Universal Dynamic Complexity as the Basis for Theoretic Ecology and Unified Civilisation Transition to Creative Global Sustainability

The recently proposed new, universally applicable, rigorously derived and reality-based concept of dynamic complexity provides a unified basis for the causally complete understanding of any real, multi-component and multi-level system of interacting entities, including the case of earth system and global civilisation development. This crucial extension with respect to other existing notions of complexity is obtained due the unrestricted, universally nonperturbative analysis of arbitrary interaction process leading to the new, rigorously derived concept of dynamically multivalued (redundant) entanglement of interacting components. Any real system with interaction is described as a sequence of autonomously emerging "levels of complexity", where each level includes unceasing, dynamically random change of multiple system configurations, or "realisations", each of them resulting from dynamic entanglement of interaction components coming, generally, from lower complexity levels. Dynamic complexity as such is universally defined as a growing function of the number of those explicitly obtained system realisations (or related rate of their change). Mathematically rigorous, realistic and universal nature of unreduced dynamic complexity determines its unique role as a basis for theoretical ecology. This conclusion is confirmed by several directions of universal complexity application to global change understanding and monitoring. They include the rigorously substantiated necessity of civilisation transition to the superior level of complexity involving new, intrinsically unified and causally complete kind of knowledge (initiated by the "universal science of complexity"), qualitatively new kind of material production, social structure, and infrastructure. We show why that new level of civilisation development is intrinsically "sustainable", i. e. characterised by creative, complexity-increasing interaction between "production" and "natural resources" that replaces current contradiction between them

Towards Sustainable Future by Transition to the Next Level Civilisation

Universal and rigorously derived concept of dynamic complexity (ccsd-00004906) shows that any system of interacting components, including society and civilisation, exists only as a process of highly inhomogeneous, qualitative development of its complexity. Modern state of civilisation corresponds to the end of unfolding of a big enough level of complexity. Such exhausted, totally “replete” structure cannot be sustainable in principle and shows instead increased instability, realising its inevitable replacement by a new kind of structure with either low or much higher level of complexity (degrading or progressive development branch, respectively). Unrestricted sustainability can emerge only after transition to the next, superior level of civilisation complexity (ccsd-00004214), which implies qualitative and unified changes in all aspects of life, including knowledge, production, social organisation, and infrastructure. These changes are specified by the rigorous analysis of underlying interaction processes. The unitary, effectively one-dimensional and rigidly fixed kind of thinking, knowledge, and social structure at the current level of complexity will be replaced by “dynamically multivalued”, intrinsically creative kind of structure at the forthcoming superior level of development. We propose mathematically rigorous description of unreduced civilisation complexity development, including universal criterion of progress. One obtains thus a working basis for the causally complete, objectively exact and reliable development science and futurology.Universal science of complexity; dynamic multivaluedness; chaos; self-organisation; dynamically probabilistic fractal; dynamic information; dynamic entropy; symmetry of complexity; Unitary System; Harmonical System; sustainability transition; Revolution of Complexity; noosphere

Describing the complexity of systems: multi-variable "set complexity" and the information basis of systems biology

Context dependence is central to the description of complexity. Keying on the pairwise definition of "set complexity" we use an information theory approach to formulate general measures of systems complexity. We examine the properties of multi-variable dependency starting with the concept of interaction information. We then present a new measure for unbiased detection of multi-variable dependency, "differential interaction information." This quantity for two variables reduces to the pairwise "set complexity" previously proposed as a context-dependent measure of information in biological systems. We generalize it here to an arbitrary number of variables. Critical limiting properties of the "differential interaction information" are key to the generalization. This measure extends previous ideas about biological information and provides a more sophisticated basis for study of complexity. The properties of "differential interaction information" also suggest new approaches to data analysis. Given a data set of system measurements differential interaction information can provide a measure of collective dependence, which can be represented in hypergraphs describing complex system interaction patterns. We investigate this kind of analysis using simulated data sets. The conjoining of a generalized set complexity measure, multi-variable dependency analysis, and hypergraphs is our central result. While our focus is on complex biological systems, our results are applicable to any complex system.Comment: 44 pages, 12 figures; made revisions after peer revie

Applications of tripled chaotic maps in cryptography

Security of information has become a major issue during the last decades. New algorithms based on chaotic maps were suggested for protection of different types of multimedia data, especially digital images and videos in this period. However, many of them fundamentally were flawed by a lack of robustness and security. For getting higher security and higher complexity, in the current paper, we introduce a new kind of symmetric key block cipher algorithm that is based on \emph{tripled chaotic maps}. In this algorithm, the utilization of two coupling parameters, as well as the increased complexity of the cryptosystem, make a contribution to the development of cryptosystem with higher security. In order to increase the security of the proposed algorithm, the size of key space and the computational complexity of the coupling parameters should be increased as well. Both the theoretical and experimental results state that the proposed algorithm has many capabilities such as acceptable speed and complexity in the algorithm due to the existence of two coupling parameter and high security. Note that the ciphertext has a flat distribution and has the same size as the plaintext. Therefore, it is suitable for practical use in secure communications.Comment: 21 pages, 10 figure