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The design of echo state network (ESN) parameters relies on the selection of the maximum eigenvalue of the linearized system around zero (spectral radius). However, this procedure does not quantify in a systematic manner the performance of the ESN in terms of approximation error. This article presents a functional space approximation framework to better understand the operation of ESNs and proposes an information-theoretic metric, the average entropy of echo states, to assess the richness of the ESN dynamics. Furthermore, it provides an interpretation of the ESN dynamics rooted in system theory as families of coupled linearized systems whose poles move according to the input signal dynamics. With this interpretation, a design methodology for functional approximation is put forward where ESNs are designed with uniform pole distributions covering the frequency spectrum to abide by the richness metric, irrespective of the spectral radius. A single bias parameter at the ESN input, adapted with the modeling error, configures the ESN spectral radius to the input-output joint space. Function approximation examples compare the proposed design methodology versus the conventional design.

Background: The rapid development of the blockchain technology and its various applications has rendered it important to understand the guidelines for adopting it. Methods: The comparative analysis method is used to analyze different dimensions of the maturity model, which is mainly based on the commonly used capability maturity model. Results: The blockchain maturity model and its adoption process have been discussed and presented. Conclusions: This study serves as a guide to institutions to make blockchain adoption decisions more systematically.

This paper describes an approved algorithm for the problems of unequal circle packing -the quasi-physical quasihuman algorithm. First, the quasi-physical approach for the general packing problems is described in solving the pure problems of unequal circle packing. The method is an analogy to the physical model in which a number of smooth cylinders are packed inside a container. A quasi-human strategy is then proposed to trigger a jump for a stuck object in order to get out of local minima. Our method has been tested in numerical experiments. The computational results are presented, showing the merits of the proposed method. Our algorithm can be thought as an adoptive algorithm of the Tabu search. Ó

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