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International Conference on Complex Systems (ICCS2006)

Measuring and Tracking Complexity in Science

J Marczyk
Ontonix s.r.l

B Deshpande
Ontonix LLC

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     Last modified: August 16, 2006

We are witnessing an inexorable increase of complexity in every sphere of life: economy, global socio-political scenarios, business processes, IT networks, engineering systems, traffic, etc. The study of complex systems such as the biosphere, gene expression data or the climate, has led to an increased understanding of their behaviour and characteristics and only now are we appreciating their overwhelming complexity. One common denominator of all these systems is, obviously, complexity. However, even though complexity is becoming an increasingly important issue in modern science and technology, there are no established and practical means of measuring it. Clearly, measurement constitutes the basis of any rigorous scientific activity. The ability to quantify something is a sine-qua-non condition towards being able to manage it.

There do exist numerous complexity measures, such as, the (deterministic) Kolmogorov-Chaitin complexity, which is the smallest length in bits of a computer program that runs on a Universal Turing Machine and produces a certain object x. There are also other measures such as Computational Complexity, Stochastic Complexity, Entropy Rate, Mutual Information, Cyclomatic Complexity, Logical Depth, Thermodynamic Depth, etc. Some of the above definitions are not easily computable. Some are specific to either computer programs, strings of bits, or mechanical or thermodynamic systems. In general, the above definitions cannot be used to treat generic multi-dimensional systems from the standpoint of structure, entropy and coarse-graining.

We develop a rigorous complexity metric and establish an innovative conceptual platform for practical and effective complexity management. The metrics established take into account all the ingredients necessary for a sound and comprehensive complexity measure, namely structure, entropy and data granularity, or coarse-graining. It is shown how via this new metric one can relate complexity to fragility and how critical threshold complexity levels may be established for a given system. This methodology is incorporated into OntoSpaceTM, an easy to use and a first of its kind complexity management software developed by Ontonix.

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