Cover Veniaminov S.S. Revealing Latent Structural Patterns in Processes and Signals: From Space Research up to Analysis of Market Trends
Id: 187441
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Revealing Latent Structural Patterns in Processes and Signals: From Space Research up to Analysis of Market Trends
Revealing Latent Structural Patterns in Processes and Signals: From Space Research up to Analysis of Market Trends
Detección de regularidades estructurales ocultas en procesos y señales: Del estudio del cosmos al análisis de tendencias del mercado. (En inglés).

URSS. 200 pp. (English). Paperback. ISBN 978-5-9710-1262-7.

Some non-traditional phenomenological approaches and methods are suggested for reconstruction of the analytical structure of observed processes and signals. These are, in particular, a family of methods for revealing latent periodicities, further generalization of the classic weighted least-squares method, the block approximation method. Along with the theoretical description and substantiation of the suggested methods, a variety of examples of application of these methods in different areas of science and engineering are given as well as the results of their comparison by efficiency with some known approaches. There are also some solved problems of reconstructing the analytical structure of processes inaccessible for solution by the classic methods.

The monograph is intended for a wide circle of researchers of processes and signals in various spheres of life, science and engineering: physics, chemistry, astronomy, space research, aviation, instrument-making, vibro-tests of various constructions, biology, medicine, sociology, statistics, economy, analysis of market trends, etc.

 Acronyms and Abbreviations
 Foreword of Scientific Editor
 Author’s preface


 Analysis of the structure and prediction of processes containing latent periodicities
  1.1.General characteristics of the problem
  1.2.Review of the known methods of revealing latent periodicities
  1.3.On the possibility and correctness of application of the Fourier harmonic analysis for revealing latent periodicities
  1.4.Family of D-methods for revealing latent periodicities
  1.5.Finite-difference pattern of D-methods for n = 1 (D1-method)
  1.6.Minimization of function DX(τ) and practical calculation of the periodicities’ parameters
  1.7.Determination of the order of the polynomial non‑periodic component
  1.8.Some peculiarities of application of the discrete algorithm of D-method
  1.9.The results of testing of D-method and its comparison with some known ones
  1.10.General qualitative features of D-methods


 Some non-traditional approaches to approximation of processes using their measurements
  2.1.Generalization of the weighted root-mean-square criterion and a notion of the weighted orthogonality
  2.2.The method of consecutive correction of the generalized polynomial coefficients
  2.3.The block approximation method
  2.4.The subcase of approximating function Φ1
  2.5.The peculiarities of algorithms of the block approximation method
  2.6.Comparison of the classical weighted root-mean-square method with its generalization and the method of consecutive correction of coefficients
  2.7.Investigation of the block approximation method using test cases
 Application of the developed methods of revealing latent periodicities and the generalized approximation methods to the analysis of structure and propagation of some real processes
  3.1.Analysis of the structure and prediction of change of the space object orbit elements
  3.2.The forecast of the solar activity
  3.3.Analysis of photometric signatures of space objects
  3.4.Analysis of radar signatures of space objects
  3.5.Analysis of radio signatures for the sake of recognition of space objects
  3.6.Analysis and prediction of processes like the transient response
  3.7.Analysis of some geo- and astrophysical processes
  3.8.Analysis of vibrograms

About the author
Stanislav S. Veniaminov

Doctor of sciences, professor, laureate of the international award of the American Association for the Advancement of Science (AAAS), academician of the International Academy for Integration of Science and Business, academician of the International Public Development Academy, member of the Interagency Space Debris Coordination Committee (since 1993), member of the Committee on Space Debris of the National Research Council of USA (1993–1995), member of the Expert Working Group on Space Threats of RAS (since 2012), co-chairman of the US–Russian Space Surveillance Workshop (since 1994). An expert in the fields of control of complex systems, operations research, mathematical methods of discrete optimization, planning the search for space objects, problems of technogenic contamination of space. Leading scientist of the Scientific Research Center “Kosmos” in the field of space surveillance. Author of more than 430 scientific publications.