Modified radial basis function neural network using output transformation

A modified radial basis function (RBF) neural network and its identification algorithm based on observational data with heterogeneous noise are introduced. The transformed system output of Box-Cox is represented by the RBF neural network. To identify the model from observational data, the singular value decomposition of the full regression matrix consisting of basis functions formed by system input data is initially carried out and a new fast identification method is then developed using Gauss-Newton algorithm to derive the required Box-Cox transformation, based on a maximum likelihood estimator (MLE) for a model base spanned by the largest eigenvectors. Finally, the Box-Cox transformation-based RBF neural network, with good generalisation and sparsity, is identified based on the derived optimal Box-Cox transformation and an orthogonal forward regression algorithm using a pseudo-PRESS statistic to select a sparse RBF model with good generalisation. The proposed algorithm and its efficacy are demonstrated with numerical examples.

Generalized neurofuzzy network modeling algorithms using Bezier-Bernstein polynomial functions and additive decomposition

This paper introduces a new neurofuzzy model construction algorithm for nonlinear dynamic systems based upon basis functions that are Bezier-Bernstein polynomial functions. This paper is generalized in that it copes with n-dimensional inputs by utilising an additive decomposition construction to overcome the curse of dimensionality associated with high n. This new construction algorithm also introduces univariate Bezier-Bernstein polynomial functions for the completeness of the generalized procedure. Like the B-spline expansion based neurofuzzy systems, Bezier-Bernstein polynomial function based neurofuzzy networks hold desirable properties such as nonnegativity of the basis functions, unity of support, and interpretability of basis function as fuzzy membership functions, moreover with the additional advantages of structural parsimony and Delaunay input space partition, essentially overcoming the curse of dimensionality associated with conventional fuzzy and RBF networks. This new modeling network is based on additive decomposition approach together with two separate basis function formation approaches for both univariate and bivariate Bezier-Bernstein polynomial functions used in model construction. The overall network weights are then learnt using conventional least squares methods. Numerical examples are included to demonstrate the effectiveness of this new data based modeling approach.

Symmetry in biology: from genetic code to stochastic gene regulation

Mathematical models, as instruments for understanding the workings of nature, are a traditional tool of physics, but they also play an ever increasing role in biology - in the description of fundamental processes as well as that of complex systems. In this review, the authors discuss two examples of the application of group theoretical methods, which constitute the mathematical discipline for a quantitative description of the idea of symmetry, to genetics. The first one appears, in the form of a pseudo-orthogonal (Lorentz like) symmetry, in the stochastic modelling of what may be regarded as the simplest possible example of a genetic network and, hopefully, a building block for more complicated ones: a single self-interacting or externally regulated gene with only two possible states: ` on` and ` off`. The second is the algebraic approach to the evolution of the genetic code, according to which the current code results from a dynamical symmetry breaking process, starting out from an initial state of complete symmetry and ending in the presently observed final state of low symmetry. In both cases, symmetry plays a decisive role: in the first, it is a characteristic feature of the dynamics of the gene switch and its decay to equilibrium, whereas in the second, it provides the guidelines for the evolution of the coding rules.

Adaptive data based neural network leader-follower control of multi-agent networks

In this paper, we propose a data based neural network leader-follower control for multi-agent networks where each agent is described by a class of high-order uncertain nonlinear systems with input perturbation. The control laws are developed using multiple-surface sliding control technique. In particular, novel set of sliding variables are proposed to guarantee leader-follower consensus on the sliding surfaces. Novel switching is proposed to overcome the unavailability of instantaneous control output from the neighbor. By utilizing RBF neural network and Fourier series to approximate the unknown functions, leader-follower consensus can be reached, under the condition that the dynamic equations of all agents are unknown. An O(n) data based algorithm is developed, using only the network’s measurable input/output data to generate the distributed virtual control laws. Simulation results demonstrate the effectiveness of the approach.

A hybrid ART-GRNN online learning neural network with a ε-insensitive loss function

In this brief, a new neural network model called generalized adaptive resonance theory (GART) is introduced. GART is a hybrid model that comprises a modified Gaussian adaptive resonance theory (MGA) and the generalized regression neural network (GRNN). It is an enhanced version of the GRNN, which preserves the online learning properties of adaptive resonance theory (ART). A series of empirical studies to assess the effectiveness of GART in classification, regression, and time series prediction tasks is conducted. The results demonstrate that GART is able to produce good performances as compared with those of other methods, including the online sequential extreme learning machine (OSELM) and sequential learning radial basis function (RBF) neural network models.

Separação cega de fontes lineares e não lineares usando algoritmo genético, redes neurais artificiais RBF e negentropia de Rényi como medida de independência

Conventional methods to solve the problem of blind source separation nonlinear, in general, using series of restrictions to obtain the solution, often leading to an imperfect separation of the original sources and high computational cost. In this paper, we propose an alternative measure of independence based on information theory and uses the tools of artificial intelligence to solve problems of blind source separation linear and nonlinear later. In the linear model applies genetic algorithms and Rényi of negentropy as a measure of independence to find a separation matrix from linear mixtures of signals using linear form of waves, audio and images. A comparison with two types of algorithms for Independent Component Analysis widespread in the literature. Subsequently, we use the same measure of independence, as the cost function in the genetic algorithm to recover source signals were mixed by nonlinear functions from an artificial neural network of radial base type. Genetic algorithms are powerful tools for global search, and therefore well suited for use in problems of blind source separation. Tests and analysis are through computer simulations

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

A DOE based approach for the design of RBF artificial neural networks applied to prediction of surface roughness in AISI 52100 hardened Steel turning

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Optimization of Radial Basis Function neural network employed for prediction of surface roughness in hard turning process using Taguchi's orthogonal arrays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Variational studies and replica symmetry breaking in the generalization problem of the binary perceptron

We analyze the average performance of a general class of learning algorithms for the nondeterministic polynomial time complete problem of rule extraction by a binary perceptron. The examples are generated by a rule implemented by a teacher network of similar architecture. A variational approach is used in trying to identify the potential energy that leads to the largest generalization in the thermodynamic limit. We restrict our search to algorithms that always satisfy the binary constraints. A replica symmetric ansatz leads to a learning algorithm which presents a phase transition in violation of an information theoretical bound. Stability analysis shows that this is due to a failure of the replica symmetric ansatz and the first step of replica symmetry breaking (RSB) is studied. The variational method does not determine a unique potential but it allows construction of a class with a unique minimum within each first order valley. Members of this class improve on the performance of Gibbs algorithm but fail to reach the Bayesian limit in the low generalization phase. They even fail to reach the performance of the best binary, an optimal clipping of the barycenter of version space. We find a trade-off between a good low performance and early onset of perfect generalization. Although the RSB may be locally stable we discuss the possibility that it fails to be the correct saddle point globally. ©2000 The American Physical Society.

Influence of the network modifier on the characteristics of MSnO 3 (M=Sr and Ca) thin films synthesized by chemical solution deposition

CaSnO3 and SrSnO3 alkaline earth stannate thin films were prepared by chemical solution deposition using the polymeric precursor method on various single crystal substrates (R- and C-sapphire and 100-SrTiO3) at different temperatures. The films were characterized by X-ray diffraction (θ-2θ, ω- and φ-scans), field emission scanning electron microscopy, atomic force microscopy, micro-Raman spectroscopy and photoluminescence. Epitaxial SrSnO3 and CaSnO 3 thin films were obtained on SrTiO3 with a high crystalline quality. The long-range symmetry promoted a short-range disorder which led to photoluminescence in the epitaxial films. In contrast, the films deposited on sapphire exhibited a random polycrystalline growth with no meaningful emission regardless of the substrate orientation. The network modifier (Ca or Sr) and the substrate (sapphire or SrTiO3) influenced the crystallization process and/or the microstructure. Higher is the tilts of the SnO6 octahedra, as in CaSnO3, higher is the crystallization temperature, which changed also the nucleation/grain growth process. © 2012 Elsevier Inc. All rights reserved.

Influence of the network modifier on the characteristics of MSnO3 (M=Sr and,Ca) thin films synthesized by chemical solution deposition

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influence of the network modifier on the characteristics of MSnO3 (M=Sr and Ca) thin films synthesized by chemical solution deposition

CaSnO3 and SrSnO3 alkaline earth stannate thin films were prepared by chemical solution deposition using the polymeric precursor method on various single crystal substrates (R- and C-sapphire and 100-SrTiO3) at different temperatures. The films were characterized by X-ray diffraction (θ-2θ, ω- and φ-scans), field emission scanning electron microscopy, atomic force microscopy, micro-Raman spectroscopy and photoluminescence. Epitaxial SrSnO3 and CaSnO3 thin films were obtained on SrTiO3 with a high crystalline quality. The long-range symmetry promoted a short-range disorder which led to photoluminescence in the epitaxial films. In contrast, the films deposited on sapphire exhibited a random polycrystalline growth with no meaningful emission regardless of the substrate orientation. The network modifier (Ca or Sr) and the substrate (sapphire or SrTiO3) influenced the crystallization process and/or the microstructure. Higher is the tilts of the SnO6 octahedra, as in CaSnO3, higher is the crystallization temperature, which changed also the nucleation/grain growth process.

Transient Activation of Meox1 Is an Early Component of the Gene Regulatory Network Downstream of Hoxa2

Hox genes encode transcription factors that regulate morphogenesis in all animals with bilateral symmetry. Although Hox genes have been extensively studied, their molecular function is not clear in vertebrates, and only a limited number of genes regulated by Hox transcription factors have been identified. Hoxa2 is required for correct development of the second branchial arch, its major domain of expression. We now show that Meox1 is genetically downstream from Hoxa2 and is a direct target. Meox1 expression is downregulated in the second arch of Hoxa2 mouse mutant embryos. In chromatin immunoprecipitation (ChIP), Hoxa2 binds to the Meox1 proximal promoter. Two highly conserved binding sites contained in this sequence are required for Hoxa2-dependent activation of the Meox1 promoter. Remarkably, in the absence of Meox1 and its close homolog Meox2, the second branchial arch develops abnormally and two of the three skeletal elements patterned by Hoxa2 are malformed. Finally, we show that Meox1 can specifically bind the DNA sequences recognized by Hoxa2 on its functional target genes. These results provide new insight into the Hoxa2 regulatory network that controls branchial arch identity.