Construction of tunable radial basis function networks using orthogonal forward selection

An orthogonal forward selection (OFS) algorithm based on leave-one-out (LOO) criteria is proposed for the construction of radial basis function (RBF) networks with tunable nodes. Each stage of the construction process determines an RBF node, namely, its center vector and diagonal covariance matrix, by minimizing the LOO statistics. For regression application, the LOO criterion is chosen to be the LOO mean-square error, while the LOO misclassification rate is adopted in two-class classification application. This OFS-LOO algorithm is computationally efficient, and it is capable of constructing parsimonious RBF networks that generalize well. Moreover, the proposed algorithm is fully automatic, and the user does not need to specify a termination criterion for the construction process. The effectiveness of the proposed RBF network construction procedure is demonstrated using examples taken from both regression and classification applications.

Neurofuzzy design and model construction of nonlinear dynamical processes from data

A common problem in many data based modelling algorithms such as associative memory networks is the problem of the curse of dimensionality. In this paper, a new two-stage neurofuzzy system design and construction algorithm (NeuDeC) for nonlinear dynamical processes is introduced to effectively tackle this problem. A new simple preprocessing method is initially derived and applied to reduce the rule base, followed by a fine model detection process based on the reduced rule set by using forward orthogonal least squares model structure detection. In both stages, new A-optimality experimental design-based criteria we used. In the preprocessing stage, a lower bound of the A-optimality design criterion is derived and applied as a subset selection metric, but in the later stage, the A-optimality design criterion is incorporated into a new composite cost function that minimises model prediction error as well as penalises the model parameter variance. The utilisation of NeuDeC leads to unbiased model parameters with low parameter variance and the additional benefit of a parsimonious model structure. Numerical examples are included to demonstrate the effectiveness of this new modelling approach for high dimensional inputs.

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.

Construction of supramolecular helices and breaking the helicity by forming supramolecular β-sheet structures using suitable self-assembling pseudopeptide building blocks

Bis-valine derivatives or malonamide (Guha,S.; Drew, M.G.B. Small 2008, 4, 1993-2005) and a bis-valine derivative of 1,1-cyclopropone dicarboxamide were used as building blocks for the construction of supramolecular helical structures. The six-membered intramolecular hydrogen-bonded scaffold is formed, and this acts as a unique supramolecular synthon for the construction of a pseudopeptide-based supramolecular helical structure. However, in absence of this intramolecular hydrogen bond. intermolecular hydrogen bonds are formed among the peptide strands. This leads to a supramolecular beta-sheet structure. Proper selection of the supramolecular synthon (six-membered intramolecular hydrogenbonded scaffold) promotes supramolecular helix formation, and a deviation from this molecular structure dictates the disruption of supramolecular helicity. In this study, six crystal structures have been used to demonstrate that a change in the central angle and/or the central core structure of dicarboxamides can be used to design either a supramolecular helix or a beta-sheet.

Stepwise construction of [Os6(CO)18(μ6-P)]-, a hexanuclear osmium cluster monoanion with trigonal-prismatic co-ordination for phosphorus: X-ray crystal structures of [Os6(μ-H)2(CO)20(MeCN)(μ3-PH)] and [PPh3Me][Os6(CO)18(μ6-P)]

Treatment of the labile cluster [Os3(CO)11(MeCN)] with PH3 affords the substituted product [Os3(CO)11(PH3)](1) in high yield. Subsequent reaction of (1) with Na2CO3 in MeOH, followed by acidification, gives the hydrido phosphido cluster [Os3(µ-H)(CO)10(µ-PH2)](2). When (2) is heated to 45–60 °C in the presence of [Os3(CO)11(MeCN)] a hexanuclear complex with the formulation [Os6(µ-H)2(CO)21(µ3-PH)](3) is obtained. If this reaction is repeated using [Os3(CO)10(MeCN)2] instead of [Os3(CO)11(MeCN)], an acetonitrile-containing product, [Os6(µ-H)2(CO)20(MeCN)(µ3-PH)](4), is obtained. An X-ray analysis of (4) shows that two Os3 triangular units are linked by a µ3-phosphinidene ligand, which symmetrically bridges an Os–Os edge of one triangle and is terminally co-ordinated to one Os atom of the second triangle. When (3) is treated with a weak base, such as [N(PPh3)2]Cl or [PPh3Me] Br, deprotonation to the corresponding cluster monoanion [Os6(µ-H)(CO)21(µ3-PH)]–(5) occurs. Treatment of (5) with a weak acid regenerates (3) in quantitative yield. Thermolysis of (3) leads to a closing up of the metal framework, affording the cluster [Os6(µ-H)(CO)18(µ6-P)], which readily deprotonates to give the anion [Os6(CO)18(µ6-P)]–(7) in the presence of [N(PPh3)2] Cl or [PPh3Me]Br. The same anion (7) may also be obtained by direct thermolysis of (5). An X-ray analysis of the [PPh3Me]+ salt of (7) confirms that the phosphorus occupies an interstitial site in a trigonal-prismatic hexaosmium framework, and co-ordinates to all six metal atoms with an average Os–P distance of 2.31 (1)Å. Proton and 31P n.m.r. data on all the new clusters are presented, and the position of the phosphorus resonance in the 31P n.m.r. spectrum is related to the changes in the environment of the phosphorus atom.