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Register a new userZipfs law, unbounded complexity and open-ended evolution
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A major problem for evolutionary theory is understanding the so called {em open-ended} nature of evolutionary change, from its definition to its origins. Open-ended evolution (OEE) refers to the unbounded increase in complexity that seems to characterise evolution on multiple scales. This property seems to be a characteristic feature of biological and technological evolution and is strongly tied to the generative potential associated with combinatorics, which allows the system to grow and expand their available state spaces. Interestingly, many complex systems presumably displaying OEE, from language to proteins, share a common statistical property: the presence of Zipfs law. Given an inventory of basic items (such as words or protein domains) required to build more complex structures (sentences or proteins) Zipfs law tells us that most of these elements are rare whereas a few of them are extremely common. Using Algorithmic Information Theory, in this paper we provide a fundamental definition for open-endedness, which can be understood as {em postulates}. Its statistical counterpart, based on standard Shannon Information theory, has the structure of a variational problem which is shown to lead to Zipfs law as the expected consequence of an evolutionary process displaying OEE. We further explore the problem of information conservation through an OEE process and we conclude that statistical information (standard Shannon information) is not conserved, resulting into the paradoxical situation in which the increase of information content has the effect of erasing itself. We prove that this paradox is solved if we consider non-statistical forms of information. This last result implies that standard information theory may not be a suitable theoretical framework to explore the persistence and increase of the information content in OEE systems.
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We statistically investigate the distribution of share price and the distributions of three common financial indicators using data from approximately 8,000 companies publicly listed worldwide for the period 2004-2013. We find that the distribution of share price follows Zipfs law; that is, it can be approximated by a power law distribution with exponent equal to 1. An examination of the distributions of dividends per share, cash flow per share, and book value per share - three financial indicators that can be assumed to influence corporate value (i.e. share price) - shows that these distributions can also be approximated by a power law distribution with power-law exponent equal to 1. We estimate a panel regression model in which share price is the dependent variable and the three financial indicators are explanatory variables. The two-way fixed effects model that was selected as the best model has quite high power for explaining the actual data. From these results, we can surmise that the reason why share price follows Zipfs law is that corporate value, i.e. company fundamentals, follows Zipfs law.
Zipfs law describes the empirical size distribution of the components of many systems in natural and social sciences and humanities. We show, by solving a statistical model, that Zipfs law co-occurs with the maximization of the diversity of the component sizes. The law ruling the increase of such diversity with the total dimension of the system is derived and its relation with Heaps law is discussed. As an example, we show that our analytical results compare very well with linguistics datasets.
Non-uniform rates of morphological evolution and evolutionary increases in organismal complexity, captured in metaphors like adaptive zones, punctuated equilibrium and blunderbuss patterns, require more elaborate explanations than a simple gradual accumulation of mutations. Here we argue that non-uniform evolutionary increases in phenotypic complexity can be caused by a threshold-like response to growing ecological pressures resulting from evolutionary diversification at a given level of complexity. Acquisition of a new phenotypic feature allows an evolving species to escape this pressure but can typically be expected to carry significant physiological costs. Therefore, the ecological pressure should exceed a certain level to make such an acquisition evolutionarily successful. We present a detailed quantitative description of this process using a microevolutionary competition model as an example. The model exhibits sequential increases in phenotypic complexity driven by diversification at existing levels of complexity and the resulting increase in competitive pressure, which can push an evolving species over the barrier of physiological costs of new phenotypic features.
It has been already shown that combinatorial evolution - the creation of new things through the combination of existing things - can be a powerful way to evolve rather than design technical objects such as electronic circuits in a computer simulation. Most intriguingly, this seems to be an ongoing and thus open-ended process to create novelty with increasing complexity. In the present paper, we want to employ combinatorial evolution in software development. While current approaches such as genetic programming are efficient in solving particular problems, they all converge towards a solution and do not create anything new anymore afterwards. Combinatorial evolution of complex systems such as languages and technology are considered open-ended. Therefore, open-ended automatic programming might be possible through combinatorial evolution. Here, we implemented a computer program simulating combinatorial evolution of code blocks stored in a database to make them available for combining. Automatic programming is achieved by evaluating regular expressions. We found that reserved key words of a programming language are suitable for defining the basic code blocks at the beginning of the simulation. We also found that placeholders can be used to combine code blocks and that code complexity can be described in terms of the importance to the programming language. As in the previous combinatorial evolution simulation of electronic circuits, complexity increased from simple keywords and special characters to more complex variable declarations, to class definitions, to methods, and to classes containing methods and variable declarations. Combinatorial evolution, therefore, seems to be a promising approach for open-ended automatic programming.
Cooperative behaviour constitutes a key aspect of both human society and non-human animal systems, but explaining how cooperation evolves represents a major scientific challenge. It is now well established that social network structure plays a central role for the viability of cooperation. However, not much is known about the importance of the positions of cooperators in the networks for the evolution of cooperation. Here, we investigate how cooperation is affected by correlations between cooperativeness and individual social connectedness. Using simulation models, we find that the effect of correlation between cooperativeness and connectedness (degree) depends on the social network structure, with positive effect in standard scale-free networks and no effect in standard Poisson networks. Furthermore, when degree assortativity is increased such that individuals cluster with others of similar social connectedness, we find that bridge areas between social clusters can act as barriers to the spread of defection, leading to strong enhancement of cooperation in particular in Poisson networks. But this effect is sensitive to the presence of Trojan horses (defectors placed within cooperator clusters). The study provides new knowledge about the conditions under which cooperation may evolve and persist, and the results are also relevant to consider in regard to human cooperation experiments.
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