#### A Synthetic Stock Exchange Played with Real Money

- Vincent Granville
- May 15, 2023

Not only that, but you can predict — more precisely compute with absolute certainty — what the value of any stock will be tomorrow. Transaction fees are well below 0.05% and the market, at least in the version presented here, is fair: in other words, a zero-sum game if you play by luck. If instead […]

Read More#### Generating and Videolizing Agglomerative Processes

- Vincent Granville
- April 17, 2023

This short article explains how to efficiently simulate the evolution of agglomerative processes, and visualize their behavior with data animations. I use a generic, simple model for illustration purposes: atoms, initially consisting of one electron, collide and merge over time, with a pre-specified maximum number of electrons per atom: the maximum limit. Given enough time, […]

Read More#### New Book: Gentle Introduction To Chaotic Dynamical Systems

- Vincent Granville
- March 21, 2023

In less than 100 pages, the book covers all important topics about discrete chaotic dynamical systems and related time series and stochastic processes, ranging from introductory to advanced, in one and two dimensions. State-of-the art methods and new results are presented in simple English. Yet, some mathematical proofs appear for the first time in this […]

Read More#### Introduction to Discrete Chaotic Dynamical Systems

- Vincent Granville
- February 21, 2023

Entitled “Introduction to Discrete Chaotic Dynamical Systems”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. This article is an extract from my book “Gentle Introduction to Chaotic Dynamical Systems”, available here. This is chapter 2 of my upcoming book on dynamical systems and related stochastic processes, expected to be […]

Read More#### Random Walks, Brownian Motions, and Related Stochastic Processes

- Vincent Granville
- February 11, 2023

Entitled “Random Walks, Brownian Motions, and Related Stochastic Processes”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. This article is an extract from my book “Gentle Introduction to Chaotic Dynamical Systems”, available here. In about 15 pages, this scratch course covers a lot more material than expected in such […]

Read More#### New Book: Synthetic Data and Generative AI

- Vincent Granville
- November 28, 2022

Synthetic data is used more and more to augment real-life datasets, enriching them and allowing black-box systems to correctly classify observations or predict values that are well outside of training and validation sets. In addition, it helps understand decisions made by obscure systems such as deep neural networks, contributing to the development of explainable AI. […]

Read More#### Dynamic Clouds and Landscape Generation: Morphing and Evolutionary Processes

- Vincent Granville
- November 5, 2022

Entitled “Dynamic Clouds and Landscape Generation: Morphing and Evolutionary Processes”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. Also discussed in details with Python code in my book “Synthetic Data”, available here. My previous article focused on map generation in 3D, and also features a fascinating video, see here. In this […]

Read More#### Weird Random Walks: Synthetizing, Testing and Leveraging Quasi-randomness

- Vincent Granville
- August 11, 2022

Entitled “Weird Random Walks: Synthetizing, Testing and Leveraging Quasi-randomness”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. I discuss different types of synthetized random walks that are almost perfectly random, in one and two dimensions. Besides the theoretical interest, it provides new modeling tools, especially for physicists, engineers, natural […]

Read More#### Detecting Subtle Departures from Randomness

- Vincent Granville
- July 23, 2022

Entitled “Detecting Subtle Departures from Randomness”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. Also discussed in details in chapter 9 in my book “Intuitive Machine Learning and Explainable AI”, available here. Figure 1 below shows two plots arising from two different, non-periodic pseudo-random sequences of +1 and -1 in […]

Read More#### Gentle Introduction to Linear Algebra, with Spectacular Applications

- Vincent Granville
- May 31, 2022

This material is also discussed in details with Python code in chapter 3 in my book “Intuitive Machine Learning and Explainable AI”, available here. This is not a traditional tutorial on linear algebra. The material presented here, in a compact style, is rarely taught in college classes. It covers a wide range of topics, while avoiding […]

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