Double synaptic weight neuron theory and its application

In this paper, a novel mathematical model of neuron-Double Synaptic Weight Neuron (DSWN)(l) is presented. The DSWN can simulate many kinds of neuron architectures, including Radial-Basis-Function (RBF), Hyper Sausage and Hyper Ellipsoid models, etc. Moreover, this new model has been implemented in the new CASSANN-II neurocomputer that can be used to form various types of neural networks with multiple mathematical models of neurons. The flexibility of the DSWN has also been described in constructing neural networks. Based on the theory of Biomimetic Pattern Recognition (BPR) and high-dimensional space covering, a recognition system of omni directionally oriented rigid objects on the horizontal surface and a face recognition system had been implemented on CASSANN-II neurocomputer. In these two special cases, the result showed DSWN neural network had great potential in pattern recognition.

Biomimetic (topological) pattern recognition - A new model of pattern recognition theory and its application

A new theoretical model of Pattern Recognition principles was proposed, which is based on "matter cognition" instead of "matter classification" in traditional statistical Pattern Recognition. This new model is closer to the function of human being, rather than traditional statistical Pattern Recognition using "optimal separating" as its main principle. So the new model of Pattern Recognition is called the Biomimetic Pattern Recognition (BPR)(1). Its mathematical basis is placed on topological analysis of the sample set in the high dimensional feature space. Therefore, it is also called the Topological Pattern Recognition (TPR). The fundamental idea of this model is based on the fact of the continuity in the feature space of any one of the certain kinds of samples. We experimented with the Biomimetic Pattern Recognition (BPR) by using artificial neural networks, which act through covering the high dimensional geometrical distribution of the sample set in the feature space. Onmidirectionally cognitive tests were done on various kinds of animal and vehicle models of rather similar shapes. For the total 8800 tests, the correct recognition rate is 99.87%. The rejection rate is 0.13% and on the condition of zero error rates, the correct rate of BPR was much better than that of RBF-SVM.

Generalized semi-geostrophic theory on a sphere

Douglas, Robert; Cullen, M.J.P.; Roulston, I.; Sewell, M.J., (2005) 'Generalized semi-geostrophic theory on a sphere', Journal of Fluid Mechanics 531 pp.123-157 RAE2008

The Oscillatory Squeeze flow rheometer: Comprehensive theory and a new experimental facility

Binding, David; Bell, D.; Walters, K., (2006) 'The Oscillatory Squeeze flow rheometer: Comprehensive theory and a new experimental facility', Rheologica Acta 46 pp.111-121 RAE2008

Mathematical modelling and optimisation of the formulation and manufacture of aggregate food products

In this PhD study, mathematical modelling and optimisation of granola production has been carried out. Granola is an aggregated food product used in breakfast cereals and cereal bars. It is a baked crispy food product typically incorporating oats, other cereals and nuts bound together with a binder, such as honey, water and oil, to form a structured unit aggregate. In this work, the design and operation of two parallel processes to produce aggregate granola products were incorporated: i) a high shear mixing granulation stage (in a designated granulator) followed by drying/toasting in an oven. ii) a continuous fluidised bed followed by drying/toasting in an oven. In addition, the particle breakage of granola during pneumatic conveying produced by both a high shear granulator (HSG) and fluidised bed granulator (FBG) process were examined. Products were pneumatically conveyed in a purpose built conveying rig designed to mimic product conveying and packaging. Three different conveying rig configurations were employed; a straight pipe, a rig consisting two 45° bends and one with 90° bend. It was observed that the least amount of breakage occurred in the straight pipe while the most breakage occurred at 90° bend pipe. Moreover, lower levels of breakage were observed in two 45° bend pipe than the 90° bend vi pipe configuration. In general, increasing the impact angle increases the degree of breakage. Additionally for the granules produced in the HSG, those produced at 300 rpm have the lowest breakage rates while the granules produced at 150 rpm have the highest breakage rates. This effect clearly the importance of shear history (during granule production) on breakage rates during subsequent processing. In terms of the FBG there was no single operating parameter that was deemed to have a significant effect on breakage during subsequent conveying. A population balance model was developed to analyse the particle breakage occurring during pneumatic conveying. The population balance equations that govern this breakage process are solved using discretization. The Markov chain method was used for the solution of PBEs for this process. This study found that increasing the air velocity (by increasing the air pressure to the rig), results in increased breakage among granola aggregates. Furthermore, the analysis carried out in this work provides that a greater degree of breakage of granola aggregates occur in line with an increase in bend angle.

Brackets in the jet-bundle approach to field theory

info:eu-repo/semantics/published

Mathematical modelling of the behaviour of granular material in a computational fluid dynamics framework using micro-mechanical models

In this paper, a Computational Fluid Dynamics framework is presented for the modelling of key processes which involve granular material (i.e. segregation, degradation, caking). Appropriate physical models and sophisticated algorithms have been developed for the correct representation of the different material components in a granular mixture. The various processes, which arise from the micromechanical properties of the different mixture species can be obtained and parametrised in a DEM / experimental framework, thus enabling the continuum theory to correctly account for the micromechanical properties of a granular system. The present study establishes the link between the micromechanics and continuum theory and demonstrates the model capabilities in simulations of processes which are of great importance to the process engineering industry and involve granular materials in complex geometries.

Inexact restoration approaches to solve mathematical program with complementarity constraints

Mathematical Program with Complementarity Constraints (MPCC) finds applica- tion in many fields. As the complementarity constraints fail the standard Linear In- dependence Constraint Qualification (LICQ) or the Mangasarian-Fromovitz constraint qualification (MFCQ), at any feasible point, the nonlinear programming theory may not be directly applied to MPCC. However, the MPCC can be reformulated as NLP problem and solved by nonlinear programming techniques. One of them, the Inexact Restoration (IR) approach, performs two independent phases in each iteration - the feasibility and the optimality phases. This work presents two versions of an IR algorithm to solve MPCC. In the feasibility phase two strategies were implemented, depending on the constraints features. One gives more importance to the complementarity constraints, while the other considers the priority of equality and inequality constraints neglecting the complementarity ones. The optimality phase uses the same approach for both algorithm versions. The algorithms were implemented in MATLAB and the test problems are from MACMPEC collection.

Dermic diffusion and stratum corneum: a state of the art review of mathematical models

Transdermal biotechnologies are an ever increasing field of interest, due to the medical and pharmaceutical applications that they underlie. There are several mathematical models at use that permit a more inclusive vision of pure experimental data and even allow practical extrapolation for new dermal diffusion methodologies. However, they grasp a complex variety of theories and assumptions that allocate their use for specific situations. Models based on Fick's First Law found better use in contexts where scaled particle theory Models would be extensive in time-span but the reciprocal is also true, as context of transdermal diffusion of particular active compounds changes. This article reviews extensively the various theoretical methodologies for studying dermic diffusion in the rate limiting dermic barrier, the stratum corneum, and systematizes its characteristics, their proper context of application, advantages and limitations, as well as future perspectives.