The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe­ matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com­ puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.

The two-volume set CCIS 1869 and 1870 constitutes the refereed proceedings of the 4th International Conference on Neural Computing for Advanced Applications, NCAA 2023, held in Hefei, China, in July 2023.The 83 full papers and 1 short paper presented in these proceedings were carefully reviewed and selected from 211 submissions. The papers have been organized in the following topical sections: Neural network (NN) theory, NN-based control systems, neuro-system integration and engineering applications; Machine learning and deep learning for data mining and data-driven applications; Computational intelligence, nature-inspired optimizers, and their engineering applications; Deep learning-driven pattern recognition, computer vision and its industrial applications; Natural language processing, knowledge graphs, recommender systems, and their applications; Neural computing-based fault diagnosis and forecasting, prognostic management, and cyber-physical system security; Sequence learning for spreading dynamics, forecasting, and intelligent techniques against epidemic spreading (2); Applications of Data Mining, Machine Learning and Neural Computing in Language Studies; Computational intelligent Fault Diagnosis and Fault-Tolerant Control, and Their Engineering Applications; and Other Neural computing-related topics.