

We argue the case for a new branch of mathematics and its applications: Mathematics for the Digital Society. There is a challenge for mathematics, a strong “pull” from new and emerging commercial and public activities; and a need to train and inspire a generation of quantitative scientists who will seek careers within the associated sectors. Although now going through an early phase of boiling up, prior to scholarly distillation, we discuss how data rich activities and applications may benefit from a wide range of continuous and discrete models, methods, analysis and inference. In ten years time such applications will be common place and associated courses may be embedded within the undergraduate curriculum.

A mathematical model, implementation and study of a swarm system

The work reported in this paper is motivated towards the development of a mathematical model for swarm systems based on macroscopic primitives. A pattern formation and transformation model is proposed. The pattern transformation model comprises two general methods for pattern transformation, namely a macroscopic transformation method and a mathematical transformation method. The problem of transformation is formally expressed and four special cases of transformation are considered. Simulations to confirm the feasibility of the proposed models and transformation methods are presented. Comparison between the two transformation methods is also reported.

Mathematical notation: help or hindrance?

In this article Geoff Tennant puts forward a range of reasons for using mathematical notation, emphasising the need to allow children learning it time and space to come to terms with it. Examples are given in furthering the argument that the time to introduce notation is after the concept is already fully understood.

Integration of chaos theory and mathematical models in building simulation: Part I: Literature review

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasingly complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I) reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develops conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to building simulation scientists, initiates a dialogue and builds bridges between scientists and engineers, and stimulates future research about a wide range of issues on building environmental systems.

Integration of chaos theory and mathematical models in building simulation: Part II: Conceptual frameworks

Current mathematical models in building research have been limited in most studies to linear dynamics systems. A literature review of past studies investigating chaos theory approaches in building simulation models suggests that as a basis chaos model is valid and can handle the increasing complexity of building systems that have dynamic interactions among all the distributed and hierarchical systems on the one hand, and the environment and occupants on the other. The review also identifies the paucity of literature and the need for a suitable methodology of linking chaos theory to mathematical models in building design and management studies. This study is broadly divided into two parts and presented in two companion papers. Part (I), published in the previous issue, reviews the current state of the chaos theory models as a starting point for establishing theories that can be effectively applied to building simulation models. Part (II) develop conceptual frameworks that approach current model methodologies from the theoretical perspective provided by chaos theory, with a focus on the key concepts and their potential to help to better understand the nonlinear dynamic nature of built environment systems. Case studies are also presented which demonstrate the potential usefulness of chaos theory driven models in a wide variety of leading areas of building research. This study distills the fundamental properties and the most relevant characteristics of chaos theory essential to (1) building simulation scientists and designers (2) initiating a dialogue between scientists and engineers, and (3) stimulating future research on a wide range of issues involved in designing and managing building environmental systems.

A simplified mathematical model for urban microclimate simulation

Techniques for modelling urban microclimates and urban block surfaces temperatures are desired by urban planners and architects for strategic urban designs at the early design stages. This paper introduces a simplified mathematical model for urban simulations (UMsim) including urban surfaces temperatures and microclimates. The nodal network model has been developed by integrating coupled thermal and airflow model. Direct solar radiation, diffuse radiation, reflected radiation, long-wave radiation, heat convection in air and heat transfer in the exterior walls and ground within the complex have been taken into account. The relevant equations have been solved using the finite difference method under the Matlab platform. Comparisons have been conducted between the data produced from the simulation and that from an urban experimental study carried out in a real architectural complex on the campus of Chongqing University, China in July 2005 and January 2006. The results show a satisfactory agreement between the two sets of data. The UMsim can be used to simulate the microclimates, in particular the surface temperatures of urban blocks, therefore it can be used to assess the impact of urban surfaces properties on urban microclimates. The UMsim will be able to produce robust data and images of urban environments for sustainable urban design.

The programming language standards scene, ten years on paper 19: Pop

This paper, one of a simultaneously published set, describes the establishment in 1990 of the UK standards project for the Pop programming language, and the progress of the project to the end of 1993.

POP-11 comes of age: the advancement of an AI programming language

In 1989, the computer programming language POP-11 is 21 years old. This book looks at the reasons behind its invention, and traces its rise from an experimental language to a major AI language, playing a major part in many innovating projects. There is a chapter on the inventor of the language, Robin Popplestone, and a discussion of the applications of POP-11 in a variety of areas. The efficiency of AI programming is covered, along with a comparison between POP-11 and other programming languages. The book concludes by reviewing the standardization of POP-11 into POP91.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

Towards a modular robotics standard for AGV design and programming

Across the world there are many bodies currently involved in researching into the design of autonomous guided vehicles (AGVs). One of the greatest problems at present however, is that much of the research work is being conducted in isolated groups, with the resulting AGVs sensor/control/command systems being almost completely nontransferable to other AGV designs. This paper describes a new modular method for robot design which when applied to AGVs overcomes the above problems. The method is explained here with respect to all forms of robotics but the examples have been specifically chosen to reflect typical AGV systems.

Manual response preparation and saccade programming are linked to attention shifts: ERP evidence for covert attentional orienting and spatially specific modulations of visual processing

The premotor theory of attention claims that attentional shifts are triggered during response programming, regardless of which response modality is involved. To investigate this claim, event-related brain potentials (ERPs) were recorded while participants covertly prepared a left or right response, as indicated by a precue presented at the beginning of each trial. Cues signalled a left or right eye movement in the saccade task, and a left or right manual response in the manual task. The cued response had to be executed or withheld following the presentation of a Go/Nogo stimulus. Although there were systematic differences between ERPs triggered during covert manual and saccade preparation, lateralised ERP components sensitive to the direction of a cued response were very similar for both tasks, and also similar to the components previously found during cued shifts of endogenous spatial attention. This is consistent with the claim that the control of attention and of covert response preparation are closely linked. N1 components triggered by task-irrelevant visual probes presented during the covert response preparation interval were enhanced when these probes were presented close to cued response hand in the manual task, and at the saccade target location in the saccade task. This demonstrates that both manual and saccade preparation result in spatially specific modulations of visual processing, in line with the predictions of the premotor theory.