Stochastic Systems

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

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 […]

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Experimental Math Featured Posts Machine Learning Stochastic Systems Synthetic Data Visualization

Detecting Subtle Departures from Randomness

Entitled “Detecting Subtle Departures from Randomness”, the full version in PDF format is accessible in the “Free Books and Articles” section, here. Figure 1 below shows two plots arising from two different, non-periodic pseudo-random sequences of +1 and -1 in about equal proportions, distributed seemingly randomly. The left one is associated to prime numbers, assumed to be […]

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Featured Posts Machine Learning Statistical Science Stochastic Systems Time Series

Gentle Introduction to Linear Algebra, with Spectacular Applications

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 excessive use of jargon or advanced math. The fundamental tool is the power of a matrix, and its byproduct, the characteristic polynomial. It […]

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New Book: Stochastic Processes and Simulations – A Machine Learning Perspective

New edition with Python code. Described as a “gem” or “masterpiece” by some readers. Buy the book here. Introduction This scratch course on stochastic processes covers significantly more material than usually found in traditional books or classes. The approach is original: I introduce a new yet intuitive type of random structure called perturbed lattice or […]

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