Quantifying 'causality' in complex systems: Understanding Transfer Entropy

'Causal' direction is of great importance when dealing with complex systems. Often big volumes of data in the form of time series are available and it is important to develop methods that can inform about possible causal connections between the different observables. Here we investigate the ability of the Transfer Entropy measure to identify causal relations embedded in emergent coherent correlations. We do this by firstly applying Transfer Entropy to an amended Ising model. In addition we use a simple Random Transition model to test the reliability of Transfer Entropy as a measure of `causal' direction in the presence of stochastic fluctuations. In particular we systematically study the effect of the finite size of data sets

Understanding Complex Systems: From Networks to Optimal Higher-Order Models

To better understand the structure and function of complex systems, researchers often represent direct interactions between components in complex systems with networks, assuming that indirect influence between distant components can be modelled by paths. Such network models assume that actual paths are memoryless. That is, the way a path continues as it passes through a node does not depend on where it came from. Recent studies of data on actual paths in complex systems question this assumption and instead indicate that memory in paths does have considerable impact on central methods in network science. A growing research community working with so-called higher-order network models addresses this issue, seeking to take advantage of information that conventional network representations disregard. Here we summarise the progress in this area and outline remaining challenges calling for more research.Comment: 8 pages, 4 figure

How can we think the complex?

In this chapter we want to provide philosophical tools for understanding and reasoning about complex systems. Classical thinking, which is taught at most schools and universities, has several problems for coping with complexity. We review classical thinking and its drawbacks when dealing with complexity, for then presenting ways of thinking which allow the better understanding of complex systems. Examples illustrate the ideas presented. This chapter does not deal with specific tools and techniques for managing complex systems, but we try to bring forth ideas that facilitate the thinking and speaking about complex systems

Topological tools for understanding complex systems

The behavior of complex systems is often influenced by their structure. In mathematics, the field of algebraic topology has been especially useful for characterizing mathematical structures. Topological data analysis (TDA) is a growing field in which methods from algebraic topology are applied to studying the structure of data. TDA has been used in a variety of applications, including biological data, granular materials, and demography. Social interactions are heavily informed by space and have complex structure due to patterns in the way humans arrange themselves geographically. Consequently, social applications can benefit from the application of TDA.In this dissertation, I develop topological methods for studying spatial networks and apply them to a wide variety of data sets. In particular, I study methods for building topological spaces (specifically, simplicial complexes) based on data. I present two novel simplicial-complex constructions, the adjacency complex and the level-set complex, for spatial data. I apply both constructions to random networks, cities, voting, and scientific images, gaining insights into the structure of these systems. I also propose a novel simplicial complex construction for studying patterns of neighborhood formation based on combining demographic and spatial data. I present case studies in neighborhood segregation for two U.S. cities. In addition to my topological research, I discuss two projects in the study of social systems using methods from network analysis. I present an extension to multilayer networks of the Hegselmann--Krause model for opinion dynamics and discuss preliminary findings on its convergence properties. I also present a framework for estimating homelessness underreporting in California Local Education agencies (LEAs)

Editorial Comment on the Special Issue of "Information in Dynamical Systems and Complex Systems"

This special issue collects contributions from the participants of the "Information in Dynamical Systems and Complex Systems" workshop, which cover a wide range of important problems and new approaches that lie in the intersection of information theory and dynamical systems. The contributions include theoretical characterization and understanding of the different types of information flow and causality in general stochastic processes, inference and identification of coupling structure and parameters of system dynamics, rigorous coarse-grain modeling of network dynamical systems, and exact statistical testing of fundamental information-theoretic quantities such as the mutual information. The collective efforts reported herein reflect a modern perspective of the intimate connection between dynamical systems and information flow, leading to the promise of better understanding and modeling of natural complex systems and better/optimal design of engineering systems

Implications of external validity for research on polycentric and complex adaptive systems

Much recent research has examined the implications of policy analysis for complex adaptive social-ecological systems. System complexity comes from both the natural environment as well as complex institutional arrangements that humans use to manage and regulate such systems. Such research has systematically investigated how the interaction of a host of variables relate to some evaluation criteria. Many scholars argue that a deep understanding of the social-ecological systems, however, comes at the expense of externally valid inferences to other systems. In this paper I argue that having a nuanced understanding of the social-ecological system actually helps one to understand which types of policy domains an analysis might be generalized. --Complex Adaptive Systems,External Validity,Polycentric Systems

Understanding community evolution in Complex systems science

International audienceComplex systems is a new approach in science that studying organized be- haviours in computer science, biology, physics, chemistry, and many other fields. By collecting articles containing topic keywords relevant for the field of complex networks from ISI Web of knowledge during 1985-2009, we construct a science network, which connects ~ 215000 articles according to the proportion of shared references. Moreover, articles' publication time makes it dynamically evolve in time. We here use a two-step approach [3] to explore community evolution and study underlying information behind community changes. We firstly detect com- munities by applying Louvain algorithm [2] on each snapshot graph, and secondly construct relationships between partitions at successive snapshot graphs [1]