Application Of The Criterion Of Links Distribution Between Elements In A Complex System For Evaluation Of Holistic Text Perfection

Application Of The Criterion Of Links Distribution Between Elements In A Complex System For Evaluation Of Holistic Text Perfection

Pavel Makagonov (Russian Presidential Academy of National Economy and Public Administration, Moscow, Russian Federation)
Copyright: © 2018 |Pages: 14
DOI: 10.4018/IJEUCD.2018010103
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It is known that texts can be examined as complex social systems and Zipf's law is used when applied for the evaluation of their perfection. It is proposed to add distribution of links between the objects of the system to the list of perfection criteria of texts viewed as complex systems. An empirical law of syntactic and linking words distribution in texts is also proposed. The examples of complex systems are examined in order to define a mathematical representation of this law. The models of such systems are associated with the graph theory, exchange of messages at internet forums, distribution of urban population across city districts, and transportation networks. At the “engineering level of rigor” it is shown that in these systems, the empirical law of links distribution between the objects has a general mathematical representation. Non-linguistic models are provided to prove the system-wide character of the distribution of links ranks feature, but the models are also suitable for the self-consistent use in the corresponding applications. The golden proportion in the number of syntactic and significant words is proposed as an additional criterion of text perfection. Perfection criteria are useful in the analysis of the quality of texts posted in the internet and in the development of recommendations for the improvement of texts used for school purposes.
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1. Introduction

It is generally accepted that a necessary characteristic of the system perfection is the compliance of a ranked distribution of objects of this system with Zipf’s law:

IJEUCD.2018010103.m01, where IJEUCD.2018010103.m02 is the value of the function F(1), K – value close to 1, and N – object rank, that is its number in the set of values F(N) arranged in the descending order. It is often easier to represent this law by taking a logarithm to any base from a hyperbolic function:

IJEUCD.2018010103.m03 or IJEUCD.2018010103.m04 (1)

In case of a linguistic system, the following equation is often considered to be close to the perfection of Zipf–Mandelbrot law: IJEUCD.2018010103.m05 where B is a certain constant.

However, a system should be characterized not only by its objects but also by links between them. That is why a complete system is characterized not only by the compliance with a high degree of distribution consistency of the main quantitative characteristic of its elements but also by the presence of a perfection criterion characterizing the links between the elements. The problem of finding this criterion is aggravated in case of the absence of an evident candidate for the role of the parameter which is supposed to characterize links between the elements defined as system objects.

Local formations or points with such characteristics as weight, mass or charge are usually considered as objects for systems having geometric or geographic characteristics. Therefore, links between the objects are defined by such characteristics as distance between these points or the strength of mutual attraction between point masses. In this case, the distribution of links according to their quantitative characteristics can be evaluated as a “rank – size” correlation where rank corresponds to the link number assigned in the descending order of link significance. The links as such can be examined either as pairwise links between system objects, or as relation of each object to a set of objects. The research considers complex systems associated with social and humanitarian sciences but only systems with easily defined statistical quantitative characteristics are taken as examples. The examples of such systems are:

  • Static time-independent systems such as holistic written works that are not subject to rewriting, or mathematical models created for theoretical study of actual systems in their fixed state;

  • Dynamically changing systems that are stabilizing their main characteristics in the course of time such as texts at Internet forums or manufacturing projects with fixed life cycle limits;

  • Dynamically developing systems with such life cycle stages that are difficult to reasonably assess, for example, settlement systems and/or systems of links between them.

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