Communication and Contacts in Massively Interconnected Systems Part 2: Connectivity Functions and Differential Equation of Connectedness


By Pavel Barseghyan, PhD

Plano, Texas, USA and Yerevan, Armenia


Because of its empirical nature the Rent’s Rule is not able to capture the essence of connectivity in many cases of practical importance. To solve these problems of capturing the wide variety of cases of connectivity there is a need for more powerful spatial and temporal models of contacts and interaction between the elements of systems.

This paper discusses the methods of the theory of massively interconnected systems, developed in the 70s and 80s of the last century, as applied to one-dimensional systems of connectivity.

The concept of one-dimensional functions of connectivity is introduced and the differential equation with respect to these functions is derived.

This differential equation has wide practical applications in organizational science and electronics. Particularly the well-known Allen Curve is a specific solution of the differential equation of connectivity. The Rent’s Rule itself can be derived from one-dimensional differential equation of connectivity.


Numerous practical application of the Rent’s Rule over the last 40-50 years have shown that its use is effective for estimating the parameters of microelectronic products, but at the same time it became clear that it has a limited scope and in many practical cases is not able adequately represent connectivity in complex systems [1, 2 ].

In particular the Rent’s Rule is not suitable for the description of connectivity in systems with mass contacts and communications, such as social networks, organizations, project teams, and others.

The main reason for this is that generally the Rent’s Rule in no way related to a particular coordinate system, while an arbitrary massively interconnected system has variable connectivity parameters and operates in real time and space.

The history of science shows that an adequate quantitative description of such systems, whose parameters vary in time and space, is usually reduced to the use of differential equations.

In this respect systems with mass communications and interactions between their elements are not particularly different from other systems with variable parameters and the natural mathematical means for their fundamental description are also differential equations with partial derivatives.

It is on the basis of such an approach the theory of massively interconnected systems is built and which in its general form is presented in [2, 3].

Some aspects of this theory related to the derivation and applications of differential equation of connectivity are presented in English in [4, 5, 6].

This paper is devoted to the presentation of a simplified one-dimensional version of this theory to illustrate its basic ideas and potentialities.


To read entire paper (click here)

About the Author 

flag-Armenia-USApavel-barseghyanPavel Barseghyan, PhD    

Dr. Pavel Barseghyan is a consultant in the field of quantitative project management, project data mining and organizational science. Has over 40 years experience in academia, the electronics industry, the EDA industry and Project Management Research and tools development. During the period of 1999-2010 he was the Vice President of Research for Numetrics Management Systems. Prior to joining Numetrics, Dr. Barseghyan worked as an R&D manager at Infinite Technology Corp. in Texas. He was also a founder and the president of an EDA start-up company, DAN Technologies, Ltd. that focused on high-level chip design planning and RTL structural floor planning technologies. Before joining ITC, Dr. Barseghyan was head of the Electronic Design and CAD department at the State Engineering University of Armenia, focusing on development of the Theory of Massively Interconnected Systems and its applications to electronic design. During the period of 1975-1990, he was also a member of the University Educational Policy Commission for Electronic Design and CAD Direction in the Higher Education Ministry of the former USSR. Earlier in his career he was a senior researcher in Yerevan Research and Development Institute of Mathematical Machines (Armenia). He is an author of nine monographs and textbooks and more than 100 scientific articles in the area of quantitative project management, mathematical theory of human work, electronic design and EDA methodologies, and tools development. More than 10 Ph.D. degrees have been awarded under his supervision. Dr. Barseghyan holds an MS in Electrical Engineering (1967) and Ph.D. (1972) and Doctor of Technical Sciences (1990) in Computer Engineering from Yerevan Polytechnic Institute (Armenia).  Pavel’s publications can be found here: http://www.scribd.com/pbarseghyan and here: http://pavelbarseghyan.wordpress.com/.  Pavel can be contacted at [email protected]