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Conceptual model for measuring the scientific knowledge diffusion in the context of digitalization

The main idea of digitalization is the transition to a new technological order and, as a result, gaining competitive advantages, therefore, measuring the diffusion of scientific knowledge in the digital economy is especially relevant. The existing articles do not offer general models for the transfer of knowledge, regardless of the digitalization industry. The authors of the article have developed a conceptual model for measuring the diffusion of scientific knowledge, which allows, according to the characteristics of knowledge carriers, to assess the proximity of their paradigms, as well as the likelihood of delays in the transfer of knowledge due to the need to relay knowledge, depending on the paradigms they use. Criteria to assess the reliability of the scientific knowledge transfer in the context of digitalization are proposed.


Introduction
Due to the rapid "digitalization" of the economy, the problem of the knowledge transfer speed between industries has sharply exacerbated. This problem is caused by the fact that the paradigms comprising the subject area description languages in which the different fields of scientific knowledge exist are developing independently, becoming increasingly complex and distant from each other. This raises the problem of a cultural barrier between carriers of different paradigms. This problem is traditionally solved either by translation from one language into another, or by educating people who can alternately use different languages, for example, for communication between representatives of science and business. However, interpreter training, like different paradigms mastering, is a timeconsuming process that inevitably leads to a lag in life due to the dynamism of both science and economics. The criticality of this gap is increasing with the widespread adoption of digital technology, as the growth of computing power and the development of communication tools in scientific social networks provide new opportunities for the transfer of knowledge between carriers of various paradigms. However, there is so much knowledge and information that it is obviously impossible to do without the automation of the knowledge transfer process. At the same time, the development of

Diffusion model of scientific knowledge in the context of digitalization
Traditionally, in the publications [14][15][16], an assessment of the information transmission quality is considered, which can be reduced either to an assessment of the signal-to-noise ratio, or to the reliability of signal conversion during transmission.
However, when it comes to the knowledge transfer between carriers of different paradigms, it is necessary to take into account that the following factors will influence the knowledge transfer quality: the accuracy of the subject areas description; the accuracy of the knowledge transfer model description; the reliability of the knowledge transfer from one paradigm to another one.
The quality assessment here can be carried out only after the fact of the transfer, and its purpose will be to improve its model. Thus, the knowledge transfer quality can be defined as the adequacy of the scientific knowledge mapping presented in the original scientific worldview into scientific knowledge for the target paradigm. And the process of diffusion of scientific knowledge 1 Sk itself, as a reflection of a certain set of knowledge that exists in terms of the original scientific worldview 1 Sv into a set of scientific knowledge 2 Sk , reformulated in terms of the paradigm 2 Sv : . In order to quantify the quality of such a display, it is necessary to introduce evaluation criteria. These criteria should assess the extent to which knowledge is transmitted fully, in a timely manner and without distortions (including semantic ones) in the context of digitalization. Then the following can be selected as the evaluation criteria: Sv ; In addition, a sufficiently universal, paradigm-independent knowledge diffusion model must be introduced as part of this problem solution to formalize the transfer process as much as possible in the digitalization context.
Then the task of the transfer quality assessing or knowledge transformation between carriers of different paradigms is reduced to the task of assessing against the three criteria above. Such an assessment is relatively easy to obtain, it is quite universal. It can also be argued that a more detailed quality assessment can be carried out after the assessment according to the above criteria has yielded a positive result. For this purpose, particular criteria describing specific areas of knowledge should be developed.
In order to solve the problem of the knowledge transfer quality assessing, it is necessary to introduce a diffusion model. Neural network models, semantic network models, multi-agent models (in particular ant colony models, artificial swarm models), and graph models have been studied for model compilation. As the result of the analysis, a choice was made in favor of probabilistic graph models, as the most flexible and suitable for describing the diffusion of scientific knowledge. By probability, in this case, we mean the frequency of interaction between subjects over a certain period of time. This is due to the fact that the semantic network models allow describing the structure well, but it is very difficult to describe the transfer of information. Neural network models are good at describing data transmission, but describing structure with them is extremely difficult. Ant colony models can in principle be applied, but the modeling performed shows their discrepancy with experimental data.
Let's describe the proposed model for the diffusion of scientific knowledge. The vertices of a directed graph are carriers of knowledge that exist within a certain paradigm, arcs are the directions of knowledge transfer. Thus, the model is a network that allows you to describe the interaction between members of scientific and technical communities who are carriers of different paradigms. The model estimates the proximity of the knowledge carriers' paradigms and the probability of delays in knowledge transfer due to the need to retransmit knowledge, depending on the paradigms they use. In this case, paradigms can be divided into: phenomenological, socio-psychological, sociocultural, rhetorical, cybernetic, semiotic and critical. For each type of paradigm, the following groups of characteristics can be distinguished: social aspects, characteristics associated with areas of education, characteristics and traditions (for example, regional), age factors (in particular, complicating the transfer of knowledge between representatives of different generations), social functions of carriers of paradigms and etc. Then the analysis of similarities and contradictions for each of the paradigms should be carried out based on the proximity function (distances) of the characteristic values. It is necessary to define a strategy for analyzing specific interactions between different carriers of paradigms.
The result of the analysis should be an oriented, connected graph that reflects the knowledge existing among carriers of different paradigms (graph vertices) and the direction of knowledge transfer (graph arcs) between carriers. In fact, such a model represents both interactions between members of the scientific and technical communities, and during refinement between any subjects of the digital economy. Refinement in this case implies the introduction of characteristics of economic entities of the digital economy into the model.
For each of the arcs, a transmission quality assessment should be made. The modern classification of methods of transferring scientific knowledge [12][13][14] suggests that they can be transferred in four ways: from implicit to implicit (for example, based on observations and copying actions), from explicit to explicit (formalization of scientific knowledge is implied before transfer) and from implicit to explicit and from explicit to implicit. This requires a formalization of the scientific knowledge diffusion quality measurement.

Formalization of the scientific knowledge diffusion quality measurement
It is proposed to assess the scientific knowledge diffusion quality according to such criteria as completeness, timeliness and reliability. Completeness refers to the success rate of knowledge transfer, i.e. the extent to which the knowledge 1 Sk (paradigm 1 Sv ) reformulated and transferred into knowledge 2 Sk , is complete for problem solving within the paradigm 2 Sv . Formally, the problem of completeness estimation can be formulated as follows. As initial data there is: Sk . At the same time, you need to consider critical tasks. Thus, we obtain the following relations: Timeliness is understood as the degree of fulfillment of time constraints at which the solution of tasks is not devalued, i.e. to what extent knowledge 1 Sk is timely transformed and transferred to solve problems within the paradigm 2 Sv . Since different knowledge can be transformed and transmitted at different rates, the time constraints characterize the average expected time for the transformation and knowledge transfer. Then it is advisable to talk about assessing the probability of exceeding a certain threshold time of knowledge transformation and transfer, for which the results will not devalue the solution of problems within the framework of another paradigm.
Formally, the task of assessing timeliness can be formulated as follows.
As initial data there is: Tt  is a set of specific scientific knowledge transfer periods. It is necessary to find the probability of the knowledge transformation and transfer in a time not exceeding R .
The mathematical model of timeliness is defined as the probability 1 () P t r  of transferring knowledge when performing critical tasks in a time t not more than a given (acceptable) r . And as the probability of performing knowledge transfer for the total number of tasks completed 2 () P t r  . An estimate of the transferring knowledge probability for critical tasks in a time not exceeding the allowable time is calculated using the formula.
where n is the number of completed transfers of critical knowledge from the total number 1 C that satisfy the inequality tr  . 2 4 () where nd is the number of completed transfers of knowledge from the total number 3 C that satisfy the inequality tr  . Then, taking into account (2) and (3), the overall assessment of the timeliness of knowledge transfer can be presented as follows: For an accurate calculation, it is necessary to obtain statistical data and define a set of constraints R , which allows obtaining an estimate of the likelihood of knowledge timely transfer.
The reliability of knowledge transfer can be defined as a property that determines the infallibility of the knowledge transformations from one paradigm to another when transferring knowledge between carriers of different paradigms. In this sense, reliability makes it possible to assess how the transmitted knowledge 2 Sk is correctly transformed (does not contain errors) for solving problems within the framework of the paradigm 2 Sv . However, the assessment of the knowledge transfer reliability is very difficult, because the quality of the conversion must be taken into account, and this cannot be done without a clear description of what is considered a transmission error. Errors can be introduced both at the level of transfer from one paradigm to another, and at the level of an erroneous description of the transfer in the model. It is also very difficult to assess which task outcome in a different paradigm clearly indicates the presence of errors. A whole system of indicators needs to be introduced to assess the validity of knowledge transfer:  the number of errors in the transmitted knowledge However, building mathematical models and collecting statistical data to calculate these indicators becomes very difficult and time consuming. It is proposed for the initial assessment to be limited to a Sv . It is necessary to find the probability of the absence of a critical number of gross errors within a given array of transferred knowledge, leading to a violation of the required accuracy of information processing in a digital environment.
The mathematical model of reliability is the probability of finding errors: The overall assessment of the quality of knowledge transfer, given, can be represented by a multiplicative convolution of the criteria (1), (4) and (5) introduced above: where i  is a weighting factor that determines the importance of indicators, such that For quality assessment, a threshold value can be specified, below which the transmission quality should be considered unsatisfactory. As a criterion (6), you can also use other principles of optimality or a combination of them.

Conclusion
This article presents a conceptual approach to solving the problem of assessing the quality of knowledge diffusion during network interaction between members of scientific and technical communities who are carriers of different paradigms in the context of digitalization. The proposed approach allows for quick assessments of the quality of knowledge transfer using the minimum amount of required data. The calculations based on the developed mathematical models are not highly accurate, but they allow saving time on assessing the quality of transmission of large scientific data in the context of digitalization.

Acknowledgments
The article is prepared with the financial support of the Russian Science Foundation, project № 18-78-10047.