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The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach,…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
We show in this pedagogical review that far from being "an apparent law of physics that stands by itself" (R. Bousso, Rev. Mod. Phys. 74 (2002), 825-874), the holographic principle (HP) is a straightforward consequence of the quantum…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
We extend the usual notion of fully commutative elements from the Coxeter groups to the complex reflection groups. Then we decompose the sets of fully commutative elements into natural subsets according to their combinatorial properties,…
A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…
In article the basic principles put in a basis of algorithmicallysoftware of hypercomplex number calculations, structure of a software, structure of functional subsystems are considered. The most important procedures included in subsystems…
If a concept is not well defined, there are grounds for its abuse. This is particularly true of complexity, an inherently interdisciplinary concept that has penetrated very different fields of intellectual activity from physics to…
We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.
Reflection principles (or dually speaking, compactness principles) often give rise to combinatorial guessing principles. Uniformization properties, on the other hand, are examples of anti-guessing principles. We discuss the tension and the…
The notion of composite system made up of distinguishable parties is investigated in the context of arbitrary convex spaces.
We develop a general formalism for representing and understanding structure in complex systems. In our view, structure is the totality of relationships among a system's components, and these relationships can be quantified using information…
Limit theorems for a linear dynamical system with random interactions are established. These theorems enable us to characterize the dynamics of a large complex system in details and assess whether a large complex system is stable or…
This chapter does not deal with specific tools and techniques for managing complex systems, but proposes some basic concepts that help us to think and speak about complexity. We review classical thinking and its intrinsic drawbacks when…
The term complexity derives etymologically from the Latin plexus, which means interwoven. Intuitively, this implies that something complex is composed by elements that are difficult to separate. This difficulty arises from the relevant…
There is a lack of formalism for some key foundational concepts in systems engineering. One of the most recently acknowledged deficits is the inadequacy of systems engineering practices for engineering intelligent systems. In our previous…
We consider extensions of the language of Peano arithmetic by transfinitely iterated truth definitions satisfying uniform Tarskian biconditionals. Without further axioms, such theories are known to be conservative extensions of the original…
A thorough investigation of the foundations of paraconsistent logics. Relations between logical principles are formally studied, a novel notion of consistency is introduced, the logics of formal inconsistency, and the subclasses of…
A general information-theoretic framework for deriving physical laws is presented and a principle of informational physics is enunciated within its context. Existing approaches intended to derive physical laws from information-theoretic…
A general theory of programs, programming and programming languages built up from a few concepts of elementary set theory. Derives, as theorems, properties treated as axioms by classic approaches to programming. Covers sequential and…