Complexity Uncategorized

Complexity, Critical Complexity and Complexity Bounds

Our complexity metric, like all good metrics rooted in physics, has a lower and an upper bound. Critical complexity, as we know, is the maximum level of complexity any given system can sustain, albeit with a feeble structure that is about to collapse. However, there is also a theoretical limit as to how complex a system can really get.

Below are indicated examples of different types of interdependencies between two variables. All images are in reality scatter plots with M data points. It is clear that a uniform distribution of all M samples leads to the highest entropy.

Evidently, the above value of maximum complexity can be significantly higher than critical complexity. In fact, when a system approaches critical complexity, the QCM algorithm starts to eliminate all insignificant interdependencies, not allowing them to reach a nearly uniform distribution.

However, the above result is still useful in that it illustrates how the maximum theoretical complexity is function the fourth power of the number of dimensions, while complexity grows with the power of three.

Established originally in 2005 in the USA, Ontonix is a technology company headquartered in Como, Italy. The unusual technology and solutions developed by Ontonix focus on countering what most threatens safety, advanced products, critical infrastructures, or IT network security - the rapid growth of complexity. In 2007 the company received recognition by being selected as Gartner's Cool Vendor. What makes Ontonix different from all those companies and research centers who claim to manage complexity is that we have a complexity metric. This means that we MEASURE complexity. We detect anomalies in complex defense systems without using Machine Learning for one very good reason: our clients don’t have the luxury of multiple examples of failures necessary to teach software to recognize them. We identify anomalies without having seen them before. Sometimes, you must get it right the first and only time!

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