To the Statement of Tasks of Research of Migration Processes in Education and Science Oleksandr Makarenko 1, Yevgen Samorodov 2 1,2 Institute of Applied System Analysis of the National Technical University of Ukraine (Kyiv Polytechnic Institute. Igor Sikorsky) Prospect Victory 37, House 35, 03056, Kiev-56, Ukraine Abstract The issue of migration of students, postgraduates and scholars abroad (as well as within the country) are considered. The problem of migration is an important component of the general problem of sustainable development of the education system and science. General consequences of such migration are discussed. For example, if all scientists and educated students and graduates will go abroad, then the education system will fall into collapse. The positive aspects relate to the exchange of scientific knowledge with developed countries. Zero migration is also not desirable because it leads to isolation. Therefore, there is an optimal migration rate. Such questions, as well as many others, can only be solved by mathematical modeling. Therefore, in this article review of some possible models and problems of research tasks. Some classes of models for students and researchers migration are compared. Differential equations, system dynamics, cellular automata, artificial life had been considered. New types of cellular automata had been proposed as the models for migration problems. Also applications of artificial life approach for considering some problems of science development are discussed. Keywords 1 Migration of students, migration of scientists, review of models, mathematical modeling, cellular automata, system dynamics, global knowledge 1. Introduction their mentality. Models for their study are described, for example, in [3]. But there are many important tasks, and Knowledge and creation is one of the main fundamental. But among the various tasks here we factors [1] and literature there. This problem has distinguish one of the tasks that is of great many aspects. So indicative is the cycle of importance, namely, the issue of migration of Schlesinger in American education with a period students, postgraduates and scholars abroad (as of 15 years [2]. According to his research, the US well as within the country). Note that the problem entrants periodically change their preferences in of migration is an important component of the higher education (with curiosity to pragmatic general problem of sustainable development of business education in curiosity to study how the the education system and science. For example, if world built). Other problems relate to the issues of all scientists and educated students and graduates optimization of the learning process, finding new will go abroad, then the education system will fall forms (for example, distance education during a into collapse. But migration has positive aspects. coronary pandemic, as well as after, in the post- They relate to the exchange of scientific modern society). Also, questions are also adjacent knowledge with developed countries. Zero to the behavior of individuals taking into account migration is also not desirable because it leads to isolation. Therefore, there is an optimal migration ISIT 2021: II International Scientific and Practical Conference «Intellectual Systems and Information Technologies», September 13–19, 2021, Odesa, Ukraine EMAIL: makalex51@gmail.com (A. 1); esamor2@gmail.com (A. 2); ORCID: 0000-0001-6728-3058 (A. 1); 0000-0002-3981-8454 (A. 2) ©️ 2021 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). CEUR Workshop Proceedings (CEUR-WS.org) rate. This question, as well as many others, can of donors and recipients are important: financial, only be solved by mathematical modeling. In cultural, social, etc. Also important parameter is general, this is a very difficult problem in this the attachment to the native country and relatives. area. Therefore, in this article we offer a review of 2.5 Multi-agent models (masses - multi-agent some possible models and problems of tasks. systems) [6]. The models of such class are considered by the team of artificial agents who 2. Possible models of scientific take some decisions in some branch, knowing the state of the environment, exchange information migration and decide. In migration models, educational agents can be equivalent to the identities, and the 2.1 The simplest model that is suitable for environment in which they are placed described such processes is to (very simplified) by external factors that meet the above aspects. consideration in terms of competitive processes. 2.6 Approach of the theory of games in the The first most famous model of this type is the problem of educating migration. Another aspect Volterra model [4]. One variable of such a model of educational and scientific migration is more corresponds to the number of students, and the detailed taking into account the competitive second variable corresponds to the total volume of aspects of this phenomenon. For such issues, a students involved. The more ready students, the methodology in the field of science called the more this variable will be. When students for theory of games is quite well suited. In the some reason becomes little, then the magnitude of problem of educational migration, there are also the second variable decreases. The disadvantages aspects of competition. Note if knowledge and of this model are that it is spatially focused. those who produce this knowledge are the main 2.2 Models in the classroom of ordinary resource of sustainable development [1], in the differential equations. One of the simpler options future, the struggle for the distribution of these is to write a system ordinary differential equations resources becomes fierce and will take new forms - one for the total number of students, (sometimes cruel). Regarding migration tasks, postgraduate students and scholars; Others for the then part of them can be adapted to the problems total number of students, scientists, etc., which go of the theory of games. The country - migrant abroad, as well as the quality of evaluation (or donor is also considered as a separate agent. even equation) for parameters describing Competition between these agents takes place for conditions abroad: the need for skilled migrants, the involvement of educated frames. In principle, financial conditions, other conditions (cultural the game should be unanimate, because in the affinity - The distance of cultures, physical normal course of things, the general goal would distance, etc.) This is one of the ways to use have to ensure the progress of the aggregate of models (that is, empirical). countries. In this case, a separate unit is a 2.3 More simplistic, but more adapted to definition, what is this progress and which quality practical tasks is the system dynamics approach, and quantity should be knowledge to ensure this launched by J. Forrester [5]. According to the goal. concept of systemic dynamics, it is necessary to 2.7 MASTER EQUATIONS. In this division, distinguish elements, their interaction between I would like to remind you of another class of them, reinforcing or inhibiting the connection models that in principle can come to migration between elements. For the field of educational tasks, namely Master Equations, or kinetic migration, it is necessary to adapt system equations. In this approach, an element that has dynamics. In principle, this can be done, but it is certain set of values and records the laws of necessary to conduct a large amount of previous evolution of these states that have physical work, including in detail by drawing the justification [8, 9] are recorded. In principle, this corresponding diagrams of system bonds. approach can solve all migration tasks, but it is 2.4 Another class of models that suits very difficult, and it is practically impossible to migration modeling is a diffusion equation. Then apply to important applications due to the migration is considered with the help of diffusion impossibility of gathering the necessary data. equations. The disadvantage of such a model is the severity of finding the diffusion coefficients and other parameters. In addition, it is very difficult to take into account the mental identities of potential migrants. In fact, important features 3. Modeling migration in the class of 4. The struggle for the allocation of cellular automata resources in science and education There is another class of models that have 4.1 Modeling the dynamics of science as a been well established for applied tasks, namely a system, with a large number of scientists, model with splitting space on cellular elements infrastructure, funding and a record of equations to change the state of The question of modeling the development of these elements. Such models are called cellular science that produces knowledge as a product of automatics models [10, 11]. Note that such evolutionary development is of great theoretical statutes exist for other models [12]. importance. A large number of studies (both 3.1 Models of scientific migration on the basis specialists in scientometrics and scientists from of cellular machines. The idea to set up the other fields: physics, mathematics, biology, method to migration is as follows. All available economics, sociology, etc.) are devoted to these geographic space is divided into geometric problems. But there is still a need to attract new elements, that is, in a simpler case, a uniform concepts, ideas, models, including the real geometric grid is imposed. At the first stage, such management of science. Therefore, here we a grid is superimposed to Ukraine. Fixed number present one approach to modeling such processes. of educated frames is one migration agent. Then In science, scientific schools, the following basic the number of agents in the cell corresponds to the components: scientists (as a rule, the association total number of educated frames. of scientists to study a particular field or more Further in a simpler case model, all countries often a scientific problem, finance allocated to the abroad can be considered as one general element. scientific field, but more often to a scientific Then in the middle of Ukraine, the process of problem, the branches of science as elements). migration is considered as a sequence of steps project) of theoretical, experimental knowledge, from the cell into a cell in the middle of Ukraine governing bodies that distribute funding (for with a final step behind the boundary in a research and training), and educational conditional general element. The model can be institutions (usually at the university level) that easily refined if and a foreign cell to break into transfer knowledge, prepare new generations of cells that meet separate foreign countries. Further, researchers and shape the preferences of as in other applications of cellular machines to graduates. spatial evolution tasks in various fields of Analyzing such aspects of science research as migration [11], the laws of changes in cell systems and its modeling, one can come to changes are recorded. These laws take into unexpected analogies with models from account all available information as external and completely different fields of research - namely mental. Note that such an approach showed with some aspects that are inherent in the so- acceptability in modeling the spatial distribution called "Artificial Life" (AL, ALife, artificial life) tasks (despite the local nature of the dynamic laws directly [13, 14]. Typical tasks there are studies of of classical cellular machines [10,11]. But you can the struggle of groups - antagonists (or generalize cellular machines under migration. The collaborators) for resources. Some key fact is that classical cellular machines were built components of the AL approach are: on the base E - classic Euclidean Dimension 1. Cell space Space 1D, 2D, ..., ND. The structure of the base 2. Spatial distribution of resources needed for life space Es set the measure of the cells. This, in turn, 3. Agents that can move through the cell space and set the local challenge cell and which determines which can be in the search for resources, the the dynamic law of the cellular automaton. To the struggle for resources, destroy each other, have base space of classical machines in the applied different preferences for behavior Tasks are tied by various thematic layers: 4. There may be associations of teams of agents financial, economic, cultural, etc. These thematic with tactics and strategies of behavior layers can be replaced by E. E. Moreover that 5. The birth of young generations of agents in the there is so formed statistics. But you can enter team and the death of the old other measures of the cells that will be taken into 6. Rules of conduct are "embedded" in individual account the formed Proximity of countries: agents historical, cultural, diplomatic. 7. The possibility of a certain combination of rules of conduct of agents of "parents" at the birth of an agent of a "child" of a new generation at a most developed in the world, but in aggressor "meeting" of "parents" and "birth" of this agent of countries, or with dictatorial regimes. It is also a new generation. important to take into account the processes of (As well as many others). aging and generational change in science and A review of the properties 1-7 above and the scientific schools. Then, in principle, it is properties of scientific activity allows us to draw necessary to build a multidimensional cell space, conclusions about some analogies that allow us to where different coordinates will correspond to apply the concept of AL to the consideration of different aspects of science as a system, and the science as a system. Let's show it at first on the echo of agents will then take place in this simplest example. multidimensional space. Example 1. The struggle of scientists for Example 2. Taking into account the change of finance. generations. Let the branches of science be placed as a In addition to the details of Example 1, "scientific" space of ideas (by the way, there are aspects of generational change and sustainable now studies to build an "atlas of science", development of science can be added. Again, let's however, without cellular concepts). Let the illustrate this with one of the simplest examples. individual scientist be presented as an agent who Suppose that only universities train and graduate can move through the cellular space of "ideas" young scientists. It is then that universities set (space of science) and funding. Scientists are priorities in the choice of scientific field and united in "scientific schools" (teams of agents). scientific tasks, ethical principles, morals. It may Note that usually there are not many schools, say also be that several teachers have the greatest 2-5. The state (or relevant institutions) provide influence at the university. Other issues can also funding for a particular field of science (distribute be considered, including external regulation of finance resources on different sets of resources). learning processes, distribution, funding Then school teams look for resources strategies for universities and specialties in them, (consciously or unconsciously), fight with each etc. Then there are also clear analogies with the other, develop, survive, or die. Note that the approaches of AL (transfer of knowledge and distribution of finances by industry is the preferences) to the next generation. management of science (of course, under many In general, a set of such models can be important other conditions - the rules of grants, selection for the management of science and education. criteria and much more). Even using such a 4.2 Extending the approach of artificial model, you can try to get a model from the class life to some problems of social relations AL to model and manage scenarios for the Let us recall an approximate description of the development of science). But this model is soft approach in artificial life. There is a space in suitable for considering the competition of stable which representatives of competing groups that / established scientific schools. can move in search of resources are located. There It is clear that considering only financial is also some location of resources in the search issues is only one aspect of science. Thus, the space. As a rule, in AL the space consisting of intellectual attractiveness of the field of association of cells is considered. In the classic knowledge for the scientific school (as well as for examples that came from ecology, resources are the individual scientist) is also important. For edible resources and artificial life means fighting example, some scientists do not want to work on for them (the example of sugar is the best known). the task of designing weapons of mass destruction It is suggested that the ideas of such a for any money. Also important in scientific description can be transferred to some tasks of discovery is often the role of individual scientists society. Such tasks can be difficult, so here we (who are distant from colleagues, or are not in the describe the idea with simpler examples. "Core" of the scientific school). Therefore, it is Let us have the task of fighting some ideas for important to introduce other (in addition to the minds of the population. Suppose there is idea financial measurements) dimensions, A with many carriers of ideas (mass media, TV, "dimensionality" (say, attractiveness, metrics of Internet) and another (antagonistic) idea B. "proximity" of different branches of science, etc.). Imagine that the population is a resource for idea Really important are the physical (geographical), A or idea B. That is, ideas are analogs of teams in political aspects of the development of science classical artificial life. Then the population is a and science schools. Yes, many scientists will not resource, and consumption of a resource by ideas want to go to work in science, which may be the A or B is analogous to consumption of an edible resource. Here it is necessary to take into account are many tasks in this issue. First, it is a problem the perception of the population to the ideas of A of new knowledge. Secondly, it is the sustainable or B, the forms of their presentation, the development of educational and scientific attractiveness of the forms of presentation of ideas infrastructure. The problem of migration belongs to the population, etc. Ideologists and flight to this range of problems. consultants of different ideas are looking for ways 5.2 General description of the migration to bring ideas to the public: what ideas; how to problem deliver them; how to take into account and make From the point of view of the approach of an ideas attractive to the population. Acceptance of artificial life it is possible to allocate such the idea of A or B by the population is analogous elements. In this problem, foreign sources provide to the classic AL: teams eat resources. Aspects of resources, and the contingent of migrants is improving the attractiveness of ideas are divided into communities from different analogous to management processes. Note that countries, which implicitly compete for resources. such a transfer of ideas is possible in the case of Resources can be money, highly qualified only one community (team, idea). Yes, migration positions and much more. It should also be noted from only one country can be considered. You can that the same indicators should be taken into also adapt artificial life ideas to some account for the internal situation in Ukraine. But cybersecurity issues. For example, the spread of we still need to take into account the "homeliness" fakes and the reaction of society to them. Then the of agents, the attractiveness of the country as a analogy is that a fake "eats" part of the population whole, the prediction of the future situation in the depending on the characteristics of society. country and other countries. In this case, the It is also possible to consider the spread of problem can be considered locally in time, ie at epidemics as the spread of a virus - an analogue of short intervals with constant conditions. If it is the virus team, and the team, which increases in desirable to study this in order to optimize the size with the spread of the epidemic. Note that scientific infrastructure, it is necessary to predict further generalization of the models leads to the changes in the world situation. At the same time problems of artificial life in another (non-cellular) there are interesting and new for the subject of space, and, for example, to the problems of artificial life issues of resource management over distribution in the network structure. You can also time. In many cases, this directly leads to a new consider problems for the dissemination of ideas issue of sustainable development of education and in a mental space other than the physical. A science. possible example is a change in scientific Here we describe informally part of the paradigms in a field of science. problem. Let 𝑅⃗𝑧 - resources for migrants abroad at the measurement scale [0, 1], 𝑅⃗𝑣 - domestic 5. Migration processes in education resources in Ukraine. When, 𝑅⃗𝑣 → 0 𝑅⃗𝑧 → , and science as an example of the 1everyone will emigrate from Ukraine, and when struggle for resources 𝑅⃗𝑣 → 1 𝑅⃗𝑧 → 0, everyone will stay in Ukraine. , Clearly, there should be an intermediate value 0 < 5.1 General problems of sustainable development in education and science 𝑅⃗ 𝑧 < 1 that should be optimal for the A separate but important task in the field of sustainable development of education and science modeling is the migration processes of highly in Ukraine. Another thing is that these educated professionals: primarily scientists, productions are part of the problem of sustainable students, graduate students and others. Scientific development. The main resource of the process of migration has two aspects - domestic and sustainable development is knowledge international aspects, ie migration abroad. Here (Makarenko, 2020). With regard to Ukraine, this we will point out one very important aspect of leads to the following issues (which still need to migration in education and science both for an be addressed): what knowledge is needed now and individual country (especially, for example, for in the future; their division into fundamental and Ukraine) and for the world community as a whole applied; how this knowledge is generated (global aspect). The main problem is the depending on the infrastructure. And all this very sustainable development of the reproduction of much depends on the number of scientists and necessary knowledge [1]. At the same time, there students 0 < 𝑁𝑣 < 1 who remain in Ukraine. 6. Discussion, conclusions and developmnt-and-principles-of-social- systems-modeling/) staging of new tasks [2] A.M. Schlesinger The cycles of American History. Houghton Mifflin Company. In the previous sections, a comparative Boston, 1986. 688 p. review of some models of scientific migration was [3] A. 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