Large-scale neural dynamics: simple and complex

We review the use of neural field models for modelling the brain at the large scales necessary for interpreting EEG, fMRI, MEG and optical imaging data. Albeit a framework that is limited to coarse-grained or mean-field activity, neural field models provide a framework for unifying data from different imaging modalities. Starting with a description of neural mass models we build to spatially extended cortical models of layered two-dimensional sheets with long range axonal connections mediating synaptic interactions. Reformulations of the fundamental non-local mathematical model in terms of more familiar local differential (brain wave) equations are described. Techniques for the analysis of such models, including how to determine the onset of spatio-temporal pattern forming instabilities, are reviewed. Extensions of the basic formalism to treat refractoriness, adaptive feedback and inhomogeneous connectivity are described along with open challenges for the development of multi-scale models that can integrate macroscopic models at large spatial scales with models at the microscopic scale.

Review of order fulfilment models for Catalogue Mass Customization

Mass Customization (MC) is not a mature business strategy and hence it is not clear that a single or small group of operational models are dominating. Companies tend to approach MC from either a mass production or a customization origin and this in itself gives reason to believe that several operational models will be observable. This paper reviews actual and theoretical fulfilment systems that enterprises could apply when offering a pre-engineered catalogue of customizable products and options. Issues considered are: How product flows are structured in relation to processes, inventories and decoupling point(s); - Characteristics of the OF process that inhibit or facilitate fulfilment; - The logic of how products are allocated to customers; - Customer factors that influence OF process design and operation. Diversity in the order fulfilment structures is expected and is found in the literature. The review has identified four structural forms that have been used in a Catalogue MC context: - fulfilment from stock; - fulfilment from a single fixed decoupling point; - fulfilment from one of several fixed decoupling points; - fulfilment from several locations, with floating decoupling points. From the review it is apparent that producers are being imaginative in coping with the demands of high variety, high volume, customization and short lead times. These demands have encouraged the relationship between product, process and customer to be re-examined. Not only has this strengthened interest in commonality and postponement, but, as is reported in the paper, has led to the re-engineering of the order fulfilment process to create models with multiple fixed decoupling points and the floating decoupling point system

Fundamental Modes of Operation for Mass Customization

The concept of Mass Customization (MC) - producing customised goods for a mass market - has received considerable attention in the research literature in recent years. However the literature is limited in providing an understanding of the content of MC strategies (the organizational structures, process technologies, etc., that are best in a particular environment) and the process of MC strategies (the sub-strategy that an enterprise should select and how they should go about implementing an MC strategy). In this paper six published classification schemes of relevance to Mass Customization are reviewed. The classification schemes are applied to five case studies of enterprises operating in an MC environment. The limitations of the schemes are analysed and their failure to distinguish key characteristics is highlighted. Analysis of the findings leads to the development of a taxonomy of operational modes for MC. Five fundamental modes of operation for Mass Customization are identified. These modes are described and justified and their application is illustrated by contrasting the information requirements of two modes. The potential of these modes to provide the foundations for detailed configurations models is discussed.

Coagulation equations with mass loss

We derive and solve models for coagulation with mass loss arising, for example, from industrial processes in which growing inclusions are lost from the melt by colliding with the wall of the vessel. We consider a variety of loss laws and a variety of coagulation kernels, deriving exact results where possible, and more generally reducing the equations to similarity solutions valid in the large-time limit. One notable result is the effect that mass removal has on gelation: for small loss rates, gelation is delayed, whilst above a critical threshold, gelation is completely prevented. Finally, by forming an exact explicit solution for a more general initial cluster size distribution function, we illustrate how numerical results from earlier work can be interpreted in the light of the theory presented herein.