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Communication complexity is the mathematical study of scenarios where several parties need to communicate to achieve a common goal, a situation that naturally appears during computation. This introduction presents the most recent developments in an accessible form, providing the language to unify several disjoint research subareas. Written as a guide for a graduate course on communication complexity, it will interest a broad audience in computer science, from advanced undergraduates to researchers in areas ranging from theory to algorithm design to distributed computing. The first part presents basic theory in a clear and illustrative way, offering beginners an entry into the field. The second part describes applications including circuit complexity, proof complexity, streaming algorithms, extension complexity of polytopes, and distributed computing. Proofs throughout the text use ideas from a wide range of mathematics, including geometry, algebra, and probability. Each chapter contains numerous examples, figures, and exercises to aid understanding.
This research intends to investigate a new hybrid artificial intelligence (AI) technique compared to some common CPT methods in estimating axial ultimate pile bearing capacity (UPBC) using cone penetration test (CPT) data in geotechnical engineering applications. A data series of 108 samples was collected in order to develop a new hybrid structure of an adaptive neuro-fuzzy inference system (ANFIS) network, and the group method of the data handling (GMDH) type neural network was optimized by applying the particle swarm optimization (PSO) algorithm over the hybrid ANFIS-GMDH topology, which leads to a new hybrid AI model called as ANFIS-GMDH-PSO. The derived database provides information related to pile load tests, in situ field CPT data, and soil–pile information for introducing the proposed hybrid neural system. The cross-section of the pile toe, average cone tip resistance along embedded pile length, and sleeve frictional resistance along the shaft had been considered as input parameters for the proposed network. The results of this research indicated that the proposed ANFIS-GMDH-PSO model predicted the UPBC with an acceptable precision compared to various CPT methods, including Schmertmann, De Kuiter & Bringen, and LPC/LPCT methods. Moreover, ANFIS-GMDH-PSO network model performance was compared to CPT-based models in terms of statistical criteria in order to achieve a best fitted model. From the statistical results, it was found that the developed ANFIS-GMDH-PSO model has achieved a higher accuracy level in terms of statistical indices compared to CPT-based empirical methods, such as Schmertmann model, De Kuiter & Beringen model, and Bustamante & Gianeselli for predicting driven pile ultimate bearing capacity.