Stefania Tomasiello

Numerical solutions of the Burgers-Huxley equation by the IDQ method

In this paper, the Burgers–Huxley equation has been solved by a generalized version of the Iterative Differential Quadrature (IDQ) method for the first time. The IDQ method is a method based on the quadrature rules. It has been proposed by the author applying to a certain class of non-linear problems. Stability and error analysis are performed, showing the efficiency of the method. Besides, an error bound is tried. In the discussion about the numerical examples, the generalized Burgers–Huxley equation is involved too.

Numerical stability of DQ solutions of wave problems

In this paper, the solution of one-dimensional (1D) wave problems, by means of the Iterative Differential Quadrature method is discussed in terms of stability and accuracy. The 1D-wave equation with different boundary and initial conditions is considered. The time advancing scheme is here presented in a form, particularly suitable to support the discussion about stability both by the matrix method and by the energy method. The stability analysis, performed by means of these two methods, confirms the conditionally stable nature of the method. The accuracy of the solutions is discussed too.

Using fuzzy transform in multi-agent based monitoring of smart grids

In this paper, we discuss the main scientific aspects of a Multi-Agent System (MAS), which was designed for monitoring Smart Grids (SGs) with assessment of optimal settings obtained through approximate Optimal Power Flow (OPF) solutions. The consideration behind the approach is that large historical operation dataset are usually available in SGs and employed to extract useful information; besides, such datasets are also expected to grow over and over because of the pervasive deployment of SGs sensors. So we use Fuzzy transform in order to respond to two issues, that is first to reduce the storage need, by compressing the historical datasets, and second to provide agents with fast and reliable actions to get accurate OPF solutions, by a similarity search throughout the compressed historical dataset. A formal discussion on properties involved by the application of the method is afforded. Numerical results, obtained both on small and large-scale power systems, support the theoretical achievements, by showing the effectiveness of the proposed methodology in the task of solving realistic smart grid operation problems.

Cubic B-spline fuzzy transforms for an efficient and secure compression in wireless sensor networks

Joining data compression and encryption is a way to keep secure data, as discussed by the current literature. While data compression responds to the great demand on data storage and transmission techniques, the encryption allows to handle some important parameters in a secure way. In wireless sensor networks the usual transform-based compression is the Discrete Wavelet Transform. In a previous paper we showed the good perfomance of the fuzzy transform (or F-trasform for short) based compression with respect to it. In this work, we propose a cubic B-spline F-transform in order to have a higher accuracy, even when data are not correlated, and a lower computational cost. Besides, in order to show the efficiency of the proposed approach, we compare it with the most recent lossless compression scheme in the field. We discuss these issues formally and numerically by using publicly available real-world data sets. The parameters required to decompress data are encrypted by means of a suitable existing encryption algorithm. We show that even if an illegal user had access to one of these parameters, our scheme would be still secure.

Some remarks on a new DQ-based method for solving a class of Volterra integro-differential equations

In this paper a numerical Picard-like method, which combines successive approximations with integral and differential quadrature, is considered to solve some Volterra integro-differential equations where rational functions are involved. Under certain conditions, the method provides solutions in explicit form, without any recursive computation, and for some cases it is possible to give a formula to compute the related error. Several numerical examples are proposed to illustrate the behaviour of the method, by comparing it, where possible, with some existing methods.

Solving 2D-wave problems by the iterative differential quadrature method

In this paper, the numerical stability of an iterative method based on differential quadrature (DQ) rules when applied to solve a two-dimensional (2D) wave problem is discussed. The physical model of a vibrating membrane, with different initial conditions, is considered. The stability analysis is performed by the matrix method generalized for a 2D space-time domain. This method was presented few years ago by the same author as an analytical support to check the stability of the iterative differential quadrature method in 1D space-time domains. The stability analysis confirms here the conditionally stable nature of the method. The accuracy of the solution is discussed too.

A note on three numerical procedures to solve Volterra integro-differential equations in structural analysis

In this paper, three numerical methods to solve Volterra integro-differential equations containing rational functions are discussed. The first one is the Differential Quadrature Method and, to the best knowledge of the author, it has never been applied to this kind of problem; the second one is a new version of the Iterative Differential Quadrature method, a method proposed by the author some years ago to solve problems in space-time domains, revised herein for the single space variable problem; the third one is a numerical Picard-like method, proposed herein to combine successive approximations with numerical integration. Stability and convergence of the second and the third method are discussed. The three methods have been applied to solve a real world problem in the field of the structural engineering and the numerical results compared.

Self-regulated learning with approximate reasoning and situation awareness

We present a decision support system for seamless and self-regulating learning. The decision support system presents a degree of novelty in supporting learners since it allows to: (1) understand the concepts that a learner may have acquired during her/his daily life activities, and (2) make the learner aware of these concepts and enforcing learning paths. Two key ideas are behind our results. The first idea relates to the identification of classes of indiscernible competences, and comes from the intuition that some real-world activities can lead to the acquisition of sets of competences (not always easy to discriminate) which can be considered as good approximations of competences related to a specific concept. Classes of indiscernible competences are building blocks that our decision support system uses to understand, with a certain degree of approximation, the concepts that a learner may have acquired, and this is an added value with regard to the self-awareness of a learner. The second idea is to allow our decision support system to identify incremental learning situations, which are situations in which a learning path is enforced or modified by the recognition that some concepts may have been learned, also during the execution of daily life activities. The decision support system grounds on three-way decisions and situation awareness. An evaluation of the system following the SAGAT approach has been done and reported in the paper.

An extended functional network model and its application for a gas sensing system

Functional networks (FNs) are a promising numerical scheme that produces accurate solutions for several problems in science and engineering with less computational effort than other conventional numerical techniques such as neural networks. By using domain knowledge in addition to data knowledge, functional networks can be regarded as a generalization of neural networks: they allow to design arbitrary functional models without neglecting possible functional constraints involved by the model. The computational efficiency of functional networks can be improved by combining this scheme with finite differences when highly oscillating systems have to be considered. The main focus of this paper is on the possible questions arising from the application of this combined scheme to an identification problem when non-smooth functions are involved and noisy data are possible. These issues are not covered by the current literature. An extended version, based on a piecewise approach, and a stability criterion are proposed and applied to the quantitative identification problem in a gas sensing system in its transient state. Numerical simulations show that our scheme allows good accuracy, avoiding the error accumulation and the sensitivity to noisy data by means of the stability criterion.

Granularity into Functional Networks

In the last years, many papers on Granular Neural Networks appeared, aiming at achieving a higher degree of transparency in the network architecture and a better understanding of the involved steps. This paper is a first attempt to emphasize and exploit the notion of granularity into Functional Networks. Functional Networks are a relatively recent alternative to Neural Networks and they have been proved to ensure better performances. We propose a revised scheme from a granular perspective with a different learning algorithm with respect to the original one. An application example shows the good performance of this new scheme.