A neurofuzzy network knowledge extraction and extended gram-Schmidt algorithm for model subspace decomposition

This paper introduces a new neurofuzzy model construction and parameter estimation algorithm from observed finite data sets, based on a Takagi and Sugeno (T-S) inference mechanism and a new extended Gram-Schmidt orthogonal decomposition algorithm, for the modeling of a priori unknown dynamical systems in the form of a set of fuzzy rules. The first contribution of the paper is the introduction of a one to one mapping between a fuzzy rule-base and a model matrix feature subspace using the T-S inference mechanism. This link enables the numerical properties associated with a rule-based matrix subspace, the relationships amongst these matrix subspaces, and the correlation between the output vector and a rule-base matrix subspace, to be investigated and extracted as rule-based knowledge to enhance model transparency. The matrix subspace spanned by a fuzzy rule is initially derived as the input regression matrix multiplied by a weighting matrix that consists of the corresponding fuzzy membership functions over the training data set. Model transparency is explored by the derivation of an equivalence between an A-optimality experimental design criterion of the weighting matrix and the average model output sensitivity to the fuzzy rule, so that rule-bases can be effectively measured by their identifiability via the A-optimality experimental design criterion. The A-optimality experimental design criterion of the weighting matrices of fuzzy rules is used to construct an initial model rule-base. An extended Gram-Schmidt algorithm is then developed to estimate the parameter vector for each rule. This new algorithm decomposes the model rule-bases via an orthogonal subspace decomposition approach, so as to enhance model transparency with the capability of interpreting the derived rule-base energy level. This new approach is computationally simpler than the conventional Gram-Schmidt algorithm for resolving high dimensional regression problems, whereby it is computationally desirable to decompose complex models into a few submodels rather than a single model with large number of input variables and the associated curse of dimensionality problem. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

The role of Wnt signalling in the development of somites and neural crest

The Wnt family of secreted signalling molecules controls a wide range of developmental processes in all metazoans. In this investigation we concentrate on the role that members of this family play during the development of (1) the somites and (2) the neural crest. (3) We also isolate a novel component of the Wnt signalling pathway called Naked cuticle and investigate the role that this protein may play in both of the previously mentioned developmental processes. (1) In higher vertebrates the paraxial mesoderm undergoes a mesenchymal-to-epithelial transformation to form segmentally organised structures called somites. Experiments have shown that signals originating from the ectoderm overlying the somites or from midline structures are required for the formation of the somites, but their identity has yet to be determined. Wnt6 is a good candidate as a somite epithelialisation factor from the ectoderm since it is expressed in this tissue. In this study we show that injection of Wnt6-producing cells beneath the ectoderm at the level of the segmental plate or lateral to the segmental plate leads to the formation of numerous small epithelial somites. We show that Wnts are indeed responsible for the epithelialisation of somites by applying Wnt antagonists which result in the segmental plate being unable to form somites. These results show that Wnt6, the only member of this family to be localised to the chick paraxial ectoderm, is able to regulate the development of epithelial somites and that cellular organisation is pivotal in the execution of the differentiation programmes. (2) The neural crest is a population of multipotent progenitor cells that arise from the neural ectoderm in all vertebrate embryos and form a multitude of derivatives including the peripheral sensory neurons, the enteric nervous system, Schwann cells, pigment cells and parts of the craniofacial skeleton. The induction of the neural crest relies on an ectodermally derived signal, but the identity of the molecule performing this role in amniotes is not known. Here we show that Wnt6, a protein expressed in the ectoderm, induces neural crest production. (3) The intracellular response to Wnt signalling depends on the choice of signalling cascade activated in the responding cell. Cells can activate either the canonical pathway that modulates gene expression to control cellular differentiation and proliferation, or the non-canonical pathway that controls cell polarity and movement (Pandur et al. 2002b). Recent work has identified the protein Naked cuticle as an intracellular switch promoting the non-canonical pathway at the expense of the canonical pathway. We have cloned chick Naked cuticle-1 (cNkd1) and demonstrate that it is expressed in a dynamic manner during early embryogenesis. We show that it is expressed in the somites and in particular regions where cells are undergoing movement. Lastly our study shows that the expression of cNkd1 is regulated by Wnt expression originating from the neural tube. This study provides evidence that non-canonical Wnt signalling plays a part in somite development.

Wnt6 controls amniote neural crest induction through the non-canonical signaling pathway

The neural crest is a multipotent embryonic cell population that arises from neural ectoderm and forms derivatives essential for vertebrate function. Neural crest induction requires an ectodermal signal, thought to be a Writ ligand, but the identity of the Wnt that performs this function in amniotes is unknown. Here, we demonstrate that Wnt6, derived from the ectoderm, is necessary for chick neural crest induction. Crucially, we also show that Wnt6 acts through the non-canonical pathway and not the beta-catenin-dependant pathway. Surprisingly, we found that canonical Wnt signaling inhibited neural crest production in the chick embryo. In light of studies in anamniotes demonstrating that canonical Wnt signaling induces neural crest, these results indicate a significant and novel change in the mechanism of neural crest induction during vertebrate evolution. These data also highlight a key role for noncanonical Wnt signaling in cell type specification from a stem population during development.

Expression and regulation of Nkd-1, an intracellular component of Wnt signalling pathway in the chick embryo

The Wnt family of secreted signalling molecules control a wide range of developmental processes in all metazoans. The intracellular response to Wnt signalling depends on the choice of signalling cascade activated in the responding cell. Cells can activate either the canonical pathway that modulates gene expression to control cellular differentiation and proliferation, or the non-canonical pathway that controls cell polarity and movement. Recent work has identified the protein Naked Cuticle to act as an intracellular switch to promote the non-canonical pathway at the expense of the canonical pathway. We have cloned chick Naked Cuticle-1 (cNkd-1) and show that it is expressed in a dynamic manner during early embryogenesis. We show that it is expressed in the somites and in particular regions where cells are undergoing movement. Lastly, we show that the expression of cNkd-1 is regulated by Wnt expression originating from the neural tube. This study provides evidence that non-canonical Wnt signalling plays a part in somite development.

Characterization of an escherichia coli elaC deletion mutant

The elaC gene of Escherichia coli encodes a binuclear zinc phosphodiesterase (ZiPD). ZiPD homologs from various species act as 3' tRNA processing endoribonucleases, and although the homologous gene in Bacillus subtilis is essential for viability [EMBO J. 22 (2003) 4534], the physiological function of E. coli ZiPD has remained enigmatic. In order to investigate the function of E. coli ZiPD we generated and characterized an E. coli elaC deletion mutant. Surprisingly, the E. coli elaC deletion mutant was viable and had wild-type like growth properties. Micro array-based transcriptional analysis indicated expression of the E. coli elaC gene at basal levels during aerobic growth. The elaC gene deletion had no effect on the expression of genes coding for RNases or amino-acyl tRNA synthetases or any other gene among a total of > 1300 genes probed. 2D-PAGE analysis showed that the elaC mutation, likewise, had no effect on the proteome. These results strengthen doubts about the involvement of E. coli ZiPD in tRNA maturation and suggest functional diversity within the ZiPD/ElaCl protein family. In addition to these unexpected features of the E. coli elaC deletion mutant, a sequence comparison of ZiPD (ElaCl) proteins revealed specific regions for either enterobacterial or mammalian ZiPD (ElaCl) proteins. (C) 2004 Elsevier Inc. All rights reserved.

Sparse model identification using orthogonal forward regression with basis pursuit and D-optimality

An efficient model identification algorithm for a large class of linear-in-the-parameters models is introduced that simultaneously optimises the model approximation ability, sparsity and robustness. The derived model parameters in each forward regression step are initially estimated via the orthogonal least squares (OLS), followed by being tuned with a new gradient-descent learning algorithm based on the basis pursuit that minimises the l(1) norm of the parameter estimate vector. The model subset selection cost function includes a D-optimality design criterion that maximises the determinant of the design matrix of the subset to ensure model robustness and to enable the model selection procedure to automatically terminate at a sparse model. The proposed approach is based on the forward OLS algorithm using the modified Gram-Schmidt procedure. Both the parameter tuning procedure, based on basis pursuit, and the model selection criterion, based on the D-optimality that is effective in ensuring model robustness, are integrated with the forward regression. As a consequence the inherent computational efficiency associated with the conventional forward OLS approach is maintained in the proposed algorithm. Examples demonstrate the effectiveness of the new approach.

M-estimator, and D-optimality model construction using orthogonal forward regression

This correspondence introduces a new orthogonal forward regression (OFR) model identification algorithm using D-optimality for model structure selection and is based on an M-estimators of parameter estimates. M-estimator is a classical robust parameter estimation technique to tackle bad data conditions such as outliers. Computationally, The M-estimator can be derived using an iterative reweighted least squares (IRLS) algorithm. D-optimality is a model structure robustness criterion in experimental design to tackle ill-conditioning in model Structure. The orthogonal forward regression (OFR), often based on the modified Gram-Schmidt procedure, is an efficient method incorporating structure selection and parameter estimation simultaneously. The basic idea of the proposed approach is to incorporate an IRLS inner loop into the modified Gram-Schmidt procedure. In this manner, the OFR algorithm for parsimonious model structure determination is extended to bad data conditions with improved performance via the derivation of parameter M-estimators with inherent robustness to outliers. Numerical examples are included to demonstrate the effectiveness of the proposed algorithm.

Robust neurofuzzy rule base knowledge extraction and estimation using subspace decomposition combined with regularization and D-optimality

A new robust neurofuzzy model construction algorithm has been introduced for the modeling of a priori unknown dynamical systems from observed finite data sets in the form of a set of fuzzy rules. Based on a Takagi-Sugeno (T-S) inference mechanism a one to one mapping between a fuzzy rule base and a model matrix feature subspace is established. This link enables rule based knowledge to be extracted from matrix subspace to enhance model transparency. In order to achieve maximized model robustness and sparsity, a new robust extended Gram-Schmidt (G-S) method has been introduced via two effective and complementary approaches of regularization and D-optimality experimental design. Model rule bases are decomposed into orthogonal subspaces, so as to enhance model transparency with the capability of interpreting the derived rule base energy level. A locally regularized orthogonal least squares algorithm, combined with a D-optimality used for subspace based rule selection, has been extended for fuzzy rule regularization and subspace based information extraction. By using a weighting for the D-optimality cost function, the entire model construction procedure becomes automatic. Numerical examples are included to demonstrate the effectiveness of the proposed new algorithm.

Genome expansion and gene loss in powdery mildew fungi reveal tradeoffs in extreme parasitism

Powdery mildews are phytopathogens whose growth and reproduction are entirely dependent on living plant cells. The molecular basis of this life-style, obligate biotrophy, remains unknown. We present the genome analysis of barley powdery mildew, Blumeria graminis f.sp. hordei (Blumeria), as well as a comparison with the analysis of two powdery mildews pathogenic on dicotyledonous plants. These genomes display massive retrotransposon proliferation, genome-size expansion, and gene losses. The missing genes encode enzymes of primary and secondary metabolism, carbohydrate-active enzymes, and transporters, probably reflecting their redundancy in an exclusively biotrophic life-style. Among the 248 candidate effectors of pathogenesis identified in the Blumeria genome, very few (less than 10) define a core set conserved in all three mildews, suggesting thatmost effectors represent species-specific adaptations.

Variable selection algorithm for the construction of MIMO operating point dependent neurofuzzy networks

An input variable selection procedure is introduced for the identification and construction of multi-input multi-output (MIMO) neurofuzzy operating point dependent models. The algorithm is an extension of a forward modified Gram-Schmidt orthogonal least squares procedure for a linear model structure which is modified to accommodate nonlinear system modeling by incorporating piecewise locally linear model fitting. The proposed input nodes selection procedure effectively tackles the problem of the curse of dimensionality associated with lattice-based modeling algorithms such as radial basis function neurofuzzy networks, enabling the resulting neurofuzzy operating point dependent model to be widely applied in control and estimation. Some numerical examples are given to demonstrate the effectiveness of the proposed construction algorithm.

Enhancement of a telemanipulator design with a human arm model

In this chapter we described how the inclusion of a model of a human arm, combined with the measurement of its neural input and a predictor, can provide to a previously proposed teleoperator design robustness under time delay. Our trials gave clear indications of the superiority of the NPT scheme over traditional as well as the modified Yokokohji and Yoshikawa architectures. Its fundamental advantages are: the time-lead of the slave, the more efficient, and providing a more natural feeling manipulation, and the fact that incorporating an operator arm model leads to more credible stability results. Finally, its simplicity allows less likely to fail local control techniques to be employed. However, a significant advantage for the enhanced Yokokohji and Yoshikawa architecture results from the very fact that it’s a conservative modification of current designs. Under large prediction errors, it can provide robustness through directing the master and slave states to their means and, since it relies on the passivity of the mechanical part of the system, it would not confuse the operator. An experimental implementation of the techniques will provide further evidence for the performance of the proposed architectures. The employment of neural networks and fuzzy logic, which will provide an adaptive model of the human arm and robustifying control terms, is scheduled for the near future.

Design of an active arm support for assisting arm movements

In this paper we have explored areas of application for health care manipulators and possible user groups. We have shown the steps in the design approach to the conceptual mechanism from the AAS. The future work will be measurement from properties of the muscle with the elbow parameterization test-bed to get a database to design one part of the control area from the AAS. More work on the mechanical design is required before a functional prototype can be built.

Adaptive least mean square CDMA detection with Gram–Schmidt pre-processing

The Gram-Schmidt (GS) orthogonalisation procedure has been used to improve the convergence speed of least mean square (LMS) adaptive code-division multiple-access (CDMA) detectors. However, this algorithm updates two sets of parameters, namely the GS transform coefficients and the tap weights, simultaneously. Because of the additional adaptation noise introduced by the former, it is impossible to achieve the same performance as the ideal orthogonalised LMS filter, unlike the result implied in an earlier paper. The authors provide a lower bound on the minimum achievable mean squared error (MSE) as a function of the forgetting factor λ used in finding the GS transform coefficients, and propose a variable-λ algorithm to balance the conflicting requirements of good tracking and low misadjustment.