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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…

Physics Education · Physics 2007-05-23 Rajesh R. Parwani

This is an essay about understanding complexity science, via some peculiarities of the field, as a meeting place for a special kind of scientist. It comes out of my hobby of reading popular-science complex systems books, and builds on notes…

Physics and Society · Physics 2022-01-12 Petter Holme

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…

Systems and Control · Electrical Eng. & Systems 2025-08-18 John W. Sheppard

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…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Carlos Gershenson , Francis Heylighen

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…

Other Computer Science · Computer Science 2021-10-05 Luciano da F. Costa , Guilherme S. Domingues

I present my viewpoint on complexity, stressing general arguments and using a rather simple language.

Statistical Mechanics · Physics 2007-05-23 Giorgio Parisi

The term {\em complexity} is used informally both as a quality and as a quantity. As a quality, complexity has something to do with our ability to understand a system or object -- we understand simple systems, but not complex ones. On…

Adaptation and Self-Organizing Systems · Physics 2009-11-19 Russell K. Standish

Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…

Adaptation and Self-Organizing Systems · Physics 2020-09-22 Karoline Wiesner , James Ladyman

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…

Other Computer Science · Computer Science 2011-09-02 Carlos Gershenson

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…

adap-org · Physics 2009-10-22 Kunihiko Kaneko , Ichiro Tsuda

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…

Software Engineering · Computer Science 2015-12-25 Alexei Botchkarev , Patrick Finnigan

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,…

Adaptation and Self-Organizing Systems · Physics 2015-02-12 Christopher R. Stephens

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.…

Data Analysis, Statistics and Probability · Physics 2013-01-18 Eugene Perevalov , David Grace

This is a very basic introduction to some notions related to logic and complexity.

Logic · Mathematics 2007-05-23 Stephen Semmes

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…

Computers and Society · Computer Science 2020-01-09 Juste Raimbault

In this chapter, I review the main methods and techniques of complex systems science. As a first step, I distinguish among the broad patterns which recur across complex systems, the topics complex systems science commonly studies, the tools…

Adaptation and Self-Organizing Systems · Physics 2007-05-23 Cosma Rohilla Shalizi

Basic problems in complex systems are surveyed in connection with Life. As a key issue for complex systems, complementarity between syntax/rule/parts and semantics/behavior/whole is stressed. To address the issue, a constructive approach…

adap-org · Physics 2007-05-23 Kunihiko Kaneko

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…

Adaptation and Self-Organizing Systems · Physics 2021-02-26 Carlos Gershenson

We give a basic overview of computational complexity, query complexity, and communication complexity, with quantum information incorporated into each of these scenarios. The aim is to provide simple but clear definitions, and to highlight…

Quantum Physics · Physics 2016-11-23 Richard Cleve

A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…

Chaotic Dynamics · Physics 2009-11-07 Ricardo Lopez-Ruiz , Hector Mancini , Xavier Calbet
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