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Associate Professor Benyamin Lichtenstein

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Professor Liz Varga

This chapter advocates a mixed methods research strategy for the types of problem generally investigated by complexity science research. Indeed complexity science thinking underpins mixed methods research through embracing different types of data found in real-world problems. The need for multiple perspectives, philosophically and theoretically, and new stances to solving paradigmatic dilemmas, are highlighted. Alternative frameworks are compared to assist in alignment with research questions and research purpose as well as recognizing practical influences on research design choice. Numerous mixed methods research designs demonstrating the integration of mixed methods are reviewed, as are techniques for integrating the data between traditional methods. Data collection and data analysis techniques are considered from a mixed methods perspective. The benefits and challenges of mixed methods research are discussed. Overall, mixed methods research has critical mass but continues to evolve and become ever more relevant to address complex systems problems.

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Carl J. Dister, Professor Brian Castellani and Dr Rajeev Rajaram

If one is to improve reliability and resilience in infrastructures, it is necessary to adopt a ‘complex, smart territory’ modelling strategy, particularly one that gives attention to the importance of social complexity. To test the veracity of their argument the authors conducted a case study on a segment of the US power grid, seeking to create a first proof-of-concept sufficient to show how thinking about infrastructures in ‘complex systems’ terms, primarily in terms of their social aspects, can prove beneficial. They employed the SACS Toolkit, which is part of the new approach to modelling complex systems, called case-based complexity. As a technique, the SACS Toolkit is a computationally grounded, case-comparative, mixed methods platform for modelling complex systems as sets of cases. In an effort to help readers make use of this technique, this chapter provides a basic overview of the research process, ending with a summary of the novel insights this approach was able to achieve.

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Professor Bill McKelvey

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Professor Patrick Beautement

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Hannah L. Brown, Chase R. Booth, Elizabeth G. Eason and Assistant Professor Damian G. Kelty-Stephen

This gender study exemplifies fields struggling to balance the deeply ingrained desire for logical formalisms and conceptually dynamic models of systems. Gender Studies grounds itself in dynamic models as seen in the popularity of ‘intersectionality theory,’ a notion of experiences as unfolding at the ‘intersections’ of classical taxonomies. This popular theory evades quantitative research because it eschews classical categorical distinctions. The authors introduce multifractal analysis and suggest that cascade dynamics and multifractal analysis provide logical and corresponding statistical frameworks to make intersectionality quantitatively and tractably expressible for gendered experiences. Recent cognitive science advances involve multifractal analysis laying bare key features of the cascades driving cognitive performance. The chapter offers similar demonstration of similar cascades in gender dynamics through multifractal analysis of web-traffic data for gender terms on Wikipedia. It concludes that cascade formalisms and multifractal analysis offer new avenues for gender studies balancing both logical formalisms and dynamic concepts.

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Professor Jeffrey Johnson, Professor Joyce Fortune and Dr Jane Bromley

Making multilevel systems well-defined is essential for the implementation of computer models to investigate the multilevel consequences of policy. This chapter shows that systems thinking can provide practical guidance to those building models of complex multilevel social systems in order to inform policymaking. Part–whole aggregation and taxonomic aggregation are described as methods of representing multilevel structure, and it is shown how they are interleaved in the construction of vocabulary to describe multilevel systems. This enables complex nested structures to be represented as a kind of backcloth that supports patterns of aggregate and disaggregate numbers that describe the day-to-day traffic of people, resources and responsibility that are essential for systems to function.

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Professor Göktuğ Morçöl and Dr Sohee Kim

In this chapter we discuss and illustrate how network text analysis and social network analysis can be used to investigate complex governance networks. After briefly defining and describing ‘governance networks,’ we discuss the importance of investigating their complex structural properties and the roles actors play in them. Then we describe and illustrate how AutoMap (network text analysis software) and ORA (dynamic network analysis software) can be used in such investigations with two applications in the cases of an urban governance network and that of a statewide policymaking processes. We also discuss the general problems in using archival data sources in network analyses, specific problems and strengths in using AutoMap in network extraction from archival data. We present the protocol we developed for the applications of AutoMap and ORA in the appendix of the chapter.

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Dr Kurt A. Richardson and Andrew Tait

Understanding the structure of complex networks and uncovering the properties of their constituents has been for many decades at the center of study of several fundamental sciences, especially in the fields of biological and social networks. Given the large scale and interconnected nature of these types of networks, there is a need for tools that enable us to make sense of these structures. This chapter explores how, for a given network, there are a range of emergent dynamic structures that support the different behaviors exhibited by the network’s various state space attractors. We use a selected Boolean Network, calculate a variety of structural and dynamic parameters, explore the various dynamic structures that are associated with it and consider the activities associated with each of the network’s nodes when in certain modes/attractors. This work is a follow-up to past work aiming to develop robust complexity-informed tools with particular emphasis on network dynamics.

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Professor James K. Hazy and Professor Peter R. Wolenski

The chapter presents a general mathematical framework to study discontinuous change in human interaction dynamics. There are two complementary perspectives: macro and micro. Regarding the macro context, the chapter proposes that levels of ordered structure in complex human organizing can be represented by a category theoretic representation that reflects informational influence acting on individual agents from sources external to the population and those internal to the population. These independent influences interact to change the set of interaction rules that are enacted locally. Regarding micro context, the authors position contagion as the mechanism whereby a common organizing state is adopted across multiple agents. They show that as a general matter, the ordered structure that emerges within a population can be indexed as the number of active degrees of freedom embedded in local rules of interaction that are guiding groups of agents. Category theoretic mathematical approaches should be more used in social science research to suggest deductive hypotheses that can be tested empirically with definitive results.