Robust fuzzy Gustafson-Kessel clustering for nonlinear system identification

This paper deals with Takagi-Sugeno (TS) fuzzy model identification of nonlinear systems using fuzzy clustering. In particular, an extended fuzzy Gustafson-Kessel (EGK) clustering algorithm, using robust competitive agglomeration (RCA), is developed for automatically constructing a TS fuzzy model from system input-output data. The EGK algorithm can automatically determine the 'optimal' number of clusters from the training data set. It is shown that the EGK approach is relatively insensitive to initialization and is less susceptible to local minima, a benefit derived from its agglomerate property. This issue is often overlooked in the current literature on nonlinear identification using conventional fuzzy clustering. Furthermore, the robust statistical concepts underlying the EGK algorithm help to alleviate the difficulty of cluster identification in the construction of a TS fuzzy model from noisy training data. A new hybrid identification strategy is then formulated, which combines the EGK algorithm with a locally weighted, least-squares method for the estimation of local sub-model parameters. The efficacy of this new approach is demonstrated through function approximation examples and also by application to the identification of an automatic voltage regulation (AVR) loop for a simulated 3 kVA laboratory micro-machine system.

Measuring the significance of inconsistency in the Viewpoints framework

Measuring inconsistency is crucial to effective inconsistency management in software development. A complete measurement of inconsistency should focus on not only the degree but also the significance of inconsistency. However, most of the approaches available only take the degree of inconsistency into account. The significance of inconsistency has not yet been given much needed consideration. This paper presents an approach for measuring the significance of inconsistency arising from different viewpoints in the Viewpoints framework. We call an individual set of requirements belonging to different viewpoints a combined requirements collection in this paper. We argue that the
significance of inconsistency arising in a combined requirements collection is closely associated with global priority levels of requirements involved in the inconsistency. Here we assume that the global priority level of an individual requirement captures the relative importance of every viewpoint including this requirement as well as the local priority level of the requirement within the viewpoint. Then we use the synthesis of global priority levels of all the requirements in a combined collection to measure the significance of the
collection. Following this, we present a scoring matrix function to measure the significance of inconsistency in an inconsistent combined requirements collection, which describes the contribution made by each subset of the requirements collection to the significance of the set of requirements involved in the inconsistency. An ordering relationship between inconsistencies of two combined requirements collections, termed more significant than, is also presented by comparing their significance scoring matrix functions. Finally, these techniques were implemented in a prototype tool called IncMeasurer, which we developed as a proof of concept.

Dynamic Distance-Based Shape Features for Gait Recognition

We propose a novel skeleton-based approach to gait recognition using our Skeleton Variance Image. The core of our approach consists of employing the screened Poisson equation to construct a family of smooth distance functions associated with a given shape. The screened Poisson distance function approximation nicely absorbs and is relatively stable to shape boundary perturbations which allows us to define a rough shape skeleton. We demonstrate how our Skeleton Variance Image is a powerful gait cycle descriptor leading to a significant improvement over the existing state of the art gait recognition rate.

A new Jacobian matrix for optimal learning of single-layer neural networks

This paper investigates the learning of a wide class of single-hidden-layer feedforward neural networks (SLFNs) with two sets of adjustable parameters, i.e., the nonlinear parameters in the hidden nodes and the linear output weights. The main objective is to both speed up the convergence of second-order learning algorithms such as Levenberg-Marquardt (LM), as well as to improve the network performance. This is achieved here by reducing the dimension of the solution space and by introducing a new Jacobian matrix. Unlike conventional supervised learning methods which optimize these two sets of parameters simultaneously, the linear output weights are first converted into dependent parameters, thereby removing the need for their explicit computation. Consequently, the neural network (NN) learning is performed over a solution space of reduced dimension. A new Jacobian matrix is then proposed for use with the popular second-order learning methods in order to achieve a more accurate approximation of the cost function. The efficacy of the proposed method is shown through an analysis of the computational complexity and by presenting simulation results from four different examples.

Combined R-matrix eigenstate basis set and finite-difference propagation method for the time-dependent Schrodinger equation: The one-electron case

In this work we present the theoretical framework for the solution of the time-dependent Schrödinger equation (TDSE) of atomic and molecular systems under strong electromagnetic fields with the configuration space of the electron’s coordinates separated over two regions; that is, regions I and II. In region I the solution of the TDSE is obtained by an R-matrix basis set representation of the time-dependent wave function. In region II a grid representation of the wave function is considered and propagation in space and time is obtained through the finite-difference method. With this, a combination of basis set and grid methods is put forward for tackling multiregion time-dependent problems. In both regions, a high-order explicit scheme is employed for the time propagation. While, in a purely hydrogenic system no approximation is involved due to this separation, in multielectron systems the validity and the usefulness of the present method relies on the basic assumption of R-matrix theory, namely, that beyond a certain distance (encompassing region I) a single ejected electron is distinguishable from the other electrons of the multielectron system and evolves there (region II) effectively as a one-electron system. The method is developed in detail for single active electron systems and applied to the exemplar case of the hydrogen atom in an intense laser field.

Exchange potential from the common energy denominator approximation for the Kohn-Sham Green's function: Application to (hyper)polarizabilities of molecular chains

An approximate Kohn-Sham (KS) exchange potential v(xsigma)(CEDA) is developed, based on the common energy denominator approximation (CEDA) for the static orbital Green's function, which preserves the essential structure of the density response function. v(xsigma)(CEDA) is an explicit functional of the occupied KS orbitals, which has the Slater v(Ssigma) and response v(respsigma)(CEDA) potentials as its components. The latter exhibits the characteristic step structure with "diagonal" contributions from the orbital densities \psi(isigma)\(2), as well as "off-diagonal" ones from the occupied-occupied orbital products psi(isigma)psi(j(not equal1)sigma). Comparison of the results of atomic and molecular ground-state CEDA calculations with those of the Krieger-Li-Iafrate (KLI), exact exchange (EXX), and Hartree-Fock (HF) methods show, that both KLI and CEDA potentials can be considered as very good analytical "closure approximations" to the exact KS exchange potential. The total CEDA and KLI energies nearly coincide with the EXX ones and the corresponding orbital energies epsilon(isigma) are rather close to each other for the light atoms and small molecules considered. The CEDA, KLI, EXX-epsilon(isigma) values provide the qualitatively correct order of ionizations and they give an estimate of VIPs comparable to that of the HF Koopmans' theorem. However, the additional off-diagonal orbital structure of v(xsigma)(CEDA) appears to be essential for the calculated response properties of molecular chains. KLI already considerably improves the calculated (hyper)polarizabilities of the prototype hydrogen chains H-n over local density approximation (LDA) and standard generalized gradient approximations (GGAs), while the CEDA results are definitely an improvement over the KLI ones. The reasons of this success are the specific orbital structures of the CEDA and KLI response potentials, which produce in an external field an ultranonlocal field-counteracting exchange potential. (C) 2002 American Institute of Physics.

CTCF modulates Estrogen Receptor function through specific chromatin and nuclear matrix interactions

Enhancer regions and transcription start sites of estrogen-target regulated genes are connected by means of Estrogen Receptor long-range chromatin interactions. Yet, the complete molecular mechanisms controlling the transcriptional output of engaged enhancers and subsequent activation of coding genes remain elusive. Here, we report that CTCF binding to enhancer RNAs is enriched when breast cancer cells are stimulated with estrogen. CTCF binding to enhancer regions results in modulation of estrogen-induced gene transcription by preventing Estrogen Receptor chromatin binding and by hindering the formation of additional enhancer-promoter ER looping. Furthermore, the depletion of CTCF facilitates the expression of target genes associated with cell division and increases the rate of breast cancer cell proliferation. We have also uncovered a genomic network connecting loci enriched in cell cycle regulator genes to nuclear lamina that mediates the CTCF function. The nuclear lamina and chromatin interactions are regulated by estrogen-ER. We have observed that the chromatin loops formed when cells are treated with estrogen establish contacts with the nuclear lamina. Once there, the portion of CTCF associated with the nuclear lamina interacts with enhancer regions, limiting the formation of ER loops and the induction of genes present in the loop. Collectively, our results reveal an important, unanticipated interplay between CTCF and nuclear lamina to control the transcription of ER target genes, which has great implications in the rate of growth of breast cancer cells.

Escape times for rigid Brownian rotators in a bistable potential from the time evolution of the Green function and the characteristic time of the probability evolution

The greatest relaxation time for an assembly of three- dimensional rigid rotators in an axially symmetric bistable potential is obtained exactly in terms of continued fractions as a sum of the zero frequency decay functions (averages of the Legendre polynomials) of the system. This is accomplished by studying the entire time evolution of the Green function (transition probability) by expanding the time dependent distribution as a Fourier series and proceeding to the zero frequency limit of the Laplace transform of that distribution. The procedure is entirely analogous to the calculation of the characteristic time of the probability evolution (the integral of the configuration space probability density function with respect to the position co-ordinate) for a particle undergoing translational diffusion in a potential; a concept originally used by Malakhov and Pankratov (Physica A 229 (1996) 109). This procedure allowed them to obtain exact solutions of the Kramers one-dimensional translational escape rate problem for piecewise parabolic potentials. The solution was accomplished by posing the problem in terms of the appropriate Sturm-Liouville equation which could be solved in terms of the parabolic cylinder functions. The method (as applied to rotational problems and posed in terms of recurrence relations for the decay functions, i.e., the Brinkman approach c.f. Blomberg, Physica A 86 (1977) 49, as opposed to the Sturm-Liouville one) demonstrates clearly that the greatest relaxation time unlike the integral relaxation time which is governed by a single decay function (albeit coupled to all the others in non-linear fashion via the underlying recurrence relation) is governed by a sum of decay functions. The method is easily generalized to multidimensional state spaces by matrix continued fraction methods allowing one to treat non-axially symmetric potentials, where the distribution function is governed by two state variables. (C) 2001 Elsevier Science B.V. All rights reserved.

Multi-zone TAP-reactors theory and application - IV. Ideal and non-ideal boundary conditions

We study the influence of non-ideal boundary and initial conditions (BIC) of a temporal analysis of products (TAP) reactor model on the data (observed exit flux) analysis. The general theory of multi-response state-defining experiments for a multi-zone TAP reactor is extended and applied to model several alternative boundary and initial conditions proposed in the literature. The method used is based on the Laplace transform and the transfer matrix formalism for multi-response experiments. Two non-idealities are studied: (1) the inlet pulse not being narrow enough (gas pulse not entering the reactor in Dirac delta function shape) and (2) the outlet non-ideality due to imperfect vacuum. The effect of these non-idealities is analyzed to the first and second order of approximation. The corresponding corrections were obtained and discussed in detail. It was found that they are negligible. Therefore, the model with ideal boundary conditions is proven to be completely adequate to the description and interpretation of transport-reaction data obtained with TAP-2 reactors.

R-matrix theory of electron molecule scattering

This paper presents an overview of R-matrix theory of electron scattering by diatomic and polyatomic molecules. The paper commences with a detailed discussion of the fixed-nuclei approximation which in recent years has been used as the basis of the most accurate ab initio calculations. This discussion includes an overview of the computer codes which enable electron collisions with both diatomic and polyatomic molecules to be calculated. Nuclear motion including rotational and vibrational excitation and dissociation is then discussed. In non-resonant energy regions, or when the scattered electron energy is not close to thresholds, the adiabatic-nuclei approximation can be successfully used. However, when these conditions are not applicable, non-adiabatic R-matrix theory must be used and a detailed discussion of this theory is given. Finally, recent applications of the theory to treat electron scattering by polyatomic molecules are reviewed and a detailed comparison of R-matrix calculations and experimental measurements for water is presented.

The 67 kDa laminin receptor: structure, function and role in disease

The 67LR (67 kDa laminin receptor) is a cell-surface receptor with high affinity for its primary ligand. Its role as a laminin receptor makes it an important molecule both in cell adhesion to the basement membrane and in signalling transduction following this binding event. The protein also plays critical roles in the metastasis of tumour cells. Isolation of the protein from either normal or cancerous cells results in a product with an approx. molecular mass of 67 kDa. This protein is believed to be derived from a smaller precursor, the 37LRP (37 kDa laminin receptor precursor). However, the precise mechanism by which cytoplasmic 37LRP becomes cell-membrane-embedded 67LR is unclear. The process may involve post-translational fatty acylation of the protein combined with either homo- or hetero-dimerization, possibly with a galectin-3-epitope-containing partner. Furthermore, it has become clear that acting as a receptor for laminin is not the only function of this protein. 67LR also acts as a receptor for viruses, such as Sindbis virus and dengue virus, and is involved with internalization of the prion protein. Interestingly, unmodified 37LRP is a ribosomal component and homologues of this protein are found in all five kingdoms. In addition, it appears to be strongly associated with histones in the eukaryotic cell nucleus, although the precise role of these interactions is not clear. Here we review the current understanding of the structure and function of this molecule, as well as highlighting areas requiring further research.