The new methods for system-cognitive analysis to identify and present graphical visualization of causal functions from the large dimension empirical data and its software tools - «EIDOS» system are discussed.
In this article application of the method of computerized system-cognitive analysis and its programmatic tooling – system "Eidoses" for detection of cause and effect associations from the trial-and-error data is considered. In the capacity of a toolkit for the formal submission of cause and effect associations cognitive functions are tendered. Cognitive functions represent many-valued interval functions of many arguments in which one various value of function in a various degree match to various value of arguments, and the quantitative standard of this correspondence appears to be the knowledge, i.e. the information about cause and effect associations in the trial-and-error data, beneficial to a goal achievement
This article briefly reviews the classical concept of functional dependence in mathematics, determines the limitations of this concept for adequate modeling of reality and formulates the problem, consisting in search of such generalization of the concept of func-tions, which is more suitable for the adequate reflec-tion of causal relationships in the real domain. Also, it discusses theoretical and practical solving the prob-lem, consisting in: (a) we suggest the universal method of calculating the amount of information in the value of argument about the meaning of the function, i.e. cognitive functions which is independent from the subject area; b) we offer software tools: Eidos intelli-gent system, allowing in practice to carry out these calculations, i.e. to build cognitive functions based on a fragmented noisy empirical data of high dimension. We also offer the concepts of nonreducing, partially and completely reduced direct and inverse, positive and negative cognitive functions and the method of formation of reduced cognitive function, which is a generalization of known weighted least-squares meth-od on the basis of observation the amount of infor-mation in the values of the argument about the values of the functions accounting
The results of cluster analysis of the operational functioning of the Russian arbitration courts of various instances are shown, and the new mathematical model of discriminant analysis to measure the efficiency of arbitration courts are presented
CLIMATIC CHANGES IN THE BLACK SEA REGION AND ELABORATION OF STRATEGY FOR ITS SUSTAINABLE DEVELOPMENT
In this article, we consider some aspects of regional development under changing climatic conditions. Further, we discuss trends and in global and regional climate in the past century and scenarios of climatic changes up to the end of the current century. The system of measures is suggested for transition to sustainable development of Russian Black Sea Coast. The conclusion is made that elaboration and correction of the regional sustainable development strategy requires wide spreading of information about climatic changes, environmental, economical and demographic conditions in the region
A simple climate–economic model based on the AK model of economic growth with the endogenous depreciation rate linear in temperature and on the exogenous climate scenario with temperature linear in time is considered. The analytical solution of the model is obtained. The uncertainty of temperature projections is introduced in the model, and the moments of model state variable are calculated analytically. Numerical examples are provided
This work studies the mathematical model of the
object “inverted pendulum” on the example of the
unstable electromechanical devices which is
balancing robot on wheel couple. Unfortunately,
many details of object model are unknown. Logical
and empirical method offers hypotheses about the
difference between the actual object model from its
mathematical approximation based on logical
analysis with subsequent refinement of this model
and testing of the hypothesis with modeling of the
systems with the updated model. As a result, the
amendments to the model have been found
containing nonlinear components. With the help of
these amendments, the dynamic characteristics of
the actuator, filters, friction and the tendency of the
object to fluctuations are better taken into account
According to measurement theory, statistical data
are measured in various scales. The most widely
used ordinal scale, scales of intervals and relations.
Statistical methods of data analysis should
correspond to the scales in which the data is
measured. The term "correspondence" is specified
with the help of the concepts of an adequate
function and an allowable scale transformation. The
main content of the article is a description of the
average values that can be used to analyze data
measured in the ordinal scale, interval and
relationship scales, and some others. The main
attention is paid to the means for Cauchy and the
means for Kolmogorov. In addition to the mean,
from this point of view, polynomials and correlation
indices are also analyzed. Detailed mathematical
proofs of characterization theorems are given for the
first time in scientific periodicals. It is shown that in
the ordinal scale there are exactly n average values,
that can be used, namely, n order statistics. The
proof is represented as a chain of 9 lemmas. In the
scale of intervals from all Kolmogorov means, only
the arithmetic mean can be used. In the scale of
relations from all the Kolmogorov means, only the
power means and the geometric mean are
permissible. The kind of adequate polynomials in
the relationship scale is indicated
The model of chaotic behavior of nucleons in nuclei, based on the model of nuclear interactions and the Fermi-Dirac statistics is discussed
Estimation of chaos and order in structure of electronic systems of atoms, protein molecules, webs of spiders, poetic products is done with the help of synergetic information theory. Existence of statistical rule of structural organization in nature is expected. This rule directs evolution of discrete system towards balance of chaos and order.