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Why We Live in Hierarchies: a Quantitative Treatise Why we live in hierarchies: a quantitative treatise by Anna Zafeiris1 and Tamás Vicsek1, 2 1Statistical and Biological Physics Research Group of HAS 2Department of Biological Physics, Eötvös University Preprint version Final version to be published by Springer as part of SpringerBriefs in Physics series. July 2017 1 Contents 1 Introduction ........................................................................................................................... 4 1.1 General considerations ................................................................................................... 4 1.2 Motivation ...................................................................................................................... 8 1.3 Hierarchical structures in space and in networks .......................................................... 9 Reference list ..................................................................................................................... 10 2 Definitions and Basic Concepts .......................................................................................... 12 2.1 Describing hierarchical structures ............................................................................... 17 2.1.1 Graphs and networks ............................................................................................ 17 2.1.2 Measuring the level of hierarchy .......................................................................... 19 2.1.3 Classification of hierarchical networks ................................................................ 28 2.2 Visualization techniques .............................................................................................. 32 2.2.1 A general overview ............................................................................................... 32 2.2.2 Techniques reflecting the overall hierarchy level ................................................. 33 Reference list ..................................................................................................................... 37 3 Observations and measurements......................................................................................... 40 3.1 Animal groups ............................................................................................................. 40 3.1.1 Dominance ............................................................................................................ 40 3.1.2 Leadership in motion ............................................................................................ 44 3.1.3 Leadership versus dominance ............................................................................... 48 3.1.4 Collective decision-making .................................................................................. 51 3.2 Hierarchy in Humans ................................................................................................... 58 3.2.1 Our biological and social heritage ........................................................................ 58 3.2.2 Large-scale hierarchies in societies ...................................................................... 60 3.2.3 Nested hierarchy structure of human societies ..................................................... 64 3.2.4 Phenomenological theory of collective decision-making ..................................... 66 Reference list ..................................................................................................................... 71 2 4 Experiments on the emergence and function ...................................................................... 76 4.1. The Liskaland camp experiment ................................................................................. 76 4.1.1. The Liska model of economy .............................................................................. 76 4.1.2 The experiment ..................................................................................................... 77 4.1.3 Results................................................................................................................... 78 4.2 Picturask ...................................................................................................................... 79 4.2.1 The ―game‖ ........................................................................................................... 79 4.2.2 Methods ................................................................................................................ 80 4.2.3 Results................................................................................................................... 81 Reference List .................................................................................................................... 83 5. Modelling emergence and control ..................................................................................... 84 5.1 Emergence of hierarchy in model systems .................................................................. 84 5.2 The complex efficiency landscape of hierarchical organizations ................................ 88 5.2.1 Modelling organizations ....................................................................................... 88 5.2.2 Simulations and results ......................................................................................... 89 5.3 Controlling hierarchical networks ............................................................................... 92 5.3.1 Structural controllability – controlling nodes ....................................................... 92 5.3.2. Switchboard dynamics – controlling edges ......................................................... 93 Reference list ..................................................................................................................... 98 6. Conclusions........................................................................................................................ 99 6.1 General features of hierarchical structures. ................................................................. 99 6.2. Origins of flow hierarchy.......................................................................................... 100 6.3 Emergence of hierarchy ............................................................................................. 101 3 1 Introduction This book is concerned with the various aspects of hierarchical collective behaviour which is manifested by most complex systems in nature. From the many of the possible topics, we plan to present a selection of those that we think are useful from the point of shedding light from very different directions onto our quite general subject. Our intention is to both present the essential contributions by the existing approaches as well as go significantly beyond the results obtained by traditional methods by applying a more quantitative approach then the common ones (there are many books on qualitative interpretations). In addition to considering hierarchy in systems made of similar kinds of units, we shall concentrate on problems involving either dominance relations or the process of collective decision-making from various viewpoints. 1.1 General considerations Since hierarchy is abundant in nature and society, but many of its quantitative aspects are still unexplored, the main goal we intend to achieve is the systematic interpretation and documentation of new unifying principles and basic laws describing the most relevant aspects of hierarchy (being perhaps the most widespread organizing principle in the Universe). To do so we shall discuss recent experiments and models that are both simple and realistic enough to reproduce the observations and develop concepts for a better understanding of the complexity of systems consisting of many organisms. We shall cover systems ranging from flocks of birds to groups of people. The related research goes beyond being interdisciplinary and can be rather described as multidisciplinary, since it involves many kinds of systems (both living and non-living), various techniques and technologies typically used in different branches of science and engineering. The topics we address might look too diverse. However, one can always think of these research directions as facets of a single, to be explored idea. Although we shall concentrate on hierarchical collective behaviour in general, there will be two aspects of it which will pop up in the majority of cases: collective motion and dynamically changing partially directed networks (and the natural relation of the two). A few of the many possible examples are visualized in Fig. 1. In addition, we give a brief description of the most relevant concepts which hierarchy is related to. Organisms versus agents, entities or “particles” Throughout of this book we shall consider systems made of many (from a few dozens to several thousands) organisms, i.e., living entities. Of course, hierarchy is present in the non-living world as well; starting from elementary particles through the solar system up to the whole universe, but that is a beautiful and long story which is not the subject of the present work. 4 Fig. 1 a Axon arborisation (the end part of a major kind of neuronal cells) shows typical hierarchical tree-like structure in space. b The wiring of a human brain. Hierarchy is not obvious, but closer inspection and additional MRI images indicate hierarchical functional operation. c And this is a possible interpretation of how we think (thoughts being one of the end products of a functioning
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