Complexity & Systems
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# The spatial meaning of Pareto's scaling exponent of city-size distribution

The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the fractal dimension. However, this viewpoint is not exact. In this paper, I will present a new interpretation of the scaling exponent of rank-size distributions. The ideas from fractal measure relation and the principle of dimension consistency are employed to explore the essence of Pareto's and Zipf's scaling exponents. The Pareto exponent proved to be a ratio of the fractal dimension of a network of cities to the average dimension of city population. Accordingly, the Zipf exponent is the reciprocal of this dimension ratio. On a digital map, the Pareto exponent can be defined by the scaling relation between a map scale and the corresponding number of cities based on this scale. The cities of the United States of America in 1900, 1940, 1960, and 1980 and Indian cities in 1981, 1991, and 2001 are utilized to illustrate the geographical spatial meaning of Pareto's exponent. The results suggest that the Pareto exponent of city-size distribution is not a fractal dimension, but a ratio of the urban network dimension to the city population dimension. This conclusion is revealing for scientists to understand Zipf's law and fractal structure of hierarchy of cities.

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# Complexity & Systems

Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex.  wikipedia (en)
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## The Hidden Power Laws of Ecosystems - Issue 29: Scaling - Nautilus

Here’s how to cause a ruckus: Ask a bunch of naturalists to simplify the world. We usually think in terms of a web of complicated…
Gary Bamford's curator insight,

The complexity of complexity!

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## Cooperation, competition and the emergence of criticality in communities of adaptive systems

The hypothesis that living systems can benefit from operating at the vicinity of critical points has gained momentum in recent years. Criticality may confer an optimal balance between too ordered and exceedingly noisy states. Here we present a model, based on information theory and statistical mechanics, illustrating how and why a community of agents aimed at understanding and communicating with each other converges to a globally coherent state in which all individuals are close to an internal critical state, i.e. at the borderline between order and disorder. We study—both analytically and computationally—the circumstances under which criticality is the best possible outcome of the dynamical process, confirming the convergence to critical points under very generic conditions. Finally, we analyze the effect of cooperation (agents trying to enhance not only their fitness, but also that of other individuals) and competition (agents trying to improve their own fitness and to diminish those of competitors) within our setting. The conclusion is that, while competition fosters criticality, cooperation hinders it and can lead to more ordered or more disordered consensual outcomes.

Via Samir, Complexity Digest
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## Organized Complexity

While I've focused this week thus far on Cities and the Wealth of Nations, Jane Jacobs' most popular book among planners is, of course, The Death and Life of Great American Cities. This is because the latter book contains all the of the happy things
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## Complexity Labs

Complexity Labs is an online resource dedicated to the area of complex systems providing a wide variety of users with information, research, learning and media content relating to this exciting new area. Our mission statement is to assist in the development of a coherent, robust and accessible framework for modelling, designing and managing complex systems.

http://complexitylabs.io

Via Complexity Digest
Complexity Digest's curator insight,

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## Collapse des systèmes complexes

Pourquoi parler d’effondrement et de collapse de notre civilisation ? Parce que le faisceau d’informations factuelles est très convergent, parce que cela a à voir avec les systèmes complexes, et parce que la résilience, individuelle et collective, commence par l’acceptation de la réalité telle qu’elle est.

Via Philippe Vallat
Pierre Mongin 's curator insight,
juin excellente synthése du film Demain
Jürgen Kanz's curator insight,
The authors are referring to the paper of Graham M. Turner "On the cusp of global collapse?". This document is available here: https://www.ethz.ch/content/dam/ethz/special-interest/usys/ites/ecosystem-management-dam/documents/EducationDOC/Readings_DOC/Turner_2012_GAIA_LimitsToGrowth.pdf
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## Hybrid Societies: Challenges and Perspectives in the Design of Collective Behavior in Self-organizing Systems

Hybrid societies are self-organizing, collective systems, which are composed of different components, for example, natural and artificial parts (bio-hybrid) or human beings interacting with and through technical systems (socio-technical). Many different disciplines investigate methods and systems closely related to the design of hybrid societies. A stronger collaboration between these disciplines could allow for re-use of methods and create significant synergies. We identify three main areas of challenges in the design of self-organizing hybrid societies. First, we identify the formalization challenge. There is an urgent need for a generic model that allows a description and comparison of collective hybrid societies. Second, we identify the system design challenge. Starting from the formal specification of the system, we need to develop an integrated design process. Third, we identify the challenge of interdisciplinarity. Current research on self-organizing hybrid societies stretches over many different fields and hence requires the re-use and synthesis of methods at intersections between disciplines. We then conclude by presenting our perspective for future approaches with high potential in this area.

Hybrid Societies: Challenges and Perspectives in the Design of Collective Behavior in Self-organizing Systems

Heiko Hamann, Yara Khaluf, Jean Botev, Mohammad Divband Soorati, Eliseo Ferrante, Oliver Kosak, Jean-Marc Montanier, Sanaz Mostaghim, Richard Redpath, Jonathan Timmis, Frank Veenstra, Mostafa Wahby, Aleš Zamuda
Front. Robot. AI, 11 April 2016 | http://dx.doi.org/10.3389/frobt.2016.00014

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## Systems tinkering versus systems thinking - All Things ITSM

Systems Thinking, is well suited to mass customization and knowledge work.Dealing with complex systems requires an experimental ‘systems tinkering’ approach
Via Jürgen Kanz
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## How Diversity Makes Us Smarter

Being around people who are different from us makes us more creative, more diligent and harder-working

Via june holley
Marcelo Errera's curator insight,
Indeed, as new ideas flow across groups of people, new degrees of freedom become available in the design evolution process.

It's a physics phenomenon.

Lexie stroud's curator insight,
Although many people, specifically from homogenous groups, might argue this, I think it is an interesting concept. I think that it is a good thing for people of different backgrounds to come together and find ways to effectively solve problems. It seems obvious that they might be better at it. L.S.
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## Some problems with the systems approach

Some problems with the systems approach Why isn't it applied more often? Simple explanations        I am convinced that the systems approach is a very good thing. Like many 'believers' it is hard for me to understand why so many people think otherwise. In other words, how non-systems practitioners can think that they can and must address…
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## The systems approach according to Churchman

The environmental fallacy and other notions The systems approach and its enemies      Too often human realities are ignored, with the result that planning efforts are sterile, unsatisfying, and irrelevant. In 'The systems approach and its enemies' (1979), Churchman draws on his wide and deep experience as a both a thinker and planner to show that…
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## [1602.09054] Lyapunov Indices and the Poincaré Mapping in a Study of the Stability of the Krebs Cycle

On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxilic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane potential formed by the respiratory chain in the plasmatic membrane of a cell. The phase-parametric characteristic of the dynamics of the ATP level depending on a given parameter is constructed. The scenario of formation of multiple autoperiodic and chaotic modes is presented. Poincar\'{e} sections and mappings are constructed. The stability of modes and the fractality of the obtained bifurcations are studied. The full spectra of Lyapunov indices, divergences, KS-entropies, horizons of predictability, and Lyapunov dimensionalities of strange attractors are calculated. Some conclusions about the structural-functional connections determining the dependence of the cell respiration cyclicity on the synchronization of the functioning of the tricarboxilic acid cycle and the electron transport chain are presented.
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## Measuring the Complexity of Continuous Distributions

We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. Given that the measures were based on Shannon’s information, the novel continuous complexity measures describe how a system’s predictability changes in terms of the probability distribution parameters. This allows us to calculate the complexity of phenomena for which distributions are known. We find that a broad range of common parameters found in Gaussian and scale-free distributions present high complexity values. We also explore the relationship between our measure of complexity and information adaptation.

Measuring the Complexity of Continuous Distributions
Guillermo Santamaría-Bonfil, Nelson Fernández,  and Carlos Gershenson

Entropy 2016, 18(3), 72

http://www.mdpi.com/1099-4300/18/3/72

Via Complexity Digest
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## Gérard Ben Arous - "Paul Lévy et les cygnes noirs"

BnF - 30 avril 2014 Conférence donnée dans le cadre du cycle "Un texte, un mathématicien", organisée par la Société…
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## How the hidden mathematics of living cells could help us decipher the brain

So will we ever be able to model something as complex as the human brain using computers? After all, biological systems use symmetry and interaction to do things that even the most powerful computers cannot do – like surviving, adapting and reproducing. This is one reason why binary logic often falls short of describing how living things or human intelligence work. But our new research suggests there are alternatives: by using the mathematics that describe biological networks in the computers of the future, we may be able to make them more complex and similar to living systems like the brain.

How the hidden mathematics of living cells could help us decipher the brain

Chrystopher Nehaniv

https://theconversation.com/how-the-hidden-mathematics-of-living-cells-could-help-us-decipher-the-brain-59483

Via Complexity Digest
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## How to get from a ‘problematic situation’ to a ‘systemic intervention’?

How to get from a 'problematic situation' to a 'systemic intervention'? While reading '15 praktijkverhalen over kennismanagement' [Dutch for '15 practical cases of knowledge management'] I came across one story (about Kennisland, Dutch for 'knowledgeland') which triggered my curiosity. It led me to MaRS (originally 'Medical and Related Sciences', but now an acronym no more),…
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## ComplexityBlog » Studying Complexity vs Studying Complex Systems

Springing from my recent post distinguishing types of inter-disciplinary research, I now will go into more detail on a related topic: the difference between studying particular systems that happen to be complex, and studying complexity itself. The main point is that complexity theory includes several commitments related to levels of organization and to there being shared principles/mechanisms underpinning the dynamics of disparate systems. Studying complexity is the overt researching of these commitments and underpinnings. However, most scientists that describe themselves as doing complexity research are not doing that. Instead they are studying particular complex systems and typically ignore the commitments and underpinnings that define complexity science.
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## Systems Science Ascending

After years of development in increasingly fracturing sub-disciplines it seems that systems science as an integrated whole domain of knowledge is rising again. For those familiar with the history of systems science you will recall that in the earl
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## case-based modeling, case based modeling, sacs toolkit, brian castellani, rajeev rajaram, sociology and complexity, complexity map

sociology and complexity science web
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## Understanding the group dynamics and success of teams

Complex problems often require coordinated group effort and can consume significant resources, yet our understanding of how teams form and succeed has been limited by a lack of large-scale, quantitative data. We analyse activity traces and success levels for approximately 150 000 self-organized, online team projects. While larger teams tend to be more successful, workload is highly focused across the team, with only a few members performing most work. We find that highly successful teams are significantly more focused than average teams of the same size, that their members have worked on more diverse sets of projects, and the members of highly successful teams are more likely to be core members or ‘leads’ of other teams. The relations between team success and size, focus and especially team experience cannot be explained by confounding factors such as team age, external contributions from non-team members, nor by group mechanisms such as social loafing. Taken together, these features point to organizational principles that may maximize the success of collaborative endeavours.

Understanding the group dynamics and success of teams
Michael Klug, James P. Bagrow

Royal Society Open Science

http://dx.doi.org/10.1098/rsos.160007

Via Complexity Digest
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## The systems approach: theory for practice

Over the past 4 years I have written a good number of posts on various aspects of the systems approach. In this post I will re-arrange more than 30 of them, to provide a more or less coherent body of theoretical insights underlying  Wicked Solutions. Along the way you will learn why “it is tempting, if the…
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## The origins of the systems approach

Churchman's personal journey This post about the origins (and future!) of the systems approach is a bit complicated. You may prefer to get yourself intellectually geared up by first reading my previous post on the reasons why people don't apply the systems approach more often. Biography of the systems approach          In the first chapter of…
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## Systems of Interaction between the First Sedentary Villages in the Near East Exposed Using Agent-Based Modelling of Obsidian Exchange

In the Near East, nomadic hunter-gatherer societies became sedentary farmers for the first time during the transition into the Neolithic. Sedentary life presented a risk of isolation for Neolithic groups. As fluid intergroup interactions are crucial for the sharing of information, resources and genes, Neolithic villages developed a network of contacts. In this paper we study obsidian exchange between Neolithic villages in order to characterize this network of interaction. Using agent-based modelling and elements taken from complex network theory, we model obsidian exchange and compare results with archaeological data. We demonstrate that complex networks of interaction were established at the outset of the Neolithic and hypothesize that the existence of these complex networks was a necessary condition for the success and spread of a new way of living.
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## [1406.5955] Simple universal models capture all spin physics

Spin models are used in virtually every study of complex systems---be it condensed matter physics [1-4], neural networks [5] or economics [6,7]---as they exhibit very rich macroscopic behaviour despite their microscopic simplicity. It has long been known that by coarse-graining the system, the low energy physics of the models can be classified into different universality classes [8]. Here we establish a counterpart to this phenomenon: by "fine-graining" the system, we prove that all the physics of every classical spin model is exactly reproduced in the low energy sector of certain `universal models'. This means that (i) the low energy spectrum of the universal model is identical to the entire spectrum of the original model, (ii) the corresponding spin configurations are exactly reproduced, and (iii) the partition function is approximated to any desired precision. We prove necessary and sufficient conditions for a spin model to be universal, which show that complexity in the ground state alone is sufficient to reproduce full energy spectra. We use this to show that one of the simplest and most widely studied models, the 2D Ising model with fields, is universal.
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## The essence of the systems approach

Why 'Wicked Solutions' works? Wicked problems now recognized         There was a time when wicked problems did not seem to exist. No matter how complex the problem, there was a general belief that a solution could be found, more typically by so-called linear problem solving methods. This changed in the early 1960s when Horst Rittel found…
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## Jean-Michel Coron - "La régulation des systèmes complexes depuis Maxwell"

BnF - 11 mai 2011 Conférence donnée dans le cadre du cycle "Un texte, un mathématicien", organisée par la Société…
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## [1602.02540] Variations on chaos in physics: from unpredictability to universal laws

The tremendous popular success of Chaos Theory shares some common points with the not less fortunate Relativity: they both rely on a misunderstanding. Indeed, ironically , the scientific meaning of these terms for mathematicians and physicists is quite opposite to the one most people have in mind and are attracted by. One may suspect that part of the psychological roots of this seductive appeal relies in the fact that with these ambiguous names, together with some superficial clichés or slogans immediately related to them ("the butterfly effect" or "everything is relative"), some have the more or less secret hope to find matter that would undermine two pillars of science, namely its ability to predict and to bring out a universal objectivity. Here I propose to focus on Chaos Theory and illustrate on several examples how, very much like Relativity, it strengthens the position it seems to contend with at first sight: the failure of predictability can be overcome and leads to precise, stable and even more universal predictions.

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