Ming Li Ordre des livres (chronologique)

Utilizing advanced mathematical techniques such as time series analysis and Fourier transforms, this book introduces fractal traffic modeling to enhance delay bounds in computer communication networks. It emphasizes improving service quality by integrating concepts like functional analysis and fractional order systems, alongside addressing noise factors. The focus on innovative computations aims to provide practical solutions for optimizing network performance.

The timeless story of the monkey-god Hanuman is that of a valiant superhero, best known for battling the demon Ravana in the classic tale Ramayana. Although Hanuman has the mystic ability to shrink and expand, and to leap great distances, it is his sensitivity and devotion to King Rama that make him such a memorable character. As a youth, Hanuman's mischievousness often landed him in trouble with the village elders. Finally they cast a spell causing him to forget his immense powers. Hanuman grew up thinking he was an ordinary monkey. His potential was realized only later when he was compelled to rescue Sita, the kidnapped wife of Rama, from the clutches of Ravana.

Briefly, we review the basic elements of computability theory and prob ability theory that are required. Finally, in order to place the subject in the appropriate historical and conceptual context we trace the main roots of Kolmogorov complexity. This way the stage is set for Chapters 2 and 3, where we introduce the notion of optimal effective descriptions of objects. The length of such a description (or the number of bits of information in it) is its Kolmogorov complexity. We treat all aspects of the elementary mathematical theory of Kolmogorov complexity. This body of knowledge may be called algo rithmic complexity theory. The theory of Martin-Lof tests for random ness of finite objects and infinite sequences is inextricably intertwined with the theory of Kolmogorov complexity and is completely treated. We also investigate the statistical properties of finite strings with high Kolmogorov complexity. Both of these topics are eminently useful in the applications part of the book. We also investigate the recursion theoretic properties of Kolmogorov complexity (relations with Godel's incompleteness result), and the Kolmogorov complexity version of infor mation theory, which we may call "algorithmic information theory" or "absolute information theory. " The treatment of algorithmic probability theory in Chapter 4 presup poses Sections 1. 6, 1. 11. 2, and Chapter 3 (at least Sections 3. 1 through 3. 4).