1

1. Kudrin B.I. Introduction to technology. - 2nd ed., Revised, add. - Tomsk: TSU, 1993 .-- 552 p.

2. Mathematical description cenoses and laws of technology. Philosophy and the formation of technology / ed. B.I. Kudrina // Cenological studies. - Issue. 1-2. - Abakan: Center systems research, 1996 .-- 452 p.

3. Gnatyuk V.I. The law of optimal construction of technocenoses: monograph. - Issue 29. Census studies. - Moscow: TSU Publishing House - Center for System Research, 2005. - 452 p. (http://www.baltnet.ru/~gnatukvi/ind.html).

4. Gurina R.V. Rank analysis of educational systems (cenological approach): guidelines for educators. - Issue 32. "Census Studies". - M .: Technetics, 2006 .-- 40 p. (http://www.gurinarv.ulsu.ru).

5. Gurina R.V., Dyatlova M.V., Khaibullov R.A. Rank analysis of astrophysical and physical systems // Kazan Science. - 2010. - No. 2. - S. 8-11.

6. Gurina R.V., Lanin A.A. The limits of applicability of the law of rank distribution // Technogenic self-organization and the mathematical apparatus of cenological research. - Issue. 28. "Census studies". - M .: Center for System Research, 2005. –S. 429-437.

7. Khaibullov R.A. Rank analysis space systems// Izvestia GAO in Pulkovo. Proceedings of the second Pulkovo youth conference. - SPb., 2009. - No. 219. - Issue. 3. - S. 95-105.

8. Uchaikin M.V. Application of the law of rank distribution to objects Solar system// Izvestia GAO in Pulkovo. Proceedings of the second Pulkovo youth conference. - SPb., 2009. - No. 219. - Issue. 3. - S. 87-95.

The rank distribution (RR) is understood as the distribution obtained as a result of the procedure for ranking the sequence of parameter values ​​assigned to the rank. Rank r is the number of the individual in order in the PP. Ranking is a procedure for ordering objects according to the severity of any quality in descending order of this quality. Real RR can be expressed by various mathematical dependencies and have a corresponding graphical form, however, the most important are hyperbolic rank distributions (HRD), since they reflect the sign of “coenosity” - the belonging of a set of ranked objects (elements, individuals) to cenoses. The theory of cenoses as applied to technical products was developed by Professor B.I. Kudrin more than 30 years ago (www kudrinbi.ru) and was successfully introduced into practice. Methods for constructing geological exploration and their subsequent use in order to optimize cenosis constitute the main meaning of rank analysis (RA) (cenological approach), the content and technology of which is a new direction that promises great practical results. The law of hyperbolic rank distribution of individuals in the technocenosis (H-distribution) has the form:

W = A / r β (1)

where W is the ranked parameter of individuals; r - rank number of an individual (1,2,3….); A is the maximum value of the parameter of the best individual with the rank r = 1, i.e. at the first point; β - rank coefficient characterizing the degree of steepness of the PP curve (for technocenoses 0.5< β < 1,5 ).

If any parameter of the cenosis is ranked, then the PP is called the rank parametric one. The subordination of the community of individuals to the GRR law (1) is the main sign of cenosis, but insufficient. In addition to this feature, cenoses, unlike other communities, have a common habitat, and its objects are included in the struggle for resources.

IN AND. Gnatyuk developed the RA method for the optimization of technical systems-cenoses. The possibilities of practical use of RA in pedagogy are described by R.V. Gurina (http://www.gurinarv.ulsu.ru), and also developed a methodology for its application in this area. The number of individuals in a cenosis determines the power of the population. The terminology came from biology, from the theory of biocenoses. "Cenos" is a community. The term biocenosis, introduced by Möbius (1877), formed the basis of ecology as a science. B.I. Kudrin transferred the concepts of "cenosis", "individual", "population", "species" and from biology to technology: in the technique of "individual" - individual technical products, technical specifications, and a large set of technical products (individuals) whose PP is expressed by law (1) is called a technocenosis.

V social sphere"Individuals" are people organized in social groups(classes, study groups), then the population power is the number of students in the group. School is also a sociocenosis, consisting of individuals - separate structural units - classes. Here, the population capacity is the number of classes in the school. The totality of schools is a cenosis of more large scale, where the individual, the structural unit of the given cenosis is the school. The ranked parameters W in technocenoses are technical or physical parameters that characterize an individual, for example, size, mass, power consumption, radiation energy, etc. In sociocenoses, in particular pedagogical cenoses, the ranked parameters are academic performance, rating in points of participants in Olympiads or testing; the number of students enrolled in universities and so on, and the ranked individuals are the students themselves, classes, study groups, schools, and so on.

Recent studies have shown that the aggregates of space objects in many systems (galaxies, the solar system, clusters of galaxies, etc.) are cenoses (cosmocenoses, astrocenoses). However, astrocenoses differ from tenocenoses and sociocenoses in that a person cannot influence the state, change and optimize them. In space, objects are rigidly interconnected by the forces of gravity, which determine their behavior. The specificity of astrocenoses has not been fully elucidated; the RA method applied to astrocenoses has not been developed, which determined the purpose of this study. The goal was divided into a number of tasks:

1. Study of the RA method, clarification of the possibility of applicability of the RA method to astrophysical systems-cenoses (ie, to what extent is RA applicable to astrocenoses).

2. Step by step description application of the RA method for astrocenoses.

After studying the technique of using RA for technocenoses, its general (universal) elements were identified, which apply to all types of cenoses. Thus, the RA method includes the following universal procedure steps.

1. Allocation of cenosis - a set of objects of the studied community (system).

2. Allocation of ranking parameters. These parameters can be the mass, size of objects, cost, energy reliability, the percentage of elements in the composition of the object under study, USE scores of test participants, etc.

3. Parametric description of the cenosis. Creation of a spreadsheet (database) containing systematized information about the parameters of individual individuals of the cenosis.

4. Construction of a tabulated empirical RR. The tabulated PP is a table of two columns: the parameters of individuals W arranged by rank and the rank number of an individual r (r = 1,2,3 ...). The first rank is the individual with the maximum parameter value, the second rank is the individual with the highest parameter value among other individuals, etc.

5. Construction of a graphical empirical RR. The graph of the empirical rank curve has the form of a hyperbola: the rank number r is plotted along the abscissa axis, the investigated parameter W is plotted along the ordinate axis, Fig. 1, a. All data is taken from the tabulated PP.

Rice. 1. Hyperbola (a) and "rectified" hyperbolic dependence on a double logarithmic scale (b); B = lnA

6. Approximation of empirical RR. The approximation and determination of the parameters of the RR, as a rule, is carried out using computer programs, with their help, the confidence interval is set, the parameters of the distribution curve A, B are found, the regression coefficient Re (or Re2) is also determined, showing the degree of approximation of the empirical hyperbola to the theoretical one. In this case, an approximation ideal curve is drawn (and, if necessary, on both sides of it, the confidence interval lines).

7. Linearization of GDG: construction of an empirical RR in logarithmic coordinates. Let us explain the process of linearization of dependence (1). Taking the logarithm of dependence (1) W = А / r β, we obtain:

lnW = lnА - β ln r (2)

Denoting:

lnW = y; lnА = В = const; ln r = x, (3)

we get (2) in the form:

y = B - β x. (4)

Equation (4) is a decreasing linear function (Fig. 1, b). Only the ordinate is lnW, and the abscissa is lnr. To construct a line graph, a table of empirical values ​​of lnW and lnr is compiled, according to the values ​​of which a graph of the dependence of lnW (lnr) is plotted using computer programs.

Manually coefficient β is determined by the formula:

β = tan α = lnA: ln r,

coefficient A is determined from the condition: r = 1, W1 = A.

8. Approximation of the empirical dependence ln W (lnr) to the linear Y = B - β x.

This procedure is also performed using computer programs; followed by finding the parameters β, A, determining the confidence interval, determining the regression coefficient Rе (or Rе 2), which expresses the degree of approximation of the empirical graph ln W (ln r) to a linear form. At the same time, an approximation line appears.

9. Optimization of cenosis (for bio, - techno, - sociocenoses).

The procedure for optimizing the system (cenosis) consists in working together with tabulated and graphical distributions and comparing the ideal curve with the real one, after which they conclude: what practically needs to be done in the cenosis so that the points of the real curve tend to lie on the ideal curve. The closer the empirical distribution curve approaches the ideal curve of the form (1), the more stable the system. The optimization stage includes the following procedures (actions).

Theoretical part: joint work with tabulated and graphical PP:

Finding anomalous points and distortions according to the schedule;

Determination of their coordinates and their identification with real individuals by tabulated distribution;

Practical part: working with real objects of the cenosis to improve it:

Analysis of the causes of anomalies and the search for ways to eliminate them (managerial, economic, production, etc.);

Elimination of anomalies in the real cenosis.

Optimization of technocenoses according to V.I. Hnatyuk is carried out in two ways:

1. Nomenclature optimization - a purposeful change in the number of cenosis, directing the real RR in form to the ideal (1). In a biocenosis, a flock is the expulsion or destruction of weak individuals, in study group it is the screening of the unsuccessful, in the technocenosis - getting rid of rubbish, transferring used equipment to the category of scrap metal.

2. Parametric optimization - purposeful improvement of the parameters of individual individuals, leading the cenosis to a more stable, efficient state. In the pedagogical cenosis - the educational group (class) - this is work with the unsuccessful - improving their performance indicators, in the technocenosis - replacing old technology with improved models.

As stated above, optimization procedure 9 is not applicable to astrocenoses. Studying their geological exploration, one can only extract one or another useful scientific information about the state of astrocenosis, thereby expanding the understanding of the astronomical picture of the World. What is the nature of deviations in real geological exploration of objects of astrophysical cenoses from the ideal H-distribution and what do they indicate? On the graphs of exploration of objects of astrocenosis systems, 2 types of distortions were found:

I. Several points fall out of the confidence interval of the GRR or the hyperbole is distorted (the presence of "humps", "valleys", "tails" (Fig. 2, a).

II. A sharp break in the logarithmic straight line lnW (lnr), dividing it into 2 segments (at an angle to each other or with an offset along the y-axis).

Figure 2, a, b - graphs of the RR of Satup satellites with distortions of the first type.

Due to the imperfection of measuring technology or methods of astronomical measurements, out of all 62 satellites of Saturn, there is information about the masses of 19 satellites and about the diameters of 45 satellites. It is clearly seen from the graphs that in a system with a large number of individuals (Fig. 2, b), the empirical points reflecting the sizes of satellites better fit the logarithmic straight line, which indicates more adequate information about the completeness of the system. The foregoing allows us to assert that the use of RA makes it possible to predict the presence of missing objects in space systems.

Rice. 2. Rank distribution of Saturn's satellites on a double logarithmic scale ln W = f (ln r); r - satellite rank number; a) RR 19 satellites by known masses; b) RR satellites in the same system with a large number of individuals - 45 satellites with known diameters

When studying the graphic RR of astrocenoses, it was found that the first type of distortions may indicate that:

Some objects do not belong to this astrocenosis (system, class);

Measurements of parameters of astrocenosis objects are not accurate;

There is not enough information about the completeness of the astrophysical system-cenosis. Moreover, the more complete the system, the greater the regression coefficient.

The second type of distortion testifies to the following.

If there is a sharp kink in the straightening graph, this means that the system consists of two subsystems. A similar case is presented by the graphs in Fig. 3, 4. At the same time, on the W (r) graph, an acute kink is formed by two hyperbolas "creeping over each other" (Fig. 3, a), while this kink is not always as pronounced as on the graph in a double logarithmic scale ( fig. 3 b, 4, b). The smaller the angle between the linearized segments on the ln W (ln r) graph, the more pronounced the kink of the hyperbola on the W (r) graph.

In fig. 3, a, b shows the graphs of the geological distribution of known galaxies in relation to the distance from our solar system (40 objects in total).

If there is a sharp kink in the straightening graph, this means that the system consists of two subsystems. RA makes it possible to theoretically divide the system of galaxies into two classes: peripheral (distant) group -1 and local (nearby) group of galaxies - 2, which corresponds to astronomical classification data.

Rice. 3. Rank distribution of galaxies by distance from the Solar System, where 1 is a peripheral group of galaxies, while Re = 0.97; 2 - local group of galaxies, Re = 0.86; W is the distance of the Galaxy, kpc; r is the rank number of the galaxy. A total of 40 objects. a) Graph W (r), Re = 0.97; b) Graph ln W = f (ln r), Re = 0.86

Rice. 4. РР of the masses of the planets of the Solar system (in terrestrial masses), where group 1 - the giant planets (Jupiter, Saturn, Uranus, Neptune); 2 - terrestrial planets; W is the mass of the planet, M; r is the rank number of the planet. A total of 8 objects; a) Graph W (r), Re = 0.99; b) Graph ln W = f (ln r), for 1 - (giant planets) Re = 0.86, for 2 also - Re = 0.86

As you know from the course of astronomy in our planetary system, there are 2 subsystems: giant planets and terrestrial planets. In fig. 4, a, b show the GRD of the planets of the Solar System by masses. Note that directly on hyperbolic RRs, the breaks may not be clearly visible, and it is impossible to distinguish subsystems on them (Fig. 4, a), therefore, it is necessary to construct the RR on a double logarithmic scale, on which the breaks are pronounced (Fig. 4, b).

Using reference books of physical quantities and an Internet resource, the construction of the geological exploration of other astrocenoses was carried out, confirming the above. The approximation was carried out using the QtiPlot program.

Thus:

The RA method for systems-cenoses by analogy with technocenoses is considered and described step by step;

The specificity of the application of RA to astrocenoses has been determined;

The possibility of applying RA to the study of astrophysical systems-cenoses in the plans has been determined:

Identification of subsystems in space systems-cenoses; the method consists in fixing and studying the breaks of the line graphs of geological exploration in a double logarithmic scale;

Prediction of the completeness of astrophysical systems-cenoses;

Further research is required in this direction confirming the conclusions drawn.

Bibliographic reference

Ustinova K.A., Kozyrev D.A., Gurina R.V. RANK ANALYSIS AS A RESEARCH METHOD AND THE POSSIBILITY OF ITS APPLICATION TO ASTROPHYSICAL SYSTEMS // International Student scientific bulletin. – 2015. – № 3-4.;
URL: http://eduherald.ru/ru/article/view?id=14114 (date accessed: 12/26/2019). We bring to your attention the journals published by the "Academy of Natural Sciences"

George Zipf empirically found that the frequency of use of the Nth most frequently used word in natural languages ​​is approximately inversely proportional to the number N and was described by the author in the book: Zipf G.R., Human Behavior and the Principle of Least Effort, 1949

“He found that the most common in English language the word ("the") is used ten times more often than the tenth most frequently used word, 100 times more often than the 100th most frequently used word, and 1000 times more often than the 1000th most frequently used word. In addition, it was found that the same pattern holds true for market share. software, soft drinks, cars, sweets and for the frequency of visits to Internet sites. [...] It became clear that in almost every field of activity, being number one is much better than number three or number ten. Moreover, the distribution of remuneration is by no means even, especially in our world entangled in various networks. And on the Internet, the stakes are even higher. The market caps of Priceline, eBay and Amazon reach 95% the aggregate market capitalization of all other areas e-business... There is no doubt that the winner gets a lot. "

Seth Godin, Idea Virus? Epidemic! Make customers work for your sales, St. Petersburg, "Peter", 2005, p. 28.

“The meaning of this phenomenon is that […] the ability of participants in creativity to enter completed works is distributed among participants in accordance with the law, the product of the number of entries by the rank of the participant (by the number of participants with the same frequency of entry), the value is constant: f r = Const. […] In the ranking list of all participants in creativity, in this case, words, the property of uneven distribution of migration ability is revealed, and with it the regularity of the relationship between quantity and quality in creative activity in general. […]

In addition to literary sources, Zipf investigated many other phenomena suspicious of rank distribution - from the distribution of the population by cities to the arrangement of tools on a carpenter's workbench, books on a table and a scientist's rack, everywhere bumping into the same pattern.

Regardless Zipf close distribution was revealed Pareto in the study of bank deposits, Urquart in the analysis of requests for literature, Tray in the analysis of the authors' productivity of scientists. Even the gods of Olympus, from the point of view of their load of skill-forming and skill-preserving functions, behave according to Zipf's law.

Through efforts Price and his colleagues, and later, through the efforts of many scientists in science, it was found that the law Zipf has a lot to do with pricing in science.

Price writes about this: “All data related to the distribution of such characteristics as the degree of perfection, usefulness, productivity, size obey several unexpected, but simple laws [...] Is the exact shape of this distribution log-normal or geometric, or inverse-square, or obeying the law Zipf, is the subject of concretization for each separate industry. What we know consists in stating the very fact that any of these distribution laws gives results close to empirical results in each of the studied industries, and that such a phenomenon common to all industries is, apparently, the result of the operation of one law. " Price D., Regular Patterns in the Organization of Science, Organon, 1965, No. 2., p. 246».

Petrov M.K. , Art and Science. Pirates of the Aegean and personality, M., “Russian Political Encyclopedia, 1995, p. 153-154.

Besides, George Zipf also found that the most frequently used words in a language that has existed for a long time are shorter than the rest. Frequent use "worn out" them ...

1 According to the methodology, the measurement and distribution of types of natural disasters is carried out on the basis of data on damage, the number of victims and deaths by types of natural disasters. Then, measures are designed to prevent possible future natural disasters. It is known that scientific forecast and timely warning can reduce environmental damage from possible natural disasters.

Before designing measures, it is proposed to determine by modeling the patterns of distribution in descending order of the number of catastrophes. For this, the values ​​of each indicator are assigned integer ranks, starting from zero. Further, according to the values ​​of indicators with integer ranks, regularities of their rank distribution are obtained.

The distributions in descending order of the number of catastrophes of the values ​​of damage, the number of victims and victims is determined by the formula common for many processes

where Y is an indicator; r is an integer rank taken from the series 0, 1, 2, 3, ...; a 1 ... a 7 are the parameters of the statistical model, which receive numerical values ​​for a specific distribution of damage, the number of injured and dead.

Wherein activity of influence natural-natural α 1 and technogenic α 2 interference in the distribution of the values ​​of the indicator Y = Y 1 + Y 2 are calculated by the formulas α 1 = Y 1 / Y and α 2 = Y 2 / Y. The adaptability of a person k to his technogenic intervention, including measures to prevent natural disasters, is determined by the ratio of the technogenic component of the general pattern to the second component, that is, by the mathematical expression k = Y 2 / Y 1.

Examples of... According to the identification data (1), regularities were obtained.

1. The number of different types of natural disasters that have occurred in the world over 30 years (1962-1992) changed in terms of material damage (Table 1) according to the pattern

Table 1. The number of disasters in the world for 30 years (1962-1992) by property damage

	disasters		Calculated values ​​(2)

Table 1 and others, the following types of disasters were adopted: GL - hunger; ЗМ - frost; ЗС - drought; ЗТ - earthquakes; IW - eruptions; ND - floods; НН - invasion of insects; OP - landslides; PZh - fires; SL - avalanche; CX - dry winds; TSh - tropical storms; TsN - tsunami; SHT - storms; ED - epidemics.

The first component (2) shows the natural process of the ranking of types of natural disasters, and the second - the stressful excitement of mankind for material damage, as a negative (“+” sign) response to insufficient prevention actions emergencies and elimination of the consequences of past disasters.

The indicators of the adequacy of the model (2) and others were determined as follows. The difference between the actual and calculated values ​​of the indicator is used to calculate the absolute error ε by the expression. The relative error Δ (%) is determined from the expression. From these residues, the maximum value of Δ max (modulo) is selected, which in table. 1 is underlined. Then the confidence probability D of the found statistical regularity will be equal to ... From the data table. 1 that the maximum relative error of formula (1) is 52.0%. At the same time, it is known that the distributions in descending order of the values ​​of the indicator have significant errors at the end of the series. Therefore, the last values ​​of the series can be neglected; at ranks 7, 8 and 9, the number of catastrophes is equal to one. They are 3 x 100/241 = 1.24%. If we exclude them, then the maximum error of formula (2) will be 20.75%. Confidence in (2) will be at least 100 - 20.75 = 79.25%. Such trust will allow the application of formula (2) in the approximate calculations of material damage from future disasters expected in the future.

Table 2. Statistical Model Analysis (2)

Table 2 shows the results of calculating both components N 1 and N 2 of formula (2), as well as the values significance factors α 1 and α 2 of these components of material damage and adaptability coefficient k of humanity (at the time of registration of the dynamics of the number of catastrophes) to the distribution of the number of catastrophes.

From the data table. 2, it can be seen that at ranks 6-9 the coefficient of adaptability of mankind to eruptions, landslides, tsunamis and frosts in terms of material damage tends to infinity.

A person cannot yet overcome fires at k = 15.00.

2. The number of types of natural disasters in the world for 30 years (1962-1992), distinguished by the number of victims, changes according to the statistical regularity (tab. 3, tab. 4)

From table. 4 shows that stress arousal is maximal for hunger (4th rank).

3. The number of types of natural disasters in the world according to the number of people killed gets a pattern (Table 5 and Table 6) according to the formula

Table 3. The number of disasters in the world in 30 years (1962-1992) by the number of victims disasters Calculated values ​​(3)

Table 4. Statistical Model Analysis (3)

Table 5. The number of disasters in the world in 30 years (1962-1992) by the number of deaths disasters Calculated values ​​(4)

Table 6. Analysis of the model (6) of the number of catastrophes

From the data table. 6 it can be seen that the stressful excitement of humanity is maximum for storms, which have the fifth rank in terms of the number of deaths.

To prove that a model of type (1) is a stable law, it is necessary that the adopted coefficients of activity and adaptability also change according to stable laws.

According to the table. 6 models were obtained for data on the death toll:

the coefficient of significance of the first component of the model (4) is

the coefficient of significance of the second component;

the coefficient of adaptability of mankind to natural disasters by the number of deaths over 30 years (1962-1992) changed according to the formula

According to three indicators, and there may be many of them, it is possible to determine ranking place m r (in these examples, without taking into account the weighting coefficients of indicators) of each type of natural (and in the future and not natural) disasters (Table 7).

	Natural disaster type	Material damage		Number of victims		The death toll
	GL - hunger
	ЗМ - frost
	ЗС - drought
	ЗТ - earthquakes
	IW - eruptions
	ND - floods
	НН - invasion of insects
	OP - landslides
	PZh - fires
	SL - avalanche
	CX - dry winds
	TSh - tropical storms
	TsN - tsunami
	PCS - storms
	ED - epidemics

Note: floods are most dangerous, and frosts are safe.

The use of the method of rank analysis in the distributions of natural disasters by type will expand the classification of disasters, in particular, with the inclusion of new types of natural disasters, and in the future, classes of any types of anthropogenic impacts.

BIBLIOGRAPHY:

1. Korobkin, V.I. Ecology: textbook for universities / V.I. Korobkin, L.V. Peredelskiy. - Rostov on Don: Publishing house "Phoenix", 2001. - 576 p.
2. Mazurkin, P.M. Statistical ecology / P.M. Mazurkin: Tutorial... - Yoshkar-Ola: MarSTU, 2004 .-- 308 p.
3. Mazurkin, P.M. Geoecology: Regularities of modern natural science: Scientific ed. / P.M. Mazurkin. - Yoshkar-Ola: MarSTU, 2006 .-- 336 p.
4. Mazurkin, P.M. Statistical modeling. Heuristic-mathematical approach / P.M. Mazurkin. - Scientific publication... - Yoshkar-Ola: MarSTU, 2001 .-- 100 p.
5. Mazurkin, P.M. Math modeling. Identification of one-factor statistical patterns: Textbook / P.M. Mazurkin, A.S. Filonov. - Yoshkar-Ola: MarSTU, 2006 .-- 292 p.

Bibliographic reference

Mazurkin P.M., Mikhailova S.I. RANGE DISTRIBUTION OF NATURAL DISASTER TYPES // Modern science-intensive technologies. - 2008. - No. 9. - S. 50-53;
URL: http://top-technologies.ru/ru/article/view?id=24197 (date accessed: 12/26/2019). We bring to your attention the journals published by the "Academy of Natural Sciences"

Lecture 5.

RANGE ANALYSIS technology

TECHNOCENOZES

Introductory remarks

Rank analysis as the main tool of the technocenological method of studying large technical systems of a certain class is based on three foundations: a technocratic approach to the surrounding reality, which goes back to the third scientific picture of the world; principles of thermodynamics; non-Gaussian mathematical statistics of stable infinitely divisible distributions.

The center of the third scientific picture of the world is a fundamental concept that complements the ontological description of the surrounding reality with a fundamentally new stratification level. This is a technocenosis, the main distinguishing feature of which is the specificity of connections between technical elements-individuals. Technocenoses today see the prototype of the future technosphere, which, in terms of the complexity of its organization and the speed of evolution, will surpass the biological reality that generates it.

The specificity of technocenoses lies in the methodological foundations of their research. Technocenoses defy description nor traditional methods Gaussian mathematical statistics, operating with the concepts of mean and variance as informatively rich convolutions of large arrays of statistical information, or imitation models that underlie reductionism. To correctly describe the technocenosis, it is necessary to constantly operate with a sample in general, no matter how great it is, which implies the construction of species and rank distributions, theoretical basis which lies in the field of non-Gaussian mathematical statistics of stable infinitely divisible distributions.

Methods for constructing species and rank distributions and their subsequent use in order to optimize the technocenosis constitute the main meaning of rank analysis, the content and technology of which is, in fact, a new fundamental scientific direction, promising great practical results.

Target setting of the lecture - to describe in detail the methodology of rank analysis, systematize its technology, including procedures for describing, processing statistics, constructing species and rank distributions, as well as nomenclature and parametric optimization of technocenoses.

5.1. Methodology for constructing rank distributions

Rank analysis is based on a very complex mathematical apparatus. However, as in any fundamental theory, there is a certain quite accessible level of problem solving, in fact, bordering on engineering methodology. Deep theoretical study, comprehensive philosophical comprehension and repeated testing in practice in various areas of human activity make it possible to consider rank analysis to be quite reliable and, as we now see, the only effective means of solving problems of a certain class (Fig.5.1).

It seems that rank analysis, allowing to solve the problems of optimal construction of technocenoses, occupies a kind of intermediate position between the simulation model

by means of which effective design is carried out certain types technology, and the methodology of operations research, which is currently used to solve the problems of geopolitical and macroeconomic planning. In this regard, it seems important to note two points. Firstly, the absence of a sufficiently deeply developed special mathematical methodology makes the apparatus of operations research very unreliable for solving problems of the corresponding macrolevel and leads, on the one hand, to numerous fruitless attempts to apply simulation modeling in the field of geopolitics and macroeconomics, and, on the other hand, generates distrust in this methodology on the part of most practitioners who still prefer to rely more on their intuition in these matters.

Secondly, all attempts to put forward requirements based on macro forecasts directly to the developers of certain types of technology or the policy of the latter, which consists in completely ignoring geopolitical and macroeconomic processes, with equal success lead to failure. It seems that it is precisely the technocenological methodology that can solve the problem of the organic connection between the extreme levels of modern technical problems (Fig. 5.1).

Within the framework of the lecture, of course, there is no opportunity to analyze in detail the technocenological approach in all its depth. We do not set ourselves such a task. However, as a first approximation (as they say, at the engineering level), it seems possible to consider rank analysis.

So, the rank analysis includes the following procedure steps:

1. Isolation of technocenosis.

2. Determination of the list of species in the technocenosis.

3. Setting species-forming parameters.

4. Parametric description of technocenosis.

5. Construction of tabulated rank distribution.

6. Construction of a graphical rank distribution of species.

7. Construction of rank parametric distributions.

8. Building a species distribution.

9. Approximation of distributions.

10. Technocenosis optimization.

Let's pay attention to one terminological feature. The fact is that the term "rank analysis", although it has already become traditional, is not entirely accurate. It would be more correct to use the term "rank analysis and synthesis", since the ten listed procedures contain both analysis and synthesis operations. However, we will not introduce new concepts and confine ourselves to the existing ones, interpreting it broadly (similar to the terms "correlation analysis", "regression analysis", "factor analysis", etc.).

Let's consider the rank analysis procedures in more detail.

1. Isolation of technocenosis

The first procedure is difficult to formalize due to the problems that in technocenological theory call conventionality of boundaries and fractality of speciation (together leading to the transcendence of technocenoses), which results in the limitations and dependence of actually existing technocenoses. Without going into the theoretical jungle, we will formulate only a number of recommendations for identifying technocenosis, which directly follow from its definition.

First, the technocenosis must be localized (delimited) in space and time. This operation requires a certain determination from the researcher, because he must understand that the technocenosanist will never be able to make an absolutely exact selection. In addition, the technocenosis is constantly changing (“living”, evolving), so it must be investigated without delay. It is also fundamental that a significant number (thousands, tens of thousands) of individual technical products should be represented in the technocenosis. different types(made according to different technical documentation), not connected with each other by strong bonds. That is, a technocenosis is not a separate product, but a multitude of them.

Secondly, a single infrastructure should be clearly visible in the technocenosis, which includes control systems and all-round support of functioning. The most important thing is that a single goal should be present and clearly formulated in the technocenosis, which, as a rule, is to obtain the greatest positive effect at the lowest cost. Of course, there can be competition among the elements of the technocenosis, but it should also be aimed at achieving a common goal. In this sense, technocenoses, as a rule, cannot be considered the workshops of an enterprise, or two or three factories that are not interconnected by a control system, or the city as a whole. Several interconnected enterprises cannot be considered a technocenosis if they constitute only a part of the system. If we talk about groupings of troops, then the technocenoses are the division, army, front, however, separately taken signal troops of the front or army aviation (like any other type of troops) are not such.

Allocation of technocenosis is accompanied by its description. It is recommended to create a special database for this, including the most systematized and standardized, sufficiently complete and at the same time, without unnecessary details, information about the species and individuals of the technocenosis. The information is structured by organizational unit. Access to it should be, if possible, automated, it is necessary to provide procedures for its analysis and generalization in an interactive mode. In this case, you should make the most of the capabilities of computer technology (in particular, standard Windows applications: Access, Excel, Fox-pro, etc.).

2. Determination of the list of species

This rank analysis procedure is just as complex and difficult to formalize. Its essence lies in the definition of a complete list of types of technology in the already identified technocenosis. This is done by analyzing the developed information base.

As we already know, the type of equipment is distinguished as a unit for which there is a separate design and technological documentation. However, there are also some nuances here. The fact is that most modern technical products consist of other products, which, in turn, also have their own documentation. Therefore, one must proceed from the fact that the type of technology should be functionally complete, relatively independent. In this sense, a shovel can be recognized as a type of technology, but a computer's processor unit is not. The shovel can perform its functions (digging the ground), and the processor unit, being taken separately, is not needed by anyone.

The difficulty lies in the fact that there are always many modifications of the same type of equipment at the same time, and at what point from the next modification arises the new kind, it is very difficult to define. It is clear that one species must differ substantially from another. The criterion for such a difference is either the difference in one of the most important classification parameters of the purpose (power, speed, voltage, frequency, range, etc.), or the presence in the design of a fundamentally new functionally important unit, block, unit (engine, generator, attachments, transport base , chassis, bodywork, etc.).

Based on the experience of researching technocenoses (in different areas human activity), in the list of species it is recommended to have two or three hundred names (with the total number of technical items-individuals up to tens of thousands of units). When compiling a list, it is important to actively use the existing standard nomenclatures, classifications, organizational structures, requirements, norms, technical descriptions, etc. However, in any case, one should strive to ensure that the list of species is, on the one hand, exhaustive, and on the other, uniform in terms of detail by modifications. It means that there should not be such a situation when one of the species is represented by only one modification, and the other - by ten.

The selected list of species should be recorded in a separate list and repeatedly checked by various specialists.

3. Specifying Species Parameters

When performing this procedure of rank analysis, it is recommended to set as species-forming several parameters that are functionally significant for the technocenosis, physically measured and accessible for research. It is desirable that they be complex and in the aggregate represent a group sufficiently complete for a qualitative description of the technocenosis from the point of view of its ultimate goal of functioning. These parameters can be cost, power capacity, structure complexity (if it can be described), reliability, survivability, number of maintenance personnel, weight and size indicators, fuel efficiency, etc. As you can see, any of the above parameters characterizes technical products very succinctly. The most important of them are the cost, energy capacity and the number of maintenance personnel (of course, including the personnel who provide comprehensive support for the operation of this type of equipment). It seems that it is these parameters that most capaciously reflect the energy embodied in a particular technical product during its manufacture.

4. Parametric description of technocenosis

After specifying the species-forming parameters, it is necessary to determine and enter into the technocenosis database the specific values ​​of these parameters that each type of equipment from its composition possesses. This is a long and painstaking statistical work, but it is quite accessible to every researcher. One should only strive to ensure that one system measurements, i.e. for different types, the parameter must be determined in the same units (kilograms, kilowatts, rubles at the same rate, man-hours, etc.). In the created information base of the technocenosis, of course, the corresponding fields should be initially provided for the subsequent entry of the values ​​of specific parameters.

The work on creating an information base of a technocenosis is completed after a multidimensional spreadsheet (a database that includes a databank and a control system) has been created, which includes a systematized in a certain order (by enlarged types of equipment, subdivisions of a technocenosis, boundary values ​​of parameters or other features ) information on the types of technical products included in the technocenosis, and the values ​​of species-forming parameters that characterize each of these types.

The key parameter, which we have not yet talked about, but which must be present in the generated database, and in the first place, is the number of units of equipment of each of the species, which they are represented in the technocenosis. We know that a group of technical products of the same type in a technocenosis is called a population, and their number is called a population power.

Here it will be useful to once again recall the fundamental difference between a species and an individual. A view is an abstract objectified concept, in fact, our internal idea of ​​the appearance of a technical product, formed on the basis of knowledge and experience. We call the type a brand or a model of technology (a ZIL-131 car, an ESB-0.5-VO power plant, a large sapper shovel, the Progress spacecraft, etc.). As part of the investigated technocenosis, a technical individual functions, for example, a specific car (brand - ZIL-131, chassis - No. 011337, serial number of the engine - 17429348, mileage at the moment - 300 thousand km, driver - Ivanov, on the left side of the body - dirty oil spot). In total, there are currently 150 ZIL-131 vehicles in the technocenosis. Thus, in the database we will have a record in some place: view - ZIL-131 car; purpose - transportation of goods; the number in the technocenosis (population capacity) - 150 units; cost - 10 thousand dollars; weight - 5 tons, etc.

5. Building a tabulated rank

distribution

The first four procedures complete the so-called information stage rank analysis. The next, analytical stage, in fact, boils down to building rank and species distributions of a technocenosis on the basis of an information database. The starting point here is the tabulated rank distribution.

In general, the rank distribution is understood as the Zipf distribution in the rank differential form, which is the result of the approximation of the non-increasing sequence of parameter values ​​assigned to the rank obtained in the procedure for ordering the types of technocenosis. The number of species in the technocenosis (population power) can be considered as a parameter. In this case, the distribution is called the rank specific distribution. Or any of the species-forming parameters may appear - then the distribution will be rank parametric. There is a significant specificity in the technology of constructing distributions, but more on that later. The rank of a species or individual is a complex characteristic that determines their place in an ordered distribution. Ranking has deep energetic rationale and fundamental philosophical significance. However, we will not go into details and say only that for us the rank is the number of the species in order in a certain distribution.

The tabulated rank distribution combines all the statistics on the technocenosis that are significant from the point of view of the technocenological approach in general. In form, this is a table. Below is a variant of this distribution (Table 5.1). As you can see, the first line of the table is occupied by the record about the most numerous video equipment (in this case, the electric power infrastructure of the grouping of forces was analyzed, and electrical equipment was considered as types). The second largest power plant was put in second place, and so on, up to unique species for a given technocenosis, of which there are only one.

Table 5.1

An example of a tabulated rank distribution of a technocenosis

Rank	ETS type	Number in the grouping, units	Species-forming parameter
			power, kWt	cost, $	m ass, kg	……
	AB-0.5-P / 30	2349				……
	ESB-0.5-VO	1760				……
	AB-1-O / 230	1590				……
	AB-1-P / 30	1338				……
	ESB-1-VO	1217		1040		……
	ESB-1-VZ	1170				……
	AB-2-O / 230	1093		1500		……
	AB-2-P / 30			1540		……
	AB-4-T / 230			1990		……
……	……	……	……	……	……	……
……	……	……	……	……	……	……
	ESD-100-VS			85000	3400	……
	ED200-T400			120000	4200	……
	ED500-T400			250000	6700	……
	ED1000-T400		1000	340000	9300	……
	PAES-2500		2500	500000	13700	……

The following regularity is essential for us: the smaller the number of a species in the technocenosis, the higher its main species-forming parameters. And although in some places there are deviations from this pattern, the general trend is obvious. And in this one of the most fundamental laws of nature finds its manifestation.

6. Building a graphical rank

species distribution

The species rank distribution can be depicted in graphical form. It represents the dependence of the number of technical individuals, to which the species is represented in the technocenosis, on the rank (Fig. 5.2 - for the example given in Table 5.1). In fact, the graph of the rank species distribution is a collection of points, however, for clarity, the figure also shows smooth approximating curves. But more about them later.

Each point of the graph corresponds to a certain type of technique. In this case, the abscissa on the graph is the rank, and the ordinate is the number of individuals that represent this species in the technocenosis. All data is taken from a tabular distribution.

7. Construction of rank parametric distributions

In the course of the rank analysis of the technocenosis by tabulated distribution, graphs of rank distributions are also constructed for each of the species-forming parameters. However, a certain specificity can be traced here, which consists in the fact that if species are ranked in the rank distribution, then in the parametric distribution - individuals. Figure 5.3 shows a graph of the parametric power distribution (in kilowatts) for the example shown in Table 5.1. Since there can be tens of thousands of technical individuals in technocenoses, it is not possible to plot the parametric distribution in one axes for the entire technocenosis. For clarity, it is divided into fragments with an appropriate scale.

As we have already noted, in the rank parametric distribution, each point corresponds not to a species, but to an individual. The first rank is assigned to an individual with greatest value parameter, the second - the individual with the highest parameter value among individuals, except for the first, and so on. A number of remarks need to be made here. First, as we now understand, the rank in Figure 5.3 (called parametric) does not correspond to the (specific) rank in Figure 5.2. In theory, there is a connection between the two, but it is extremely complex. Secondly, because within a species, we take the value of the species-forming parameter to be the same, then on the parametric distribution graph, all individuals of this species will be depicted by points with the same ordinates. The number of these points will be equal to the number of individuals of this species in the technocenosis. The graph itself consists, as it were, of horizontal segments of various lengths. Third, the species on the rank species distribution and individuals on the rank parametric distribution that have the same ordinates are ranked arbitrarily. Fourthly, the ranking of individuals according to various parameters, although generally similar, never exactly corresponds to one another, which is also important to take into account so as not to be mistaken. Each parametric distribution has its own rank.

8. Construction of species distribution

Among the distributions of rank analysis, a specific place is occupied by the species. It is believed that it is the most fundamental. There is a theoretical substantiation and empirical confirmation that, on the one hand, the species and rank species are reciprocal forms of one distribution, and on the other hand, that an infinite set (continuum) of rank parametric distributions of a technocenosis mathematically collapses into one specific distribution.

By definition, a species distribution is understood as an infinitely divisible distribution that establishes, in a continuous or discrete form, an ordered relationship between the set of possible numbers of technocenosis individuals and the number of species of these individuals, actually represented in the technocenosis by a fixed number.

The species distribution in graphical form (Fig. 5.4) is built according to the tabulated distribution. The figure shows the distribution (which is, strictly speaking, a collection of points) for the example given earlier in Table 5.1. It is clear that it, like the rank parametric one, is practically impossible to depict in some axes, therefore, the species distribution is usually depicted in fragments with a convenient scale (one of such fragments is shown in Fig. 5.4).

Let us clarify once again how the species distribution is constructed. So, the abscissa shows the possible number of individuals of one species (possible population capacity) in the technocenosis. Obviously, there can be one, two, three individuals, etc. up to the figure corresponding to the maximum population in terms of volume. In other words, it is a series of natural numbers in ascending order. The ordinate shows the number of species represented in the analyzed technocenosis by a given number. As can be seen from the tabulated rank distribution, we have four species represented by one individual (ED200-T400, ED500-T400, ED1000-T400, PAES-2500). Therefore, we set aside a point with coordinates (1,4). Three species are represented by two individuals - point (2,3); by three individuals, two species - point (3,2); four, five, seven and eight individuals are represented by one species - points (4,1); (5.1); (7.1); (8,1), but no species is represented by six individuals, therefore, among the points of the graph there is a point with coordinates (6,0). The last point has coordinates (2349.1).

Let's make a few more important points. First, all points with zero ordinates must be taken into account in the subsequent approximation procedure. Secondly, theoretically, the species distribution contains a fundamental tendency: the greater the number in the technocenosis (the larger the number on the abscissa), the less the species diversity (the smaller the number of species on the ordinate). This is the law of nature. However, unlike rank distributions (which are always decreasing), the species distribution is not ranked; therefore, its graph contains points that seem to deviate abnormally from the rule formulated above. In Figure 5.4, such points are visible (for example, (6,0)). Where there is a thickening of abnormally deviated points (both in one direction and in the other direction), we fix the so-called zones of nomenclature disturbances in the technocenosis.

Let's try to figure out what abnormal deviations in species distribution mean (while recalling the law of optimal construction of technocenoses). If the points deviate below some smooth approximating curve, this means that in the anomalous zone of the nomenclature series of the technocenosis, an overestimated unification of technology is noted. And we know that any unification leads to a decrease in functional indicators, i.e. this technique is not reliable enough, maintainable , worse weight and dimensions, etc. If the points deviate above the curve, then there is an unjustifiably large variety of equipment, which will certainly affect (for the worse) the functioning of the supporting systems (it is more difficult to get spare parts, cook service staff, pick up the tool, etc.) In any case, the deviation is an anomaly.

In conclusion, we note that for clarity, sometimes species distributions are plotted in the form of histograms, but this has no theoretical value.

9. Approximation of distributions

As we have already noted, strictly mathematically, each distribution in graphical form is a set of points obtained from empirical data:

(x 1, y 1); (x 2, y 2); ...; (x i, y i); ...; (x n, y n), (5.1)

where i–Formal index;

n – total amount points.

The points are the result of the analysis of the tabulated rank distribution of the technocenosis. Each of the distributions has its own number of points (which is the abscissa in the distribution, and which is the ordinate, we already know). From the point of view of the subsequent optimization of the technocenosis, the approximation of empirical distributions is of great importance. Its task is to select an analytical dependence that best describes the set of points (5.1). We ask as a standard form, a hyperbolic analytic expression of the form

(5.2)

where A and α - options.

The choice of form (5.2) is explained by the traditionally established approach among researchers engaged in rank analysis. Undoubtedly, given form far from the most perfect, but it has an undeniable advantage - it reduces the problem of approximation to the determination of only two parameters: A and α ... This problem is solved (also traditionally) by the least squares method.

The essence of the method is to find such parameters of the analytical dependence (5.2) A and α that minimize the sum of the squares of the deviations actually obtained in the course of the rank analysis of the technocenosis of empirical values y i on the values ​​calculated from the approximation dependence (5.2), i.e.:

(5.3)

It is known that the solution of problem (5.3) is reduced to the solution of a system of differential equations (for (5.2) - two with two unknowns):

Below is the text of the program:

As a result, after approximation, we obtain a two-parameter dependence of the form (5.2) for each of the distributions. This is where the actual analytical part of the rank analysis ends.

5.2. Technocenosis optimization based on

rank distributions

Ranking analysis never ends with the determination of the corresponding distributions of the technocenosis. It is always followed by optimization, since our main task is always to determine the directions and criteria for improving the existing technocenosis. Optimization is one of the most difficult problems of technocenological theory. A significant number of works are devoted to this area of ​​research. And although this is a separate serious conversation, we will nevertheless consider several of the simplest optimization procedures that have been well tested in practice.

The first procedure is to determine the direction of transformation of the rank species distribution. It is based on the concept of an ideal distribution (Fig. 5.5), which is indicated in the figure with the number 2. The unit denotes the rank species distribution actually obtained as a result of the analysis of the technocenosis. Here Λ Is the number of species, and r in- species rank (see Fig. 5.2).

As the many years of experience in the study of technocenoses from various fields of human activity shows, the best is the state of technocenosis, in which in the approximation expression of the rank species distribution

(5.13)

parameter β is within

0,5 ≤ β ≤ 1,5.(5.14)

By the way, the law of optimal construction of technocenoses says that the optimal state is achieved when β = 1. However, this applies only to a certain ideal technocenosis, which functions absolutely in isolation. Such in practice does not exist, therefore, one can use the interval estimate (5.14). Figure 5.5 shows the ideal curve for better understanding (with β = 1), but not a strip satisfying requirement (5.14).

It can be seen from the figure that the real distribution differs sharply from the ideal one, and the curves intersect at the point R... Hence the conclusion: among the types of equipment with ranks r in< R the variety should be increased, and at the same time, where r in> R on the contrary, to carry out unification, which is illustrated by arrows in the figure. This seems to be the first optimization procedure.

The second procedure is the elimination of anomalous deviations in the species distribution. As already noted, in the species distribution of the technocenosis, areas of maximum anomalous deviations can be distinguished (they are shown, albeit rather tentatively, in Figure 5.6).

Here we clearly see at least three pronounced anomalies, where the empirical points actually obtained during the analysis clearly deviate from the smooth approximation curve. In this case, the curve is constructed, as we already know, by the least squares method according to the tabulated rank distribution data and is described by the expression

(5.15)

where Ω - the number of species (see Fig. 5.4.);

NS- continuous analogue of the population power;

ω 0 and α - distribution parameters.

After identifying anomalies in the species distribution, according to the same tabulated distribution, the types of equipment "responsible" for the anomalies are determined, and priority measures are outlined for their elimination. At the same time, upward deviations from the approximating curve indicate insufficient unification, and downward - on the contrary, excessive.

It should be noted that the first and second procedures are interrelated, with the first showing the strategic direction of changing the species structure of the technocenosis as a whole, and the second helping to locally identify the "most painful" zones in the nomenclature (list of types) of technology.

The third procedure is the verification of the nomenclature optimization of the technocenosis (Fig. 5.7). Obviously, in any real technocenosis, nomenclature optimization carried out within the first and second procedures can be performed only for a long period of time. In addition, the implementation in practice of the proposed measures may run into a number of subjective difficulties. Therefore, an additional optimization procedure - verification (Fig. 5.7) seems to be very useful.

Its implementation requires statistical information on the state of the technocenosis for a foreseeable period of time. This will allow the researcher to plot the dependence of the parameter β rank species distribution in time t... Suppose that this dependence turned out as shown in Figure 5.7. That is, the species composition of the technocenosis has transformed over time, and the parameter β ... With addiction β (t) on one graph it is necessary to compare the dependence E (t), where E- some key parameter characterizing the functioning of the technocenosis as a whole, for example, profit. If additional correlation analysis shows that interdependence E and β significant, a comparison of their time dependences will make it possible to draw a number of extremely important conclusions. As an example, in Figure 5.7 arrows show a method for determining the optimal value β opt.

The fourth procedure is parametric optimization (Figure 5.8). Strictly speaking, the first three optimization procedures refer to the so-called nomenclature optimization. The fourth, although considered in this case as additional to the previous ones, belongs to a slightly different sphere and is called, as already indicated, parametric. Let us give precise definitions.

The nomenclature optimization of a technocenosis is understood as a purposeful change in the set of types of technology (nomenclature), directing the species distribution of the technocenosis in form to the canonical (exemplary, ideal). Parametric optimization is a purposeful change in the parameters of certain types of technology, leading the technocenosis to a more stable and, therefore, effective state.

To date, it has been theoretically shown that there is a relationship between the nomenclature and parametric optimization procedures, when it is practically impossible to carry out one procedure without the other. Both of them are, in fact, different sides of the same process. There is a concept of optimization of technocenoses, according to which the nomenclature optimization sets the final state of the technocenosis to which it aims, and the parametric one determines the detailed mechanism of this process. We will not delve into the essence of this concept (due to its sufficient complexity), we will restrict ourselves only to an extremely simplified version of the parametric optimization procedure.

Earlier we got acquainted with the process of obtaining the rank parametric distribution. Consider an abstract example of the distribution of technocenosis by parameter W(fig. 5.8). From the law of optimal construction, it follows that for any technocenosis, the form of the so-called ideal rank parametric distribution can be theoretically specified. In the figure, it is depicted by the curve indicated by the number 2 (real - 1). It is clearly seen that these two distributions differ significantly, which indicates omissions in the scientific and technical policy pursued during the formation of the technocenosis.

If we apply the hyperbolic form of distributions that has already become traditional for us

(5.16)

where r- parametric rank;

W 0 and β - distribution parameters,

then the ideal distribution will be specified by an interval estimate of the requirements for the parameter β , and

0,5 £ β £ 1,5.(5.17)

Based on the same considerations that are given in the comments to expression (5.14), in this case, the interval estimate is replaced by a specific value β = 1... Therefore, in Figure 5.8, instead of the bar, curve 2 is shown.

The essence of parametric optimization in this case boils down to the fact that after identifying in the species distribution the types of equipment “responsible” for abnormal deviations (the second optimization procedure), the parametric ranks of these types are determined. In Figure 5.8, a similar view corresponds to a point with coordinates (r t,W 1)... Further, according to the optimal curve 2, the value is determined W 2 corresponding to the same abscissa (r t). It's obvious that W 2 can be interpreted as a kind of requirement for developers of types of equipment for a given, specific parameter (the direction of optimization is shown in the figure with an arrow). If a similar operation is carried out in the rank distributions for all the main parameters, we can talk about setting the complex technical requirements for the development or modernization of types of technical products.

There are a number of remarks to all that has been said. First, the obtained technical requirements do not have to be implemented in practice by developing new or modernizing the exploited species. It is enough to find an existing sample that meets the requirements (if, of course, it exists somewhere) and include it in the nomenclature instead of the one that does not satisfy us.

Secondly, which is extremely important to understand, in the technocenosis there is a deep, fundamental relationship between the number of types of technology (population size) and the level of their main species-forming parameters. Therefore, optimization can be carried out not only by changing the parameters, but also by changing the number of individuals of a given species in the technocenosis. The choice of the path depends entirely on the specific situation. Here we omit how this is done and refer those interested to special literature.

And finally, a final comment on the fourth optimization procedure. In its simplest version, presented here, purely technical difficulties may arise in determining the parametric rank r t... The fact is that according to the tabulated distribution, we can directly determine only the species rank, since the table provides a list of species. And on the rank parametric distributions, all individuals are ranked. Let us repeat ourselves and note that, theoretically, there is a fundamental relationship between parametric and species ranks, but it is very complex. You can get out of this situation as follows. After identifying a species requiring parametric optimization (and this is done by species distribution), its species rank is determined. Moreover, according to the species distribution, only the abundance of this species in the technocenosis is determined, and only then, taking into account the abundance, the species rank is determined according to the rank species distribution (and the actual brand of this type of equipment). If several species have the same number, then it is up to the researcher to decide which one to optimize. Knowing the species rank, using the tabulated distribution, we determine the value of the parameter corresponding to this kind... We postpone it on the rank parametric distribution (in Fig.5.8, this value W 1) and then proceed in accordance with the above procedure.

We conclude the presentation of general questions of rank analysis. In this lecture, relatively simple techniques were proposed, and this is natural, since it is necessary to start comprehending the technocenological method “from the simple”. However, the experience of many years of research on real technocenoses shows that even relatively simple methods are effective and very useful. There is even reason to say that for a certain class of problems the technocenological method in general and rank analysis in particular are the only correct methods of research and optimization.