87 resultados para Systems of linear equations


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The technique of linear responsibility analysis is used for a retrospective case study of a private development consisting of an extension to an existing building to provide a wholesale butchery facility. The project used a conventionally organized management process. The organization structure adopted on the project is analysed using concepts from the systems theory, which are included in Walkers theoretical model of the structure of building project organizations. This model proposes that the process of building provision can be viewed as systems and sub-systems that are differentiated from each other at decision points. Further to this, the sub-systems can be viewed as the interaction of managing system and operating system. Using Walkers model, a systematic analysis of the relationships between the contributors gives a quantitative assessment of the efficiency of the organizational structure used. The project's organization structure diverged from the models propositions resulting in delay to the project's completion and cost overrun but the client was satisfied with the project functionally.

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The technique of linear responsibility analysis is used for a retrospective case study of a private industrial development consisting of an engineering factory and offices. A multi-disciplinary professional practice was used to manage and design the project. The organizational structure adopted on the project is analysed using concepts from systems theory which are included in Walker's theoretical model of the structure of building project organizations (Walker, 1981). This model proposes that the process of buildings provision can be viewed as systems and sub-systems which are differentiated form each other at decision points. Further to this, the sub-systematic analysis of the relationship between the contributors gives a quantitative assessment of the efficiency of the organizational structure used. There was a high level of satisfaction with the completed project and this is reflected by the way in which the organization structure corresponded to the model's proposition. However, the project was subject to string environmental forces which the project organization was not capable of entirely overcoming.

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The influence matrix is used in ordinary least-squares applications for monitoring statistical multiple-regression analyses. Concepts related to the influence matrix provide diagnostics on the influence of individual data on the analysis - the analysis change that would occur by leaving one observation out, and the effective information content (degrees of freedom for signal) in any sub-set of the analysed data. In this paper, the corresponding concepts have been derived in the context of linear statistical data assimilation in numerical weather prediction. An approximate method to compute the diagonal elements of the influence matrix (the self-sensitivities) has been developed for a large-dimension variational data assimilation system (the four-dimensional variational system of the European Centre for Medium-Range Weather Forecasts). Results show that, in the boreal spring 2003 operational system, 15% of the global influence is due to the assimilated observations in any one analysis, and the complementary 85% is the influence of the prior (background) information, a short-range forecast containing information from earlier assimilated observations. About 25% of the observational information is currently provided by surface-based observing systems, and 75% by satellite systems. Low-influence data points usually occur in data-rich areas, while high-influence data points are in data-sparse areas or in dynamically active regions. Background-error correlations also play an important role: high correlation diminishes the observation influence and amplifies the importance of the surrounding real and pseudo observations (prior information in observation space). Incorrect specifications of background and observation-error covariance matrices can be identified, interpreted and better understood by the use of influence-matrix diagnostics for the variety of observation types and observed variables used in the data assimilation system. Copyright © 2004 Royal Meteorological Society

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In this paper new robust nonlinear model construction algorithms for a large class of linear-in-the-parameters models are introduced to enhance model robustness, including three algorithms using combined A- or D-optimality or PRESS statistic (Predicted REsidual Sum of Squares) with regularised orthogonal least squares algorithm respectively. A common characteristic of these algorithms is that the inherent computation efficiency associated with the orthogonalisation scheme in orthogonal least squares or regularised orthogonal least squares has been extended such that the new algorithms are computationally efficient. A numerical example is included to demonstrate effectiveness of the algorithms. Copyright (C) 2003 IFAC.

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The identification of non-linear systems using only observed finite datasets has become a mature research area over the last two decades. A class of linear-in-the-parameter models with universal approximation capabilities have been intensively studied and widely used due to the availability of many linear-learning algorithms and their inherent convergence conditions. This article presents a systematic overview of basic research on model selection approaches for linear-in-the-parameter models. One of the fundamental problems in non-linear system identification is to find the minimal model with the best model generalisation performance from observational data only. The important concepts in achieving good model generalisation used in various non-linear system-identification algorithms are first reviewed, including Bayesian parameter regularisation and models selective criteria based on the cross validation and experimental design. A significant advance in machine learning has been the development of the support vector machine as a means for identifying kernel models based on the structural risk minimisation principle. The developments on the convex optimisation-based model construction algorithms including the support vector regression algorithms are outlined. Input selection algorithms and on-line system identification algorithms are also included in this review. Finally, some industrial applications of non-linear models are discussed.

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In this paper, we initiate the study of a class of Putnam-type equation of the form x(n-1) = A(1)x(n) + A(2)x(n-1) + A(3)x(n-2)x(n-3) + A(4)/B(1)x(n)x(n-1) + B(2)x(n-2) + B(3)x(n-3) + B-4 n = 0, 1, 2,..., where A(1), A(2), A(3), A(4), B-1, B-2, B-3, B-4 are positive constants with A(1) + A(2) + A(3) + A(4) = B-1 + B-2 + B-3 + B-4, x(-3), x(-2), x(-1), x(0) are positive numbers. A sufficient condition is given for the global asymptotic stability of the equilibrium point c = 1 of such equations. (c) 2005 Elsevier Ltd. All rights reserved.

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We use a spectral method to solve numerically two nonlocal, nonlinear, dispersive, integrable wave equations, the Benjamin-Ono and the Intermediate Long Wave equations. The proposed numerical method is able to capture well the dynamics of the solutions; we use it to investigate the behaviour of solitary wave solutions of the equations with special attention to those, among the properties usually connected with integrability, for which there is at present no analytic proof. Thus we study in particular the resolution property of arbitrary initial profiles into sequences of solitary waves for both equations and clean interaction of Benjamin-Ono solitary waves. We also verify numerically that the behaviour of the solution of the Intermediate Long Wave equation as the model parameter tends to the infinite depth limit is the one predicted by the theory.

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We investigate the spectrum of certain integro-differential-delay equations (IDDEs) which arise naturally within spatially distributed, nonlocal, pattern formation problems. Our approach is based on the reformulation of the relevant dispersion relations with the use of the Lambert function. As a particular application of this approach, we consider the case of the Amari delay neural field equation which describes the local activity of a population of neurons taking into consideration the finite propagation speed of the electric signal. We show that if the kernel appearing in this equation is symmetric around some point a= 0 or consists of a sum of such terms, then the relevant dispersion relation yields spectra with an infinite number of branches, as opposed to finite sets of eigenvalues considered in previous works. Also, in earlier works the focus has been on the most rightward part of the spectrum and the possibility of an instability driven pattern formation. Here, we numerically survey the structure of the entire spectra and argue that a detailed knowledge of this structure is important within neurodynamical applications. Indeed, the Amari IDDE acts as a filter with the ability to recognise and respond whenever it is excited in such a way so as to resonate with one of its rightward modes, thereby amplifying such inputs and dampening others. Finally, we discuss how these results can be generalised to the case of systems of IDDEs.

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This paper is concerned with the uniformization of a system of afine recurrence equations. This transformation is used in the design (or compilation) of highly parallel embedded systems (VLSI systolic arrays, signal processing filters, etc.). In this paper, we present and implement an automatic system to achieve uniformization of systems of afine recurrence equations. We unify the results from many earlier papers, develop some theoretical extensions, and then propose effective uniformization algorithms. Our results can be used in any high level synthesis tool based on polyhedral representation of nested loop computations.

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We present a kinetic double layer model coupling aerosol surface and bulk chemistry (K2-SUB) based on the PRA framework of gas-particle interactions (Poschl-Rudich-Ammann, 2007). K2-SUB is applied to a popular model system of atmospheric heterogeneous chemistry: the interaction of ozone with oleic acid. We show that our modelling approach allows de-convoluting surface and bulk processes, which has been a controversial topic and remains an important challenge for the understanding and description of atmospheric aerosol transformation. In particular, we demonstrate how a detailed treatment of adsorption and reaction at the surface can be coupled to a description of bulk reaction and transport that is consistent with traditional resistor model formulations. From literature data we have derived a consistent set of kinetic parameters that characterise mass transport and chemical reaction of ozone at the surface and in the bulk of oleic acid droplets. Due to the wide range of rate coefficients reported from different experimental studies, the exact proportions between surface and bulk reaction rates remain uncertain. Nevertheless, the model results suggest an important role of chemical reaction in the bulk and an approximate upper limit of similar to 10(-11) cm(2) s(-1) for the surface reaction rate coefficient. Sensitivity studies show that the surface accommodation coefficient of the gas-phase reactant has a strong non-linear influence on both surface and bulk chemical reactions. We suggest that K2-SUB may be used to design, interpret and analyse future experiments for better discrimination between surface and bulk processes in the oleic acid-ozone system as well as in other heterogeneous reaction systems of atmospheric relevance.

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A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

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This study describes the validation of short tandem repeat (STR) systems for the resolution of cases of disputed parentage where only a single parent is available for testing or where the claimed relationship of both parents is in doubt and also cases where sibship must be tested. Three separate multiplex systems the Second Generation Multiplex, Powerplex 1.2 and FFFL have been employed, giving a total of 16 STR loci. Both empirical and theoretical approaches to the validation have been adopted. Appropriate equations have been derived to calculate likelihood ratios for different relationships, incorporating a correction for subpopulation effects. An F(ST) point estimate of 1% has been applied throughout. Empirically, 101 cases of alleged father, alleged mother and child where analysed using six SLP systems and also using the three multiplex STR systems. Of the 202 relationships tested, 197 were independently resolved by both systems, providing either clear evidence of non-parentage or strong support for the relationship.

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We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

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A two-dimensional X-ray scattering system developed around a CCD-based area detector is presented, both in terms of hardware employed and software designed and developed. An essential feature is the integration of hardware and software, detection and sample environment control which enables time-resolving in-situ wide-angle X-ray scattering measurements of global structural and orientational parameters of polymeric systems subjected to a variety of controlled external fields. The development and operation of a number of rheometers purpose-built for the application of such fields are described. Examples of the use of this system in monitoring degrees of shear-induced orientation in liquid-crystalline systems and crystallization of linear polymers subsequent to shear flow are presented.

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We consider the two-point boundary value problem for stiff systems of ordinary differential equations. For systems that can be transformed to essentially diagonally dominant form with appropriate smoothness conditions, a priori estimates are obtained. Problems with turning points can be treated with this theory, and we discuss this in detail. We give robust difference approximations and present error estimates for these schemes. In particular we give a detailed description of how to transform a general system to essentially diagonally dominant form and then stretch the independent variable so that the system will satisfy the correct smoothness conditions. Numerical examples are presented for both linear and nonlinear problems.