## Recent Publications

## Books

Hypernetworks in the Science of Complex Systems Jeffrey Johnson This book sets out the theory of hypernetworks that underlies the work of VSL. Imperial College Press. 2014 |
Non-Equilibrium Social Science and Policy Introduction and Essays on New and Changing Paradigms in Socio-Economic Thinking Editors: Johnson, J., Nowak, A., Ormerod, P., Rosewell, B., Zhang, Y.-C. The overall aim of this book, an outcome of the European FP7 FET Open NESS project, is to contribute to the ongoing effort to put the quantitative social sciences on a proper footing for the 21st century. A key focus is economics, and its implications on policy making, where the still dominant traditional approach increasingly struggles to capture the economic realities we observe in the world today - with vested interests getting too often in the way of real advances. |

## Research Papers and Book Chapters

### Global Systems Science and Policy

Ralph Dum and Jeffrey Johnson

J. Johnson et al. (eds.), Non-Equilibrium Social Science and Policy: Understanding Complex Systems, 2017, DOI 10.1007/978-3-319-42424-8_14

Abstract: The vision of Global Systems Science (GSS) is to provide scientific evidence and means to engage into a reflective dialogue to support policy-making and public action and to enable civil society to collectively engage in societal action in response to global challenges like climate change, urbanisation, or social inclusion. GSS has four elements: policy and its implementation, the science of complex systems, policy informatics, and citizen engagement. It aims to give policy makers and citizens a better understanding of the possible behaviours of complex social systems. Policy informatics helps generate and evaluate policy options with computer-based tools and the abundance of data available today. The results

they generate are made accessible to everybody—policymakers, citizens—through intuitive user interfaces, animations, visual analytics, gaming, social media, and so on. Examples of Global Systems include epidemics, finance, cities, the Internet, trade systems and more. GSS addresses the question of policies having desirable outcomes, not necessarily optimal outcomes. The underpinning idea of GSS is not to precisely predict but to establish possible and desirable futures and their likelihood. Solving policy problems is a process, often needing the requirements, constraints,

and lines of action to be revisited and modified, until the problem is ‘satisficed’, i.e. an acceptable compromise is found between competing objectives and constraints. Thus policy problems and their solutions coevolve much as in a design process. Policy and societal action is as much about attempts to understand objective facts as it is about the narratives that guide our actions. GSS tries to reconcile these apparently contradictory modes of operations. GSS thus provides policy makers and society guidance on their course of action rather than proposing (illusionary) optimal solutions.

### Systems, Networks, and Policy

Jeffrey Johnson, Joyce Fortune, and Jane Bromley

J. Johnson et al. (eds.), Non-Equilibrium Social Science and Policy: Understanding Complex Systems, 2017, DOI 10.1007/978-3-319-42424-8_14

Abstract: Systems theory is fundamental to understanding the dynamics of the complex social systems of concern to policy makers. A system is defined as: (1) an assembly of components, connected together in an organised way; (2) the components are affected by being in the system and the behaviour of the systems is changed if they leave it; (3) the organised assembly of components does something; and (4) the assembly has been identified as being of particular interest. Feedback is central to system behaviour at all levels, and can be responsible for systems behaving in complex and unpredictable ways. Systems can be represented by networks and there is a growing literature that shows how the behaviour of individuals is highly dependent on their social networks. This includes copying or following the advice of others when making decisions. Network theory gives insights into social phenomena such as the spread of information and the way people form social groups which then constrain their behaviour. It is emerging as a powerful way of examining the dynamics of social systems. Most systems relevant to policy have many levels, from the individual to local and national and international organisations and institutions. In many social systems the micro, meso and macrolevel dynamics are coupled, meaning that they cannot be studied or modified in isolation. Systems and network science allow computer simulations to be used to investigate possible system behaviour. This science can be made available to policy makers through policy informatics which involves computer-based simulation, data, visualisation, and interactive interfaces. The future of science-based policy making is seen to be through Global Systems Science which combines complex systems science and policy informatics to inform policy makers and facilitate citizen engagement. In this context, systems theory and network science are fundamental for modelling far-from-equilibriumsystems for policy purposes.

### Open Questions in Multidimensional Multilevel Network Science

Jeffrey Johnson

E. Shmueli et al. (eds.), 3rd Int Winter School & Conference on Network Science, Springer Proceedings in Complexity, DOI 10.1007/978-3-319-55471-6 10, 2017

Abstract: It is shown that the theory of networks has a natural multidimensional extension through n-ary relations with n > 2. An ordered set of vertices under a general n-ary relation is defined to be a simplex, or a hypersimplex when the defining n-ary relation is made explicit. This leads to a theory of multilevel systems for any number of levels in which the structure of the generalised networks is considered to be a relatively static backcloth supporting relatively dynamic patterns of numbers called the system traffic. This enables the exploration of multilevel coupled dynamics, and the evolution of multilevel systems. It is suggested that the structures presented are necessary to understand the dynamics of complex multilevel systems. However there are many open questions, and some of these are presented for consideration by the network community.

### Hypernetworks: Multidimensional relationships in multilevel systems

Jeffrey Johnson

Eur. Phys. J. Special Topics 225, 1037–1052 (2016), DOI: 10.1140/epjst/e2016-02653-4

Abstract. Networks provide a powerful way of modelling the dynamics of complex systems. Going beyond binary relations, embracing n-ary

relations in network science can generalise many structures. This starts with hypergraphs and their Galois structures. Simplicial complexes

generalise hypergraphs by adding orientation. Their multidimensional q-connectivity structure generalises connectivity in networks. Hypersimplices

generalise simplices by making the relational structure explicit in the notation. This gives a new way of representing multilevel systems and their dynamics, leading to a new fragment-recombine operator to model the complex dynamics of interacting multilevel systems.

### Embracing n-ary relations in network science

Jeffrey Johnson

Jeffrey Johnson

NetSciX 2016, Advances in Network Science, A. Wierzbicki, U. Brandes, F. Schweitzer, D. Pedreschi (Eds), Springer, 2016

**Abstract**: Most network scientists
restrict their attention to relations between pairs of things, even
though most complex systems have structures

and dynamics determined by n-ary relation where n is greater than two.
Various examples are given to illustrate this. The basic mathematical
structures allowing more than two vertices have existed for more than
half a century, including hypergraphs and simplicial complexes. To
these can be added hypernetworks which, like multiplex networks, allow
many relations to be dened on the vertices. Furthermore,
hypersimplices provide an essential formalism for representing
multilevel partwhole and taxonomic structures for integrating the
dynamics of systems between levels. Graphs, hypergraphs, networks,
simplicial complex, multiplex network and hypernetworks form a coherent
whole from which, for any particular application, the scientist can
select the most suitable.