The Problem of Constructing the GMDH Neural Networks with Active Neurons

Characteristics of the existing neural networks of GMDH with active neurons are given and their main advantages and disadvantages are analyzed. An approach to increasing the efficiency of inductive construction of complex system models from statistical data based on the creation of a new class of GMDH neural networks with active neurons using methods of computational intelligence is proposed.

Educating for “Buoyancy”

The future of education matters to all of us. This chapter presents a theoretical-inductive construction of the future of education, inspired by the advancements envisaged in the Fourth Industrial Revolution (also abbreviated to Industry 4.0 or IR4.0). Recent developments in the technological field make it imperative that university syllabi foster and grow technological and non-cognitive soft skills in tandem. The latter—socio-emotional skills—are considered crucial skills that endow “buoyancy” and resilience to the workforce. Empathy, cultural sensitivity, and tolerance are the key professional skills that should be nurtured among the upcoming generation of digital natives. The chapter builds on a previous publication and aims at advancing concrete proposals for the future of university education.

Symbol Separation in Double Occurrence Words

A double occurrence word (DOW) is a word in which every symbol appears exactly twice. We define the symbol separation of a DOW [Formula: see text] to be the number of letters between the two copies of a symbol, and the separation of [Formula: see text] to be the sum of separations over all symbols in [Formula: see text]. We then analyze relationship among size, reducibility and separation of DOWs. Specifically, we provide tight bounds of separations of DOWs with a given size and characterize the words that attain those bounds. We show that all separation numbers within the bounds can be realized. We present recursive formulas for counting the numbers of DOWs with a given separation under various restrictions, such as the number of irreducible factors. These formulas can be obtained by inductive construction of all DOWs with the given separation.

Location-scale matching for approximate quasi-order sampling

Quasi-orders are reflexive and transitive binary relations and have many applications. Examples are the dependencies of mastery among the problems of a psychological test, or methods such as item tree or Boolean analysis that mine for quasi-orders in empirical data. Data mining techniques are typically tested based on simulation studies with unbiased samples of randomly generated quasi-orders. In this paper, we develop techniques for the approximately representative sampling of quasi-orders. Polynomial regression curves are fitted for the mean and standard deviation of quasi-order size as a function of item number. The resulting regression graphs are seen to be quadratic and linear functions, respectively. The extrapolated values for the mean and standard deviation are used to propose two quasi-order sampling techniques. The discrete method matches these location and scale measures with a transformed discrete distribution directly obtained from the sample. The continuous method uses the normal density function with matched expectation and variance. The quasi-orders are constructed according to the biased randomized doubly inductive construction, however they are resampled to become approximately representative following the matched discrete and continuous distributions. In simulations, we investigate the usefulness of these methods. The location-scale matching approach can cope with very large item sets. Close to representative samples of random quasi-orders are constructed for item numbers up to n = 400.