Related papers: How can we think the complex?
The classical simulation of physical processes using standard models of computation is fraught with problems. On the other hand, attempts at modelling real-world computation with the aim of isolating its hypercomputational content have…
A general notion of information-related complexity applicable to both natural and man-made systems is proposed. The overall approach is to explicitly consider a rational agent performing a certain task with a quantifiable degree of success.…
The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides…
Many undergraduate students of engineering and the exact sciences have difficulty with their mathematics courses due to insufficient proficiency in what we in this paper have termed clear thinking. We believe that this lack of proficiency…
Implicit computational complexity, which aims at characterizing complexity classes by machine-independent means, has traditionally been based, on the one hand, on programs and deductive formalisms for free algebras, and on the other hand on…
Complex systems' modeling and simulation are powerful ways to investigate a multitude of natural phenomena providing extended knowledge on their structure and behavior. However, enhanced modeling and simulation require integration of…
The world is changing at an ever-increasing pace. And it has changed in a much more fundamental way than one would think, primarily because it has become more connected and interdependent than in our entire history. Every new product, every…
In these notes we review emergent phenomena in complex systems, emphasizing ways to identify potential underlying universal mechanisms that generates complexity. The discussion is centered around the emergence of collective behavior in…
Basic problems of complex systems are outlined with an emphasis on irreducibility and dynamic many-to-many correspondences. We discuss the importance of a constructive approach to artificial reality and the significance of an internal…
Explaining the behaviour of intelligent systems will get increasingly and perhaps intractably challenging as models grow in size and complexity. We may not be able to expect an explanation for every prediction made by a brain-scale model,…
Building software-driven systems that are easily understood becomes a challenge, with their ever-increasing complexity and autonomy. Accordingly, recent research efforts strive to aid in designing explainable systems. Nevertheless, a common…
Complex systems and their underlying convoluted networks are ubiquitous, all we need is an eye for them. They pose problems of organized complexity which cannot be approached with a reductionist method. Complexity science and its emergent…
Complexity theory provides a wealth of complexity classes for analyzing the complexity of decision and counting problems. Despite the practical relevance of enumeration problems, the tools provided by complexity theory for this important…
Simplicial complexes are a versatile and convenient paradigm on which to build all the tools and techniques of the logic of knowledge, on the assumption that initial epistemic models can be described in a distributed fashion. Thus, we can…
The science of complexity is far from being fully understood and even its foundations are not well established. On the other hand, during the last decade, the random motion of particles or waves - the so-called diffusion - has been known…
Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter…
Complex systems are characterized by specific time-dependent interactions among their many constituents. As a consequence they often manifest rich, non-trivial and unexpected behavior. Examples arise both in the physical and non-physical…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
This article summarises a Web-book on "Complexity" that was developed to introduce undergraduate students to interesting complex systems in the biological, physical and social sciences, and the common tools, principles and concepts used for…
Systems are growing into more complex ones for developing and maintaining. Existing systems which do not have much in common on the first look are connected, due to the technical progress, even if it was never intended that way. It is an…