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The universal unfolding of a normal form can be employed to reveal the general behaviors of a specific local bifurcation, while the computation of the normal form for high codimensional bifurcation still remains unsolved. This paper focuses on a vector field with codimension-3 triple Hopf bifurcation. Besides 1:1 internal resonance for two frequencies in semi-simple form, two cases are considered, corresponding to internal resonance and noninternal resonance between the first two frequencies and the third frequency, respectively. Based on a combination of center manifold and normal theory, all the coefficients in the normal form and the nonlinear transformation are derived explicitly in terms of the coefficients of the original vector field. Upon the recursive procedure established, a user friendly computer program can be easily developed using a symbolic computation language Maple to compute the coefficients up to an arbitrary order for a specific vector field with triple Hopf bifurcation. Furthermore, universal unfolding of the normal form is obtained, which can be used to display the topological structure in the neighborhood of bifurcation point. It is pointed out that different choices of the remaining terms in the nonlinear transformation may lead to different expressions of the normal form and the unfolding, which are qualitatively equivalent to each other. [ABSTRACT FROM AUTHOR]

In this paper, we present an Intelligent Tutoring System (ITS), for use in teaching the logic of computer programming and the programming language 'C'. The aim of the ITS is to adapt the delivered learning material and the lesson sequence to the knowledge level and learning needs of each individual student. The adaptation of the presented ITS is based on fuzzy logic and a machine learning technique. Particularly, the system uses the distance weighted k-nearest neighbor algorithm to detect the learner's knowledge level and abilities concerning computer programming during her/ his first interaction with the system. Next and during subsequent interactions of the learner with the system, fuzzy logic is used to identify the learner's current knowledge level and potential misconceptions. The system takes into consideration the knowledge dependencies that exist among the domain concepts of the learning material and, applying fuzzy rules, decides about the learning material that has to be delivered to the learner as well as the lesson sequence. The system has been fully implemented and evaluated through t-tests. The evaluation results show that the combination of machine learning (for initially identifying the student's learning abilities and needs) with fuzzy logic (for the continuous identification of the learner's current knowledge level and misconceptions) provides more personalized learning experience, promotes the active participation of students in the learning process and results in decrease in the number of dropouts. [ABSTRACT FROM AUTHOR]

In a broad spectrum, software metrics play a vital role in attribute assessment, which successively moves software projects. The metrics measure gives many crucial facets of the system, enhancing the system quality of software developed. Moreover, maintenance is the correction process that works out in the software system once the software is initially made. The noteworthy characteristic of any software is 'change,' and as a result, additional concern ought to be taken in developing software. So, the software is expected to be modified effortlessly (maintainable). Predicting software maintainability is still challenging, and accurate prediction models with low error rates are required. Since there are so many modern programming languages on the horizon. To accurately measure software maintainability, new techniques have to been introduced. This paper proposes a maintainability index (MI) by considering various software metrics by which the error gets minimized. It also intends to adopt a renowned optimization algorithm, namely Firefly (FF), for the optimum result. The proposed Base Model-FF is compared to other traditional models like BM-Differential Evolution (BM-DE), BM-Artificial Bee Colony (BM-ABC), BM-Particle Swarm Optimization (BM-PSO), and BM-Genetic Algorithm (BM- GA) in terms of performance metrics like Differential ratio, correlation coefficient, and Random Mean Square Error (RMSE). [ABSTRACT FROM AUTHOR]