Fundamenta Informaticae - Volume 146, issue 3

Authors: Arqub, Omar Abu

Article Type: Research Article

Abstract: This paper presents novel reproducing kernel algorithm for obtaining the numerical solutions of differential algebraic systems with nonclassical boundary conditions for ordinary differential equations. The representation of the exact and the numerical solutions is given in the W [0, 1] and H [0, 1] inner product spaces. The computation of the required grid points is relying on the Rt (s ) and rt (s ) reproducing kernel functions. An efficient construction is given to obtain the numerical solutions for the systems together with an existence proof of the exact solutions based upon the reproducing …kernel theory. Numerical solutions of such nonclassical systems are acquired by interrupting the η -term of the exact solutions. In this approach, numerical examples were analyzed to illustrate the design procedure and confirm the performance of the proposed algorithm in the form of tabulate data and numerical comparisons. Finally, the utilized results show the significant improvement of the algorithm while saving the convergence accuracy and time. Show more

Keywords: Differential algebraic systems, Nonclassical boundary conditions, Reproducing kernel theory, Fourier series expansion

DOI: 10.3233/FI-2016-1384

Citation: Fundamenta Informaticae, vol. 146, no. 3, pp. 231-254, 2016

Authors: Kheirfam, Behrouz

Article Type: Research Article

Abstract: In this paper, we propose an arc-search infeasible interior point algorithm for symmetric optimization using the negative infinity neighborhood of the central path. The algorithm searches the optimizers along the ellipses that approximate the entire central path. The convergence of the algorithm is shown for the set of commutative scaling class, which includes some of the most interesting choice of scalings such as xs , sx and the Nesterov-Todd scalings.

Keywords: Symmetric optimization, arc-search directions, infeasible interior-point method, the negative infinity neighborhood, polynomial complexity

DOI: 10.3233/FI-2016-1385

Citation: Fundamenta Informaticae, vol. 146, no. 3, pp. 255-269, 2016

Authors: Mandal, Bimal | Stănică, Pantelimon | Gangopadhyay, Sugata | Pasalic, Enes

Article Type: Research Article

Abstract: Two (so-called 𝒞, D) classes of permutation-based bent Boolean functions were introduced by Carlet [4] two decades ago, but without specifying some explicit construction methods for their construction (apart from the subclass 𝒟0 ). In this article, we look in more detail at the 𝒞 class, and derive some existence and nonexistence results concerning the bent functions in the 𝒞 class for many of the known classes of permutations over 𝔽2n . Most importantly, the existence results induce generic methods of constructing bent functions in class 𝒞 which possibly do not belong to the completed Maiorana-McFarland class. The …question whether the specific permutations and related subspaces we identify in this article indeed give bent functions outside the completed Maiorana-McFarland class remains open. Show more

Keywords: Boolean functions, bent functions, permutation polynomials, MSC 2010: 05A05, 06E30, 11T55, 94C10

DOI: 10.3233/FI-2016-1386

Citation: Fundamenta Informaticae, vol. 146, no. 3, pp. 271-292, 2016

Authors: Qi, Ji | Ohsawa, Yukio

Article Type: Research Article

Abstract: Previous seriation algorithms are confronted with a balance problem. Some approaches provide permutations with perfect wholeness, where matrix rows/columns are associated with increasing or decreasing gradient. However, this smooth permutation may lead to the blurred representation of the data structure, such as clustering structures and detailed structures inside clusters. Some other approaches indicate these structures well by tighter aggregating similar rows/columns, but this aggregation is alway at the cost of losing necessary coherence of the matrix rows/columns. In this paper, we introduce a seriation algorithm that aims at balancing the smoothness of the permutation and the clarity of the matrix …structure. The permutation algorithm greedily and recursively replaces high-dissimilar object pairs with low-dissimilar ones, and the optimization algorithm searches the global optimizing solution by applying the simulated annealing algorithm. A comparison study shows both empirical and statistical evidence that Recut can provide more accurate and visually appropriate permutation by considering the balance problem. Show more

Keywords: Seriation, Matrix Reordering, Matrix Visualization, Data Visualization, Data Analysis

DOI: 10.3233/FI-2016-1387

Citation: Fundamenta Informaticae, vol. 146, no. 3, pp. 293-304, 2016

Authors: Teh, Wen Chean

Article Type: Research Article

Abstract: Since the introduction of the Parikh matrix mapping, its injectivity problem is on top of the list of open problems in this topic. In 2010 Salomaa provided a solution for the ternary alphabet in terms of a Thue system with an additional feature called counter. This paper proposes the notion of a Parikh rewriting system as a generalization and systematization of Salomaa’s result. It will be shown that every Parikh rewriting system induces a Thue system without counters that serves as a feasible solution to the injectivity problem.

Keywords: Parikh matrix, subword, injectivity problem, Parikh rewriting system, M-equivalence

DOI: 10.3233/FI-2016-1388

Citation: Fundamenta Informaticae, vol. 146, no. 3, pp. 305-320, 2016

Authors: Wedley, William C. | Choo, Eng U. | Wijnmalen, Diederik J. D.

Article Type: Research Article

Abstract: The true pairwise comparison matrix is simulated and used as a benchmark for evaluating different priority vectors derived from a decision maker’s pairwise comparison matrix. The accuracy of the decision maker’s comparisons are progressively improved until they emulate the true values. Using four different distance measures to evaluate five different methods of deriving priorities, the geometric mean, normalized column mean, and right eigenvector techniques are more accurate. All methods exhibit rare reversals in accuracy as the comparison values approach the true values.

Keywords: Ratio comparison matrices, accuracy, priority vectors

DOI: 10.3233/FI-2016-1389

Citation: Fundamenta Informaticae, vol. 146, no. 3, pp. 321-338, 2016