Analysis of natural convection from a column of cold horizontal cylinders using Artificial Neural Network

Artificial Neural Networks (ANNs) offer an alternative way to tackle complex problems. They can learn from the examples and once trained can perform predictions and generalizations at high speed. They are particularly useful in behavior or system identification. According to the above advantages of ANN in the present paper ANN is used to predict natural convection heat transfer and fluid flow from a column of cold horizontal circular cylinders having uniform surface temperature. Governing equations are solved in a few specified cases by finite volume method to generate the database for training the ANN in the range of Rayleigh numbers of 10⁵–10⁸ and a range of cylinder spacing of 0.5, 1.0, and 1.5 diameters, thereafter a Multi-Layer Perceptron (MLP) network is used to capture the behavior of flow and temperature fields and then generalized this behavior to predict the flow and temperature fields for any other Rayleigh numbers. Different training algorithms are used and it is found that the resilient back-propagation algorithm is the best algorithm regarding the faster training procedure. To validate the accuracy of the trained network, comparison is performed among the ANN and available CFD results. It is observed that ANN can be used more efficiently to determine cold plume and thermal field in lesser computational time. Based on the generalized results from the ANN new correlations are developed to estimate natural convection from a column of cold horizontal cylinders with respect to a single horizontal cylinder.     

Regression and ANN models for estimating minimum value of machining performance

Surface roughness is one of the most common performance measurements in machining process and an effective parameter in representing the quality of machined surface. The minimization of the machining performance measurement such as surface roughness (R_a) must be formulated in the standard mathematical model. To predict the minimum R_a value, the process of modeling is taken in this study. The developed model deals with real experimental data of the R_a in the end milling machining process. Two modeling approaches, regression and Artificial Neural Network (ANN), are applied to predict the minimum R_a value. The results show that regression and ANN models have reduced the minimum R_a value of real experimental data by about 1.57% and 1.05%, respectively.     

A combination of testability and decodability by tensor products

Ben‐Sasson and Sudan (RSA 2006) showed that taking the repeated tensor product of linear codes with very large distance results in codes that are locally testable. Due to the large distance requirement the associated tensor products could be applied only over sufficiently large fields. Then Meir (SICOMP 2009) used this result to present a combinatorial construction of locally testable codes with largest known rate. As a consequence, this construction was obtained over sufficiently large fields. In this paper we improve the result of Ben‐Sasson and Sudan and show that for any linear codes the associated tensor products are locally testable. Consequently, the construction of Meir can be taken over any field, including the binary field. Moreover, a combination of our result with the result of Spielman (IEEE IT, 1996) implies a construction of linear codes (over any field) that combine the following properties:

• have constant rate and constant relative distance;
• have blocklength n and are testable with n^? queries, for any constant ? > 0;
• linear time encodable and linear‐time decodable from a constant fraction of errors.

Furthermore, a combination of our result with the result of Guruswami et al. (STOC 2009) implies a similar corollary for list‐decodable codes. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46, 572–598, 2015     

A Comparison of Discriminant Analysis versus Artificial Neural Networks

Artificial Neural Network (ANN) techniques have recently been applied to many different fields and have demonstrated their capabilities in solving complex problems. In a business environment, the techniques have been applied to predict bond ratings and stock price performance. In these applications, ANN techniques outperformed widely-used multivariate statistical techniques. The purpose of this paper is to compare the ANN method with the Discriminant Analysis (DA) method in order to understand the merits of ANN that are responsible for the higher level of performance. The paper provides an overview of the basic concepts of ANN techniques in order to enhance the understanding of this emerging technique. The similarities and differences between ANN and DA techniques in representing their models are described. This study also proposes a method to overcome the limitations of the ANN approach, Finally, a case study using a data set in a business environment demonstrates the superiority of ANN over DA as a method of classification of observations.     

Mean curvature of hypersurfaces in Killing submersions with bounded shadow

Given a complete hypersurface isometrically immersed in an ambient manifold, in this paper we provide a lower bound for the norm of the mean curvature vector field of the immersion assuming that:

• 1) The ambient manifold admits a Killing submersion with unit-length Killing vector field.
• 2) The projection of the image of the immersion is bounded in the base manifold.
• 3) The hypersurface is stochastically complete, or the immersion is proper.

     

Hybrid artificial neural networks for efficient valuation of real options and financial derivatives

A hybrid valuation methodology is proposed and tested for improving the efficiency of contingent claims pricing by combining Artificial Neural Networks (ANN) and conventional parametric option pricing techniques. With one application on financial derivatives and one on real options the methods superiority is demonstrated. The resulting efficiency is instrumental for real time applications.MSC code: 90-08 Acknowledgements: Both authors are thankful for partial financial support to the HERMES European Center of Excellence on Computational Finance and Economics of the University of Cyprus and a University of Cyprus grant for research in ANNs and Derivatives, and to the anonymous referees for their helpful comments and discussions.     

A hybrid wrapper–filter approach to detect the source(s) of out-of-control signals in multivariate manufacturing process

With modern data-acquisition equipment and on-line computers used during production, it is now common to monitor several correlated quality characteristics simultaneously in multivariate processes. Multivariate control charts (MCC) are important tools for monitoring multivariate processes. One difficulty encountered with multivariate control charts is the identification of the variable or group of variables that cause an out-of-control signal. Expert knowledge either in combination with wrapper-based supervised classifier or a pre-filter with wrapper are the standard approaches to detect the sources of out-of-control signal. However gathering expert knowledge in source identification is costly and may introduce human error. Individual univariate control charts (UCC) and decomposition of T²$T^2$ statistics are also used in many cases simultaneously to identify the sources, but these either ignore the correlations between the sources or may take more time with the increase of dimensions. The aim of this paper is to develop a source identification approach that does not need any expert-knowledge and can detect out-of-control signal in less computational complexity. We propose, a hybrid wrapper–filter based source identification approach that hybridizes a Mutual Information (MI) based Maximum Relevance (MR) filter ranking heuristic with an Artificial Neural Network (ANN) based wrapper. The Artificial Neural Network Input Gain Measurement Approximation (ANNIGMA) has been combined with MR (MR-ANNIGMA) to utilize the knowledge about the intrinsic pattern of the quality characteristics computed by the filter for directing the wrapper search process. To compute optimal ANNIGMA score, we also propose a Global MR-ANNIGMA using non-functional relationship between variables which is independent of the derivative of the objective function and has a potential to overcome the local optimization problem of ANN training. The novelty of the proposed approaches is that they combine the advantages of both filter and wrapper approaches and do not require any expert knowledge about the sources of the out-of-control signals. Heuristic score based subset generation process also reduces the search space into polynomial growth which in turns reduces computational time. The proposed approaches were tested by exhaustive experiments using both simulated and real manufacturing data and compared to existing methods including independent filter, wrapper and Multivariate EWMA (MEWMA) methods. The results indicate that the proposed approaches can identify the sources of out-of-control signals more accurately than existing approaches.     

Prediction of bond ratings using statistical and neural networks techniques

Quantitative models have been developed to predict bond ratings of firms in the Indian manufacturing sector, using financial leverage, profitability, asset management ability, stability and market sensitivity of the firm, which totally involved 16 variables. These 16 independent variables are first reduced to seven orthogonal variables using principal component analysis. Then these variables are used to build three types of models, namely Multiple Discriminant Analysis (MDA), Multinomial Logistic Regression (MLR) and Artificial Neural Networks (ANN). Based on both in-sample classification and out-sample validation it is found that both MLR and ANN models are superior to MDA, with little difference in performance between themselves. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A unified framework for testing linear‐invariant properties

In the study of property testing, a particularly important role has been played by linear invariant properties, i.e., properties of Boolean functions on the hypercube which are closed under linear transformations of the domain. Examples of such properties include linearity, Reed‐Muller codes, and Fourier sparsity. In this work, we describe a framework that can lead to a unified analysis of the testability of all linear‐invariant properties, drawing on techniques from additive combinatorics and from graph theory. Our main contributions here are the following:

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多风险因素的投标报价决策方法

本文讨论工程项目投标报价的多风险因素层次模型，系统地介绍了90年代以来发展出的多风险因素条件下投标报价的5种主要决策方法，即层次分析法（AHP）、人工神经网络（ANN）、模糊评价法（Fuzzy）、专家系统（ES）和基于事例推理（CBR）。本文也对中国在该领域的研究现状作一个简单的评述。     

TRANSFORM-ANN for online optimization of complex industrial processes: Casting process as case study

Artificial Neural Networks (ANNs) are well known for their credible ability to capture non-linear trends in scientific data. However, the heuristic nature of estimation of parameters associated with ANNs has prevented their evolution into efficient surrogate models. Further, the dearth of optimal training size estimation algorithms for the data greedy ANNs resulted in their overfitting. Therefore, through this work, we aim to contribute a novel ANN building algorithm called TRANSFORM aimed at simultaneous and optimal estimation of ANN architecture, training size and transfer function. TRANSFORM is integrated with three standalone Sobol sampling based training size determination algorithms which incorporate the concepts of hypercube sampling and optimal space filling. TRANSFORM was used to construct ANN surrogates for a highly non-linear industrially validated continuous casting model from steel plant. Multiobjective optimization of casting model to ensure maximum productivity, maximum energy saving and minimum operational cost was performed by ANN assisted Non-dominated Sorting Genetic Algorithms (NSGA-II). The surrogate assisted optimization was found to be 13 times faster than conventional optimization, leading to its online implementation. Simple operator's rules were deciphered from the optimal solutions using Pareto front characterization and K-means clustering for optimal functioning of casting plant. Comprehensive studies on (a) computational time comparisons between proposed training size estimation algorithms and (b) predictability comparisons between constructed ANNs and state of art statistical models, Kriging Interpolators adds to the other highlights of this work. TRANSFORM takes physics based model as the only input and provides parsimonious ANNs as outputs, making it generic across all scientific domains.     

Low‐density barriers for controlling plant crowd diseases: How far and fast can pathogens spread?

We explore numerically the possibility of controlling the spread of plant diseases characterized by relatively low dispersal (crowd diseases) through the introduction of a spatial barrier with low density of susceptible hosts. We use the diffusion approximation to Kendall's spatially extended version of the Kermack–McKendrick epidemic model and illustrate our findings within the context of a representative viral disease that affects cocoa trees. RECOMMENDATIONS FOR MANAGERS:

• Our numerical results suggest that using low‐density barriers of hosts in crowd plant diseases might be an effective way of halting the spatial dispersal of pathogens. The introduction of these barriers may reduce the economic impact when compared with other methods of controlling the disease spread.
• Before using the model to approximate suitable sizes of barriers, it is necessary to execute an exhaustive assessment of the model appropriateness for any particular disease under consideration.
• Our results suggest that to improve the efficiency of low‐density barriers it is important to explore their use in combination of current alternative control methods.

     

An empirical comparison of conventional techniques,neural networks and the three stage hybrid Adaptive Neuro Fuzzy Inference System (ANFIS) model for credit scoring analysis: The case of Turkish credit card data

The number of Non-Performing Loans has increased in recent years, paralleling the current financial crisis, thus increasing the importance of credit scoring models. This study proposes a three stage hybrid Adaptive Neuro Fuzzy Inference System credit scoring model, which is based on statistical techniques and Neuro Fuzzy. The proposed model’s performance was compared with conventional and commonly utilized models. The credit scoring models are tested using a 10-fold cross-validation process with the credit card data of an international bank operating in Turkey. Results demonstrate that the proposed model consistently performs better than the Linear Discriminant Analysis, Logistic Regression Analysis, and Artificial Neural Network (ANN) approaches, in terms of average correct classification rate and estimated misclassification cost. As with ANN, the proposed model has learning ability; unlike ANN, the model does not stay in a black box. In the proposed model, the interpretation of independent variables may provide valuable information for bankers and consumers, especially in the explanation of why credit applications are rejected.     

The lotto numbers L(n,3,p,2)

An (n,k,p,t)‐lotto design is an n‐set N and a set of k‐subsets of N (called blocks) such that for each p‐subset P of N, there is a block for which . The lotto number L(n,k,p,t) is the smallest number of blocks in an (n,k,p,t)‐lotto design. The numbers C(n,k,t) = L(n,k,t,t) are called covering numbers. It is easy to show that, for n ≥ k(p ? 1), For k = 3, we prove that equality holds if one of the following holds:

• (i) n is large, in particular
• (ii)
• (iii) 2 ≤ p ≤ 6.

© 2006 Wiley Periodicals, Inc. J Combin Designs 14: 333–350, 2006     

Two‐Timing Hypothesis,Distinguished Limits,Drifts, and Pseudo‐Diffusion for Oscillating Flows

The aim of this paper is: using the two‐timing method to study and classify the multiplicity of distinguished limits and asymptotic solutions for the advection equation with a general oscillating velocity field. Our results are:

• (i) the dimensionless advection equation that contains two independent small parameters, which represent the ratio of two characteristic time‐scales and the spatial amplitude of oscillations; the related scaling of the variables and parameters uses the Strouhal number;
• (ii) an infinite sequence of distinguished limits has been identified; this sequence corresponds to the successive degenerations of a drift velocity;
• (iii) we have derived the averaged equations and the oscillatory equations for the first four distinguished limits; derivations are performed up to the fourth orders in small parameters;
• (v) we have shown, that each distinguished limit generates an infinite number of parametric solutions; these solutions differ from each other by the slow time‐scale and the amplitude of the prescribed velocity;
• (vi) we have discovered the inevitable presence of pseudo‐diffusion terms in the averaged equations, pseudo‐diffusion appears as a Lie derivative of the averaged tensor of quadratic displacements; we have analyzed the matrix of pseudo‐diffusion coefficients and have established its degenerated form and hyperbolic character; however, for one‐dimensional cases, the pseudo‐diffusion can appear as ordinary diffusion;
• (vii) the averaged equations for four different types of oscillating velocity fields have been considered as the examples of different drifts and pseudo‐diffusion;
• (viii) our main methodological result is the introduction of a logical order into the area and classification of an infinite number of asymptotic solutions; we hope that it can help in the study of the similar problems for more complex systems;
• (ix) our study can be used as a test for the validity of the two‐timing hypothesis, because in our calculations we do not employ any additional assumptions.

     

A 2-component Camassa-Holm Equation,Euler-Bernoulli Beam Problem,and Noncommutative Continued Fractions

A new approach to the Euler-Bernoulli beam based on an inhomogeneous matrix string problem is presented. Three ramifications of the approach are developed:

1. motivated by an analogy with the Camassa-Holm equation a class of isospectral deformations of the beam problem is formulated;
2. a reformulation of the matrix string problem in terms of a certain compact operator is used to obtain basic spectral properties of the inhomogeneous matrix string problem with Dirichlet boundary conditions;
3. the inverse problem is solved for the special case of a discrete Euler-Bernoulli beam. The solution involves a noncommutative generalization of Stieltjes’ continued fractions, leading to the inverse formulas expressed in terms of ratios of Hankel-like determinants.

© 2022 Courant Institute of Mathematics and Wiley Periodicals LLC.     

A new model for automatic normalization of multitemporal satellite images using Artificial Neural Network and mathematical methods

Relative Radiometric Normalization is often required in remote sensing image analyses particularly in the land cover change detection process. Normalization process minimizes the radiometric differences between two images caused by inequalities in the acquisition conditions rather than changes in surface reflectance. A wide range of RRN methods have been developed to adjust linear models. This paper proposes an automated Relative Radiometric Normalization (RRN) method to adjust a non-linear model based on an Artificial Neural Network (ANN) and unchanged pixels. The proposed method includes the following stages: (1) automatic detection of unchanged pixels based on a new idea that uses CVA (Change Vector Análysis) method, PCA (Principal Component Analysis) transformation and K-means clustering technique, (2) evaluation of different architectures of perceptron neural networks to find the best architecture for this specific task and (3) use of the aforementioned network for normalizing the subject image. The method has been implemented on two images taken by the TM sensor. Experimental results confirm the effectiveness of the presented technique in the automatic detection of unchanged pixels and minimizing imaging condition effects (i.e., atmosphere and other effective parameters).     

Dynamical behavior of fractional‐order energy‐saving and emission‐reduction system and its discretization

This paper attempts to explore dynamical behavior and mathematical properties of the three‐dimensional fractional‐order energy‐saving and emission‐reduction system. Theoretically, the conditions of local stability of fractional‐order system's equilibrium points are obtained. Numerical investigations on the dynamics of this system are carried out, and the existence of the asymptotically stable attractor is found. Combined with the fractional‐order subsystem, we discuss the relationship between energy‐saving and emission‐reduction and economic growth, and carbon emissions and economic growth. Furthermore, we discretize the fractional‐order system and give necessary and sufficient conditions of its stabilization. It is shown that the stability of the discretization system is impacted by the system's fractional parameter. Numerical simulations show the richer dynamical behavior of the fractional‐order system and verify the theoretical results. Recommendations for Resource Managers

• The impact of carbon emissions on economic growth is one of the main reasons for energy‐saving and emission‐reduction.
• Control measures on people's low‐carbon life through government intervention are required to protect the natural environment.
• New energy‐saving and emission‐reduction technologies should be implemented to achieve sustainable social and economic development.

     

Packing k‐edge trees in graphs of restricted vertex degrees

Let denote the set of graphs with each vertex of degree at least r and at most s, v(G) the number of vertices, and τ_k (G) the maximum number of disjoint k‐edge trees in G. In this paper we show that

• (a1) if G ∈ and s ≥ 4, then τ₂(G) ≥ v(G)/(s + 1),
• (a2) if G ∈ and G has no 5‐vertex components, then τ₂(G) ≥ v(G)4,
• (a3) if G ∈ and G has no k‐vertex component, where k ≥ 2 and s ≥ 3, then τ_k(G) ≥ (v(G) ‐k)/(sk ‐ k + 1), and
• (a4) the above bounds are attained for infinitely many connected graphs.

Our proofs provide polynomial time algorithms for finding the corresponding packings in a graph. © 2007 Wiley Periodicals, Inc. J Graph Theory 55: 306–324, 2007     

Novel method of virtual embryogenesis for structuring Artificial Neural Network controllers

The organization of an Artificial Neural Network (ANN; e.g. the organization in layers, the number of cells per layer and the degree of connectivity between the cells) has a big influence on its abilities (e.g. learning ability). In this article, we present a novel method to organize the nodes and links of an ANN in a biologically motivated manner using virtual embryogenesis (VE). The VE mimics processes observable in biology, like interaction of cells via chemical substances or tissue differentiation. In our system, a virtual embryo consists of individual cells controlled by a genome. These cells can develop to nodes in the ANN during the embryogenetic process. The embryo is implemented as a spatially and temporally discrete multi-agent model. The cells in our model interact with each other via virtual physics and virtual chemistry. With the work at hand, we show that patterns developing in VE are comparable to patterns found during natural embryogenesis. We plan to combine VE with Evolutionary Algorithms to optimize the genome of the embryo. We expect the described model of VE (in combination with Evolutionary Algorithms) to lead to novel, evolutionary shaped net structures of ANNs.