Teoria dos Números Visual – Divisão

Vou começar uma série de artigos, explicando a bela Teoria dos Números a partir de uma abordagem visual, que chamei de “álgebra de pedrinhas”.

A motivação é que os livros comuns de matemática exploram pouco os recursos visuais, e a matemática fica mais intuitiva com objetos do mundo real.

Vamos começar com a divisão.

Definição. Se a e b são inteiros, dizemos que a divide b, denotando por a|b, se existir um inteiro c tal que b = a*c.

Por exemplo, 12 dividido por 4 = 3, pode ser interpretado por 12 bolinhas, dispostas em 4 colunas, cada coluna com 3 bolinhas de altura.

Convido o leitor a experimentar o algoritmo em:


Definição: O algoritmo da divisão.

Dados dois inteiros a e b, b>0, existe um único par de inteiros q e r tais que:

a = q*b+r,

com 0<= r < b

q é chamado…

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Predições analytics 2022

Fonte: Informs (https://pubsonline.informs.org/do/10.1287/LYTX.2022.01.12/full/)

Scott Zoldi, chief analytics officer, FICO

  • Data will continue its mass expansion and integration into everyday business practices. With that, there is an increased responsibility to track data provenance and ensure proper consent before harnessing the data in new AI applications. Responsible businesses will treat new data both as opportunity and liability. Businesses that establish strong data governance guide rails will earn customer trust and will receive customers’ data assets.
  • When looking ahead to a future filled with data-driven automation, AI will again be at the forefront of delivering increased value based on this incremental data. Big data will be out and small data will be in, with savvy practitioners weighing the benefits and risks with surgical precision prior to use.
  • Ethical AI starts with data and recognizing the biases that exist within it. Expanded data use will be coupled with contracting, selective use of the right data, supercharging the analytic power of AI applications responsibly.
  • Digital transformation is still an omnipresent directive, but the days of “big data appetites” will be replaced with a combined reliance on strong data governance and responsible AI practices of using only carefully selected portions of data in explainable and justifiable ways.

Ryan Welsh, founder and CEO, Kyndi

  • 2022: The year when humans and AI work together to drive enterprise performance. With the proliferation of unstructured text, knowledge workers are struggling to gain insights from the volume of information they must comb through. In 2022, organizations will look for AI technologies that remove the barriers of traditional supervised learning models so that they can more easily and quickly turn these troves of data into usable information. AI vendors will flip the script and deliver solutions that do not require the time, resources and expense required for supervised learning models. They will deliver solutions that provide highly relevant and context-driven information with unprecedented speed and precision so that humans are empowered to do their most meaningful work. Rather than replacing human intervention, these modern – and evolving – AI technologies will allow people to analyze and use unstructured as well as structured data in a smarter, faster and more natural way.
  • Organizations will focus on AI initiatives that augment human performance, not replace humans with machines. Up until now, the goal of machine learning for most applications has been the replacement of human effort with machine effort. 2022 will see machines performing tedious, tactical tasks such as information retrieval, etc., which will enable humans to focus on higher-level, strategic tasks and decision-making. … In the coming year, expect AI providers to focus on delivering platforms that centralize data/content for use across multiple business processes.
  • In 2022, organizations will demand AI vendors begin developing specific AI-enabled solutions that can be immediately implemented without coding. By focusing on providing human-centered solutions to business users, vendors will enable individuals to immediately generate insights that drive decision-making. Consequently, organizations will shift their investments in AI, moving away from highly customized solutions in favor of configurable (off-the-shelf) options.
  • Zero-code solutions that provide greater transparency will become paramount. Much has been written about the “democratization” of AI and the delivery of platforms that can be used without additional coding. Frankly, this is a benefit more often enjoyed by IT than business users who do not make buying decisions simply because no coding is required. Meeting a buyer’s need is less about democratization and more about the “universality” of AI. Universal AI will be embedded in a suite of configurable business solutions that do not require coding.
  • In 2022, with the focus shifting to AI-enabled solutions targeted to line-of-business teams with specific business problems, expect to see a corresponding shift away from point solutions to suite-oriented solutions that allow other lines of business users to capitalize on the same institutional knowledge. Attention will shift to the platform’s ability to support the suite along with a rich user experience instead of simply focusing on the platform and tools.

Alan Jacobson, chief data and analytics officer, Alteryx

  • Digital transformation 2.0 will usher in a culture of analytics across business units as more larger enterprises provide the self-service technologies and training to ensure the average knowledge worker is set up for success and able to directly perform analytics.
  • Fragmentation in the data and analytics space will level off. In recent years, the AI/ML space has been complex, with more companies entering the space than the year prior. However, we will begin to see this trend curve and plateau as we enter a more mature space with increased consolidation in 2022.

David Sweenor, senior director of product marketing, Alteryx

  • 2022 will usher in the age of the consumerization of analytics. Organizations will invest in code-free analytics applications to solve business-specific problems across business units, “mass produce” impactful business applications, and enable business users to step into the roles of analyst and advanced analyst.
  • Data is not the new oil; data is a renewable energy source. Data, after it is transformed into useful insight through analytics, continues to increase in value and that value will exist in perpetuity as opposed to oil, which is burned and then gone.
  • We will see the rise of data trusts and frameworks evolve and organizations will shift their mindsets to sharing rather than data hoarding. We’ll see increasing use of synthetic data, differential privacy, other techniques to ensure security, privacy and legit use of data.
  • More responsible AI will bridge the gap from design to innovation. While companies are starting to think about and discuss AI ethics, their actions are nascent, but within the next year we will see an event that will force companies to be more serious about AI ethics.
  • The role of the “citizen data scientist” will evolve within vertical markets like fintech. Organizations will focus more on the relationship between people and AI, leading to increased spend on upskilling people as data literacy evolves into AI literacy. We will move away from the term “citizen data scientist” and toward “AI or analytics literate.” Businesses will become more dependent on collective intelligence, the idea that better business decisions can be made by machines and humans working together. 

Libby Duane Adams, chief advocacy officer and co-founder, Alteryx

  • Businesses are forced to fast-track employee upskilling programs. While many businesses are talking about ways to upskill their employees and equip them with the tools they need to deliver analytics for business impact, a recent Alteryx survey found that the majority of workers believe more training in data work would result in better (75%) and faster (69%) decisions. As businesses seek to gain competitive insights and value from their data, they will need to quickly address upskilling needs if they want to keep pace with the market.
  • The reliance on data analytics process automation is increasing with exponential growth of business data used by fintech organizations to innovate. With the speed at which business happens, business professionals need data-driven insights that answer key questions faster to drive process improvement and identify opportunities to increase revenue, improve efficiencies and reduce risk. The ability to automate data analytics has greatly impacted the speed to insight, and business leaders are no longer satisfied waiting days or weeks for answers they know they need to receive in minutes or hours.

Jay Henderson, VP product management, Alteryx

  • Data scientists will no longer be the only workers that understand analytics. As we continue to democratize analytics and empower teams with the skills needed to understand data, organizations will no longer need to rely solely on a data scientist to make sense, and gain insights, from data. This will empower a much larger group to create insights and allow data scientists to focus on the problems where they can have the most impact.
  • Businesses will move from being data-hoarders to driving real insights and democratizing analytics. Right now, organizations are drowning in data but still thirsty for insights. The arrival of cheap cloud storage and the ever-expanding digital exhaust has caused organizations to simply capture and store as much data as possible, without doing much with it. Adopting solutions that speed the time to meaningful business insight from their analytic platforms will allow enterprises to drive business forward with data-driven intelligence. The emergence of AI-driven auto-insights capabilities are a key enabler of this change.
  •  Next year, analytics finally crosses the chasm into the cloud. Cloud adoption is steadily growing as businesses seek to leverage big data already in cloud repositories, take advantage of cloud native computing, and provide easier access to analytics.

Empilhamento de cartas e série harmônica

Quantas cartas consigo empilhar, de modo que a borda das superiores saiam da mesa e elas se sustentem apenas por gravidade? Qual distância máxima consigo chegar?

Este probleminha é relativamente simples, e interessante, por remeter à série harmônica.

Para analisar o raciocínio, deve-se pensar da carta de cima para as cartas de baixo.

Com uma carta, posso colocar o centro de gravidade exatamente na borda da mesa (representada pelo triângulo). Ou seja, ando lateralmente meia carta. Como hipótese, podemos considerar que a carta tem tamanho 2, sendo assim, meia carta tem tamanho 1, para facilitar as contas seguintes.

Com duas cartas, considera-se que o centro de gravidade da primeira carta está exatamente na borda da segunda carta. O ponto de equílibro do centro de gravidade do sistema é dado por pela soma de distâncias* pesos.

Nesse caso: (1-x) P = x*P

-> x = 1/2

Com três cartas e…

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I’m very proud to share this course achievement: Quantum Algorithms for CyberSecurity, Chemistry and Optimization, in MIT xPRO.

It is a very high level course: video classes, thoughtful questions and exercises in the end of the session, with some of the legendary professors of this field: Will Oliver, Peter Shor and Isaac Chuang.

It explains clearly the main concepts and applications of quantum computing. It deepens a bit in the subjects, but not too much, being specially good for those who want to have at the same time a broad overview, and also a bit of the details on each topic.

Como resolver o Cubo Dino

O Cubo Dino é um cubo com peças triangulares, como o da foto.

Ele é mais simples do que resolver do que o Cubo Rubik 3x3x3. Basta a aplicação de poucos movimentos, acertando localmente as peças.

Para ilustrar os movimentos, vamos “desdobrar” o cubo conforme esquema abaixo.

Primeiro, a notação.

O Movimento R (right) significa um movimento da peça da direita, no sentido horário.

Apesar de parecer um pouco confuso, basta imaginar um triângulo girando, conforme indica o esquema. As demais peças permanecem inalteradas.

O movimento L (left) é semelhante, mas do outro lado, conforme o diagrama.

Vale a pena registrar o movimento R’, ou seja, o movimento R no sentido oposto, anti-horário.

Analogamente, o movimento L’, conforme diagrama abaixo.

Daí, o segredo para resolver o cubo é fazer uma série de movimentos à direita e à esquerda, e desfazer o movimento logo a seguir.

Movimento RL’-R’L:

Notar o efeito…

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Prêmio Brasil referência Data Science

Bom dia, rede. Estou concorrendo ao Prêmio Brasil, como referência em Data Science, patrocinado pela Cognitivo AI.

Lidero um time que faz Advanced Analytics na gigante #Klabin S.A.

A operação florestal Klabin PR é uma das mais complexas do mundo em um único site. Há camadas de planejamento desde o longo prazo (30 anos) até on-line. Trabalhos incluem programação linear inteira para otimização do planejamento, algoritmos de roteirização e despacho de veículos, simulador da cadeia, obviamente com apoio de muitas outras mãos.

Na área industrial e outras áreas, calendário e trim da máquina de papel, forecasts, simuladores de cenários e diversos outros.

Para fortalecer a comunidade de Data Science:

– Administro uma lista de Excel VBA, com mais de 250 pessoas

– Sou divulgador da Computação Quântica no Brasil, sendo IBM Qiskit Advocate desde ago/21.

– Convido todos a visitar o meu blog: Ideias Esquecidas.

Peço apoio de vocês para votar e divulgar, no link abaixo:


Escaravelho Dourado: decifre o enigma de Allan Poe com Python

“O Escaravelho Dourado” é um pequeno conto, do escritor americano Edgar Allan Poe, publicado em 1843.

O enredo narra a história de William Legrand, supostamente picado por um escaravelho dourado. Seu servo Júpiter teme que Legrand fique louco, e com a ajuda do narrador anônimo, partem para uma aventura que envolve uma mensagem criptografada e um tesouro escondido.

Sem mais delongas, os aventureiros se depararam com a seguinte mensagem.

53‡‡†305))6;4826)4‡.)4‡);80 6;48†8¶60))85;1‡(;:‡8†83(88) 5†;46(;8896?;8)‡(;485);5





A primeira informação é que a mensagem está em inglês. O narrador cita que, tendo decifrado inúmeras mensagens criptogradas, é essencial saber qual a linguagem em que este está escrito.

A seguir, ele faz uma contagem dos caracteres existentes.

Em Python, podemos utilizar um set para listar os caracteres únicos, como mostra o código a seguir.

strOriginal = "53‡‡†305))6;4826)4‡.)4‡);806;48†8¶60))85;1‡(;:‡8†83(88)5

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Exercício – cifra de substituição simples

Aproveitando a onda do post anterior (https://ideiasesquecidas.com/2021/10/11/escaravelho-dourado-decifre-o-enigma-de-allan-poe-com-python/), segue um pequeno exercício.

Qual a mensagem abaixo, sabendo que é uma cifra de substituição simples, e está escrito em português brasileiro?



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Prova visual da divergência da série harmônica

A série harmônica é dada por:

Ela tem esse nome por conta do conceito de harmônicas, em música. Imagine prender uma corda de piano a um tamanho 1, depois a metade do tamanho, 1/3 do tamanho, etc.

É um resultado conhecido desde Bernoulli, no séc XVII, que a série harmônica diverge: o somatório dos termos tende a infinito.

A prova dos livros de matemática consiste em comparar com uma série conhecidamente divergente:

1/2 + 1/2 + 1/2 + …

Se eu somar o número 1/2 infinitamente, claramente a série vai divergir.

A série harmônica é maior do que a série divergente acima, basta rearranjar os termos. A figura acima ilustra as operações envolvidas.

Embora a série harmônica divirja, ela o faz muito lentamente.

Um programinha de 4 linhas em Python, para 1000 termos:

for i in range(1,1001):
harmonic += 1/i

Para 1000 termos, a soma dá 7,48.


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