Horseshoe in a model of artificial neural network

In this paper, we study a three-dimensional general model of artificial neural network (ANN). To confirm the chaotic behavior in this neural network demonstrated in numerical studies, we consider a cross-section properly chosen for the attractor obtained and study the dynamics of the corresponding Poincaré map, and rigorously verify the existence of horseshoe by computer-assisted verification arguments.     

A hybrid algorithm to optimize RBF network architecture and parameters for nonlinear time series prediction

This paper proposes a novel hybrid algorithm for automatic selection of the proper input variables, the number of hidden nodes of the radial basis function (RBF) network, and optimizing network parameters (weights, centers and widths) simultaneously. In the proposed algorithm, the inputs and the number of hidden nodes of the RBF network are represented by binary-coded strings and evolved by a genetic algorithm (GA). Simultaneously, for each chromosome with fixed inputs and number of hidden nodes, the corresponding parameters of the network are real-coded and optimized by a gradient-based fast-converging parameter estimation method. Performance of the presented hybrid approach is evaluated by several benchmark time series modeling and prediction problems. Experimental results show that the proposed approach produces parsimonious RBF networks, and obtains better modeling accuracy than some other algorithms.     

神经网络优化组合预测模型在油气产量预测中的应用

采用组合预测方法对油气产量预测进行研究,首先选取油藏工程领域多种油气产量预测模型建立组合预测模型库,基于权系数的时效性,利用三层前馈BP神经网络建立油气产量变权组合预测模型,并进行实例分析,结果表明该方法能提高预测精度,增强预测模型的实用性.     

An analytic network process approach to operationalization of five forces model

The five forces model has been one of the most influential frameworks for strategic management. In contrast to its importance as a centerpiece of textbooks, however, it has attracted less attention from both academic researchers and practicing managers. This is due to its innate weakness, difficulty in operationalization. The vital requisites for operationalizing the five forces model are to deal with it as a complex system composed of interrelated forces and their sub-forces, and to prioritize them with consideration of their interdependency. The tenet of this study is the requisites can be achieved through the analytic network process (ANP). The ANP, which is a generalization of the analytic hierarchy process (AHP), produces priorities of elements in a complex network model with consideration of interdependency among elements. The five forces model is transformed into a network model of the ANP. The ANP procedure is then carried out to obtain the priority weights of the forces. Combining the derived weights and ratings on the forces produces the state-of-industry-competition index (SICI) values that represent the overall competitive condition of a given industry. The working of the proposed approach is provided with the help of a case study example of the Web portal Industry of Korea. The proposed ANP approach is expected to expand the five forces model into a workable system of analysis by improving its analytical power.     

Nonparametric conditional autoregressive expectile model via neural network with applications to estimating financial risk

The parametric conditional autoregressive expectiles (CARE) models have been developed to estimate expectiles, which can be used to assess value at risk and expected shortfall. The challenge lies in parametric CARE modeling is the specification of a parametric form. To avoid any model misspecification, we propose a nonparametric CARE model via neural network. The nonparametric CARE model can be estimated by a classical gradient based nonlinear optimization algorithm, and the consistency of nonparametric conditional expectile estimators is established. We then apply the nonparametric CARE model to estimating value at risk and expected shortfall of six stock indices. Empirical results for the new model is competitive with those classical models and parametric CARE models. Copyright © 2016 John Wiley & Sons, Ltd.     

Radial basis neural tree model for improving waste recovery process in a paper industry

In this article, we propose a novel hybridization of regression trees (RTs) and radial basis function networks, namely, radial basis neural tree model, for waste recovery process (WRP) improvement in a paper industry. As a by‐product of the paper manufacturing process, a lot of waste along with valuable fibers and fillers come out from the paper machine. The WRP involves separating the unwanted materials from the valuable ones so that the recovered fibers and fillers can be further reused in the production process. This job is done by fiber‐filler recovery equipment (FFRE). The efficiency of FFRE depends on several crucial process parameters, and monitoring them is a difficult proposition. The proposed model can be useful to find the essential parameters from the set of available data and to perform prediction task to improve WRP efficiency. An idea of parameter optimization along with regularity conditions for the universal consistency of the proposed model is given. The proposed model has the advantages of easy interpretability and excellent performance when applied to the FFRE efficiency improvement problem. Improved waste recovery will help the industry to become environmentally friendly with less ecological damage apart from being cost‐effective.     

Convergence for a family of neural network operators in Orlicz spaces

In this paper, we develop the theory for a family of neural network (NN) operators of the Kantorovich type, in the general setting of Orlicz spaces. In particular, a modular convergence theorem is established. In this way, we study the above family of operators in many instances of useful spaces by a unique general approach. The above NN operators provide a constructive approximation process, in which the coefficients, the weights, and the thresholds of the networks needed in order to approximate a given function f , are known. At the end of the paper, several examples of Orlicz spaces, and of sigmoidal activation functions for which the present theory can be applied, are studied in details.     

Simulation of nonlinear fractional dynamics arising in the modeling of cognitive decision making using a new fractional neural network

By the rapid growth of available data, providing data-driven solutions for nonlinear (fractional) dynamical systems becomes more important than before. In this paper, a new fractional neural network model that uses fractional order of Jacobi functions as its activation functions for one of the hidden layers is proposed to approximate the solution of fractional differential equations and fractional partial differential equations arising from mathematical modeling of cognitive-decision-making processes and several other scientific subjects. This neural network uses roots of Jacobi polynomials as the training dataset, and the Levenberg-Marquardt algorithm is chosen as the optimizer. The linear and nonlinear fractional dynamics are considered as test examples showing the effectiveness and applicability of the proposed neural network. The numerical results are compared with the obtained results of some other networks and numerical approaches such as meshless methods. Numerical experiments are presented confirming that the proposed model is accurate, fast, and feasible.     

A diagram approach to the strong coupling in the single-impurity Anderson model

We propose a diagram theory around the atomic limit for the single-impurity Anderson model in which the strongly correlated impurity electrons hybridize with free (uncorrelated) conduction electrons. Using this diagram approach, we prove a linked-cluster theorem for the vacuum diagrams and derive Dyson-type equations for localized and conduction electrons and the corresponding equations for mixed propagators. The system of equations can be closed by summing an infinite series of ladder diagrams containing irreducible Green’s functions. The result allows discussing resonances associated with quantum transitions at the impurity site. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 3, pp. 474–497, June, 2008.     

An analytical method for cost analysis in multi-stage supply chains: A stochastic network model approach

This paper studies the cost distribution characteristics in multi-stage supply chain networks. Based on the graphical evaluation and review technique, we propose a novel stochastic network mathematical model for cost distribution analysis in multi-stage supply chain networks. Further, to investigate the effects of cost components, including the procurement costs, inventory costs, shortage costs, production costs and transportation costs of supply chain members, on the total supply chain operation cost, we propose the concept of cost sensitivity and provide corresponding algorithms based on the proposed stochastic network model. Then the model is extended to analyze the cost performance of supply chain robustness under different order compensation ability scenarios and the corresponding algorithms are developed. Simulation experiment shows the effectiveness and flexibility of the proposed model, and also promotes a better understanding of the model approach and its managerial implications in cost management of supply chains.     

A fuzzy adaptive network approach to parameter estimation in cases where independent variables come from an exponential distribution

In a regression analysis, it is assumed that the observations come from a single class in a data cluster and the simple functional relationship between the dependent and independent variables can be expressed using the general model; Y=f(X)+ε. However; a data cluster may consist of a combination of observations that have different distributions that are derived from different clusters. When faced with issues of estimating a regression model for fuzzy inputs that have been derived from different distributions, this regression model has been termed the ‘switching regression model’ and it is expressed with . Here l_i indicates the class number of each independent variable and p is indicative of the number of independent variables [J.R. Jang, ANFIS: Adaptive-network-based fuzzy inference system, IEEE Transaction on Systems, Man and Cybernetics 23 (3) (1993) 665–685; M. Michel, Fuzzy clustering and switching regression models using ambiguity and distance rejects, Fuzzy Sets and Systems 122 (2001) 363–399; E.Q. Richard, A new approach to estimating switching regressions, Journal of the American Statistical Association 67 (338) (1972) 306–310].In this study, adaptive networks have been used to construct a model that has been formed by gathering obtained models. There are methods that suggest the class numbers of independent variables heuristically. Alternatively, in defining the optimal class number of independent variables, the use of suggested validity criterion for fuzzy clustering has been aimed. In the case that independent variables have an exponential distribution, an algorithm has been suggested for defining the unknown parameter of the switching regression model and for obtaining the estimated values after obtaining an optimal membership function, which is suitable for exponential distribution.