Related papers: Identifying Complexity by Means of Matrices
Complexity is an inherent attribute of any project. The purpose of defining and documenting complexity is to have an early warning tool allowing a project team to focus on certain areas and aspects of the project in order to prevent and…
Except for crystalline or random structures, an agreed definition of complexity for intermediate and hence interesting cases does not exist. We fill this gap with a notion of complexity that characterises shapes formed by any finite number…
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…
The complexity of a system, in general, makes it difficult to determine some or almost all matrix elements of its operators. The lack of accuracy acts as a source of randomness for the matrix elements which are also subjected to an external…
Emergence and causality are two fundamental concepts for understanding complex systems. They are interconnected. On one hand, emergence refers to the phenomenon where macroscopic properties cannot be solely attributed to the cause of…
Complex systems are typically represented by large ensembles of observations. Correlation matrices provide an efficient formal framework to extract information from such multivariate ensembles and identify in a quantifiable way patterns of…
The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to…
The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…
Nowadays the question `what is complexity?' is a challenge to be answered. This question is triggering a great quantity of works in the frontier of physics, biology, mathematics and computer science. Even more when this century has been…
Complexity remains one of the central challenges in science and technology. Although several approaches at defining and/or quantifying complexity have been proposed, at some point each of them seems to run into intrinsic limitations or…
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…
Complexity of patterns is a key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal…
Herein we consider various concepts of entropy as measures of the complexity of phenomena and in so doing encounter a fundamental problem in physics that affects how we understand the nature of reality. In essence the difficulty has to do…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a…
The evolution of complexity has been a central theme for Biology [2] and Artificial Life research [1]. It is generally agreed that complexity has increased in our universe, giving way to life, multi-cellularity, societies, and systems of…
There is no single definition of complexity (Edmonds 1999; Gershenson 2008; Mitchell 2009; De Domenico, et al., 2019), as it acquires different meanings in different contexts. A general notion is the amount of information required to…
In this paper we examine the concept of complexity as it applies to generative art and design. Complexity has many different, discipline specific definitions, such as complexity in physical systems (entropy), algorithmic measures of…
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…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…