Scientific Journal of KubSAU

One of the "points of growth" of applied statistics is methods of reducing the dimension of statistical data. They are increasingly used in the analysis of data in specific applied research, such as sociology. We investigate the most promising methods to reduce the dimensionality. The principal components are one of the most commonly used methods to reduce the dimensionality. For visual analysis of data are often used the projections of original vectors on the plane of the first two principal components. Usually the data structure is clearly visible, highlighted compact clusters of objects and separately allocated vectors. The principal components are one method of factor analysis. The new idea of factor analysis in comparison with the method of principal components is that, based on loads, the factors breaks up into groups. In one group of factors, new factor is combined with a similar impact on the elements of the new basis. Then each group is recommended to leave one representative. Sometimes, instead of the choice of representative by calculation, a new factor that is central to the group in question. Reduced dimension occurs during the transition to the system factors, which are representatives of groups. Other factors are discarded. On the use of distance (proximity measures, indicators of differences) between features and extensive class are based methods of multidimensional scaling. The basic idea of this class of methods is to present each object as point of the geometric space (usually of dimension 1, 2, or 3) whose coordinates are the values of the hidden (latent) factors which combine to adequately describe the object. As an example of the application of probabilistic and statistical modeling and the results of statistics of non-numeric data, we justify the consistency of estimators of the dimension of the data in multidimensional scaling, which are proposed previously by Kruskal from heuristic considerations. We have considered a number of consistent estimations of dimension of models (in regression analysis and in theory of classification). We also give some information about the algorithms for reduce the dimensionality in the automated system-cognitive analysis

Insects are a major component of natural biocenoses and agrocenoses. One of the largest and most numerous families are ground beetles (Carabidae); their number, according to various estimates, is more than 30,000 species. For Carabidae beetles it is common to have different ways of eating, a place of habitation, occupied layers, seasonal and daily activity. They live both on the surface and in the soil, more rarely on bushes and trees. The types of the family of ground beetles – active beetles with long, thin antennae of uniform thickness, long elytra and long legs, adapted to running. Their sizes vary from a few millimeters to 10 cm. As active predators, ground beetles play a huge practical importance, destroying pests before reaching the last threshold, thereby providing a natural regulation. Based on the fact, that the number of beetles is large, and their sizes are sometimes only a few millimeters, there is a problem of determining the species of these insects (or their identification), therefore it took a special tool, which, on the one hand, facilitate obtaining data about these insects, and on the other hand, would increase their accuracy. This article proposes a new (to this subject area) approach to identify different species of ground beetles along their outer contour with the use of software tools for automated system-cognitive analysis (ASC-analysis) – the universal cognitive analytical system called "Eidos," which is well-proven in the study of other objects. The reason why it was decided to use this system is that normal (standard) identification of ground beetles, have certain disadvantages: the human factor (manifest error in the determination); quite time consuming; the inability to increase the number of criteria to improve the reliability of the model comparison. This article aims to overcome these drawbacks, by the use of universal cognitive analytical system "Eidos", the automated system-cognitive analysis (ASC-analysis). A numerical example is given

In criminology, there are actual problems of determining the type (machine gun, rifle, large caliber, pistol) and a particular model of small rifle for its ammunition, in particular, discovered in the use of weapons. The article proposes a solution to this problem with the use of a new innovative method of artificial intelligence: automated system-cognitive analysis (ASCanalysis) and its programmatic toolkit – a universal cognitive analytical system called "Eidos". In the system of "Eidos", we have implemented a software interface that provides input to the system images, and the identification of their external contours on the basis of luminance and color contrast. Typing by multiparameter contour images of specific ammunition, we create and verify the system-cognitive model, with the use of which (if the model is sufficiently reliable), we can solve problems of system identification, classification, study of the simulated object by studying its model and others. For these tasks we perform the following steps: 1) enter the images of ammunitions into the system of "Eidos" and create mathematical models of their contours; 2) synthesis and verification of models of the generalized images of ammunition for types of weapons based on the contour images of specific munitions (multivariate typology); 3) quantification of the similarities-differences of the specific ammunition with generalized images of ammunition of various types and models of small rifle (system identification); 4) quantification of the similarities-differences of the types of munitions, i.e. cluster-constructive analysis

Classical combinatorial formula to calculate the number of combinations from n on m: C(n,m)=n!/(m!(nm)!) involves the intermediate calculation of factorials, which is often impossible when n>170, due to limitations in the capacity of numbers that are used in programming languages and created through these systems. However, in some cases it is necessary to calculate the number of combinations for n and m much larger than this limit, such as when a value greater than 10000. In such cases, there is a definite problem, which manifests itself, for example in the fact that many on-line services meant to calculate the number of combinations with these parameters do not work properly. In this article, we present its solution in the form of an algorithm and software implementation. The essence of the approach is to first decompose the factorials into prime factors and reduce them, and then to produce multiplication. This approach differs from those cited in the Internet

The article proposes to use the automated systemcognitive analysis (ASC-analysis) and its software tool which is "Eidos" system to solving multiparameter typing, system identification and cartographic visualization of spatially-distributed natural, environmental and socio-economic systems. Imagine, that we have an original point cloud with coordinates (X,Y,Z), each with known values of gradation descriptive scales of nominal, ordinal, or numeric type S(s1,s2,...,sn). Then the "Eidos" system provides: 1) building a model that contains generalized knowledge about the strength and the direction of the influence of descriptive gradations of scales at Z=M(S); 2) estimation of the values of Z for points (X,Y) described in the same descriptive scales S(s1,s2,...,sn), but not a part of the original point cloud; 3) a cartographic visualization of the spatial distribution of values of the function Z=M(S) for points outside the initial cloud, using Delaunay triangulation. Basically, this means that the "Eidos" system ensures recovery of the unknown function values on the grounds of the argument and implements it in a generic setting, independent of subject area. We propose a new scientific concept called "Geo-cognition system", which is defined as a software system that provides conversion of source data into information, and knowledge in visualization and mapping of this knowledge, resulting in the cognitive map becomes graphics. This feature can be used to quantify the degree of suitability of the watersheds for cultivation of certain crops, the evaluation of the ecological situation on particular territories on the structure and intensity of anthropogenic load, visualization of results of forecasting of earthquakes and other unwanted risks or emergencies, as well as for solving many other similar mathematical essence of tasks in a variety of subject areas. We have also shown a simple numerical example

In forensics there is an urgent need to determine the type of rifle (automatic, rifle, large caliber pistol) depending on its used ammunition found at the scene of the use of weapons. We offer a solution to this problem with the use of new innovative method of artificial intelligence: automated system-cognitive analysis (ASC-analysis) and its program toolkitwhich is a universal cognitive analytical system called "Eidos". In the "Eidos" system we have implemented the software interface that allows posting of images and identifying their outer contours. By multivariable typing, the system creates a systemic-cognitive model, the use of which, if the model is sufficiently accurate, may be helpful in solving problems of system identification, prediction, classification, decision support and research of the modeled object by studying its model. For this task the following stages: 1) input images of ammunitions into the "Eidos" system and creation of their mathematical models; 2) the synthesis and verification of the models of generalized images of ammunition for types of weapons based on the contour images of specific munitions (multiparameter typing); 3) improving the quality of the model by separating classes for typical and atypical parts; 4) quantification of the similarities-the differences between specific types of munitions with generic images of different types of ammunition of the weapon (system identification); 5) quantification of the similarity-differences between types of ammunition, i.e. cluster-constructive analysis of generalized images of ammunition. A numerical example is given. We also possess a successful experience of solving similar problems in other subject areas

The article proposes using the automated system-cognitive analysis (ASC-analysis) and its software tool, which is the system called "Eidos" for synthesis and application of adaptive intelligent measuring systems to measure values of parameters of objects, and for system state identification of complex multivariable nonlinear dynamic systems. The article briefly describes the mathematical method of ASC-analysis, implemented in the software tool – universal cognitive analytical system named "Eidos-X++". The mathematical method of ASC-analysis is based on system theory of information (STI) which was created in the conditions of implementation of program ideas of generalizations of all the concepts of mathematics, in particularly, the information theory based on the set theory, through a total replacement of the concept of “many” with the more general concept of system and detailed tracking of all the consequences of this replacement. Due to the mathematical method, which is the basis of ASC-analysis, this method is nonparametric and allows you to process comparably tens and hundreds of thousands of gradations of factors and future conditions of the control object (class) in incomplete (fragmented), noisy data numeric and non-numeric nature which are measured in different units of measurement. We provide a detailed numerical example of the application of ASC-analysis and the system of "Eidos-X++" as a synthesis of systemic-cognitive model, providing a multiparameter typization of the states of complex systems, and system identification of their states, as well as for making decisions about managing the impact of changing the composition of the control object to get its quality (level of consistency) maximally increased at minimum cost. For a numerical example of a complex system we have selected the team of the company, and its component – employees and applicants (staff). However, it must be noted that this example should be considered even wider, because the ASC-analysis and the "Eidos" system were developed and implemented in a very generalized statement, not dependent on the subject area, and can successfully be applied in other areas

The article discusses the application of automated system-cognitive analysis (ASC-analysis), its mathematical model is a system of information theory and implements, its software tools – intellectual system called "Eidos" for solving one of the important tasks of ampelography: to quantify the similarities and differences of different clones of grapes using contours of the leaves. To solve this task we perform the following steps: 1) digitization of scanned images of the leaves and creation their mathematical models; 2) formation mathematical models of specific leaves with the application of information theory; 3) modeling the generalized images of leaves of different clones on the basis of specific leaves (multiparameter typing); 4) verification of the model by identifying specific leaf images with generic clones, i.e., classes (system identification); 5) quantification of the similarities and differences of the clones, i.e. cluster-constructive analysis of generalized images of leaves of various clones. The specific shape of the contour of the leaf is regarded as noise information on the clone to which it relates, including information about the true shape of a leaf of this clone (clean signal) and noise, which distort the real shape, due to the random influence of the environment. Software tools of ASA-analysis which is intellectual "Eidos" system provides the noise suppression and the detection of a signal about the true shape of a leaf of each clone on the basis of a number of noisy concrete examples of the leaves of this clone. This creates a single image of the shape of the leaf of each clone, independent of their specific implementations, i.e. "Eidos" of these images (in the sense of Plato) - the prototype or archetype (in the Jungian sense) of the images

Intuitively everyone understands that noise is a signal in which there no information is, or which in practice fails to reveal the information. More precisely, it is clear that a certain sequence of elements (the number) the more is the noise, the less information is contained in the values of some elements on the values of others. It is even stranger, that noone has suggested the way, but even the idea of measuring the amount of information in some fragments of signal of other fragments and its use as a criterion for assessing the degree of closeness of the signal to the noise. The authors propose the asymptotic information criterion of the quality of noise, and the method, technology and methodology of its application in practice. As a method of application of the asymptotic information criterion of noise quality, we offer, in practice, the automated systemcognitive analysis (ASC-analysis), and as a technology and software tools of ASC-analysis we offer the universal cognitive analytical system called "Eidos". As a method, we propose a technique of creating applications in the system, as well as their use for solving problems of identification, prediction, decision making and research the subject area by examining its model. We present an illustrative numerical example showing the ideas presented and demonstrating the efficiency of the proposed asymptotic information criterion of the quality of the noise, and the method, technology and methodology of its application in practice

It has been proved that theoretical scientific models created as a result of the learning process, reflect not the reality of "what it really is" and only the reality "what it is" in the process of interaction with tools of empirical knowledge, i.e. the organs of perception of a certain organism that supports a corresponding form of consciousness, experimental instruments and information-measuring systems of a certain functional level. Examples and consequences of the major mistakes that have been historically made by scientists for the substantial interpretation of theoretical scientific models: this error is unwarranted giving the model the ontological status ("hypostatizations") and its associated error model giving the status of universality. The history of the emergence and development of science was viewed as a process of sequential application of natural scientific method to the study of objects of knowledge, previously studied in the framework of philosophy. We have formulated a promising idea of solving problems of philosophy of natural science methods. In the framework of implementation of this idea, we have proposed a natural-scientific formulation and solution of the basic question of philosophy. This new scientific concept of "Relatively objective and Relatively subjective" and discusses the relationship of the content of these concepts from forms of consciousness. The article gives a natural-scientific definition of consciousness and offers periodic multi-criteria classification of forms of consciousness, including 49 forms of consciousness: the 7 types of 7 consciousness and cognition methods. It examines the dialectics of the changing ideological paradigms from antiquity to the present day and a place of scientific paradigms in the process. It also describes the law of denial-denial in the change of ideological paradigms and on the basis; it explores the hypothesis about the main features of the future ideological paradigm, formed in the present. We have formulated the correct principles of interpreting scientific models of natural-scientific method – scientific method of induction and the principles of open consciousness, i.e. the principles, opening the way for the formation of new, improved and more adequate models of reality than the existing ones which were considered the only true models