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.
In this paper, we propose, discuss, and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers, and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call “expansion entropy,” and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy to which it is equivalent under appropriate conditions. We also present example illustrations, discuss computational implementations, and point out issues arising from attempts at giving definitions of chaos that are not entropy-based.
Italian New Public Management (NPM) has been mainly characterized by a political orientation toward power decentralization to local governments and privatization of public companies. Nowadays, local utilities in Italy are often run by joint stock companies controlled by public agencies such as Regional and Municipal Administrations. Due to this transformation, these companies must comply with a set of diverse expectations coming from a wide range of stakeholders, related to their financial, competitive and social performance. Such fragmented governance increases the presence of “wicked” problems in the decision-making sphere of these entities. Given this multi-level governance structure, how do these agents influence public services performance? In recent years, coordination and inter-institutional joint action have been identified as possible approaches for dealing with governance fragmentation and wicked problems deriving from it. How can we adapt a performance management perspective in order to help us reform the system and so have a better collaboration between the stakeholders involved? In order to address and discuss these research questions, a case study will be developed. The case concerns AMAT, the local utility providing the public transportation service in the Municipality of Palermo (Italy). The result of this study is a dynamic model including a set of performance indicators that help us in understanding the impact of the governing structure on the system’s performance.
We discuss how understanding the nature of chaotic dynamics allows us to control these systems. A controlled chaotic system can then serve as a versatile pattern generator that can be used for a range of application. Specifically, we will discuss the application of controlled chaos to the design of novel computational paradigms. Thus, we present an illustrative research arc, starting with ideas of control, based on the general understanding of chaos, moving over to applications that influence the course of building better devices.
“Chaos is found in greatest abundance wherever order is being sought. It always defeats order, because it is better organized” Terry Pratchett A brief review is presented of some recent findings in the theory of chaotic dynamics. We also prove a statement that could be naturally considered as a dual one to the Poincaré theorem on recurrences. Numerical results demonstrate that some parts of the phase space of chaotic systems are more likely to be visited earlier than other parts. A new class of chaotic focusing billiards is discussed that clearly violates the main condition considered to be necessary for chaos in focusing billiards.
Represented as graphs, real networks are intricate combinations of order and disorder. Fixing some of the structural properties of network models to their values observed in real networks, many other properties appear as statistical consequences of these fixed observables, plus randomness in other respects. Here we employ the dk-series, a complete set of basic characteristics of the network structure, to study the statistical dependencies between different network properties. We consider six real networks---the Internet, US airport network, human protein interactions, technosocial web of trust, English word network, and an fMRI map of the human brain---and find that many important local and global structural properties of these networks are closely reproduced by dk-random graphs whose degree distributions, degree correlations, and clustering are as in the corresponding real network. We discuss important conceptual, methodological, and practical implications of this evaluation of network randomness.
How random are complex networks Chiara Orsini, Marija Mitrović Dankulov, Almerima Jamakovic, Priya Mahadevan, Pol Colomer-de-Simón, Amin Vahdat, Kevin E. Bassler, Zoltán Toroczkai, Marián Boguñá, Guido Caldarelli, Santo Fortunato, Dmitri Krioukov
This special issue brings together articles that illustrate the recent advances of studying complex adaptive systems in industrial ecology (IE). The authors explore the emergent behavior of sociotechnical systems, including product systems, industrial symbiosis (IS) networks, cities, resource consumption, and co-authorship networks, and offer application of complex systems models and analyses. The articles demonstrate the links, relevance, and implications of many (often emerging) fields of study to IE, including network analysis, participatory modeling, nonequilibrium thermodynamics, and agent-based modeling. Together, these articles show that IE itself is a complex adaptive system, where knowledge, frameworks, methods, and tools evolve with and by their applications and use in small and large case studies—multidisciplinary knowledge ecology.
Complexity in Industrial Ecology: Models, Analysis, and Actions Gerard P.J. Dijkema, Ming Xu, Sybil Derrible and Reid Lifset
Journal of Industrial Ecology Special Issue: Advances in Complex Adaptive Systems and Industrial Ecology Volume 19, Issue 2, pages 189–194, April 2015
We examine all possible statistical pictures of violent conflicts over common era history with a focus on dealing with incompleteness and unreliability of data. We apply methods from extreme value theory on log-transformed data to remove compact support, then, owing to the boundedness of maximum casualties, retransform the data and derive expected means. We find the estimated mean likely to be at least three times larger than the sample mean, meaning severe underestimation of the severity of conflicts from naive observation. We check for robustness by sampling between high and low estimates and jackknifing the data. We study inter-arrival times between tail events and find (first-order) memorylessless of events. The statistical pictures obtained are at variance with the claims about "long peace".
On the tail risk of violent conflict and its underestimation Pasquale Cirillo, Nassim Nicholas Taleb
Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example.
Historical knowledge is essential to practical applications of ecological economics. Systems of problem solving develop greater complexity and higher costs over long periods. In time such systems either require increasing energy subsidies or they collapse. Diminishing returns to complexity in problem solving limited the abilities of earlier societies to respond sustainably to challenges, and will shape contemporary responses to global change. To confront this dilemma we must understand both the role of energy in sustaining problem solving, and our historical position in systems of increasing complexity.
This paper describes a new concept of cellular automata (CA). XCA consists of a set of arcs (edges). These arcs correspond to cells in CA. At a definite time, the arcs are connected to a directed graph. With each next time step, the arcs are exchanging their neighbors (adjacent arcs) according to rules that are dependent on the status of the adjacent arcs. With the extended cellular automaton (XCA) an artificial world may be simulated starting with a Big Bang. XCA does not require a grid like CA do. However, it can create one, just as the real universe after the big bang generated its own space, which previously did not exist. Examples with different rules show how manifold the concept of XCA is. Like the game of life simulates birth, survival, and death, this game should simulate a system that starts from a singularity, and evolves to a complex space.
Random walk is a fundamental concept with applications ranging from quantum physics to econometrics. Remarkably, one specific model of random walks appears to be ubiquitous across many fields as a tool to analyze transport phenomena in which the dispersal process is faster than dictated by Brownian diffusion. The Lévy-walk model combines two key features, the ability to generate anomalously fast diffusion and a finite velocity of a random walker. Recent results in optics, Hamiltonian chaos, cold atom dynamics, biophysics, and behavioral science demonstrate that this particular type of random walk provides significant insight into complex transport phenomena. This review gives a self-consistent introduction to Lévy walks, surveys their existing applications, including latest advances, and outlines further perspectives.
Lévy walks V. Zaburdaev, S. Denisov, and J. Klafter Rev. Mod. Phys. 87, 483
A new offering from SFI’s online education resource,Complexity Explorer, gives complexity enthusiasts quantitative tools for distinguishing the "complex" aspects of a system from the merely "complicated."
Any national cuisine is a sum total of its variety of regional cuisines, which are the cultural and historical identifiers of their respective regions. India is home to a number of regional cuisines that showcase its culinary diversity. Here, we study recipes from eight different regional cuisines of India spanning various geographies and climates. We investigate the phenomenon of food pairing which examines compatibility of two ingredients in a recipe in terms of their shared flavor compounds. Food pairing was enumerated at the level of cuisine, recipes as well as ingredient pairs by quantifying flavor sharing between pairs of ingredients. Our results indicate that each regional cuisine follows negative food pairing pattern; more the extent of flavor sharing between two ingredients, lesser their co-occurrence in that cuisine. We find that frequency of ingredient usage is central in rendering the characteristic food pairing in each of these cuisines. Spice and dairy emerged as the most significant ingredient classes responsible for the biased pattern of food pairing. Interestingly while individual spices contribute to negative food pairing, dairy products on the other hand tend to deviate food pairing towards positive side. Our data analytical study highlighting statistical properties of the regional cuisines, brings out their culinary fingerprints that could be used to design algorithms for generating novel recipes and recipe recommender systems. It forms a basis for exploring possible causal connection between diet and health as well as prospection of therapeutic molecules from food ingredients. Our study also provides insights as to how big data can change the way we look at food.
The Slime Mould Collective is a portal for interesting, progressive and ground breaking research and creative practice working with the simple yet intelligent organisms. If you are involved with or interested in slime moulds as a scientist, artist (or somewhere in between or other) please join and share what you do...
Critical transitions in multistable systems have been discussed as models for a variety of phenomena ranging from the extinctions of species to socio-economic changes and climate transitions between ice-ages and warm-ages. From bifurcation theory we can expect certain critical transitions to be preceded by a decreased recovery from external perturbations. The consequences of this critical slowing down have been observed as an increase in variance and autocorrelation prior to the transition. However especially in the presence of noise it is not clear, whether these changes in observation variables are statistically relevant such that they could be used as indicators for critical transitions. In this contribution we investigate the predictability of critical transitions in conceptual models. We study the the quadratic integrate-and-fire model and the van der Pol model, under the influence of external noise. We focus especially on the statistical analysis of the success of predictions and the overall predictability of the system. The performance of different indicator variables turns out to be dependent on the specific model under study and the conditions of accessing it. Furthermore, we study the influence of the magnitude of transitions on the predictive performance.
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