Measuring Features of Complex Systems

2020 ◽  
pp. 87-116
Author(s):  
J. Ladyman ◽  
K. Wiesner
Keyword(s):  
Information Processing ◽  
Complex Systems ◽  
Complexity Science ◽  
Effective Measure ◽  
Statistical Complexity ◽  
Universal Behaviour

This chapter offers a guide to quantifying complexity based on the fruits of the analysis of the previous chapters. Many measures of complexity have been proposed since scientists first began to study complex systems, and the list is still growing. If complexity is a collection of features rather than a single phenomenon, then all quantitative measures of complexity can quantify only aspects of complexity rather than complexity as such. The chapter demonstrates the truism of complexity science that it is computational and probabilistic. It also further explains some of the new kinds of invariance and forms of universal behaviour that emerge when complex systems are modelled as networks and information-processing systems. The chapter then looks at a few, by now classic, measures of complexity from the 1980s and 1990s, including effective complexity, effective measure complexity, statistical complexity, and logical depth.

scholarly journals New Inequalities between Information Measures of Network Information Content

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Pantelimon-George Popescu ◽  
Florin Pop ◽  
Alexandru Herişanu ◽  
Nicolae Ţăpuş
Keyword(s):  
Information Processing ◽  
Complex Systems ◽  
Complex Networks ◽  
Information Content ◽  
Discrete Case ◽  
Network Information ◽  
Information Inequalities ◽  
Information Measures ◽  
New Inequalities

We refine a classical logarithmic inequality using a discrete case of Bernoulli inequality, and then we refine furthermore two information inequalities between information measures for graphs, based on information functionals, presented by Dehmer and Mowshowitz in (2010) as Theorems 4.7 and 4.8. The inequalities refer to entropy-based measures of network information content and have a great impact for information processing in complex networks (a subarea of research in modeling of complex systems).

scholarly journals The sleeping brain as a complex system

2011 ◽  
Vol 369 (1952) ◽  
pp. 3697-3707 ◽  
Author(s):  
Eckehard Olbrich ◽  
Peter Achermann ◽  
Thomas Wennekers
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Systems Approach ◽  
Complex Dynamics ◽  
Activity Patterns ◽  
Complexity Science ◽  
Sleep Stages ◽  
Sleep Regulation ◽  
Theme Issue ◽  
The Brain

‘Complexity science’ is a rapidly developing research direction with applications in a multitude of fields that study complex systems consisting of a number of nonlinear elements with interesting dynamics and mutual interactions. This Theme Issue ‘The complexity of sleep’ aims at fostering the application of complexity science to sleep research, because the brain in its different sleep stages adopts different global states that express distinct activity patterns in large and complex networks of neural circuits. This introduction discusses the contributions collected in the present Theme Issue. We highlight the potential and challenges of a complex systems approach to develop an understanding of the brain in general and the sleeping brain in particular. Basically, we focus on two topics: the complex networks approach to understand the changes in the functional connectivity of the brain during sleep, and the complex dynamics of sleep, including sleep regulation. We hope that this Theme Issue will stimulate and intensify the interdisciplinary communication to advance our understanding of the complex dynamics of the brain that underlies sleep and consciousness.

Empirical Tests of Scale-Free Geometry in NASA DATA

2011 ◽  
Vol 301-303 ◽  
pp. 762-767
Author(s):  
Fang Jun Wu
Keyword(s):  
Complex Systems ◽  
21St Century ◽  
Complexity Science ◽  
Scientific Development ◽  
Software Systems ◽  
Scale Free ◽  
Structure Characteristics ◽  
Empirical Tests ◽  
Behavior Characteristics ◽  
And Behavior

Complex systems and complexity science to be home and abroad are believed as the 21st century scientific development frontier by numerous scientists. At present, the complex network and software engineering crossover study has just started. The research results of complex systems and complex networks provide a powerful support for exploring the structure characteristics and behavior characteristics of software systems. This paper tests scale free characteristics on NASA data empirically. More specially, this paper checks whether two of Chidamber and Kemerer metrics suite, namely, CBO and WMC follow power law or not.

scholarly journals Exploring Links between Complexity Constructs and Children’s Knowledge Formation: Implications for Science Learning

2021 ◽  
Author(s):  
Michael J. Droboniku ◽  
Heidi Kloos ◽  
Dieter Vanderelst ◽  
Blair Eberhart
Keyword(s):  
Science Education ◽  
Complex Systems ◽  
Science Learning ◽  
Complexity Science ◽  
Close Correspondence ◽  
Ongoing Controversy ◽  
Preliminary Step ◽  
The Past ◽  
Open Questions ◽  
Knowledge Formation

This essay brings together two lines of work—that of children’s cognition and that of complexity science. These two lines of work have been linked repeatedly in the past, including in the field of science education. Nevertheless, questions remain about how complexity constructs can be used to support children’s learning. This uncertainty is particularly troublesome given the ongoing controversy about how to promote children’s understanding of scientifically valid insights. We therefore seek to specify the knowledge–complexity link systematically. Our approach started with a preliminary step—namely, to consider issues of knowledge formation separately from issues of complexity. To this end, we defined central characteristics of knowledge formation (without considerations of complexity), and we defined central characteristics of complex systems (without considerations of cognition). This preliminary step allowed us to systematically explore the degree of alignment between these two lists of characteristics. The outcome of this analysis revealed a close correspondence between knowledge truisms and complexity constructs, though to various degrees. Equipped with this insight, we derive complexity answers to open questions relevant to science learning.

Complex Systems and How Complex Non-Profits can Harness the Flow of Information

2020 ◽  
Vol 19 (03) ◽  
pp. 2050027
Author(s):  
Darin Freeburg
Keyword(s):  
Complex Systems ◽  
Communities Of Practice ◽  
Information Seeking ◽  
Complexity Science ◽  
Non Profit ◽  
Innovation Model ◽  
Flow Of Information ◽  
Role Of Information

Non-profits must continuously adapt themselves to changing circumstances, but they often lack the resources necessary to adapt successfully. This paper proposes a model to help non-profits overcome this challenge. It explains the role of information in the adaptation of complex systems and suggests a process that non-profits can follow to direct the flow of this information. The Information for Innovation Model (IIM) presented in the paper explains how the inflow and outflow of information influences a system’s adaptation. A series of steps are then proposed for the design of Communities of Practice (CoP) that can help organisations implement the model. Librarians, trained in information-seeking and focused on increasing their reach beyond the library, can support a non-profit following these steps. This paper contributes to the literature on complexity science by articulating a process that organisations can follow to influence the inflow and outflow of information. This process highlights new roles for both CoPs and librarians within non-profits. This is important because non-profits often lack resources necessary for innovation, and librarians are looking for new ways to extend their reach.

scholarly journals Filtering Statistics on Networks

Entropy ◽  
2020 ◽  
Vol 22 (10) ◽  
pp. 1149
Author(s):  
G. J. Baxter ◽  
R. A. da Costa ◽  
S. N. Dorogovtsev ◽  
J. F. F. Mendes
Keyword(s):  
Exact Solution ◽  
Information Processing ◽  
Complex Systems ◽  
Random Graphs ◽  
Strong Dependence ◽  
Initial Configuration ◽  
Final States ◽  
Two Factors ◽  
Processing Information ◽  
Simple Filter

Compression, filtering, and cryptography, as well as the sampling of complex systems, can be seen as processing information. A large initial configuration or input space is nontrivially mapped to a smaller set of output or final states. We explored the statistics of filtering of simple patterns on a number of deterministic and random graphs as a tractable example of such information processing in complex systems. In this problem, multiple inputs map to the same output, and the statistics of filtering is represented by the distribution of this degeneracy. For a few simple filter patterns on a ring, we obtained an exact solution of the problem and numerically described more difficult filter setups. For each of the filter patterns and networks, we found three key numbers that essentially describe the statistics of filtering and compared them for different networks. Our results for networks with diverse architectures are essentially determined by two factors: whether the graphs structure is deterministic or random and the vertex degree. We find that filtering in random graphs produces much richer statistics than in deterministic graphs, reflecting the greater complexity of such graphs. Increasing the graph’s degree reduces this statistical richness, while being at its maximum at the smallest degree not equal to two. A filter pattern with a strong dependence on the neighbourhood of a node is much more sensitive to these effects.

Complexity

2016 ◽  
Author(s):  
David Colander ◽  
Roland Kupers
Keyword(s):  
Complex Systems ◽  
Computer Analysis ◽  
Scientific Community ◽  
Complexity Science ◽  
Computational Tools ◽  
Complex Processes ◽  
Scientific Establishment ◽  
New Vision

This chapter focuses on Stephen Wolfram, an early advocate of the importance of complexity science. He founded the Journal of Complex Systems back in 1987, and saw the transformational aspect of computer analysis long before it was generally understood. But his ego and his disdain for standard scientific conventions kept him and the complexity science he favored outside the mainstream scientific establishment that discourages such grandiose claims. In 2002, his self-published book A New Kind of Science was seen by the scientific community as the delusions of a former wunderkind. It is argued that Wolfram’s book represents the insights of a brilliant visionary about “a new tool of science”—computational tools that earlier scientists could hardly have imagined. These computational tools provide not only new tools for analysis, but also a new vision of how to frame thinking about complex processes. It is the blending of the computational tools and the vision that makes up complexity science.

scholarly journals Insights from the study of complex systems for the ecology and evolution of animal populations

2019 ◽  
Vol 66 (1) ◽  
pp. 1-14 ◽  
Author(s):  
David N Fisher ◽  
Jonathan N Pruitt
Keyword(s):  
Population Dynamics ◽  
Complex Systems ◽  
Complexity Theory ◽  
Complexity Science ◽  
Self Organization ◽  
Emergent Properties ◽  
Ecological Data ◽  
Animal Populations ◽  
Key Characteristics ◽  
And Behavior

Abstract Populations of animals comprise many individuals, interacting in multiple contexts, and displaying heterogeneous behaviors. The interactions among individuals can often create population dynamics that are fundamentally deterministic yet display unpredictable dynamics. Animal populations can, therefore, be thought of as complex systems. Complex systems display properties such as nonlinearity and uncertainty and show emergent properties that cannot be explained by a simple sum of the interacting components. Any system where entities compete, cooperate, or interfere with one another may possess such qualities, making animal populations similar on many levels to complex systems. Some fields are already embracing elements of complexity to help understand the dynamics of animal populations, but a wider application of complexity science in ecology and evolution has not occurred. We review here how approaches from complexity science could be applied to the study of the interactions and behavior of individuals within animal populations and highlight how this way of thinking can enhance our understanding of population dynamics in animals. We focus on 8 key characteristics of complex systems: hierarchy, heterogeneity, self-organization, openness, adaptation, memory, nonlinearity, and uncertainty. For each topic we discuss how concepts from complexity theory are applicable in animal populations and emphasize the unique insights they provide. We finish by outlining outstanding questions or predictions to be evaluated using behavioral and ecological data. Our goal throughout this article is to familiarize animal ecologists with the basics of each of these concepts and highlight the new perspectives that they could bring to variety of subfields.

scholarly journals Engineering Resilient Complex Systems: The Necessary Shift Toward Complexity Science

2020 ◽  
Vol 14 (3) ◽  
pp. 3865-3874 ◽  
Author(s):  
Giuliano Punzo ◽  
Anurag Tewari ◽  
Eugene Butans ◽  
Massimiliano Vasile ◽  
Alan Purvis ◽  
...  
Keyword(s):  
Complex Systems ◽  
Complexity Science
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