Preface

**Section 2**

Sizes

Plants

FGM Copula *by Franck Adékambi*

Networks

**II**

From a Formalization of Uncertainities to Probabilistic Modeling, **165**

**Chapter 7 167**

**Chapter 8 191**

**Chapter 9 221**

**Chapter 10 245**

**Chapter 11 259**

**Chapter 12 271**

**Chapter 13 293**

**Chapter 14 309**

Reasonable Control and Artificial Intelligence

*by Victor Korolev and Alexander Zeifman*

Combinatorial Enumeration of Graphs

Uncertain Costs at Known Locations *by Davood Shiri and F. Sibel Salman*

A Geometrical Realisation of Quasi-Cyclic Codes *by Cristina Martinez Ramirez and Alberto Besana*

*Dmitriy Olegovich Reznikov*

*by Carlos Rodríguez Lucatero*

From Asymptotic Normality to Heavy-Tailedness via Limit Theorems for Random Sums and Statistics with Random Sample

Probability Modeling Taking into Account Nonlinear Processes of a Deformation and Fracture for the Equipment of Nuclear Power

*by Nikolay Andreevich Makhutov, Mikhail Matveevich Gadenin, Igor Alexandrovich Razumovskiy, Sergey Valerievich Maslov and*

New Variations of the Online *k*-Canadian Traveler Problem:

Moments of the Discounted Aggregate Claims with Delay Inter-Occurrence Distribution and Dependence Introduced by a

Modelling the Information- Psychological Impact in Social

*by Igor Goncharov, Nikita Goncharov, Pavel Parinov,*

*Sergey Kochedykov and Alexander Dushkin*

Combinatorial Cosmology

*by Martin Tamm*

Since ancient times combinatorics and probability theory have been closely interrelated. Combinatorial techniques were used for the calculation of probabilities even when the latter were not directly assumed and were hidden behind the concept of "chances." After the notion of probability appeared, was acknowledged and comprehended, this interrelation became even stronger. Now probabilistic and combinatorial techniques are often used for solving advanced problems. The union of probability and combinatorics becomes more and more actual within the problem of Big Data, which assumes the possibility of detection of latent regularities or relations in new non-structured data types and construction of predictive models. One of the most urgent directions of the development of methods for Big Data analysis is their application in artificial intelligence systems. The problems of adequate modeling involve the development of the mathematical apparatus for the construction of reasonable models of statistical regularities and the study of their analytical and asymptotic properties. Whereas for a layman probability is still associated with divination on daisies, for specialists these methods long ago became powerful tools in predicting successes or failures, preventive management and achieving the desired successes. Some of these applicable techniques are demonstrated in this book. It is worth noting that to a great extent the calculus of probabilities became a mathematical theory due to the findings and works of the representatives of the Russian mathematical school: P.L. Chebyshev (1821–1894), A. A. Markov (1856–1922), A.M. Lyapunov (1857–1918), S.N. Bernstein (1880–1968), A.Ya. Khinchin (1894–1959), A.N. Kolmogorov (1903–1987), B.V. Gnedenko (1912– 1995), Yu.V. Prokhorov (1929–2013), who by all means deserve to be remembered along with the famous creators of probability theory J. Bernoulli (1655–1705), P.-S. Laplace (1749–1827), S.D. Poisson (1781–1840), C.F. Gauss (1777–1855) and others.

This book is very unusual. It is not at all a random collection on a topic devoted to a formalization of uncertainties. Considering that because of high complexity and uncertainties the existing probabilistic models can't be used sometimes directly to predict and estimate desired results, the initial concept of the book is as follows:


• to demonstrate analytical possibilities and practical effects for solving different system problems on each life cycle stage.

For example, the described approaches are applicable:


Of course, the described approaches do not exhaust all existing views on the problems of "probability, combinatorics and control." Nevertheless, after competent application of the proposed models, we are sure the reader will be able to trace distinctly the following chain of purposeful actions of the authors of this book:

1.From a formalization of uncertainties - to probabilistic modeling;

2.From probabilistic modeling - to reasonable control;

3.From reasonable control - to artificial intelligence;


We wish you, dear readers, the patience in understanding the book's ideas and their successful implementations in different theoretical and applications areas. It will allow to control effects in time and to achieve sustainable harmony in system engineering, your creative life and activity.

> **Andrey Kostogryzov** Federal Research Center "Computer Science and Control" of the Russian Academyof Sciences, Gubkin Russian State University of Oil and Gas, Russia
