Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of complex systems can be modeled as an organization of many embedded levels (potentially infinite in number), all of them following the same universal growth principle known as preferential attachment. We give examples of such hierarchy in real systems, for instance, in the pyramid of production entities of the film industry. More importantly, we show how real complex networks can be interpreted as a projection of our model, from which their scale independence, their clustering, their hierarchy, their fractality, and their navigability naturally emerge. Our results suggest that complex networks, viewed as growing systems, can be quite simple, and that the apparent complexity of their structure is largely a reflection of their unobserved hierarchical nature.
Complex networks as an emerging property of hierarchical preferential attachment Laurent Hébert-Dufresne, Edward Laurence, Antoine Allard, Jean-Gabriel Young, and Louis J. Dubé Phys. Rev. E 92, 062809
In this paper we provide a survey of the most relevant work on dynamical criticality, with particular emphasis on the criticality hypothesis, which states that systems in a dynamical regime between order and chaos have evolutionary advantages with respect to ordered and disordered (chaotic) systems. We review the main contributions concerning dynamics and information processing at the edge of chaos, and we illustrate the main achievements in the detection of critical dynamics in biological systems. Finally, we discuss open questions and outlook future work.
Dynamical criticality: overview and open questions Andrea Roli, Marco Villani, Alessandro Filisetti, Roberto Serra
One of the most important tasks in science is to understand the self-organization's arrow of time. To attempt this we utilize the connection between self-organization and non-equilibrium thermodynamics. Eric Chaisson calculated an exponential increase of Free Energy Rate Density (FERD) in Cosmic Evolution, from the Big Bang until now, paralleling the increase of system's structure. We term these studies "Devology". We connect FERD to the principle of least action for complex systems, driving their increase of action efficiency. We study CPUs as a specific system in which the organization, the total amount of action and FERD are connected in a positive feedback loop, providing exponential growth of all three and power law relations between them. This is a deep connection, reaching to the first principles of physics: the least action principle and the second law of thermodynamics. We propose size-density and complexity-density rules in addition to the established size-complexity one.
Free Energy Rate Density and Self-organization in Complex Systems Georgi Yordanov Georgiev, Erin Gombos, Timothy Bates, Kaitlin Henry, Alexander Casey, Michael Daly
Recent increases in food prices are linked to widespread hunger and social unrest. The causes of high food prices have been debated. Here we rule out explanations that are not consistent with the data and construct a dynamic model of food prices using two factors determined to have the largest impact: corn-to-ethanol conversion and investor speculation. We overcome limitations of equilibrium theories that are unable to quantify the impact of speculation by using a dynamic model of trend following. The model accurately fits the data. Ethanol conversion results in a smooth price increase, whereas speculation results in bubbles and crashes. These findings significantly inform the discussion about food prices and market equilibrium and have immediate policy implications.
Accurate market price formation model with both supply-demand and trend-following for global food prices providing policy recommendations
Marco Lagi, Yavni Bar-Yam, Karla Z. Bertrand, and Yaneer Bar-Yam
In 1898, Italian biologist Camillo Golgi saw something odd in the slices of brain tissue he examined under his micro scope: weblike lattices surrounding many neurons. Golgi could not discern their purpose, and many dismissed the nets as an artifact of his staining technique. For the next century, the lattices remained largely obscure. But last week at the annual meeting of the Society for Neuroscience here, researchers offered tantalizing new evidence that holes in these nets could be the storage sites for long-term memories.
Perineuronal nets (PNNs), as they are known today, are scaffolds of linked proteins and sugars that resemble cartilage. A growing body of research suggests that PNNs may control the formation and function of synapses, the microscopic junctions between neurons that allow cells to communicate and that may play a role in learning and memory, says neuroscientist Sakina Palida (...)
Lifelong memories may reside in nets around brain cells Emily Underwood
To ensure that no government, company or person with sole control of digital filters can manipulate our decisions, we need information systems that are transparent, trustworthy and user-controlled. Each of us must be able to choose, modify and build our own tools for winnowing information.
Society: Build digital democracy Dirk Helbing & Evangelos Pournaras
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 exceedingly ordered and too noisy states. We here 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 try to enhance not only their fitness, but also that of other individuals) and competition (agents try 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 solutions.
Cooperation, competition and the emergence of criticality in communities of adaptive systems Jorge Hidalgo, Jacopo Grilli, Samir Suweis, Amos Maritan, Miguel A. Munoz
The engineering of large-scale decentralised systems requires sound methodologies to guarantee the attainment of the desired macroscopic system-level behaviour given the microscopic individual-level implementation. While a general-purpose methodology is currently out of reach, specific solutions can be given to broad classes of problems by means of well-conceived design patterns. We propose a design pattern for collective decision making grounded on experimental/theoretical studies of the nest-site selection behaviour observed in honeybee swarms (Apis mellifera). The way in which honeybee swarms arrive at consensus is fairly well-understood at the macroscopic level. We provide formal guidelines for the microscopic implementation of collective decisions to quantitatively match the macroscopic predictions. We discuss implementation strategies based on both homogeneous and heterogeneous multiagent systems, and we provide means to deal with spatial and topological factors that have a bearing on the micro-macro link. Finally, we exploit the design pattern in two case studies that showcase the viability of the approach. Besides engineering, such a design pattern can prove useful for a deeper understanding of decision making in natural systems thanks to the inclusion of individual heterogeneities and spatial factors, which are often disregarded in theoretical modelling.
We propose a method to decompose a multivariate dynamical system into weakly-coupled modules based on the idea that module boundaries constrain the spread of perturbations. Using a novel quality function called 'perturbation modularity', we find system coarse-grainings that optimally separate the dynamics of perturbation spreading into fast intra-modular and slow inter-modular components. Our method is defined directly in terms of system dynamics, unlike approaches that find communities in networks (whether in structural networks or 'functional networks' of statistical dependencies) or that impose arbitrary dynamics onto graphs. Due to this, we are able to capture the variation of modular organization across states, timescales, and in response to different perturbations, aspects of modularity which are all relevant to real-world dynamical systems. However, in certain cases, mappings exist between perturbation modularity and community detection methods of `Markov stability' and Newman's modularity. Our approach is demonstrated on several examples of coupled logistic maps. It uncovers hierarchical modular organization present in a system's coupling matrix. It also identifies the onset of a self-organized modular regime in coupled map lattices, where it is used to explore dependence of modularity on system state, parameters, and perturbations.
Modularity and the Spread of Perturbations in Complex Dynamical Systems Artemy Kolchinsky, Alexander J. Gates, Luis M. Rocha
Can a human society be organized in such a way that self-organization will always tend to produce outcomes that advance the goals of the society? Such a society would be self-organizing in the sense that agents which pursue only their own interests would none-the-less act in the interests of the society as a whole, irrespective of any intention to do so. In contrast to current human societies, such a society would have a resilient and universal tendency to self-organize “the good” (however “the good” is defined by the society). The paper sketches an agent-based model that identifies the conditions that must be met if self-organizing societies are to emerge. The model draws heavily on an understanding of how self-organizing societies have emerged repeatedly during the evolution of life on Earth (e.g. evolution has produced societies of molecular processes, of simple cells, of eukaryote cells and of multicellular organisms). The model suggests that the key enabling requirement for a self-organizing society is consequence-capture: all agents that comprise the society must capture sufficient of the benefits (and harms) of the impacts of their actions on the goals of the society (if this condition is not met, agents that invest resources in actions that produce global benefits will be outcompeted by those that do not). This condition can be met where a society is managed by appropriate systems of evolvable constraints that suppress free riders and support pro-social actions. In human societies these management constraints include governance and enculturated pre-dispositions such as norms. Appropriate management can produce a self-organizing society in which the interests of all agents (including individuals, associations, firms, multi-national corporations, political organizations, institutions and governments) are aligned with those of the society as a whole. In such a society, agents that pursue only their immediate self-interest will advance societal goals.
Adaptive Individuals in Evolving Populations: Models and Algorithms (Santa Fe Institute Studies in the Sciences of Complexity, Proceedings Vol 26) [Richard K. Belew, Melanie Mitchell] on Amazon.com. *FREE* shipping on qualifying offers. The theory of evolution has been most successful explaining the emergence of new species in terms of their morphological traits. Ethologists teach that behaviors
In 2012 the world's population exceeded 7 billion, and since 2008 the number of individuals living in urban areas has surpassed that of rural areas. This is the result of an overall increase of life expectancy in many countries that has caused an unprecedented growth of the world's total population during recent decades, combined with a net migration flow from rural villages to urban agglomerations. While it is clear that the rate of natural increase and migration flows are the driving forces shaping the spatial distribution of population, a general consensus on the mechanisms that characterise the urbanisation process is still lacking. Here we present two fundamental laws of urbanisation that are quantitatively supported by empirical evidence: 1) the number of cities in a country is proportional to the country's total population, irrespective of the country's area, and 2) the average distance between cities scales as the inverse of the square root of the country's population density. We study the spatio-temporal evolution of population considering two classes of models, Gravity and Intervening Opportunities, to estimate migration flows and show that they produce different spatial patterns of cities.
Discovering the laws of urbanisation Filippo Simini, Charlotte James
A central task in analyzing complex dynamics is to determine the loci of information storage and the communication topology of information flows within a system. Over the last decade and a half, diagnostics for the latter have come to be dominated by the transfer entropy. Via straightforward examples, we show that it and a derivative quantity, the causation entropy, do not, in fact, quantify the flow of information. At one and the same time they can overestimate flow or underestimate influence. We isolate why this is the case and propose alternate measures for information flow. An auxiliary consequence reveals that the proliferation of networks as a now-common theoretical model for large-scale systems in concert with the use of transfer-like entropies has shoehorned dyadic relationships into our structural interpretation of the organization and behavior of complex systems, despite the occurrence of polyadic dependencies. The net result is that much of the sophisticated organization of complex systems goes undetected.
Information Flows? A Critique of Transfer Entropies Ryan G. James, Nix Barnett, James P. Crutchfield
Can we quantify the change of complexity throughout evolutionary processes? We attempt to address this question through an empirical approach. In very general terms, we simulate two simple organisms on a computer that compete over limited available resources. We implement Global Rules that determine the interaction between two Elementary Cellular Automata on the same grid. Global Rules change the complexity of the state evolution output which suggests that some complexity is intrinsic to the interaction rules themselves. The largest increases in complexity occurred when the interacting elementary rules had very little complexity, suggesting that they are able to accept complexity through interaction only. We also found that some Class 3 or 4 CA rules are more fragile than others to Global Rules, while others are more robust, hence suggesting some intrinsic properties of the rules independent of the Global Rule choice. We provide statistical mappings of Elementary Cellular Automata exposed to Global Rules and different initial conditions onto different complexity classes.
To maintain stability yet retain the flexibility to adapt to changing circumstances, social systems must strike a balance between the maintenance of a shared reality and the survival of minority opinion. A computational model is presented that investigates the interplay of two basic, oppositional social processes—conformity and anticonformity—in promoting the emergence of this balance. Computer simulations employing a cellular automata platform tested hypotheses concerning the survival of minority opinion and the maintenance of system stability for different proportions of anticonformity. Results revealed that a relatively small proportion of anticonformists facilitated the survival of a minority opinion held by a larger number of conformists who would otherwise succumb to pressures for social consensus. Beyond a critical threshold, however, increased proportions of anticonformists undermined social stability. Understanding the adaptive benefits of balanced oppositional forces has implications for optimal functioning in psychological and social processes in general.
The Critical Few: Anticonformists at the Crossroads of Minority Opinion Survival and Collapse by Matthew Jarman, Andrzej Nowak, Wojciech Borkowski, David Serfass, Alexander Wong and Robin Vallacher http://jasss.soc.surrey.ac.uk/18/1/6.html
The distribution of firms' growth and firms' sizes is a topic under intense scrutiny. In this paper, we show that a thermodynamic model based on the maximum entropy principle, with dynamical prior information, can be constructed that adequately describes the dynamics and distribution of firms' growth. Our theoretical framework is tested against a comprehensive database of Spanish firms, which covers, to a very large extent, Spain's economic activity, with a total of 1 155 142 firms evolving along a full decade. We show that the empirical exponent of Pareto's law, a rule often observed in the rank distribution of large-size firms, is explained by the capacity of economic system for creating/destroying firms, and that can be used to measure the health of a capitalist-based economy. Indeed, our model predicts that when the exponent is larger than 1, creation of firms is favoured; when it is smaller than 1, destruction of firms is favoured instead; and when it equals 1 (matching Zipf's law), the system is in a full macroeconomic equilibrium, entailing ‘free’ creation and/or destruction of firms. For medium and smaller firm sizes, the dynamical regime changes, the whole distribution can no longer be fitted to a single simple analytical form and numerical prediction is required. Our model constitutes the basis for a full predictive framework regarding the economic evolution of an ensemble of firms. Such a structure can be potentially used to develop simulations and test hypothetical scenarios, such as economic crisis or the response to specific policy measures.
Thermodynamics of firms' growth Eduardo Zambrano, Alberto Hernando, Aurelio Fernández Bariviera, Ricardo Hernando, Angelo Plastino
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 interactions among animals, plants, microbes, earth, wind, and fire—what Darwin called “the entangled bank.” Reducing the bank’s complexity to broad generalizations can seem dishonest. So when Tony Ives, a theoretical ecologist at the University of Wisconsin, prodded his colleagues at the 2013 meeting of the Ecological Society of America by calling for a vote on whether they ought to seek out general laws, it probably wasn’t surprising that two-thirds of the room voted no.1 Despite the skepticism, the kinds of general laws made possible by simplification have remarkable predictive powers. They could let us calculate how many species there are in ecosystems that are too big to sample thoroughly, or how many will be lost after habitat destruction.
We extend previously proposed measures of complexity, emergence, and self-organization to continuous distributions using differential entropy. 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, Carlos Gershenson
Many complex systems can be described as networks exhibiting inner organization as communities of nodes. The identification of communities is a key factor to understand community-based functionality. We propose a family of measures based on the weighted sum of two dissimilarity quantifiers that facilitates efficient classification of communities by tuning the quantifiers’ relative weight to the network’s particularities. Additionally, two new dissimilarities are introduced and incorporated in our analysis. The effectiveness of our approach is tested by examining the Zachary’s Karate Club Network and the Caenorhabditis elegans reactions network. The analysis reveals the method’s classification power as confirmed by the efficient detection of intrapathway metabolic functions in C. elegans.
Inspired by Adam Smith and Friedrich Hayek, many economists have postulated the existence of invisible forces that drive economic markets. These market forces interact in complex ways making it difficult to visualize or understand the interactions in every detail. Here I show how these forces can transcend a zero-sum game and become a win-win business interaction, thanks to emergent social synergies triggered by division of labor. Computer simulations with the model Sociodynamica show here the detailed dynamics underlying this phenomenon in a simple virtual economy. In these simulations, independent agents act in an economy exploiting and trading two different goods in a heterogeneous environment. All and each of the various forces and individuals were tracked continuously, allowing to unveil a synergistic effect on economic output produced by the division of labor between agents. Running simulations in a homogeneous environment, for example, eliminated all benefits of division of labor. The simulations showed that the synergies unleashed by division of labor arise if: Economies work in a heterogeneous environment; agents engage in complementary activities whose optimization processes diverge; agents have means to synchronize their activities. This insight, although trivial if viewed a posteriori, improve our understanding of the source and nature of synergies in real economic markets and might render economic and natural sciences more consilient.
Agent based simulations visualize Adam Smith's invisible hand by solving Friedrich Hayek's Economic Calculus Klaus Jaffe
Human history has been marked by social instability and conflict, often driven by the irreconcilability of opposing sets of beliefs, ideologies, and religious dogmas. The dynamics of belief systems has been studied mainly from two distinct perspectives, namely how cognitive biases lead to individual belief rigidity and how social influence leads to social conformity. Here we propose a unifying framework that connects cognitive and social forces together in order to study the dynamics of societal belief evolution. Each individual is endowed with a network of interacting beliefs that evolves through interaction with other individuals in a social network. The adoption of beliefs is affected by both internal coherence and social conformity. Our framework explains how social instabilities can arise in otherwise homogeneous populations, how small numbers of zealots with highly coherent beliefs can overturn societal consensus, and how belief rigidity protects fringe groups and cults against invasion from mainstream beliefs, allowing them to persist and even thrive in larger societies. Our results suggest that strong consensus may be insufficient to guarantee social stability, that the cognitive coherence of belief-systems is vital in determining their ability to spread, and that coherent belief-systems may pose a serious problem for resolving social polarization, due to their ability to prevent consensus even under high levels of social exposure. We therefore argue that the inclusion of cognitive factors into a social model is crucial in providing a more complete picture of collective human dynamics.
Collective dynamics of belief evolution under cognitive coherence and social conformity Nathaniel Rodriguez, Johan Bollen, Yong-Yeol Ahn
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