Fractal geometry and architecture design: case study review

The idea of buildings in harmony with nature can be traced back to ancient times. The increasing concerns on sustainability oriented buildings have added new challenges in building architectural design and called for new design responses. Sustainable design integrates and balances the human geometries and the natural ones. As the language of nature, it is, therefore, natural to assume that fractal geometry could play a role in developing new forms of aesthetics and sustainable architectural design. This paper gives a brief description of fractal geometry theory and presents its current status and recent developments through illustrative review of some fractal case studies in architecture design, which provides a bridge between fractal geometry and architecture design.

Design and optimisation of a large-area process-based model for annual crops

The formulation of a new process-based crop model, the general large-area model (GLAM) for annual crops is presented. The model has been designed to operate on spatial scales commensurate with those of global and regional climate models. It aims to simulate the impact of climate on crop yield. Procedures for model parameter determination and optimisation are described, and demonstrated for the prediction of groundnut (i.e. peanut; Arachis hypogaea L.) yields across India for the period 1966-1989. Optimal parameters (e.g. extinction coefficient, transpiration efficiency, rate of change of harvest index) were stable over space and time, provided the estimate of the yield technology trend was based on the full 24-year period. The model has two location-specific parameters, the planting date, and the yield gap parameter. The latter varies spatially and is determined by calibration. The optimal value varies slightly when different input data are used. The model was tested using a historical data set on a 2.5degrees x 2.5degrees grid to simulate yields. Three sites are examined in detail-grid cells from Gujarat in the west, Andhra Pradesh towards the south, and Uttar Pradesh in the north. Agreement between observed and modelled yield was variable, with correlation coefficients of 0.74, 0.42 and 0, respectively. Skill was highest where the climate signal was greatest, and correlations were comparable to or greater than correlations with seasonal mean rainfall. Yields from all 35 cells were aggregated to simulate all-India yield. The correlation coefficient between observed and simulated yields was 0.76, and the root mean square error was 8.4% of the mean yield. The model can be easily extended to any annual crop for the investigation of the impacts of climate variability (or change) on crop yield over large areas. (C) 2004 Elsevier B.V. All rights reserved.

Implementation of a Bayesian design in a dose-escalation study of an experimental agent in healthy volunteers

Bayesian decision procedures have recently been developed for dose escalation in phase I clinical trials concerning pharmacokinetic responses observed in healthy volunteers. This article describes how that general methodology was extended and evaluated for implementation in a specific phase I trial of a novel compound. At the time of writing, the study is ongoing, and it will be some time before the sponsor will wish to put the results into the public domain. This article is an account of how the study was designed in a way that should prove to be safe, accurate, and efficient whatever the true nature of the compound. The study involves the observation of two pharmacokinetic endpoints relating to the plasma concentration of the compound itself and of a metabolite as well as a safety endpoint relating to the occurrence of adverse events. Construction of the design and its evaluation via simulation are presented.

m-aminobenzoic acid inserted beta-turn in acyclic tripeptides: a peptidomimetic design

X-ray diffraction studies show that peptides Boc-Leu-Aib-m-ABA-OMe (I) (Aib, alpha-aminoisobutyric acid; m-ABA, meta-aminobenzoic acid) and Boc-Phe-Aib-m-ABA-OMe, (II) adopt a type-II beta-turn conformation, solely stabilized by co-operative steric interactions amongst the amino acid residues. This type of U-turn without any intramolecular hydrogen bonding is generally referred to as an open turn. Although there are some examples of constrained cyclic peptides in which o-substituted benzenes have been inserted to mimic the turn region of the neurotrophin, a nerve growth factor, peptides I and II present novel two examples where m-aminobenzoic acid has been incorporated in the beta-turn of acyclic tripeptides. The result also demonstrates the first crystallographic evidence of a beta-turn structure containing an inserted m-aminobenzoic acid, which can be considered as a rigid gamma-aminobutyric acid with an all-trans extended configuration. (c) 2005 Elsevier Ltd. All rights reserved.

Design of a turn-linker-turn foldamer by incorporating meta-amino benzoic acid in the middle of a helix forming hexapeptide sequence: A helix breaking approach

Single crystal X-ray diffraction studies reveal that the incorporation of meta-amino benzoic acid in the middle of a helix forming hexapeptide sequence such as in peptide I Boc-Ile(1)-Aib(2)-Val(3)-m-ABA(4)-Ile(5)-Aib(6)-Leu(7)-OMe (Aib: alpha-amino isobutyric acid: m-ABA: meta-amino benzoic acid) breaks the helix propagation to produce a turn-linker-turn (T-L-T) foldamer in the solid state. In the crystalline state two conformational isomers of peptide I self-assemble in antiparallel fashion through intermolecular hydrogen bonds and aromatic pi-pi interactions to form a molecular duplex. The duplexes are further interconnected through intermolecular hydrogen bonds to form a layer of peptides. The layers are stacked one on top of the other through van der Waals interactions to form hydrophilic channels filled with solvent methanol. (C) 2009 Elsevier B.V. All rights reserved.

Design of a new foldamer turn-linker-turn in acyclic hexapeptides and formation of channels through self-assembly

Single crystal X-ray diffraction studies and solvent dependent NMR titration reveal that the designed pepticles I and 11, Boc-Xx(1)-Aib(2)-Yy(3)-NH(CH2)(2)NH-Yy(3)-Aib(2)-Xx(1)-Boc, where Xx and Yy are lie and Leu in peptide I and Leu and Val in peptide 11, respectively, fold into a turn-linker-turn (T-L-T) conformation both in the solid state and in solution. In the crystalline state the T-L-T foldamers; of peptide I and II self-assemble to form a three-dimensional framework of channels. The insides of the channels are hydrophilic and found to contain solvent CHCl3 hydrogen bonded to exposed C=O of Aib located at the turn regions. (c) 2008 Elsevier B.V. All rights reserved.

Design of supramolecular beta-sheet forming beta-turns containing aromatic rings and non-coded alpha-aminoisobutyric acid and the formation of flat fibrillar structures through self-assembly

Single crystal X-ray diffraction studies show that the three designed tripeptides Boc-Leu-Aib-m-NA-NO2 (I), Boc-Phe-Aib-m-NA-NO2 (II) and Boc-Pro-Aib-m-ABA-OMe (III) (Aib, -aminoisobutyric acid; m-NA, m-nitroaniline; m-ABA, m-aminobenzoic acid; Boc, t-butyloxycarbonyl) containing aromatic rings in the backbones adopt -turn structures that are self-assembled through intermolecular hydrogen bonds and van der Waals interactions to create layers of -sheets. Solvent-dependent NMR titration and CD studies show that the -turn structures of the peptides also exist in the solution phase. The field emission scanning electron microscopic and transmission electron microscopic images of the peptides in the solid state reveal fibrillar structures of flat morphology that are formed through -sheet mediated self-assembly of the preorganised -turn building blocks.

A facile one step synthesis of N-2 substituted 3-phenyliminoisoindolinones from N-(2-carboxybenzoyl)-anthranilic acid and the design of reverse-turn mimetics

Stirring of N-(2-carboxybenzoyl) anthranilic acid with anilines and amines such as p-toluidine, benzylamine, methyl esters of Leu, Phe, Ile and Val in presence of DCC produces N- 2 substituted 3-phenyliminoisoindolinones in very good yields. Single crystal X-ray diffraction studies and solution phase NMR and CD studies reveal that the 3-phenyliminoisoindolinone moiety is a turn-inducing scaffold which should be useful for reverse-turn mimetics.

RBF equalizer design using directional evolutionary multi-objective optimization

Whilst radial basis function (RBF) equalizers have been employed to combat the linear and nonlinear distortions in modern communication systems, most of them do not take into account the equalizer's generalization capability. In this paper, it is firstly proposed that the. model's generalization capability can be improved by treating the modelling problem as a multi-objective optimization (MOO) problem, with each objective based on one of several training sets. Then, as a modelling application, a new RBF equalizer learning scheme is introduced based on the directional evolutionary MOO (EMOO). Directional EMOO improves the computational efficiency of conventional EMOO, which has been widely applied in solving MOO problems, by explicitly making use of the directional information. Computer simulation demonstrates that the new scheme can be used to derive RBF equalizers with good performance not only on explaining the training samples but on predicting the unseen samples.

Sparse kernel density estimator using orthogonal regression based on D-optimality experimental design

A novel sparse kernel density estimator is derived based on a regression approach, which selects a very small subset of significant kernels by means of the D-optimality experimental design criterion using an orthogonal forward selection procedure. The weights of the resulting sparse kernel model are calculated using the multiplicative nonnegative quadratic programming algorithm. The proposed method is computationally attractive, in comparison with many existing kernel density estimation algorithms. Our numerical results also show that the proposed method compares favourably with other existing methods, in terms of both test accuracy and model sparsity, for constructing kernel density estimates.

Sparse multioutput radial basis function network construction using combined locally regularised orthogonal least square and D-optimality experimental design

A construction algorithm for multioutput radial basis function (RBF) network modelling is introduced by combining a locally regularised orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximised model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious RBF network model with excellent generalisation performance. The D-optimality design criterion enhances the model efficiency and robustness. A further advantage of the combined approach is that the user only needs to specify a weighting for the D-optimality cost in the combined RBF model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

Sparse kernel regression modeling using combined locally regularized orthogonal least squares and D-optimality experimental design

The note proposes an efficient nonlinear identification algorithm by combining a locally regularized orthogonal least squares (LROLS) model selection with a D-optimality experimental design. The proposed algorithm aims to achieve maximized model robustness and sparsity via two effective and complementary approaches. The LROLS method alone is capable of producing a very parsimonious model with excellent generalization performance. The D-optimality design criterion further enhances the model efficiency and robustness. An added advantage is that the user only needs to specify a weighting for the D-optimality cost in the combined model selecting criterion and the entire model construction procedure becomes automatic. The value of this weighting does not influence the model selection procedure critically and it can be chosen with ease from a wide range of values.

Experimental design and model construction algorithms for radial basis function networks

New construction algorithms for radial basis function (RBF) network modelling are introduced based on the A-optimality and D-optimality experimental design criteria respectively. We utilize new cost functions, based on experimental design criteria, for model selection that simultaneously optimizes model approximation, parameter variance (A-optimality) or model robustness (D-optimality). The proposed approaches are based on the forward orthogonal least-squares (OLS) algorithm, such that the new A-optimality- and D-optimality-based cost functions are constructed on the basis of an orthogonalization process that gains computational advantages and hence maintains the inherent computational efficiency associated with the conventional forward OLS approach. The proposed approach enhances the very popular forward OLS-algorithm-based RBF model construction method since the resultant RBF models are constructed in a manner that the system dynamics approximation capability, model adequacy and robustness are optimized simultaneously. The numerical examples provided show significant improvement based on the D-optimality design criterion, demonstrating that there is significant room for improvement in modelling via the popular RBF neural network.