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Register a new userA Theory of Discrete Hierarchies as Optimal Cost-Adjusted Productivity Organisations
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Hierarchical structures are ubiquitous in human and animal societies, but a fundamental understanding of their raison d^etre has been lacking. Here, we present a general theory in which hierarchies are obtained as the optimal design that strikes a balance between the benefits of group productivity and the costs of communication for coordination. By maximising a generic representation of the output of a hierarchical organization with respect to its design, the optimal configuration of group sizes at different levels can be determined. With very few ingredients, a wide variety of hierarchically ordered complex organisational structures can be derived. Furthermore, our results rationalise the ubiquitous occurrence of triadic hierarchies, i.e., of the universal preferred scaling ratio between $3$ and $4$ found in many human and animal hierarchies, which should occur according to our theory when production is rather evenly contributed by all levels. We also provide a systematic approach for optimising team organisation, helping to address the question of the optimal `span of control. The significantly larger number $sim 3-20$ of subordinates a supervisor typically manages is rationalised to occur in organisations where the production is essentially done at the bottom level and in which the higher levels are only present to optimise coordination and control.
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Rapid economic growth in China has lead to an increasing energy demand in the country. In combination with Chinas emission control and clean air initiatives, it has resulted in large-scale expansion of the leading renewable energy technologies, wind and solar power. Their intermittent nature and uneven geographic distribution, however, raises the question of how to best exploit them in a future sustainable electricity system, where their combined production may very well exceed that of all other technologies. It is well known that interconnecting distant regions provides more favorable production patterns from wind and solar. On the other hand, long-distance connections challenge traditional local energy autonomy. In this paper, the advantage of interconnecting the contiguous provinces of China is quantified. To this end, two different methodologies are introduced. The first aims at gradually increasing heterogeneity, that is non-local wind and solar power production, to minimize production costs without regard to the match between production and demand. The second method optimizes the trade-off between low cost production and high utility value of the energy. In both cases, the study of a 100% renewable Chinese electricity network is based on 8 years of high-resolution hourly time series of wind and solar power generation and electricity demand for each of the provinces. From the study we conclude that compared to a baseline design of homogeneously distributed renewable capacities, a heterogeneous network not only lowers capital investments but also reduces backup dispatches from thermal units. Installing more capacity in provinces like Inner Mongolia, Jiangsu, Hainan and north-western regions, heterogeneous layouts may lower the levelized cost of electricity (LCOE) by up to 27%, and reduce backup needs by up to 64%.
We propose a formal framework that supports a model of agent-based Virtual Organisations (VOs) for service grids and provides an associated operational model for the creation of VOs. The framework is intended to be used for describing different service grid applications based on multiple agents and, as a result, it abstracts away from any realisation choices of the service grid application, the agents involved to support the applications and their interactions. Within the proposed framework VOs are seen as emerging from societies of agents, where agents are abstractly characterised by goals and roles they can play within VOs. In turn, VOs are abstractly characterised by the agents participating in them with specific roles, as well as the workflow of services and corresponding contracts suitable for achieving the goals of the participating agents. We illustrate the proposed framework with an earth observation scenario.
We introduce two models of inclusion hierarchies: Random Graph Hierarchy (RGH) and Limited Random Graph Hierarchy (LRGH). In both models a set of nodes at a given hierarchy level is connected randomly, as in the ErdH{o}s-R{e}nyi random graph, with a fixed average degree equal to a system parameter $c$. Clusters of the resulting network are treated as nodes at the next hierarchy level and they are connected again at this level and so on, until the process cannot continue. In the RGH model we use all clusters, including those of size $1$, when building the next hierarchy level, while in the LRGH model clusters of size $1$ stop participating in further steps. We find that in both models the number of nodes at a given hierarchy level $h$ decreases approximately exponentially with $h$. The height of the hierarchy $H$, i.e. the number of all hierarchy levels, increases logarithmically with the system size $N$, i.e. with the number of nodes at the first level. The height $H$ decreases monotonically with the connectivity parameter $c$ in the RGH model and it reaches a maximum for a certain $c_{max}$ in the LRGH model. The distribution of separate cluster sizes in the LRGH model is a power law with an exponent about $-1.25$. The above results follow from approximate analytical calculations and have been confirmed by numerical simulations.
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.
A detailed empirical analysis of the productivity of non financial firms across several countries and years shows that productivity follows a non-Gaussian distribution with power law tails. We demonstrate that these empirical findings can be interpreted as consequence of a mechanism of exchanges in a social network where firms improve their productivity by direct innovation or/and by imitation of other firms technological and organizational solutions. The type of network-connectivity determines how fast and how efficiently information can diffuse and how quickly innovation will permeate or behaviors will be imitated. From a model for innovation flow through a complex network we obtain that the expectation values of the productivity level are proportional to the connectivity of the network of links between firms. The comparison with the empirical distributions reveals that such a network must be of a scale-free type with a power-law degree distribution in the large connectivity range.
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