Kennedy E. Ehimwenma

Kennedy E. Ehimwenma, Hongyu Zhou, Junfeng Wang et al.

Double-black (DB) nodes have no place in red-black (RB) trees. So when DB nodes are formed, they are immediately removed. The removal of DB nodes that cause rotation and recoloring of other connected nodes poses greater challenges in the teaching and learning of RB trees. To ease this difficulty, this paper extends our previous work on the symbolic arithmetic algebraic (SA) method for removing DB nodes. The SA operations that are given as, Red + Black = Black; Black - Black = Red; Black + Black = DB; and DB - Black = Black removes DB nodes and rebalances black heights in RB trees. By extension, this paper projects three SA mathematical equations, namely, general symbolic arithmetic rule; partial symbolic arithmetic rule1; and partial symbolic arithmetic rule2. The removal of a DB node ultimately affects black heights in RB trees. To balance black heights using the SA equations, all the RB tree cases, namely, LR, RL, LL, and RR, were considered in this work; and the position of the nodes connected directly or indirectly to the DB node was also tested. In this study, to balance a RB tree, the issues considered w.r.t. the different cases of the RB tree were i) whether a DB node has an inner, outer, or both inner and outer black nephews; or ii) whether a DB node has an inner, outer or both inner and outer red nephews. The nephews r and x in this work are the children of the sibling s to a DB, and further up the tree, the parent p of a DB is their grandparent g. Thus, r and x have indirect relationships to a DB at the point of formation of the DB node. The novelty of the SA equations is in their effectiveness in the removal of DB that involves rotation of nodes as well as the recoloring of nodes along any simple path so as to balance black heights in a tree.

Kennedy Efosa Ehimwenma, Safiya Al Sharji, Maruf Raheem

The probability of an event is in the range of [0, 1]. In a sample space S, the value of probability determines whether an outcome is true or false. The probability of an event Pr(A) that will never occur = 0. The probability of the event Pr(B) that will certainly occur = 1. This makes both events A and B thus a certainty. Furthermore, the sum of probabilities Pr(E1) + Pr(E2) + ... + Pr(En) of a finite set of events in a given sample space S = 1. Conversely, the difference of the sum of two probabilities that will certainly occur is 0. Firstly, this paper discusses Bayes' theorem, then complement of probability and the difference of probability for occurrences of learning-events, before applying these in the prediction of learning objects in student learning. Given the sum total of 1; to make recommendation for student learning, this paper submits that the difference of argMaxPr(S) and probability of student-performance quantifies the weight of learning objects for students. Using a dataset of skill-set, the computational procedure demonstrates: i) the probability of skill-set events that has occurred that would lead to higher level learning; ii) the probability of the events that has not occurred that requires subject-matter relearning; iii) accuracy of decision tree in the prediction of student performance into class labels; and iv) information entropy about skill-set data and its implication on student cognitive performance and recommendation of learning [1].

Kennedy E. Ehimwenma, Sujatha Krishnamoorthy

Agent unified modeling languages (AUML) are agent-oriented approaches that supports the specification, design, visualization and documentation of an agent-based system. This paper presents the use of Prometheus AUML approach for the modeling of a Pre-assessment System of five interactive agents. The Pre-assessment System, as previously reported, is a multi-agent based e-learning system that is developed to support the assessment of prior learning skills in students so as to classify their skills and make recommendation for their learning. This paper discusses the detailed design approach of the system in a step-by-step manner; and domain knowledge abstraction and organization in the system. In addition, the analysis of the data collated and models of prediction for future pre-assessment results are also presented.

Kennedy E. Ehimwenma, Martin Beer, Paul Crowther

Student modelling and agent classified rules learning as applied in the development of the intelligent Preassessment System has been presented in [10],[11]. In this paper, we now demystify the theory behind the development of the pre-assessment system followed by some computational experimentation and graph visualisation of the agent classified rules learning algorithm in the estimation and prediction of classified rules. In addition, we present some preliminary results of the pre-assessment system evaluation. From the results, it is gathered that the system has performed according to its design specification.

Kennedy E. Ehimwenma, Paul Crowther, Martin Beer

Objects or structures that are regular take uniform dimensions. Based on the concepts of regular models, our previous research work has developed a system of a regular ontology that models learning structures in a multiagent system for uniform pre-assessments in a learning environment. This regular ontology has led to the modelling of a classified rules learning algorithm that predicts the actual number of rules needed for inductive learning processes and decision making in a multiagent system. But not all processes or models are regular. Thus this paper presents a system of polynomial equation that can estimate and predict the required number of rules of a non-regular ontology model given some defined parameters.