Editing Complexity (section)

== Topics ==

=== Behaviour ===
The behavior of a complex system is often said to be due to emergence and self-organization. Chaos theory has investigated the sensitivity of systems to variations in initial conditions as one cause of complex behaviour.

===Mechanisms ===
Recent developments in [[artificial life]], [[evolutionary computation]] and [[genetic algorithm]]s have led to an increasing emphasis on complexity and complex adaptive systems.

=== Simulations ===
In [[social science]], the study on the emergence of macro-properties from the micro-properties, also known as macro-micro view in [[sociology]]. The topic is commonly recognized as [[social complexity]] that is often related to the use of computer simulation in social science, i.e. [[computational sociology]].

=== Systems ===
{{main article|Complex system}}
[[Systems theory]] has long been concerned with the study of complex systems (in recent times, ''complexity theory'' and ''complex systems'' have also been used as names of the field). These systems are present in the research of a variety of disciplines, including [[biology]], [[economics]], social studies and [[technology]]. Recently, complexity has become a natural domain of interest of real-world socio-cognitive systems and emerging [[systemics]] research. Complex systems tend to be high-[[dimension]]al, non-linear, and difficult to model. In specific circumstances, they may exhibit low-dimensional behaviour.

=== Data ===
In [[information theory]], algorithmic information theory is concerned with the complexity of strings of [[data]].

Complex strings are harder to compress. While intuition tells us that this may depend on the [[codec]] used to compress a string (a codec could be theoretically created in any arbitrary language, including one in which the very small command "X" could cause the computer to output a very complicated string like "18995316"), any two [[Turing completeness|Turing-complete]] languages can be implemented in each other, meaning that the length of two encodings in different languages will vary by at most the length of the "translation" language – which will end up being negligible for sufficiently large data strings.

These algorithmic measures of complexity tend to assign high values to [[signal noise|random noise]]. However, under a certain understanding of complexity, arguably the most intuitive one, random noise is meaningless and so not complex at all.

[[Information entropy]] is also sometimes used in information theory as indicative of complexity, but entropy is also high for randomness. In the case of complex systems, [[information fluctuation complexity]] was designed so as not to measure randomness as complex and has been useful in many applications. More recently, a complexity metric was developed for images that can avoid measuring noise as complex by using the minimum description length principle.<ref>Mahon, L.; Lukasiewicz, T. (2023). "[https://www.sciencedirect.com/science/article/pii/S0031320323005873 Minimum Description Length Clustering to Measure Meaningful Image Complexity]". Pattern Recognition, 2023 (144).</ref>

===Classification Problems===
There has also been interest in measuring the complexity of classification problems in [[Supervised learning|supervised machine learning]]. This can be useful in [[meta-learning (computer science)|meta-learning]] to determine for which data sets filtering (or removing suspected noisy instances from the training set) is the most beneficial<ref>{{cite journal|title= Predicting Noise Filtering Efficacy with Data Complexity Measures for Nearest Neighbor Classification|journal= Pattern Recognition|volume= 46|pages= 355–364|doi= 10.1016/j.patcog.2012.07.009|year= 2013|last1= Sáez|first1= José A.|last2= Luengo|first2= Julián|last3= Herrera|first3= Francisco|issue= 1|bibcode= 2013PatRe..46..355S}}</ref> and could be expanded to other areas. For [[binary classification]], such measures can consider the overlaps in feature values from differing classes, the separability of the classes, and measures of geometry, topology, and density of [[manifold]]s.<ref>Ho, T.K.; Basu, M. (2002). "[https://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=990132&tag=1 Complexity Measures of Supervised Classification Problems]". IEEE Transactions on Pattern Analysis and Machine Intelligence 24 (3), pp 289–300.</ref>

For non-binary classification problems, instance hardness<ref>Smith, M.R.; Martinez, T.; Giraud-Carrier, C. (2014). "[https://link.springer.com/article/10.1007%2Fs10994-013-5422-z An Instance Level Analysis of Data Complexity]". Machine Learning, 95(2): 225–256.</ref>  is a bottom-up approach that first seeks to identify instances that are likely to be misclassified (assumed to be the most complex). The characteristics of such instances are then measured using [[supervised learning|supervised]] measures such as the number of disagreeing neighbors or the likelihood of the assigned class label given the input features.

=== In molecular recognition ===
A recent study based on [[Molecular modelling|molecular simulations]] and compliance constants describes [[molecular recognition]] as a phenomenon of organisation.<ref>{{cite journal | title=Complexity in molecular recognition | author=Jorg Grunenberg | journal=Phys. Chem. Chem. Phys. | year=2011 | volume=13 | issue=21 | pages= 10136–10146 | doi=10.1039/c1cp20097f| pmid=21503359 | bibcode=2011PCCP...1310136G }}</ref>
Even for small molecules like [[carbohydrates]], the recognition process can not be predicted or designed even assuming that each individual [[hydrogen bond]]'s strength is exactly known.

=== The law of requisite complexity ===
Deriving from the [[Variety (cybernetics)#Law of requisite variety|law of requisite variety]], Boisot and McKelvey formulated the ‘Law of Requisite Complexity’, that holds that, in order to be efficaciously adaptive, the internal complexity of a system must match the external complexity it confronts.<ref>{{Cite journal|last1=Boisot|first1=M.|last2=McKelvey|first2=B.|date=2011|title=Complexity and organization-environment relations: revisiting Ashby's law of requisite variety|journal=P. Allen, the Sage Handbook of Complexity and Management|language=en|pages=279–298}}</ref>

=== Positive, appropriate and negative complexity ===
The application in project management of the Law of Requisite Complexity, as proposed by Stefan Morcov, is the analysis of [[Project complexity#Positive, appropriate (requisite), and negative complexity|positive, appropriate and negative complexity]].<ref>{{Cite journal|last1=Morcov|first1=Stefan|last2=Pintelon|first2=Liliane|last3=Kusters|first3=Rob J.|date=2020|title=IT Project Complexity Management Based on Sources and Effects: Positive, Appropriate and Negative|journal=Proceedings of the Romanian Academy - Series A|language=en|volume=21|issue=4|pages=329–336|url=https://acad.ro/sectii2002/proceedings/doc2020-4/05-Morcov.pdf |archive-url=https://web.archive.org/web/20201230142223/https://acad.ro/sectii2002/proceedings/doc2020-4/05-Morcov.pdf |archive-date=2020-12-30 |url-status=live}}</ref><ref name="Morcov2021">Morcov, S. (2021). Managing Positive and Negative Complexity: Design and Validation of an IT Project Complexity Management Framework. KU Leuven University. Available at https://lirias.kuleuven.be/retrieve/637007 {{Webarchive|url=https://web.archive.org/web/20211107081756/https://lirias.kuleuven.be/retrieve/637007 |date=2021-11-07 }}</ref>

=== In [[project management]] ===
[[Project complexity]] is the property of a project which makes it difficult to understand, foresee, and keep under control its overall behavior, even when given reasonably complete information about the project system.<ref>{{Cite book|last1=Marle|first1=Franck|last2=Vidal|first2=Ludovic-Alexandre|date=2016|title=Managing Complex, High Risk Projects - A Guide to Basic and Advanced Project Management|location=London|publisher=Springer-Verlag}}</ref><ref>{{Cite journal|last1=Morcov|first1=Stefan|last2=Pintelon|first2=Liliane|last3=Kusters|first3=Rob J.|date=2020|title=Definitions, characteristics and measures of IT Project Complexity - a Systematic Literature Review|journal=International Journal of Information Systems and Project Management|language=en|volume=8|issue=2|pages=5–21|doi=10.12821/ijispm080201|s2cid=220545211|url=http://www.sciencesphere.org/ijispm/archive/ijispm-080201.pdf |archive-url=https://web.archive.org/web/20200711093800/http://www.sciencesphere.org/ijispm/archive/ijispm-080201.pdf |archive-date=2020-07-11 |url-status=live}}</ref>

=== In systems engineering ===
Maik Maurer considers complexity as a reality in engineering. He proposed a methodology for '''managing complexity in systems engineering''' <ref>{{Cite book|last=Maurer|first=Maik|url=https://www.worldcat.org/oclc/973540283|title=Complexity management in engineering design -- a primer|date=2017|isbn=978-3-662-53448-9|location=Berlin, Germany|oclc=973540283}}</ref>''':'''

                             1.           Define the system.

                             2.           Identify the type of complexity.

                             3.           Determine the strategy.

                             4.           Determine the method.

                             5.           Model the system.

                             6.           Implement the method.