The world may seem orderly, but randomness and chaos shape everything in the universe, from enormous galaxies all the way down to subatomic particles. Take a chilly window sheeting over with ice: even ...

Abstract: The Collatz conjecture, which posits that any positive integer will eventually reach 1 through a specific iterative process, is a classic unsolved problem in mathematics. This research ...

Abstract: Dynamic software watermarking is one of the major countermeasures against software licensing violations. However, conventional dynamic watermarking approaches have exhibited a number of ...

Please note that these are just the code examples accompanying the book, which we uploaded for your convenience; be aware that these notebooks may not be useful without the formulae and descriptive ...

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