相关论文: Empirical Tests of Zipf's law Mechanism In Open So…
Context: Over the last decades, open-source software has pervaded the software industry and has become one of the key pillars in software engineering. The incomparable growth of open source reflected that pervasion: Prior work described…
Research collaborations provide the foundation for scientific advances, but we have only recently begun to understand how they form and grow on a global scale. Here we analyze a model of the growth of research collaboration networks to…
The science of cities seeks to understand and explain regularities observed in the world's major urban systems. Modelling the population evolution of cities is at the core of this science and of all urban studies. Quantitatively, the most…
Many complex systems are composed of disparate, interacting types of varying sizes: Species abundances in ecosystems, firm sizes in markets, city populations in countries, word counts in language, etc. A longstanding mystery of complex…
Using an exhaustive list of Japanese bankruptcy in 1997, we discover a Zipf law for the distribution of total liabilities of bankrupted firms in high debt range. The life-time of these bankrupted firms has exponential distribution in…
Most of various large-size complex systems in nature and society can be well described as complex networks (graphs) to better understand the evolutional mechanisms and dynamical functions behind themselves. Of some part follow scale-free…
Zipf's law predicts a power-law relationship between word rank and frequency in language communication systems, and is widely reported in texts yet remains enigmatic as to its origins. Computer simulations have shown that language…
We address the general problem of testing a power law distribution versus a log-normal distribution in statistical data. This general problem is illustrated on the distribution of the 2000 US census of city sizes. We provide definitive…
In this article, I conduct a textual and contextual analysis of the empirical literature on Zipf's law for cities. Building on previous meta-analysis material openly available, I collect full texts and bibliographies of 66 scientific…
The rank-size regularity known as Zipf's law is one of scaling laws and frequently observed within the natural living world and in social institutions. Many scientists tried to derive the rank-size scaling relation by entropy-maximizing…
Zipf's law states that the frequency of an observation with a given value is inversely proportional to the square of that value; Taylor's law, instead, describes the scaling between fluctuations in the size of a population and its mean.…
We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract…
Zipf's, Heaps' and Taylor's laws are ubiquitous in many different systems where innovation processes are at play. Together, they represent a compelling set of stylized facts regarding the overall statistics, the innovation rate and the…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
In a recent paper, Krapivsky and Redner (Phys. Rev. E, 71 (2005) 036118) proposed a new growing network model with new nodes being attached to a randomly selected node, as well to all ancestors of the target node. The model leads to a…
"Evolution behaves like a tinkerer" (Francois Jacob, Science, 1977). Software systems provide a unique opportunity to understand biological processes using concepts from network theory. The Debian GNU/Linux operating system allows us to…
When following a sequence - such as reading a text or tracking a user's activity - one can measure how the "dictionary" of distinct elements (types) grows with the number of observations (tokens). When this growth follows a power law, it is…
Distributed systems in which concurrent proposals are mutually exclusive face a fundamental stability constraint under network delay. In open systems where global state progression is event-driven rather than round-driven, propagation delay…
The growth dynamics of complex systems often exhibit statistical regularities involving power-law relationships. For real finite complex systems formed by countable tokens (animals, words) as instances of distinct types (species, dictionary…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…