Home About us Contact
|
Home About us Contact | ||
|
|
||
Function Approximation (function + approximation)
Selected AbstractsAn Approximate Bayesian Algorithm for Combining Forecasts,DECISION SCIENCES, Issue 3 2001Kim-Hung Li Abstract In this paper we propose a consensus forecasting method based on a convex combination of individual forecast densities. The exact Bayesian updating of the convex combination weights is very complex and practically prohibitive. We propose a simple sequential updating alternative method based on function approximation. Several examples illustrate the method. [source] Nonlinear multiple regression methods: a survey and extensionsINTELLIGENT SYSTEMS IN ACCOUNTING, FINANCE & MANAGEMENT, Issue 1 2010Kenneth O. Cogger Abstract This paper reviews some nonlinear statistical procedures useful in function approximation, classification, regression and time-series analysis. Primary emphasis is on piecewise linear models such as multivariate adaptive regression splines, adaptive logic networks, hinging hyperplanes and their conceptual differences. Potential and actual applications of these methods are cited. Software for implementation is discussed, and practical suggestions are given for improvement. Examples show the relative capabilities of the various methods, including their ability for universal approximation. Copyright © 2010 John Wiley & Sons, Ltd. [source] High dimensional model representation for piece-wise continuous function approximationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008Rajib Chowdhury Abstract High dimensional model representation (HDMR) approximates multivariate functions in such a way that the component functions of the approximation are ordered starting from a constant and gradually approaching to multivariance as we proceed along the terms like first-order, second-order and so on. Until now HDMR applications include construction of a computational model directly from laboratory/field data, creating an efficient fully equivalent operational model to replace an existing time-consuming mathematical model, identification of key model variables, global uncertainty assessments, efficient quantitative risk assessments, etc. In this paper, the potential of HDMR for tackling univariate and multivariate piece-wise continuous functions is explored. Eight numerical examples are presented to illustrate the performance of HDMR for approximating a univariate or a multivariate piece-wise continuous function with an equivalent continuous function. Copyright © 2007 John Wiley & Sons, Ltd. [source] Unified formulation of radiation conditions for the wave equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2002Steen Krenk Abstract A family of radiation boundary conditions for the wave equation is derived by truncating a rational function approximation of the corresponding plane wave representation, and it is demonstrated how these boundary conditions can be formulated in terms of fictitious surface densities, governed by second-order wave equations on the radiating surface. Several well-established radiation boundary conditions appear as special cases, corresponding to different choices of the coefficients in the rational approximation. The relation between these choices is established, and an explicit formulation in terms of selected directions with ideal transmission is presented. A mechanical interpretation of the fictitious surface densities enables identification of suitable conditions at corners and boundaries of the radiating surface. Numerical examples illustrate excellent results with one or two fictitious layers with suitable corner and boundary conditions. Copyright © 2001 John Wiley & Sons, Ltd. [source] Properties and performance of orthogonal neural network in function approximationINTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 12 2001Chieh F. Sher Backpropagation neural network has been applied successfully to solving uncertain problems in many fields. However, unsolved drawbacks still exist such as the problems of local minimum, slow convergence speed, and the determination of initial weights and the number of processing elements. In this paper, we introduce a single-layer orthogonal neural network (ONN) that is developed based on orthogonal functions. Since the processing elements are orthogonal to one another and there is no local minimum of the error function, the orthogonal neural network is able to avoid the above problems. Among the five existing orthogonal functions, Legendre polynomials and Chebyshev polynomials of the first kind have the properties of recursion and completeness. They are the most suitable to generate the neural network. Some typical examples are given to show their performance in function approximation. The results show that ONN has excellent convergence performance. Moreover, ONN is capable of approximating the mathematic model of backpropagation neural network. Therefore, it should be able to be applied to various applications that backpropagation neural network is suitable to solve. © 2001 John Wiley & Sons, Inc. [source] Passive rational fitting of a network transfer function from its real partINTERNATIONAL JOURNAL OF RF AND MICROWAVE COMPUTER-AIDED ENGINEERING, Issue 3 2008Anne Y. Woo Abstract A methodology is presented for the rational function approximation of a passive network function from sampled values of its real part over the bandwidth of interest. The accuracy and validity of the proposed methodology are demonstrated through its application to the fitting of several broadband, multiport transfer functions. © 2008 Wiley Periodicals, Inc. Int J RF and Microwave CAE, 2008. [source] Molecular Modeling and Receptor-Dependent (RD) 3D-QSAR Approach to a Set of Antituberculosis DerivativesMOLECULAR INFORMATICS, Issue 11-12 2009Fernanda, Kerly, Mesquita Pasqualoto Abstract In this study, receptor-dependent (RD) 3D-QSAR models were built for a set of thirty-seven isoniazid derivatives bound to the enoyl-acp reductase from M. tuberculosis, called InhA (PDB entry code 1zid). Ligand-receptor (L-R) molecular dynamics (MD) simulations [500,000 steps; the step size was 0.001,ps (1,fs)] were carried out at 310,K (biological assay temperature). The hypothesized active conformations resulting from a previously reported receptor-independent (IR) 4D-QSAR analysis were used as the molecular geometries of each ligand in this structure-based L-R binding research. The dependent variable is the reported MIC values against M. tuberculosis var. bovis. The independent variables (descriptors) are energy terms of a modified first-generation AMBER force field combined with a hydration shell aqueous solvation model. Genetic function approximation (GFA) formalism and partial least squares (PLS) regression were employed as the fitting functions to develop 3D-QSAR models. The bound ligand solvation energy, the sum of electrostatic and hydrogen bonding energies of the unbound ligand, the bending energy of the unbound ligand, the electrostatic intermolecular L-R energy, and the change in hydrogen bonding energy upon binding were found as important energy contributions to the binding process. The 3D-QSAR model at 310,K has good internal and external predictability and may be regarded as representative of the binding process of ligands to InhA. [source] Dependence of the band-gap pressure coefficients of self-assembled InAs/GaAs quantum dots on the quantum dot sizePHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 1 2007C. Kristukat Abstract We report on low-temperature photoluminescence experiments on self-assembled InAs/GaAs quantum dots under high hydrostatic pressure up to 8 GPa using a diamond anvil cell. The sample exhibits a multimodal size distribution of the quantum dots, which gives rise to a characteristic emission profile displaying up to nine clearly separable peaks attributed to the ground-state recombination from each quantum dot subensemble with different size. Structural analysis revealed that their size differs in entire monolayer steps. The measured pressure coefficients for each subensemble show a linear dependence on their zero-pressure emission energy ranging from 65 meV/GPa for the largest dots to 112 meV/GPa for the smallest ones. Pressure dependent strain simulations based on an atomistic valence-force field yield that the pressure coefficient of the InAs band-gap is strongly reduced when InAs is embedded in a GaAs matrix. Taking into account confinement effects within the envelope function approximation, the calculated pressure coefficients are in good agreement with the experimental findings. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Symmetry of electron states and optical transitions in GaN/AlN hexagonal quantum dotsPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 13 2004P. Tronc Abstract The exact symmetry of hexagonal quantum dots (QDs) made of materials with the wurtzite structure such as GaN/AlN QDs for example, is described by the C3v point group and does not depend on the existence of a wetting layer. We have determined the possible exact symmetries of electron states and vibration modes in the dots and derived the optical selection rules. The vibration modes involved in the Frölich interaction are totally symmetric with respect to the C3v group and can induce transitions only between states with the same symmetry. The not totally symmetric modes provide other channels for lowering the energy of excited carriers and excitons by connecting states with symmetries different one from another. The rapid decay of created polarons, due to the short lifetime of vibration modes, releases the carriers and excitons into ground levels. In the envelope function approximation (EFA), the symmetry of the dots is represented by the C6v point group. Interband transitions are allowed only between states whose envelope functions have the same symmetry. EFA artificially increases the number of dark exciton symmetries. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Contactless electroreflectance studies of II,VI nanostructures grown by molecular beam epitaxyPHYSICA STATUS SOLIDI (B) BASIC SOLID STATE PHYSICS, Issue 3 2004Martín Muńoz Abstract The interband transitions of a single quantum well structure of Zn0.53Cd0.47Se/Zn0.27Cd0.23Mg0.50Se, lattice matched to InP, and of a capped CdSe quantum dot structure have been investigated using contactless electroreflectance. From a comparison of the quantum well optical transitions with those calculated using the envelope function approximation we determined the band offsets for this system. The electroreflectance spectrum of the quantum dot structure shows transitions originating from all the portions of the sample including the quantum dots and the wetting layer. Assuming a lens shape geometry and that the effective height-to-radius ratio observed in uncapped quantum dots is preserved, the size of the capped quantum dots was determined using the observed electroreflectance transitions, and the effective mass approximation. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source] Design of the pH Profile for Asymmetric Bioreduction of Ethyl 4-Chloro-3-oxobutyrate on the Basis of a Data-Driven MethodBIOTECHNOLOGY PROGRESS, Issue 6 2002Junghui Chen The goal of this paper was to design the optimal time-varying operating pH profile in the asymmetric reduction of ethyl 4-chloro-3-oxobutyrate by baker's yeast. Ethyl ( S)-4-chloro-3-hydroxybutyrate was produced to reach two important quality indices: reaction yield and product optical purity. The method integrated an orthogonal function approximation and an orthogonal array. The technique used a set of orthonormal functions as the basis for representing the possible profile. The optimal profile could be obtained if the orthogonal coefficients were properly adjusted. The orthogonal array was used to design and analyze the effect of each orthogonal coefficient in order to reach the optimal objective (quality) function. The performance based on the proposed strategy was significantly improved by over 10% compared with the traditional fixed pH or uncontrolled pH values during the reaction. The proposed method can be applied to the required dynamic profile in the bioreactor process to effectively improve the product quality, given good design directions and the advantage of the traditional statistical approach. [source] An adaptive dynamic programming algorithm for a stochastic multiproduct batch dispatch problemNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 7 2003Katerina P. Papadaki We address the problem of dispatching a vehicle with different product classes. There is a common dispatch cost, but holding costs that vary by product class. The problem exhibits multidimensional state, outcome and action spaces, and as a result is computationally intractable using either discrete dynamic programming methods, or even as a deterministic integer program. We prove a key structural property for the decision function, and exploit this property in the development of continuous value function approximations that form the basis of an approximate dispatch rule. Comparisons on single product-class problems, where optimal solutions are available, demonstrate solutions that are within a few percent of optimal. The algorithm is then applied to a problem with 100 product classes, and comparisons against a carefully tuned myopic heuristic demonstrate significant improvements. © 2003 Wiley Periodicals, Inc. Naval Research Logistics 50: 742,769, 2003. [source] | |||||||||||||