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The Pythagorean Theorem is one of the oldest, more famous and more useful theorems of Mathematics, and possibly the one that has had the most impact in the evolution of this and other sciences. In this article, we look at it from different perpectives, some of them uncommon. We recall some of its history, some well known applications and generalizations, other less known ones, and show it still has many surprising facets which are usually ignored. (O Teorema de Pit\'agoras (TP) \'e um dos mais antigos, famosos e \'uteis teoremas da Matem\'atica, e possivelmente o que maior impacto teve na evolu\c{c}\~ao desta e outras ci\^encias. Neste artigo, vamos olhar para este velho conhecido de diferentes perspectivas, algumas pouco usuais. Iremos lembrar um pouco da sua hist\'oria, algumas aplica\c{c}\~oes e generaliza\c{c}\~oes bem conhecidas, outras nem tanto, e ver que ele guarda muitas facetas surpreendentes e geralmente ignoradas.), Comment: in Portuguese language

Since the development of lasers, we have continuously sought to advance techniques and theory to obtain beams with a high degree of coherence, as natural light sources provide incoherent light. However, there are applications where it is advantageous to use partially coherent (PC) beams in a controlled manner, such as in propagation through turbulent media. To generate a PC beam in the laboratory or in simulations, specific theories and methods are required. In this article, we provide an introduction to PC beam theory, describing how to generate them through modal decompositions and a step-by-step guide for simulating and analyzing beam generation inspired by experiments. To illustrate the methods, we present Gaussian Schell-Model beams as an example., Comment: 12 pages, in Portuguese language, 11 figures

The thought-provoking analogy between AI and electricity, made by computer scientist and entrepreneur Andrew Ng, summarizes the deep transformation that recent advances in Artificial Intelligence (AI) have triggered in the world. This chapter presents an overview of the ever-evolving landscape of AI, written in Portuguese. With no intent to exhaust the subject, we explore the AI applications that are redefining sectors of the economy, impacting society and humanity. We analyze the risks that may come along with rapid technological progress and future trends in AI, an area that is on the path to becoming a general-purpose technology, just like electricity, which revolutionized society in the 19th and 20th centuries. A provocativa compara\c{c}\~ao entre IA e eletricidade, feita pelo cientista da computa\c{c}\~ao e empreendedor Andrew Ng, resume a profunda transforma\c{c}\~ao que os recentes avan\c{c}os em Intelig\^encia Artificial (IA) t\^em desencadeado no mundo. Este cap\'itulo apresenta uma vis\~ao geral pela paisagem em constante evolu\c{c}\~ao da IA. Sem pretens\~oes de exaurir o assunto, exploramos as aplica\c{c}\~oes que est\~ao redefinindo setores da economia, impactando a sociedade e a humanidade. Analisamos os riscos que acompanham o r\'apido progresso tecnol\'ogico e as tend\^encias futuras da IA, \'area que trilha o caminho para se tornar uma tecnologia de prop\'osito geral, assim como a eletricidade, que revolucionou a sociedade dos s\'eculos XIX e XX., Comment: In Portuguese

In this article, we present several apparent paradoxes of special relativity and their respective solutions. These paradoxes have appeared since the advent of relativity in 1905, and in fact they are never paradoxes. From a didactic point of view, paradoxes are an excellent learning tool. They lead the student to confront, and abandon, several central concepts of Galilean theory, such as simultaneity and rigidity of extended bodies. In particular, we review a new and simple solution to the twin paradox, recently found by one of the present authors [1]. It does not need to consider reference accelerators or light signals, which are the solutions presented in the literature., Comment: in Portuguese language, paper accepted for publication in Revista Brasileira do Ensino de F\'isica

This article presents initiatives aimed at promoting female participation in STEM fields, with the goal of encouraging more women to pursue careers in these areas. One of these initiatives is the Em\'ilias - Arma\c{c}\~ao em Bits Project, which organizes workshops in schools. Additionally, a podcast has been created to foster interaction between young people and professionals in the field of computing, while also contributing to the establishment of female role models in the industry. The results of these initiatives have been promising, as 70.6% of the students who participated in the workshops expressed an interest in computing. Furthermore, according to Spotify, the podcast's audience consists of 53% females, 44% males, and 3% unspecified, indicating that it has successfully reached a female demographic. Resumo. Este artigo apresenta iniciativas que t\^em como objetivo promover a participa\c{c}\~ao das mulheres nas \'areas de STEM, buscando encorajar mais mulheres a seguirem carreiras nesses campos. O Projeto Em\'ilias - Arma\c{c}\~ao em Bits desenvolve oficinas nas escolas e tamb\'em um podcast, promovendo a intera\c{c}\~ao entre jovens e profissionais da \'area de computa\c{c}\~ao, al\'em de contribuir para a forma\c{c}\~ao de modelos femininos nesse campo. Os resultados demonstraram que 70,6% das estudantes demonstraram interesse pela computa\c{c}\~ao ap\'os participarem das oficinas. Em rela\c{c}\~ao aos ouvintes do podcast, dados do Spotify indicaram que 53% do p\'ublico se identifica como feminino, 44% como masculino, e 3% n\~ao especificaram o g\^enero, o que mostra que o podcast tem alcan\c{c}ado um p\'ublico feminino., Comment: In Portuguese. 10 pages. Accepted for XVII Women in Information Technology (WIT 2023)

This work presents the design and implementation of a decentralized application (DApp) that aims to guarantee the privacy of data related to the health area, which are stored and shared within a blockchain network. For this, encryption with RSA, ECC and AES algorithms is used. The platforms, technologies, tools and libraries required for development are presented, as well as implementation details., Comment: in Portuguese language

The universe is composed of galaxies that have diverse shapes. Once the structure of a galaxy is determined, it is possible to obtain important information about its formation and evolution. Morphologically classifying galaxies means cataloging them according to their visual appearance and the classification is linked to the physical properties of the galaxy. A morphological classification made through visual inspection is subject to biases introduced by subjective observations made by human volunteers. For this reason, systematic, objective and easily reproducible classification of galaxies has been gaining importance since the astronomer Edwin Hubble created his famous classification method. In this work, we combine accurate visual classifications of the Galaxy Zoo project with \emph {Deep Learning} methods. The goal is to find an efficient technique at human performance level classification, but in a systematic and automatic way, for classification of elliptical and spiral galaxies. For this, a neural network model was created through an Ensemble of four other convolutional models, allowing a greater accuracy in the classification than what would be obtained with any one individual. Details of the individual models and improvements made are also described. The present work is entirely based on the analysis of images (not parameter tables) from DR1 (www.datalab.noao.edu) of the Southern Photometric Local Universe Survey (S-PLUS). In terms of classification, we achieved, with the Ensemble, an accuracy of $\approx 99 \%$ in the test sample (using pre-trained networks)., Comment: 18 pages, 13 figures, codes and data available at https://natanael.net, text in portuguese

The increase in data traffic on the internet has significantly increased the relevance of data and image encryption. Among the techniques most used in cryptography, chaotic systems have received great attention due to their easy implementation. However, it has recently been observed that these systems can lose their chaotic properties due to the finite precision of computers. In this work, we intend to investigate flexible computing tools, particularly interval analysis, to reduce this problem. We opted for the Lorenz System, as it is one of the few systems whose chaoticity is proven analytically. The results of this study, based on the correlation and entropy indexes, were superior to other studies published in the recent literature., Comment: DINCON 2019 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes. Sao Carlos (SP). Brazil. 7 pages. In Portuguese

This work presents a new meta-heuristic approach to model structure selection of polynomial NARX models. In this respect, the technique penalizes the models based on the individual contribution of each regressor in representing the system. The new algorithm is tested on two experimental case studies: the identification of an electromechanical system and a eletric heater. The results are compared with Error Reduction Ratio and another meta-heuristic approach. The proposed method shows its advantages over compared methods in terms of the trade-off between prediction accuracy and model interpretability. The results are quantified and compared using the Mean Squared Error (MSE) indices., Comment: in Portuguese, SBAI 2019 - Simp\'osio Brasileiro de Automa\c{c}\~ao Inteligente - Ouro Preto. 6 pages

The surface electromyography (sEMG) analysis can provide information on muscle fatigue status by estimation of muscle fibre conduction velocity (MFCV), a measure of the travelling speed of motor unit action potentials in muscle tissue. This paper proposes a technique for MFCV estimation using cross-correlation methods and variable bitstream modulation. The technique displays an estimate based on a set of data generated by the gain variation modulation, providing an average estimate of the MFCV. The observed trend of MFCV decrease correlates with the fatigue state of the observed muscle. Finally, the values found were compared with information from the literature, validating the method and showing the advantages of using variable modulation., Comment: SBAI 2019 - Simposio Brasileiro de Automacao Inteligente - Ouro Preto. 6 pages. In Portuguese

Chaotic systems have been investigated in several areas of engineering. In control theory, such systems have instigated the emergence of new techniques as well, have been used as a source of noise generation. The application of chaotic systems as pseudo-random numbers has also been widely employed in cryptography. One of the central aspects of these applications in high performance situations, such as those involving a large amount of data (Big Data), is the response of these systems in a short period of time. Despite the great advances in the design of chaotic systems in analog circuits, it is perceived less attention in the optimized design of these systems in the digital domain. In this work, the polarized fixed point representation is applied to reduce the number of digital elements. Using this approach, it was possible to significantly reduce the number of logic gates in the subtraction operation. When compared to other works in the literature, it has been viable to reduce by 50 \% the number of elements per bit of the digital representation of the tent map. The chaoticity was evidenced with the calculation of the Lyapunov exponent. Histogram, entropy and autocorrelation tests were used satisfactorily to evaluate the randomness of the represented system., Comment: SBAI 2019 - Simposio Brasileiro de Automacao Inteligente - Ouro Preto. 6 pages. In Portuguese

An evergreen scientific feature is the ability for scientific works to be reproduced. This feature allows researchers to understand, enhance, or even question works that have been developed by other scientists. In control theory the importance of modeling and simulation of systems is widely recognized. Despite this recognition, less attention is paid to the effects of finite precision of computers on the simulation reproducibility of nonlinear dynamic systems. In this work, a case study of reproducibility is presented in the simulation of a chaotic Jerk circuit, using the software LtSpice. In order to do so, we performed simulations of the circuit in the same version of the software on different computers, in order to collect the data and compare them with experimental results. The comparison was made with the NRMSE (Normalized Root Mean Square Error), in order to identify the computer with the highest prediction horizon. Tests performed in 4 different configurations showed the difficulties of simulation reproducibility in LtSpice. The methodology developed was efficient in identifying the computer with better performance, which allows applying it to other cases in the literature., Comment: SBAI 2019 - Simposio Brasileiro de Automacao Inteligente - Ouro Preto. 6 pages. In Portuguese

This is a set of lecture notes for an introductory course (advanced undergaduates or the 1st graduate course) on foundations of supervised machine learning (in Portuguese). The topics include: the geometry of the Hamming cube, concentration of measure, shattering and VC dimension, Glivenko-Cantelli classes, PAC learnability, universal consistency and the k-NN classifier in metric spaces, dimensionality reduction, universal approximation, sample compression. There are appendices on metric and normed spaces, measure theory, etc., making the notes self-contained. Este \'e um conjunto de notas de aula para um curso introdut\'orio (curso de gradua\c{c}\~ao avan\c{c}ado ou o 1o curso de p\'os) sobre fundamentos da aprendizagem de m\'aquina supervisionada (em Portugu\^es). Os t\'opicos incluem: a geometria do cubo de Hamming, concentra\c{c}\~ao de medida, fragmenta\c{c}\~ao e dimens\~ao de Vapnik-Chervonenkis, classes de Glivenko-Cantelli, aprendizabilidade PAC, consist\^encia universal e o classificador k-NN em espa\c{c}os m\'etricos, redu\c{c}\~ao de dimensionalidade, aproxima\c{c}\~ao universal, compress\~ao amostral. H\'a ap\^endices sobre espa\c{c}os m\'etricos e normados, teoria de medida, etc., tornando as notas autosuficientes., Comment: 390 pp. + vii, in Portuguese, a preliminary version, to be published by IMPA as a book of lectures of the 23nd Brazilian Math Colloquium (July 28 - Aug 2, 2019), submitted to arXiv upon IMPA permission

Chaotic systems have been investigated in the most diverse areas. One of the first steps in chaotic system research is the detection of chaos. The largest Lyapunov exponent (LLE) is one of the most widely used techniques for this purpose. Recently, techniques for calculating LLE have been developed taking into account the error due to the finite precision of computers. Recursive methods were employed to improve such algorithms. However, this method uniformly weighed the data used to calculate the LLE. This paper investigates the different weighing of the data based on the hypothesis that the initial data have a higher precision than the last data processed by the algorithm, since the process is subject to error accumulation. In five tested systems, the proposed method obtained more accurate results in three. However, there was an increase in the variance of the result obtained for two of the evaluated systems., Comment: SBAI 2019 - Simposio Brasileiro de Automacao Inteligente - Ouro Preto. 6 pages. In Portuguese

Data classification is present in different real problems, such as recognizing patterns in images, differentiating defective parts in a production line, classifying benign and malignant tumors, among many others. Many of these problems have data patterns that are hard to identify, which requires more advanced techniques for resolution. Recently, several works addressing different artificial neural network architectures have been applied to solve classification problems. When the classification problem must be obtained through images, currently, the standard methodology is the use of convolutional neural networks. Thus, in this report convolutional neural networks are used to classify fish species. Classifica\c{c}\~ao de dados est\'a presente em diversos problemas reais, tais como: reconhecer padr\~oes em imagens, diferenciar pe\c{c}as defeituosas em uma linha de produ\c{c}\~ao, classificar tumores benignos e malignos, dentre diversas outras. Muitos desses problemas possuem padr\~oes de dados dif\'iceis de serem identificados, o que requer, consequentemente, t\'ecnicas mais avan\c{c}adas para sua resolu\c{c}\~ao. Recentemente, diversos trabalhos abordando diferentes arquiteturas de redes neurais artificiais v\^em sendo aplicados para solucionar problemas de classifica\c{c}\~ao. Quando a classifica\c{c}\~ao do problema deve ser obtida por meio de imagens, atualmente a metodologia padr\~ao \'e uso de redes neurais convolucionais. Sendo assim, neste trabalho s\~ao utilizadas redes neurais convolucionais para classifica\c{c}\~ao de esp\'ecies de peixes., Comment: in Portuguese

Designing problems using matrices is very important in Computer Science. Fields like graph computer, graphs theory, and machine learning use matrices very often to solve their own problems. The most often matrix operation is the multiplication. It may be time-consuming if the matrices to be multiplied are large. For this reason, the parallel computer became a must to tackle this problem. In this report, it is presented a comparison between sequential and parallel approaches to computing the matrix multiplication using CUDA and openMP. The results show the importance of parallelizing mainly when the matrices are large. A modelagem de problemas utilizando matrizes \'e de extrema import\^ancia para Ci\^encia da Computa\c{c}\~ao. \'Areas como computa\c{c}\~ao gr\'afica, grafos e aprendizado de m\'aquina utilizam matrizes com alta frequ\^encia para solucionar seus respectivos problemas. Dessa forma, operar matrizes de maneira eficiente \'e muito importante para o desempenho de algoritmos. Uma das opera\c{c}\~oes de matrizes mais utilizadas \'e a multiplica\c{c}\~ao, que se torna um empecilho para o desempenho computacional de algoritmos na medida que o tamanho das matrizes a serem multiplicadas aumentam. Por conta disso, a computa\c{c}\~ao paralela se tornou uma solu\c{c}\~ao padr\~ao para abordar tal problema. Neste trabalho \'e apresentado uma compara\c{c}\~ao entre as abordagens sequencial e paralela para multiplica\c{c}\~ao de matrizes utilizando CUDA e OpenMP. O resultado da an\'alise realizada entre o tamanho da matriz e o desempenho da multiplica\c{c}\~ao mostra a import\^ancia da paraleliza\c{c}\~ao principalmente para matrizes de ordem elevada., Comment: in Portuguese

This paper presents a study on the reduction of the sampling frequency of the current signals of an induction motor, the reductions are performed by means time-decimation technique for digital signal processing. We have used the Fast Fourier Transform to obtain the fault signal spectrum of broken bars. The results have shown how the decimation technique significantly reduces the number of operations and the time required to calculate the Fast Fourier Transform without loss of information. This approach provides a better performance of embedded systems for fault diagnosis based on characteristic of amplitude signal modulation., Comment: in Portuguese

Differences between computer simulation of dynamical systems and laboratory experiments are common in teaching and research in engineering. Normally, numerical inaccuracy and the non-ideal behaviour of the devices involved in the experiment are the most common explanations. With the application of interval analysis, it is possible to incorporate the numerical and parametric uncertainties in the simulation, allowing a better understanding of the play between simulation and experiment. This article presents a case study in which an step input is applied to an RLC circuit. Using the toolbox Intlab for Matlab, it was possible to present a computer simulation with the range that encompasses the experimental results . Comparison of simulation with experimental data show the success of the technique and indicates a potential content to be delivered to undergraduate engineering courses., Comment: CBA 2016 - XXI Congresso Brasileiro de Automatica, Vitoria, p. 1-6, In Portuguese

There is a great need to stock materials for production, but storing materials comes at a cost. Lack of organization in the inventory can result in a very high cost for the final product, in addition to generating other problems in the production chain. In this work we present mathematical and statistical methods applicable to stock management. The stock analysis using ABC curves serves to identify which are the priority items, the most expensive and with the highest turnover (demand), and thus determine, through stock control models, the purchase lot size and the periodicity that minimize the total costs of storing these materials. Using the Economic Order Quantity (EOQ) model and the (Q,R) model, the inventory costs of a company were minimized. The comparison of the results provided by the models was performed., Comment: In Portuguese, 17 pages, 12 figures, 7 tables. Conference SEMAT2017

This article investigates the maximum time of simulation in which the phenomenon of the intermittence can be observed with numerical confidence in discrete maps. Interval analysis and the lower error limit were used. As a result, it was observed that the reliability of the intermittency is dependent on the initial condition. Four numerical examples show the efficiency of the proposal., Comment: DINCON 2017 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes - Sao Jose do Rio Preto - Brazil. 7 pages. In Portuguese

The Luruaco Lake located in the Department of Atl\'antico, Colombia, is damaged by the discharge of untreated sewage, bringing risks to the health of all who use its waters. The present study aims to perform the numerical simulation of the concentration dynamics of fecal coliforms in the lake. The simulation of the hydrodynamic flow is carried out by means of a two-dimensional horizontal (2DH) model, given by a Navier-Stokes system. The simulation of fecal coliform transport is described by a convective-dispersive-reactive equation. These equations are solved numerically by the Finite Difference Method (FDM) and the Mark and Cell (MAC) method, in generalized coordinates. Regarding the construction of the computational mesh of the Luruaco Lake, the cubic spline and multiblock methods were used. The results obtained in the simulations allow a better understanding of the dynamics of fecal coliforms in the Luruaco Lake, showing the more polluted regions. They can also advise public agencies on identifying the emitters of pollutants in the lake and on developing an optimal treatment for the recovery of the polluted environment., Comment: 13 pages, in Portuguese, 4 figures

This paper proposes a model validation method that incorporates error due to numerical procedures. Two identified models for Sine Map and Duffing-Ueda Circuit systems have been investigated. The indexes RMSE and MAPE have been applied. We have shown that after some few iterates, it is possible to notice some significative difference between index provided in the literature. This difference has been computed in around 34%., Comment: DINCON 2017 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes - Sao Jose do Rio Preto - Brazil. 7 pages. In Portuguese

In this work the non-linear and chaotic behaviour for the RLD circuit is analysed, which is modelled by state space and numerically simulated considering the diode model an association between nonlinear resistances and capacitances. It has been possible to characterize the dynamics of the circuit through period doubles and chaotic behaviour. The Lyapunov exponent is calculated to show the chaotic behaviour of this circuit. Simulated results are in good agreement with experimental data., Comment: DINCON 2017 - Conferencia Brasileira de Dinamica, Controle e Aplicacoes - Sao Jose do Rio Preto - Brazil. 7 pages. In Portuguese

This article presents a design of the logistic map by means of FPGA (Field Programmable Gate Ar-ray) under fixed-point standard and 32-bits of precision. The design was carried out with Altera Quartus platform. The hardware description language VHDL-93 has been adopted and the results were simulated by means of Altera ModelSim package. The main of the project was to produce a cha-otic system with a low energy and time cost. Using the VHDL, it was possible to use only 1439 logical gates from 114480 available. The Lyapunov exponent has been calculated with good agreement with literature reference, which shows the effectiveness the proposed method., Comment: XIII Simposio Brasileiro de Automacao Inteligente - SBAI2017 - Porto Alegre - Brazil. In Portuguese

This paper aims to identify three electrical systems: a series RLC circuit, a motor/generator coupled system, and the Duffing-Ueda oscillator. In order to obtain the system's models was used the error reduction ratio and the Akaike information criterion. Our approach to handle the numerical errors was the interval arithmetic by means of the resolution of the least squares estimation. The routines was implemented in Intlab, a Matlab toolbox devoted to arithmetic interval. Finally, the interval RMSE was calculated to verify the quality of the obtained models. The applied methodology was satisfactory, since the obtained intervals encompass the system's data and allow to demonstrate how the numerical errors affect the answers., Comment: SBAI 2017 - XIII Simp\'osio Brasileiro de Automa\c{c}\~ao Inteligente, Porto Alegre, p. 1-6, In Portuguese. arXiv admin note: text overlap with arXiv:1612.02674

This paper presents an application with ROS, Aria and RosAria to control a ModelSim simulated Pioneer 3-DX robot. The navigation applies a simple autonomous algorithm and a teleoperation control using an Android device sending the gyroscope generated information., Comment: in Portuguese

An interesting physical phenomenon, which contradicts our common sense, is concerned with the dynamics of motion of a spinning ellipsoid in a non smooth surface. A hard-boiled egg spinning on a table with a rough surface is an example. In this article, we present a theoretical explanation, of the dynamics of motion of this ellipsoid, that describes the axis raising phenomenon, from the horizontal to the vertical. The equations of motion were obtained with Lagrangian formalism., Comment: The article is written in Portuguese and was accepted for publication in the journal "Brasileira de Ensino de F\'isica"

We define a new class of numbers based on the first occurrence of certain patterns of zeros and ones in the expansion of irracional numbers in a given basis and call them Sagan numbers, since they were first mentioned, in a special case, by the North-american astronomer Carl E. Sagan in his science-fiction novel "Contact." Sagan numbers hold connections with a wealth of mathematical ideas. We describe some properties of the newly defined numbers and indicate directions for further amusement., Comment: LaTeX2e, 17 pages, 2 figures, 26 references. English version of an article originally published in Portuguese. Keywords: Recreational mathematics, science fiction, normal numbers, BBP-type formulae