On dispersion curve coloring for mechanical metafilters.

This paper formalizes smooth curve coloring (i.e., curve identification) in the presence of curve intersections as an optimization problem, and investigates theoretically properties of its optimal solution. Moreover, it presents a novel automatic technique for solving such a problem. Formally, the proposed algorithm aims at minimizing the summation of the total variations over a given interval of the first derivatives of all the labeled curves, written as functions of a scalar parameter. The algorithm is based on a first-order finite difference approximation of the curves and a sequence of prediction/correction steps. At each step, the predicted points are attributed to the subsequently observed points of the curves by solving an Euclidean bipartite matching subproblem. A comparison with a more computationally expensive dynamic programming technique is presented. The proposed algorithm is applied with success to elastic periodic metamaterials for the realization of high-performance mechanical metafilters. Its output is shown to be in excellent agreement with desirable smoothness and periodicity properties of the metafilter dispersion curves. Possible developments, including those based on machine-learning techniques, are pointed out.

A machine learning approach to economic complexity based on matrix completion.

This work applies Matrix Completion (MC) - a class of machine-learning methods commonly used in recommendation systems - to analyze economic complexity. In this paper MC is applied to reconstruct the Revealed Comparative Advantage (RCA) matrix, whose elements express the relative advantage of countries in given classes of products, as evidenced by yearly trade flows. A high-accuracy binary classifier is derived from the MC application to discriminate between elements of the RCA matrix that are, respectively, higher/lower than one. We introduce a novel Matrix cOmpletion iNdex of Economic complexitY (MONEY) based on MC and related to the degree of predictability of the RCA entries of different countries (the lower the predictability, the higher the complexity). Differently from previously-developed economic complexity indices, MONEY takes into account several singular vectors of the matrix reconstructed by MC. In contrast, other indices are based only on one/two eigenvectors of a suitable symmetric matrix derived from the RCA matrix. Finally, MC is compared with state-of-the-art economic complexity indices, showing that the MC-based classifier achieves better performance than previous methods based on the application of machine learning to economic complexity.