A proposta deste artigo foi estudar a evolução do tamanho das cidades dos estados do nordeste do Brasil para os anos de 1990, 2000 e 2010 através da regularidade empírica conhecida como lei de Zipf, a qual pode ser representada por meio da distribuição de Pareto. Por meio da análise na dinâmica da distribuição das populações através do tempo, o crescimento urbano revelou uma persistência hierárquica das cidades de Salvador, Fortaleza e Recife, enquanto que São Luís experimentou o quarto lugar no rankinging das maiores cidades, que persistiu nas duas últimas décadas. A lei de Zipf não se verificou quando se considerou as cidades do Nordeste em conjunto, que pode ser devido ao menor grau de desenvolvimento urbano das cidades dessa região. Na análise dos estados em separado, também não se observou a lei de Zipf, embora tenha se verificado a lei de Gibrat, a qual postula que o crescimento das cidades é independente de seu tamanho. Por fim, acredita-se que a instalação do complexo minerometalúrgico do Maranhão tenha contribuído para o desenvolvimento e para a redução da desigualdade urbana intracidade nesta área.

This paper analyzes an iterative kernel partitioning clustering algorithm that dynamically merges, removes and adds clusters using some characteristics, like the radii and diameters of the clusters, and distance between centers. The clustering is carried out in feature space in terms of a kernel function so that non-linearly separable clusters are identified. The preliminary experiments with seven datasets show that the proposed algorithm is able to successfully converge to the expected clustering. It is also shown that the algorithm performance is sensitive to the parameter σ of the Gaussian kernel.

Assessment of environmental contamination is increasingly a concern in nowadays soci- ety. The maximum levels for pollutants are heavily regulated, being necessary to ensure compliance. Consequently, it becomes important to construct probability maps of the observation region, showing the complementary value of the distribution function of the variable involved at regulatory thresholds. These are usually called risk maps in the environmental setting. In this work, two kernel-type estimators of the spatial distribution function are constructed, which de- part from approximating the distribution at the sampled sites and then obtaining a weighted average of the resulting values, to derive a valid estimator at any random location. Consistency of both ap- proaches is proved under rather general conditions, such as local stationarity and the existence of a number of derivatives of the distribution function. Unlike other alternatives, the new proposals pro- vide non-decreasing functions and do not require a previous estimation of the indicator variogram or the trend function. However, appropriate bandwidths parameters are needed and selection of them in practice needs to be addressed. Numerical studies are carried out, aiming at comparing the current proposal with more usual methods, such as those based on the sill estimation or the indicator kriging, described in Journel (1983) or Goovaerts (1997), respectively, and redesigned in García-Soidán and Menezes (2012). Finally, the new proposal is applied to arsenic data from Portugal, so that pollution risk maps of the referred region are constructed. Moreover, accuracy maps of the probability estimates might be constructed based on bootstrap replicas, as described in García-Soidán, Menezes and Rubiños (2014).

Abstract Kolmogorov-Arnold Networks (KANs) represent a breakthrough in deep learning by generalizing the Kolmogorov-Arnold Theorem (KAT) to networks of arbitrary depth and width. This theorem facilitates the decomposition of multivariate functions into constituent one-dimensional elements, with learnable activation functions on weights and the sum operator on nodes. KANs have been shown to exhibit robust performance in function approximation, validated across mathematical, physical, and practical domains such as traffic prediction and medical diagnostics. This study focuses on 3 objectives: (1) validating that KANs may be used in classification tasks applied to the real-world by comprehensive evaluations on OpenML, Kaggle and UCI datasets, (2) enhancing Human Activity Recognition (HAR) systems using KANs, and (3) applying these networks to Real-Time HAR in mobile devices. Tests were conducted to evaluate KANs with 7 different kernels. They demonstrate high classification performance compared to conventional machine learning approaches and MLP, and showcase reasonable latency for real-time HAR detection. These findings underscore KANs’ potential as scalable, interpretable tools in modern machine learning applications given their favorable neural scaling laws.

Kolmogorov-Arnold Networks (KANs) represent a breakthrough in deep learning, diverging from Multi-Layer Perceptrons (MLPs) by generalizing the Kolmogorov-Arnold representation theorem (KAT) to networks of arbitrary depth and width. This theorem facilitates the decomposition of multivariate functions into constituent one-dimensional elements, with learnable activation functions on weights and the sum operator on nodes. KANs have been shown to exhibit robust performance in function approximation, validated across mathematical, physical, and practical domains such as traffic prediction and medical diagnostics. Our study investigates KANs’ efficacy through comprehensive evaluations on OpenML, Kaggle and UCI datasets, with a focus on enhancing Human Activity Recognition systems. They demonstrate high classification performance compared to conventional machine learning approaches and MLPs. These findings underscore KANs’ potential as scalable, interpretable tools in modern machine learning applications given their favorable neural scaling laws.