Diversity of cluster size has been used as a measurement of complexity in several systems that generate a statistical distribution of clusters. Using Monte Carlo simulations, we present a statistical analysis of the cluster size diversity and the number of clusters generated on randomly occupied lattices for the Euclidean dimensions 1 to 6. A tuning effect for diversity of cluster size and critical probabilities associated with the maximum diversity and the maximum number of clusters are reported. The probability of maximum diversity is related to the percolation threshold and several scaling relations between the variables measured are reported. The statistics of cluster size diversity has important consequences in the statistical description of the Universe as a complex system.

The distribution of living languages is investigated and scaling relations are found for the diversity of languages as a function of country area and population. These results are compared with data from Ecology and from computer simulations of fragmentation dynamics where similar scalings appear. The language size distribution is also studied and shown to display two scaling regions: (i) one for the largest (in population) languages and (ii) another one for intermediate-size languages. It is then argued that these two classes of languages may have distinct growth dynamics, being distributed on sets of different fractal dimensions.

We present an algorithm to identify and count different lattice animals (LA's) in the site-percolation model. This algorithm allows a definition of clusters based on the distinction of cluster shapes, in contrast with the well-known Hoshen-Kopelman algorithm, in which the clusters are differentiated by their sizes. It consists in coding each unit cell of a cluster according to the nearest neighbors (NN) and ordering the codes in a proper sequence. In this manner, a LA is represented by a specific code sequence. In addition, with some modification the algorithm is capable of differentiating between fixed and free LA's. The enhanced Hoshen-Kopelman algorithm [J. Hoshen, M. W. Berry, and K. S. Minser, Phys. Rev. E 56, 1455 (1997)] is used to compose the set of NN code sequences of each cluster. Using Monte Carlo simulations on planar square lattices up to 2000x2000, we apply this algorithm to the percolation model. We calculate the cluster diversity and cluster entropy of the system, which leads to the determination of probabilities associated with the maximum of these functions. We show that these critical probabilities are associated with the percolation transition and with the complexity of the system.

We propose a spiking neural network (SNN) approach for radar-based hand gesture recognition (HGR), using frequency modulated continuous wave (FMCW) millimeter-wave radar. After pre-processing the range-Doppler or micro-Doppler radar signal, we use a signal-to-spike conversion scheme that encodes radar Doppler maps into spike trains. The spike trains are fed into a spiking recurrent neural network, a liquid state machine (LSM). The readout spike signal from the SNN is then used as input for different classifiers for comparison, including logistic regression, random forest, and support vector machine (SVM). Using liquid state machines of less than 1000 neurons, we achieve better than state-of-the-art results on two publicly available reference datasets, reaching over 98% accuracy on 10-fold cross-validation for both data sets.

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