Two fundamental issues surrounding research on Zipf’s law regarding city sizes are whether and why Zipf’s law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf’s law holds in a global setting, thus involving all cities around the world. Unlike previous studies, which have mainly relied on conventional census data, and census- bureau-imposed definitions of cities, we adopt naturally and objectively delineated cities, or natural cities, to be more precise, in order to examine Zipf’s law. We find that Zipf’s law holds remarkably well for all natural cities at the global level, and remains almost valid at the continental level except for Africa at certain time instants. We further examine the law at the country level, and note that Zipf’s law is violated from country to country or from time to time.

Nobody agrees on how to define a city. But the emergence of “natural cities” from social media data sets may change that, say computational geographers. A city is a large, permanent human settlement. But try and define it more carefully and you’ll soon run into trouble. A settlement that qualifies as a city in Sweden may not qualify in China, for example. And the reasons why one settlement is classified as a town while another as a city can sometimes seem almost arbitrary. City planners know this problem well. They tend to define cities by administrative, legal or even historical boundaries that have little logic to them. Indeed, the same city can sometimes be defined in various different ways. That causes all kinds of problems from counting the total population to working out who pays for the upkeep of the place. Which definition do you use?

We introduce a model to study the effects of social influences in opinion dynamics. In particular, we analyze the voter model, from a socio psychological perspective, by considering the role of conformity. Conformity is a central issue in social psychology as it represents one of people’s behaviors that emerge as result of their interactions. We introduce a voter model where agents, linked in a network, change their opinion according to those of their neighbors and to their degree of conformity. In particular, agents can behave as conformists or non-conformists. In the former case, agents change opinion according to that of the majority of their social circle (i.e., the majority of their neighbors); in the latter case, they do the opposite, i.e., they assume the opposite opinion. We perform a computational study of the proposed model, with the aim to analyze the role of conformity in the voter model. Moreover, we want to investigate whether it is possible to achieve some kind of equilibrium or of order in the system. The two more interesting results are that the amount of non-conformist agents in the population plays a central role in these dynamics, and the topology of the agent network has not a prominent role in the proposed model. Finally, we study the outcomes of the model by considering that agents can change also their degree of conformity over time, i.e., they can turn their behavior from conformist to non-conformist and vice-versa.

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed «exponential allometry», which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the abovementioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed «logistic allometry». The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.

We compared entropy for texts written in natural languages (English, Spanish) and artificial languages (computer software) based on a simple expression for the entropy as a function of message length and specific word diversity. Code text written in artificial languages showed higher entropy than text of similar length expressed in natural languages. Spanish texts exhibit more symbolic diversity than English ones. Results showed that algorithms based on complexity measures differentiate artificial from natural languages, and that text analysis based on complexity measures allows the unveiling of important aspects of their nature. We propose specific expressions to examine entropy related aspects of tests and estimate the values of entropy, emergence, self-organization and complexity based on specific diversity and message length.

This chapter reviews the purpose and use of models from the field of complex systems and, in particular, the implications of trying to use models to understand or make decisions within complex situations, such as policy makers usually face. A discussion of the different dimensions one can formalise situations, the different purposes for models and the different kinds of relationship they can have with the policy making process, is followed by an examination of the compromises forced by the complexity of the target issues. Several modelling approaches from complexity science are briefly described, with notes as to their abilities and limitations. These approaches include system dynamics, network theory, information theory, cellular automata, and agent-based modelling. Some examples of policy models are presented and discussed in the context of the previous analysis. Finally we conclude by outlining some of the major pitfalls facing those wishing to use such models for policy evaluation.

The recovery of society after a large scale disaster generally consists of two phases, short- and long-term recoveries. The problem of short-term recovery is rather close to the problem of resilience in their goal, namely, bouncing the damaged system back to the operating standards. The present paper proposes an algorithm for the vital resource redistribution required for implementation of the short-term recovery. The developed model is based on the cooperative interaction of cities during the resource redistribution, ordering the cities according to their priority in resource delivery, and a generating a semi-optimal plan for the desired redistribution. Nonlinear effects caused by the city limit capacities are taken into account.

The scaling exponent of a hierarchy of cities used to be regarded as a fractal parameter. The Pareto exponent was treated as the fractal dimension of size distribution of cities, while the Zipf exponent was treated as the reciprocal of the fractal dimension. However, this viewpoint is not exact. In this paper, I will present a new interpretation of the scaling exponent of rank-size distributions. The ideas from fractal measure relation and the principle of dimension consistency are employed to explore the essence of Pareto’s and Zipf’s scaling exponents. The Pareto exponent proved to be a ratio of the fractal dimension of a network of cities to the average dimension of city population. Accordingly, the Zipf exponent is the reciprocal of this dimension ratio. On a digital map, the Pareto exponent can be defined by the scaling relation between a map scale and the corresponding number of cities based on this scale. The cities of the United States of America in 1900, 1940, 1960, and 1980 and Indian cities in 1981, 1991, and 2001 are utilized to illustrate the geographical spatial meaning of Pareto’s exponent. The results suggest that the Pareto exponent of city-size distribution is not a fractal dimension, but a ratio of the urban network dimension to the city population dimension. This conclusion is revealing for scientists to understand Zipf’s law and fractal structure of hierarchy of cities.

Despite its obvious relevance, meaning has been outside most theoretical approaches to information in biology. As a consequence, functional responses based on an appropriate interpretation of signals has been replaced by a probabilistic description of correlations between emitted and received symbols. This assumption leads to potential paradoxes, such as the presence of a maximum information associated to a channel that would actually create completely wrong interpretations of the signals. Game-theoretic models of language evolution use this view of Shannon’s theory, but other approaches considering embodied communicating agents show that the correct (meaningful) match resulting from agent-agent exchanges is always achieved and natural systems obviously solve the problem correctly. How can Shannon’s theory be expanded in such a way that meaning -at least, in its minimal referential form- is properly incorporated?

A large variety of complex systems in ecology, climate science, biomedicine and engineering have been observed to exhibit tipping points, where the internal dynamical state of the system abruptly changes. For example, such critical transitions may result in the sudden change of ecological environments and climate conditions. Data and models suggest that some of these drastic events may be preceded by detectable early-warning signs. This view is also corroborated by abstract mathematical theory for generic bifurcations in stochastic multi-scale systems. Whether early-warnings are also present in social networks that anticipate \textit{a-priori unknown} events in society is an open problem to which only highly speculative answers can be given at present. Here, we focus on \textit{a-priori known} events and analyze a social network data set with a focus on classical variance and autocorrelation warning signs. We find that several a-priori known events are preceded by variance and autocorrelation growth as predicted by mathematical theory.