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Publications of Shpirko Sergey
History magazine - researches, 2020-2
Shpirko S. - A Variational Model for Historical Systems of Rural Settlement (on the Example of the Derevskaya Pyatina on the Territory of Novgorod) pp. 49-62


Abstract: The research subject of this article is the mathematical modeling of the process of spatial settlement among medieval rural populations. Due to the heterogeneous features of land in different regions, the distribution of populations is not uniform. Along with the system of ordinary settlements, the presented model examines the system of the centers serving them. As such, there are settlements that have concentrated on themselves the functions of serving the entire surrounding population (for example, tribute collection centers or parish centers). The model assumes that the distribution of the system of centers is not uniform. The aim of the developed model is to describe the laws of such settlement systems. In order to achieve this goal, an innovative variational approach is developed, the essence of whichconsists in considering the process of historical settlement as a self-developing system, characterized by its parameters and needs. The use of the mathematical methods of variation calculations within the framework of this approach allowed the author to find the parameters of the existing systems for establishing centers and to quantitatively describe the relevant phenomena occurring within them. The testing of the proposed model is carried out on the basis of one rural settlement structure from the late 15th - early 16th centuries (Derevskaya Pyatina on the territory of Novgorod). A high degree of correspondence in the obtained theoretical results from empirical data allows the author to consider mathematical modeling as an adequate and convenient auxiliary tool for studying the process of historical settlement.
Historical informatics, 2018-4
Shpirko S. - The Variation Approach to Model Medieval Distribution of Population (the Example of Derevskaya Pyatina of Novgorodskaya Land in the Late 15th Century) pp. 22-38


Abstract: Mathematical modeling is increasingly popular to study spatial distribution of population. This trend is determined by the necessity to study the dynamics of population quantity and density, reconstruct lacking data, search for population displacement factors and evaluate their influence on this process. The current study develops the model describing the system of centers distribution (the settlement structure) of the one-level hierarchy. Such a modeling aims at searching for basic factors and evaluating their influence on the process, associating optimum parameters which characterize the system of centers distribution. The model developed by the author is based on the innovative approach of S.M. Gusein-Zade which makes it possible to describe the regularities in the location (distribution) of heterogeneous settlements and other centers on the territories. The variations calculus methods applied as well as the concept of Pareto optimality allows one to find parameters of the existing systems of centers location and quantitatively describe the phenomena occurring in them. The model has been tested to study a medieval rural settlement and has proven adequate and correct.It has been demonstrated that the process of free population displacement was caused by two counterbalancing factors: a centripetal one (concentration of settlements around their centers) and a centrifugal one (displacement of population near the farmland).
History magazine - researches, 2017-5
Shpirko S., Barankova G. - The Application of One Mathematical Approach to the Task of Genealogically Classifying Copies of Medieval Texts (on the Example of the Zakon Sudnyj Ljudem) pp. 37-69


Abstract: The subject of this study is the formalized classification of the surviving copies of the medieval Slavic text "Zakon Sudnyj Ljudem", which is the oldest transferred monument of Slavic law and one of the earliest texts in the Slavic language. To resolve the difficulty of textological classification, the authors propose a model based on natural assumptions regarding the process of copying texts and have developed a method using the idea of applying the fuzzy set theory. The advantage of the fuzzy approach is the building of a stemma of the existing copies with their given level of reliability, taking into account their possible contamination. The proposed method is based on a formalized analysis of the fuzzy relation preference matrix, formulated as a result of a pairwise textual comparison of copies. To quantify the contribution of every reading discrepancy, a typology of readings was created, as well as an indirect estimation method was developed. This article describes the first experiment of applying the fuzzy genealogical classification method to a large manuscript tradition (57 copies, about 6500 readings). The obtained results as a whole do not contradict the results of the traditional textological analysis or other formalized methods and allow us to specify the grouping of copies and their interrelations. The developed approach is universal and can be applied to the classification of other manuscript texts.
History magazine - researches, 2017-1
Shpirko S., Barankova G. - On Some Aspects of the Establishment of a Formal Genealogical Classification of Text Lists of Medieval Compositions Using the Theory of Fuzzy Sets (on the Material of Zakon Sudnyi Liudem)


Abstract: The article examines the issue of the genealogical classification preserved in the copies of Medieval texts. For its understanding the authors propose an approach based on the use of the theory of fuzzy sets. This approach utilizes the matrix of the fuzzy preference relation, which is founded on the pairwise comparison of the lists with each other. Each element of this matrix is the summation of its components, whose value is determined by the end set of different value factors (types of lection). These factors are considered in their total sum in the form of weight coefficients, which are determined through expert means. In order to eliminate the unavoidable subjectivity in evaluating them, the authors of this work developed an indirect method of expertise. The aim of the proposed method lies in that the given factors are compared pairwise in their value with each other. This way the initial complex problem is substituted by the entirety of more simple ones. Meanwhile the experts operate not with quantitative, but qualitative evaluations. The proposed new approach of expert evaluation allows in a formal way to assess the value of one or another discrepancy in the text. Thus the use of the proposed method plays a key role in the fuzzy classification of the list of Medieval compositions (establishing a genealogical stemming). The use of the examined method is illustrated on a specific example of discrepancy typology.
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