Philological researches in the context of transdisciplinarity: a fractal scale-free derivational network modeling

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Sumy State University

Philological researches in the context of transdisciplinarity: a fractal scale-free derivational network modeling

Shchyhlo L.V., Vorfolomeiev M.S.

Introduction

A person who has become a supporter of a new paradigm at an early stage of development must believe in the success of this paradigm.

Thomas Kuhn

After stage of interdisciplinary researches should expect a higher stage - transdisdisciplinary, which is not limited to interdisciplinary relations, and will place these relations within the global system, without strict boundaries between disciplines.

J. Piaget

The latest stage in the development of science is characterized by the formation of “concepts, theoretical constructs, which significantly transformed the general cultural intellectual continuum (complexity, bifurcation, order parameter, emergence, complexity, recursion...) and, of course, transdisciplinarity. Transdisciplinarity has become a hallmark of synergistic and, at the same time, post-non-classical researches” [1, P. 172 ].

Linguistic scientific thought is constantly in searching of effective philological cognition ways. We believe that the main vector of qualitative rethinking of philological studies should be based on the formation of a new theoretical and methodological synthesis taking into account the convergence of humanities and natural sciences in the context of transdisciplinary system worldview.

According to the researches of the Belgian scientist E. Judge, there are four types of transdisciplinarity in the modern scientific space:

- transdisciplinarity 1 (the formal relationship of separate disciplines understanding; provides the formation of logical metarestrictions, based on which knowledge can be integrated at a higher level of abstraction than in the field of interdisciplinarity);

- transdisciplinarity 2 (a close internal connection with the personal experience of the researcher, which includes meditation);

- transdisciplinarity 3 (the usage of basic metaphors that have a fundamental cognitive value; the focus is on unicentricity and concreteness of veracity;

- transdisciplinarity 4 ( the understanding, cognition and description of the object as part of a single streamlined environment, a way to manage the state (harmonization) of the object and the natural environment of its existence, is realized in two directions - gaining new knowledge about the world, searching for ways to solve complex multifactorial problems of nature and society.The basic principle - the concreteness of truth - determines a single order, where the transdisciplinary system is represented by spatial, informational and temporal units of this order) [2].

Word-formation as a hierarchically organized dynamic system can be represented in the context of transdisciplinarity as a fractal scale-free network with preferential attachment between its constituents, which is reflected in the internal valence, meant as the ability to implement the laws of language elements combination at the word-forming level. It reflects linguistic potential units of this level due to the formation of different in size derivational clusters.

Presentation of the main material

Recently, a new direction of scientific research has been successfully developed, the so-called theory of complex networks (Network Science), which focuses on the study of large-scale network structures, for example, the Internet, social networks and so on. As it is known, the graph theory (the basis of graph theory was laid by L. Euler) is used to analyze graphs of small size or special structure compared to the theory of complex networks, which describes a significant quantity of usually randomly connected nodes [3, P. 8].

It is important to point out that the first model of the preferential attachment network was proposed by A.-L. Barabasi and R. Albert, the physicists at the University of Notre Dame (USA) [4, P. 509-512]. They studied the law of distribution of real networks nodes by the number of connections. As it turned out, for many networks, and the structure of the Internet in particular, instead of the expected probabilistic distribution of nodes according to Poisson's law, the obtained distribution roughly corresponded to the power law inherent in all critical states. Hence, in many real networks, a small quantity of nodes holds a significant number of connections (they are called “hubs”), and a huge number of nodes concentrates only a few connections. Such networks are called scale-free networks (see Fig. 1).

Fig. 1. Scale-free networks [5, P. 50].

This name is borrowed from the theory of critical phenomena, where fluctuations in critical states are also subject to the power law, and the theory of scale-free networks is considered as one of the scenarios for complex systems to reach a critical state.

The Figure 1is illustrated scale-free networks of the U.S. airline system contain hubs (red) - nodes with a very high number of links. In such networks, the distribution of node linkages follows a power law (see Fig. 2) in that most nodes have just a few connections and some have a tremendous number of links [5, P. 50]. philological transdisciplinary linguistic science

Fig. 2. Power law distribution of node linkages [5, P. 50]

The dynamics of the scale-free network formation depends on its two main conditions: growth and preferential attachment. These mechanisms form a hub-dominated structure: a new element joins the node with the largest number of connections as shown in Figure 3.

Fig. 3. The birth of scale-free networkfrom 2 to 11 nodes [5, P. 55].

Let us consider the main parameters for a scale-free network modeling:

1. Node degree. The node degree is a reflection of the number of its connections. Degree is a local property that characterizes a single node.

2. The short paths. The path in the network is measured by the appropriate number of steps to cover the distance, in order to get from one node to another one. The term “the short path” is relevant to the minimum number of steps that is to be done from a to b. If there is only one path between a and b, it is “the short path”.

3. Centrality measure. The centrality measure allows to rank the nodes in the network by their relative weight. Conventionally, weight is understood as the responsibility of a node for network connectivity (for its sections), however, specific interpretations are variable ones. An example of a centrality measure is the estimation of the node (the betweenness of a node). This measure was proposed by D. Freeman, on the basis of the sociological data [6, P.14].

Similar to the concept of “the centrality measure” is the concept of “the fragmentation coefficient” [7, P. 131-147]. This measure allows to identify key nodes, the removal of which contributes to the emergence of significant lengthening of short paths and network disruption. In the extreme case, the removal of key nodes causes complete fragmentation of the network into individual components.

It is worth noting that such a critical number does not exist for scale-free networks. Numerous experiments show that even if 80% of nodes are removed, the remaining nodes continue to form a linked cluster.

Hence, scale-free networks are very resistant to accidental damage or accidental external influence. This stability is explained by the inhomogeneous topological structure of these networks. However, such networks have a peculiar Achilles'Heel [5, P. 55], as “they are extremely vulnerable to coordinated attacks”, which can lead to partial or complete disorganization of the network [5, P. 52].

In the process of analysis of complex networks, as in the theory of graphs, the parameters of individual nodes, network parameters in general, network substructures are studied. In recent decades, scientists have identified a large number of different scale-free structures: a virtual network of hyperlinked web pages; a network of scientific articles related by hyper-references; contact networks of programmers and other specialists. The theory of scale-free networks is widely used to reveal the principles of formation and functioning of network structures in economics, biology, medicine, society and so on. Scientists point out that understanding the structural features of the network allows researchers to hypothesize about the evolutionary mechanisms that cause the emergence of a structure and allow computer simulations of network growth processes [8, P. 268-276). An example of the above phenomenon is a network containing 470,000 words of the BNC (British National Corpus), in which the distribution of degrees corresponds to two modes of the power law. In addition, the exponent of one of them correlates with A.- L. Barabasi's model.

R. Ferrer-i-Kancho and R. Sole testify that due to the presence of two modes in the lexical structure, division into a group of core words used by all members of the social group of native speakers and a group of peripheral words known only to some users becomes possible. These scholars believe that the accumulation of lexicon is subject to preferential attachment, in which the network grows around the core, which contains the most context-independent words [9, P. 788-791].

4. Clustering coefficient. The clustering coefficient reflects

Fig. 4. The clustering coefficient (C) in a scale-free network, where C = 0 is no connections between nodes; C = 1/3 is one connection between nodes C = 3 \ 3 is all nodes are connected to each other .

Summerising, a scale-free network is a graph of nodes and edges (connections).

The path in the network is determined by a sequence of steps between nodes, in which the step is equal to one edge, i.e. the path length between a and b is n -1, where n is the number of nodes from the initial to the final one.

Our observations suggest that the scale-free network is a relevant and convenient unit for researching the dynamic development of word-formation, as it reproduces positive feedback, which serves for making derivational clusters in which “the chain reactions” of preferential derivational interaction are realized.

According to the synergetic theories such as the theory of scale-free networks and the theory of tractality, the network model of the word-formation system of the German language can be represented as a nonlinear scale-free clustered structure with fractal properties. The basic characteristics of such network model are:

1. The presence of hub nodes with a significant quantity of connections that unite the network into a single entity, i.e. form “a node-shaped core”. This, in turn, contributes to the formation of a stable, but at the same time vulnerable to targeted influences, the structure of connections, which is a key feature of scale-free networks in general, and the network model of German word formation in particular. The main hub-nodes in the wordformation system of the German language are the bases of verbs, because due to their poly-combinability they form derivational clusters that contain derivatives of different parts of speech.

2. Power distribution of the number of connections between network nodes: the greater the number of direct connections in the hub is, the fewer hubs with such a number of direct connections in the network are available.

3. Self-similarity of the network: word-formation as a complex network, characterized by the presence of some hierarchy of nodes. High / medium / low linked clusters that combine into a single entity allow the network to function as a structural-semantic one.

4. Small diameter of the network: one of the important characteristics is “the diameter of the network” - the maximum length of the shortest paths between any nodes of the network. The formation and development of the network is not accidental, the new elements are mostly joined to hub nodes, which have more connections.

In addition, another mechanism for the formation of connections in a scale-free network is assortment - the advantage in the formation of connections within a group of nodes compared to the formation of external ones, which enhances clustering in a growing scale-free network. Due to these two mechanisms - preferential attachment and assortment - the scale-free network saves the properties irrespective of the size.

Based on the results of the valence potential analysis of the creative and derivative bases of verbs, it has been possible to determine that the network model of German word-formation developed by us is a position-oriented network, as in this network the edges act as derivational vectors of word-forming derivation with the inherent direction, i.e. the degree of derivation. The degree of derivation is the degree of word-forming distance of a derived word from a cognate non-derivative, which is determined by the number of derivational units in the process of wordforming act (a step). It is shown in the Figure 5.

Fig. 5. The path in the German fractal scale-free derivational network.

As it is known, the ascending unit of valence analysis is a word that performs the function of a formative basis. The latter one can be underived (simple) and derived. A derived unit of the language contains not only a formative basis, but also a wordforming formant with valence features available in it. Derivational capacity of the word base are determined by the formal- morphological and semantic valence of potentially combinable elements: affixes and bases (or lexical bases) [11; 12; 13].

In our opinion, a derivational nest as a network formation, the clusters of which are derivational paradigms - a set of common root derivative units that reflect the relationship of similarity (the creative basis) and difference (the derivational formant), where the order parameter is the degree of derivation.

As you can see from the Figure 6, the derivational nest is a bright exponent of the network model of the word-formation of the German language. The first degree of derivation turned out to be the most copious with derivatives. Further step-by-step movement of the word-formation process on the horizontal and vertical axes demonstrates the elimination of either parts of speech, or word-forming meanings, or word-forming types from the sphere of realizations, extinction of individual branches and almost complete exhaustion of derivation potential at the fourth stage of derivation.

Fig. 6. The derivational nest as a subgraph of the German fractal scale-free derivational network

So, the derivational nest as a complex hierarchically organized macro-construct of the fractal-network type is a continuum of language units characterized by the common baseconcentrator with a common element of meaning for all words, i.e. the words have semantic and material integrity. It is in the derivational nest that the generative ability of the creative word basis is represented, the structural-semantic relations between the members of the nest are traced, the peculiarities of the derivational structure of derived words are clarified, the meaning of the creative word basis in the semantics of the basis of derivative language units are reproduced.

Conclusions and perspectives

Based on the synergetic theory of scale-free networks, the word-formation of the German language is a nonlinear hierarchically organized system that can be modeled as a fractal scale-free network, which is reflected in the internal valence of the word base as a representation of its word-formation potential. According to the represented by us the German fractal scale-free derivational network, a plurality of derivatives is formed from the primary basis of the word with the participation of the corresponding word-forming units and different ways of word-formation. Derivatives are combined into clusters, the hub nodes of which are the word bases, that in turn form other derived units of the language on a fractal basis. Hence, the word-formation of the German language is a nonlinear hierarchically clustered scale-free network with fractal properties that is capable of reconfiguration and expansion. In addition, the application of the concept of scale-free networks, as it seems to us, will allow the development of a new effective theory for identifying the linguistic potential of language.

The German fractal scale-free derivational network model can be used both in projects related to the development of tools for computer (automated) word-formation analysis, and in quantitative researches. It is worth noting that research based on network modeling can be useful for further development of universal NLP (“natural language processing”) tools, i.e. methods of automated and semiautomated processing for different languages [14].

References

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2. Judge A. Conference Paper. 1-st World Congress of Transdisciplinarity. Union of International Associations. URL: http://www.uia.org/uiadocs/aadocnd4.htm (дата звернення 02.06.2022).

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4. Barabasi A.-L., Albert R. Emergence of scaling in random networks. 1999. Science. № 5439 (286). pp. 509-512.

5. Barabasi A.-L., Bonabeau E. Scale-free networks. URL: https://barabasi.com/fZ124.pdf (accessed: 21.06. 2022).

6. Freeman L. 1977. A set of measures of centrality based upon betweenness. Sociometry. № 40 (1). pp. 35-41.

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8. Strogatz S.H. Exploring complex networks. Nature. 2001. № 410. pp. 268-276.

9. Ferrer-i-Cancho, R., Sole R.V. Least effort and the origins of scaling in human language. Proceedings of the National Academy of Sciences. 2003. № 100 (3). pp.788-791.

10. Clusteringcoefficient.URL:https://en.wikipedia.org/wiki/ Clustering_coefficit (accessed: 21.06. 2022).

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Аннотация

Филологические исследования в контексте трансдисциплинарности: моделирование фрактальной словообразовательной сети без масштабирования

Новейший этап в развитии науки характеризуется формированием “концепций, теоретических построений, которые существенно преобразовали общекультурный интеллектуальный континуум (сложность, бифуркация, параметр порядка, эмерджентность, комплексность, рекурсия...) и, конечно же, трансдисциплинарность. Трансдисциплинарность стала отличительной чертой синергетических и, в то же время, постнеклассических исследований” [1, с. 172].

Лингвистическая научная мысль постоянно находится в поиске эффективных путей филологического познания. Мы считаем, что основной вектор качественного переосмысления филологических исследований должен основываться на формировании нового теоретико-методологического синтеза, учитывающего конвергенцию гуманитарных и естественных наук в контексте трансдисциплинарного системного мировоззрения.

Согласно исследованиям бельгийского ученого Э. Джаджа, в современном научном пространстве существует четыре типа трансдисциплинарности:

- трансдисциплинарность 1 (формальная взаимосвязь понимания отдельных дисциплин; обеспечивает формирование логических метарестрикций, на основе которых знания могут быть интегрированы на более высоком уровне абстракции, чем в области междисциплинарности);

- трансдисциплинарность 2 (тесная внутренняя связь с личным опытом исследователя, включающая медитацию);

- трансдисциплинарность 3 (использование базовых метафор, имеющих фундаментальную когнитивную ценность; акцент делается на одноцентричности и конкретности достоверности;

- трансдисциплинарность 4 (понимание, познание и описание объекта как части единой упорядоченной среды, способ управления состоянием (гармонизации) объекта и естественной среды его существования, реализуется в двух направлениях - получение новых знаний о мире, поиск путей решения сложных задач). многофакторные проблемы природы и общества.

Основной принцип - конкретность истины - определяет единый порядок, где трансдисциплинарная система представлена пространственными, информационными и временными единицами этого порядка) [2].

Словообразование как иерархически организованная динамическая система может быть представлено в контексте трансдисциплинарности как фрактальная безмасштабная сеть с преимущественной привязанностью между ее составляющими, что отражается во внутренней валентности, понимаемой как способность реализовывать законы сочетания языковых элементов на словообразовательном уровне. В нем отражен лингвистический потенциал единиц данного уровня за счет формирования различных по размеру словообразовательных кластеров.

Выводы и перспективы. Основываясь на синергетической теории безмасштабных сетей, словообразование немецкого языка представляет собой нелинейную иерархически организованную систему, которую можно смоделировать как фрактальную безмасштабную сеть, что отражается во внутренней валентности основы слова как представлении ее словообразовательного потенциала. Согласно представленной нами немецкой безфрактальной словообразовательной сети, множество производных образуется из первичной основы слова с участием соответствующих словообразовательных единиц и различных способов словообразования. Производные объединяются в кластеры, узловыми точками которых являются основы слов, которые, в свою очередь, формируют другие производные единицы языка на фрактальной основе. Следовательно, словообразование немецкого языка представляет собой нелинейную иерархически сгруппированную безмасштабную сеть с фрактальными свойствами, способную к реконфигурации и расширению. Кроме того, применение концепции безмасштабных сетей, как нам кажется, позволит разработать новую эффективную теорию для выявления лингвистического потенциала языка.

Немецкая модель фрактальной словообразовательной сети без масштабирования может быть использована как в проектах, связанных с разработкой инструментов для компьютерного (автоматизированного) словообразовательного анализа, так и в количественных исследованиях. Стоит отметить, что исследования, основанные на сетевом моделировании, могут быть полезны для дальнейшей разработки универсальных инструментов NLP (“обработки естественного языка”), то есть методов автоматизированной и полуавтоматизированной обработки для различных языков [14].

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