Evolution of Structures in a University System.

      Аннотация: This book presents Markov chains as a practical tool in evaluating the structure of a multi-echelon educational system. It is a research-level book since its contents are too advanced for courses. The book is written at a graduate level for researchers in the field of manpower and educational planning. The impressive contributions are in the evaluation of career patterns, the attainability of structures, the estimation of transition probabilities and the development of continuous-time Markov chains from sparse matrices. For instance, in predicting enrolment, the school's differential variables are systematically inscribed in the estimation of transition probabilities. Moreover, the book identifies future research directions which may stimulate postgraduate research projects. The motivations for this book emanate from the unstable transition durations in the university system in Nigeria and the ill-posed problem of the discrete-time Markov chain in an attempt to recover the one-step transition matrix from the higher-order transition matrix. These twofold motivations are gaps in existing literature. This book attempts to bridge these gaps.

Ключевые слова: Admission, carrying capacity, educational system, Enrolment, Entropy, Markov Chain, Promotion, Random variable, recruitment, Shannon Entropy, Staff, stock, Structure, student, Relative structure, Stochastic Matrix, Sub-stochastic matrix, Transition Matrix, Sparse Matrix, University system, Transition Probability, wastage, Attainability, Graded system, Career pattern, Binomial logistic model, manpower system, Fractional-flow models, Maximum likelihood method, Multinomial Distribution, Transient state, Absorbing state, Fundamental matrix, Block matrix, Career length, Markov generator, Euclidean norm, Log-likelihood function, Boltzmann entropy, Empirical transition matrix, Binomial Distribution, Iteratively reweighted least squares algorithm, Gani-type model, Young/Almond-type model, Diagonal adjustment regularization method, Euler summation formula, Demotion, Information matrix, Stable growth rate, Projection model, Markov replacement process, Non-homogeneous Markov chain, Homogeneous Markov chain, Discrete-time Markov chain, Continuous-time Markov chain, Imbedded Markov chain, Absorbing Markov chain, Push flow, Closed System, Open System