A robust controller design method for feedback substitution schemes using genetic algorithms

Controllers for feedback substitution schemes demonstrate a trade-off between noise power gain and normalized response time. Using as an example the design of a controller for a radiometric transduction process subjected to arbitrary noise power gain and robustness constraints, a Pareto-front of optimal controller solutions fulfilling a range of time-domain design objectives can be derived. In this work, we consider designs using a loop shaping design procedure (LSDP). The approach uses linear matrix inequalities to specify a range of objectives and a genetic algorithm (GA) to perform a multi-objective optimization for the controller weights (MOGA). A clonal selection algorithm is used to further provide a directed search of the GA towards the Pareto front. We demonstrate that with the proposed methodology, it is possible to design higher order controllers with superior performance in terms of response time, noise power gain and robustness.

Spectroscopic properties of alkenylferrocenes; crystal and molecular structure of (Z)-(1,2-diphenylethenyl)ferrocene

Studies of the 1H n.m.r. and electronic spectra of a series of alkenylferrocenes including (E) and (Z) stereoisomers of various styrylferrocenes, have provided methods of structure elucidation. Crystals of the title compound are monoclinic, space group P21/c with Z= 4 in a unit cell of dimensions a= 17.603(2), b= 10.218(2), c= 10.072 Å, β= 103.27(2)°. The structure has been determined by the heavy-atom method from diffractometer data and refind by full-matrix least-squares techniques to R= 0.043 for 2 219 unique reflections.

Linear and nonlinear generalized Fourier transforms

This article presents an overview of a transform method for solving linear and integrable nonlinear partial differential equations. This new transform method, proposed by Fokas, yields a generalization and unification of various fundamental mathematical techniques and, in particular, it yields an extension of the Fourier transform method.

A new linear initialization in SOM for biomolecular data

In the past decade, the amount of data in biological field has become larger and larger; Bio-techniques for analysis of biological data have been developed and new tools have been introduced. Several computational methods are based on unsupervised neural network algorithms that are widely used for multiple purposes including clustering and visualization, i.e. the Self Organizing Maps (SOM). Unfortunately, even though this method is unsupervised, the performances in terms of quality of result and learning speed are strongly dependent from the neuron weights initialization. In this paper we present a new initialization technique based on a totally connected undirected graph, that report relations among some intersting features of data input. Result of experimental tests, where the proposed algorithm is compared to the original initialization techniques, shows that our technique assures faster learning and better performance in terms of quantization error.

An old problem revisited - and solved: Upton and Dalton's linear production response: A note

This note presents a robust method for estimating response surfaces that consist of linear response regimes and a linear plateau. The linear response-and-plateau model has fascinated production scientists since von Liebig (1855) and, as Upton and Dalton indicated, some years ago in this Journal, the response-and-plateau model seems to fit the data in many empirical studies. The estimation algorithm evolves from Bayesian implementation of a switching-regression (finite mixtures) model and demonstrates routine application of Gibbs sampling and data augmentation-techniques that are now in widespread application in other disciplines.

Influence-matrix diagnostic of a data assimilation system

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

Declining survival rates in a reintroduced population of the Mauritius kestrel: evidence for non-linear density dependence and environmental stochasticity

1. We studied a reintroduced population of the formerly critically endangered Mauritius kestrel Falco punctatus Temmink from its inception in 1987 until 2002, by which time the population had attained carrying capacity for the study area. Post-1994 the population received minimal management other than the provision of nestboxes. 2. We analysed data collected on survival (1987-2002) using program MARK to explore the influence of density-dependent and independent processes on survival over the course of the population's development. 3.We found evidence for non-linear, threshold density dependence in juvenile survival rates. Juvenile survival was also strongly influenced by climate, with the temporal distribution of rainfall during the cyclone season being the most influential climatic variable. Adult survival remained constant throughout. 4. Our most parsimonious capture-mark-recapture statistical model, which was constrained by density and climate, explained 75.4% of the temporal variation exhibited in juvenile survival rates over the course of the population's development. 5. This study is an example of how data collected as part of a threatened species recovery programme can be used to explore the role and functional form of natural population regulatory processes. With the improvements in conservation management techniques and the resulting success stories, formerly threatened species offer unique opportunities to further our understanding of the fundamental principles of population ecology.

A mechanistic study of the low pressure pyrolysis of linear siloxanes

Matrix isolation IR spectroscopy has been used to study the vacuum pyrolysis of 1,1,3,3-tetramethyldisiloxane (L1), 1,1,3,3,5,5-hexamethyltrisiloxane (L2) and 3H,5H-octamethyltetrasiloxane (L3) at ca. 1000 K in a flow reactor at low pressures. The hydrocarbons CH3, CH4, C2H2, C2H4, and C2H6 were observed as prominent pyrolysis products in all three systems, and amongst the weaker features are bands arising from the methylsilanes Me2SiH2 (for L1 and L2) and Me3SiH (for L3). The fundamental of SiO was also observed very weakly. By use of quantum chemical calculations combined with earlier kinetic models, mechanisms have been proposed involving the intermediacy of silanones Me2Si = O and MeSiH = O. Model calculations on the decomposition pathways of H3SiOSiH3 and H3SiOSiH2OSiH3 show that silanone elimination is favoured over silylene extrusion.

The gas-phase reactions Of SiCl4 and Si2Cl6 with CH3OH and C2H5OH: an investigation by mass spectrometry and matrix-isolation infrared spectroscopy

The gas phase reactions Of SiCl4 and Si2Cl6 With CH3OH and C2H5OH have been investigated using both mass spectrometry and matrix isolation techniques. SiCl4 reacts with both CH3OH and C2H5OH upon mixing of the vapours for times in excess of 3 h to generate the HCl-elimination products SiCl3OR (R = CH3 or C2H5). The identity of these products is confirmed by deuteration experiments and by ab initio calculations at the HF/6-31G(d) level. Further products are generated when the mixture is passed through a tube heated to 750degreesC. Si2Cl6 reacts with CH3OH and C2H5OH via a different mechanism in which the Si-Si bond is cleaved to yield SiCl3OR and HCl. Other products of the type SiCl4-n(OCH3)(n) are tentatively identified by a combination of mass spectrometric and matrix isolation measurements. These latter products indicate further replacement of Cl atoms by OR groups as a result of reaction of CH3OH or C2H5OH with the initial product.

Parallel Hybrid Monte Carlo Algorithms for Matrix Computations

In this paper we consider hybrid (fast stochastic approximation and deterministic refinement) algorithms for Matrix Inversion (MI) and Solving Systems of Linear Equations (SLAE). Monte Carlo methods are used for the stochastic approximation, since it is known that they are very efficient in finding a quick rough approximation of the element or a row of the inverse matrix or finding a component of the solution vector. We show how the stochastic approximation of the MI can be combined with a deterministic refinement procedure to obtain MI with the required precision and further solve the SLAE using MI. We employ a splitting A = D – C of a given non-singular matrix A, where D is a diagonal dominant matrix and matrix C is a diagonal matrix. In our algorithm for solving SLAE and MI different choices of D can be considered in order to control the norm of matrix T = D –1C, of the resulting SLAE and to minimize the number of the Markov Chains required to reach given precision. Further we run the algorithms on a mini-Grid and investigate their efficiency depending on the granularity. Corresponding experimental results are presented.

Monte Carlo methods for matrix computations on the grid

Many scientific and engineering applications involve inverting large matrices or solving systems of linear algebraic equations. Solving these problems with proven algorithms for direct methods can take very long to compute, as they depend on the size of the matrix. The computational complexity of the stochastic Monte Carlo methods depends only on the number of chains and the length of those chains. The computing power needed by inherently parallel Monte Carlo methods can be satisfied very efficiently by distributed computing technologies such as Grid computing. In this paper we show how a load balanced Monte Carlo method for computing the inverse of a dense matrix can be constructed, show how the method can be implemented on the Grid, and demonstrate how efficiently the method scales on multiple processors. (C) 2007 Elsevier B.V. All rights reserved.

A sparse parallel hybrid Monte Carlo algorithm for matrix computations

In this paper we introduce a new algorithm, based on the successful work of Fathi and Alexandrov, on hybrid Monte Carlo algorithms for matrix inversion and solving systems of linear algebraic equations. This algorithm consists of two parts, approximate inversion by Monte Carlo and iterative refinement using a deterministic method. Here we present a parallel hybrid Monte Carlo algorithm, which uses Monte Carlo to generate an approximate inverse and that improves the accuracy of the inverse with an iterative refinement. The new algorithm is applied efficiently to sparse non-singular matrices. When we are solving a system of linear algebraic equations, Bx = b, the inverse matrix is used to compute the solution vector x = B(-1)b. We present results that show the efficiency of the parallel hybrid Monte Carlo algorithm in the case of sparse matrices.

Monte Carlo numerical treatment of large linear algebra problems

In this paper we deal with performance analysis of Monte Carlo algorithm for large linear algebra problems. We consider applicability and efficiency of the Markov chain Monte Carlo for large problems, i.e., problems involving matrices with a number of non-zero elements ranging between one million and one billion. We are concentrating on analysis of the almost Optimal Monte Carlo (MAO) algorithm for evaluating bilinear forms of matrix powers since they form the so-called Krylov subspaces. Results are presented comparing the performance of the Robust and Non-robust Monte Carlo algorithms. The algorithms are tested on large dense matrices as well as on large unstructured sparse matrices.

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.