One of the most challenging problems in the optimal control theory consists of solving the nonsmooth optimal control problems where several discontinuities may be present in the control variable and derivative of the state variable. Recently some extended spectral collocation methods have been introduced for solving such problems, and a matrix of differentiation is usually used to discretize and to approximate the derivative of the state variable in the particular collocation points. In such methods, there is typically no condition for the continuity of the state variable at the switching points. In this article, we propose an efficient hp spectral collocation method for the general form of nonsmooth optimal control problems based on the operational integration matrix. The time interval of the problem is first partitioned into several variable subintervals, and the problem is then discretized by considering the Legendre-Gauss-Lobatto collocation points. Here, the switching points are unknown parameters, and having solved the final discretized problem, we achieve some approximations for the optimal solutions and the switching points. We solve some comparative numerical test problems to support of the performance of the suggested approach.
Time series forecasting, such as stock price prediction, is one of the most important complications in the financial area as data is unsteady and has noisy variables, which are affected by many factors. This study applies a hybrid method of Genetic Algorithm (GA) and Artificial Neural Network (ANN) technique to develop a method for predicting stock price and time series. In the GA method, the output values are further fed to a developed ANN algorithm to fix errors on exact point. The analysis suggests that the GA and ANN can increase the accuracy in fewer iterations. The analysis is conducted on the 200-day main index, as well as on five companies listed on the NASDAQ. By applying the proposed method to the Apple stocks dataset, based on a hybrid model of GA and Back Propagation (BP) algorithms, the proposed method reaches to 99.99% improvement in SSE and 90.66% in time improvement, in comparison to traditional methods. These results show the performances and the speed and the accuracy of the proposed approach.
Artificial Neural Network (ANN) is the primary automated AI system preferred for medical applications. Even though ANN possesses multiple advantages, the convergence of the ANN is not always guaranteed for the practical applications. This often results in the local minima problem and ultimately yields inaccurate results. This convergence problem is common among ANNs and especially in Kohonen neural networks which employ unsupervised training methodology. In this work, an Efficient Kohonen Fuzzy Neural (EKFN) network is proposed to eliminate the iteration dependent nature of the conventional system. The suitability of this hybrid automated system is illustrated in the context of pathology identification in retinal images. This disease identification system includes anatomical structure segmentation from retinal images followed by image classification. The performance measures used are accuracy, sensitivity, specificity, positive predictive value and positive likelihood ratio. Experimental results show promising possibilities for the hybrid systems in terms of performance measures.
This paper presents an efficient learning algorithm that generates radial basis function neural network with few neurons. The neural network adds neurons according to a growth criterion defined by the current output error, the current input's distance to the nearest center, and the root-mean-square output error over a sliding windows, deletes neurons by a pruning strategy based on the error reduction rates, and updates the output-layer weights with a Givens QR decomposition based on the orthogonalized least square algorithm. Simulations on two benchmark problems demonstrate that the algorithm produces smaller networks than RAN, RANEKF, and MRAN, and consumes less training time than RAN, RANEKF, MRAN, and GAP-RBF.
Support vector machine (SVM) has become one of the most popular machine-learning methods during the last years. The design of an efficient model and the proper adjustment of the SVMs parameters are integral to reducing the testing time and enhancing performance. In this paper, a new bipartite objective function consisted of the sparseness property and generalization performance is proposed. Since the proposed objective function is based on selecting fewer numbers of the support vectors, the model complexity is reduced while the performance accuracy remains at an acceptable level. Due to the model complexity reduction, the testing time is decreased and the ability of SVM in practical applications is increased Moreover, to prove the performance of the proposed objective function, a comparative study was carried out on the proposed objective function and the conventional objective function, which is only based on the generalization performance, using the Binary Genetic Algorithm (BGA) and Real-valued vectors GA (RGA). The effectiveness of the proposed cost function is demonstrated based on the results of the comparative study on four real-world datasets of UCI database.
Linear discriminant analysis (LDA) is a versatile method in all pattern recognition fields but it suffers from some limitations. In a multi-class problem, when samples of a class are far from other classes samples, it leads to bias of the whole decision boundaries of LDA in favor of the farthest class. To overcome this drawback, this study is aimed at minimizing this bias by redefining the between- and within-class scatter matrices via incorporating weight vectors derived from Fisher value of classes pairs. After projecting the input patterns into a lower-dimensional space in which the class samples are more separable, a new version of nearest neighbor (NN) method with an adaptive distance measure is employed to classify the transformed samples. To speed up the adaptive distance routine, an iterative learning algorithm that minimizes the error rate is presented. This efficient method is applied to six standard datasets driven from the UCI repository dataset and test results are evaluated from three aspects in terms of accuracy, robustness, and complexity. Results show the supremacy of the proposed two-layer classifier in comparison with the combination of different versions of LDA and NN methods from the three points of view. Moreover, the proposed classifier is assessed in the noisy environment of those datasets and the achieved results confirm the high robustness of the introduced scheme when compared to others.
An Electronic Performance Support System (EPSS) introduces challenges on contextualized and personalized information delivery. Recommender systems aim at delivering and suggesting relevant information according to users preferences, thus EPSSs could take advantage of the recommendation algorithms that have the effect of guiding users in a large space of possible options. The JUMP project (JUst-in-tiMe Performance support systém for dynamic organizations, co-funded by POR Puglia 2000-2006 - Mis. 3.13, Sostegno agli Investimenti in Ricerca Industriale, Sviluppo Precompetitivo e Trasferimento Tecnologico) aims at integrating an EPSS with a hybrid recommender system.
Collaborative and content-based filtering are the recommendation techniques most widely adopted to date. The main contribution of this paper is a content-collaborative hybrid recommender which computes similarities between users relying on their content-based profiles in which user preferences are stored, instead of comparing their rating styles. A distinctive feature of our systém is that a statistical model of the user interests is obtained by machine learning techniques integrated with linguistic knowledge contained in WordNet. This model, named ``semantic user profile'', is exploited by the hybrid recommender in the neighborhood formation process.
t is commonly known that absolute gauge integrability, or Henstock-Kurzweil (H-K) integrability implies Lebesgue integrability. In this article, we are going to present another proof of that fact which utilizes the basic definitions and properties of the Lebesgue and H-K integrals.
The main purpose of this paper is to prove that the elliptic curve $E\colon y^2=x^3+27x-62$ has only the integral points $(x, y)=(2, 0)$ and $(28844402, \pm 154914585540)$, using elementary number theory methods and some known results on quadratic and quartic Diophantine equations.
We consider the weighted space $W_1^{(2)}(\mathbb R,q)$ of Sobolev type $$ W_1^{(2)}(\mathbb R,q)=\left \{y\in A_{\rm loc}^{(1)}(\mathbb R)\colon \|y''\|_{L_1(\mathbb R)}+\|qy\|_{L_1(\mathbb R)}<\infty \right \} $$ and the equation $$ - y''(x)+q(x)y(x)=f(x),\quad x\in \mathbb R. \leqno (1) $$ Here $f\in L_1(\mathbb R)$ and $0\le q\in L_1^{\rm loc}(\mathbb R).$ \endgraf We prove the following: \item {1)} The problems of embedding $W_1^{(2)}(\mathbb R,q)\hookrightarrow L_1(\mathbb R)$ and of correct solvability of (1) in $L_1(\mathbb R) $ are equivalent; \item {2)} an embedding $W_1^{(2)}(\mathbb R,q)\hookrightarrow L_1(\mathbb R) $ exists if and only if $$\exists a>0\colon \inf _{x\in \mathbb R}\int _{x-a}^{x+a} q(t) {\rm d} t>0.$$.