Many complex phenomena, from trait selection in biological systems to hierarchy formation in social and economic entities, show signs of competition and heterogeneous performance in the temporal evolution of their components, which may eventually lead to stratified structures such as the worldwide wealth distribution. However, it is still unclear whether the road to hierarchical complexity is determined by the particularities of each phenomena, or if there are generic mechanisms of stratification common to many systems. Human sports and games, with their (varied but simple) rules of competition and measures of performance, serve as an ideal test-bed to look for universal features of hierarchy formation. With this goal in mind, we analyse here the behaviour of performance rankings over time of players and teams for several sports and games, and find statistical regularities in the dynamics of ranks. Specifically the rank diversity, a measure of the number of elements occupying a given rank over a length of time, has the same functional form in sports and games as in languages, another system where competition is determined by the use or disuse of grammatical structures. We use a Gaussian random walk model to reproduce the rank diversity of the studied sports and games. We also discuss the relation between rank diversity and the cumulative rank distribution. Our results support the notion that hierarchical phenomena may be driven by the same underlying mechanisms of rank formation, regardless of the nature of their components. Moreover, such regularities can in principle be used to predict lifetimes of rank occupancy, thus increasing our ability to forecast stratification in the presence of competition.
The recent dramatic increase in online data availability has allowed researchers to explore human culture with unprecedented detail, such as the growth and diversification of language. In particular, it provides statistical tools to explore whether word use is similar across languages, and if so, whether these generic features appear at different scales of language structure. Here we use the Google Books N -grams dataset to analyze the temporal evolution of word usage in several languages. We apply measures proposed recently to study rank dynamics, such as the diversity of N -grams in a given rank, the probability that an N -gram changes rank between successive time intervals, the rank entropy, and the rank complexity. Using different methods, results show that there are generic properties for different languages at different scales, such as a core of words necessary to minimally understand a language. We also propose a null model to explore the relevance of linguistic structure across multiple scales, concluding that N -gram statistics cannot be reduced to word statistics. We expect our results to be useful in improving text prediction algorithms, as well as in shedding light on the large-scale features of language use, beyond linguistic and cultural differences across human populations.
In 2009, Melones Oil Terminal Inc. (MOTI) embarked on a $90 million program to develop a 2-million-bbls capacity, bunker fuel transfer facility at Melones Island, a small rock outcrop located 8 nautical miles from the Pacific entrance of the Panama Canal. The MOTI facility comprises 16 storage tanks and a T-shaped pier configured for the simultaneous berthing of a 70,000-tonne dead weight tonnage (DWT) tanker and two 9,000-tonne DWT bunker transfer barges, or four bunkering barges. The marine structure consists of a 345-meter-long pier connected to the island via a 130-meter-long access trestle. The trestle length was selected so as to provide the required 15-meter water depth along the main berth without rock dredging. The pier structure consists of a series of breasting/mooring dolphins interconnected with modified AASHTO Type II pre-topped girders. When completed, the terminal will store and distribute bunker and diesel fuel to vessels transiting the Panama Canal. This paper describes the challenges associated with the structural design and construction of the marine facilities at the island site.Because of the soft and variable overburden layer between the seabed and underlying rock formation, the pile installation was the most challenging aspect of the project. Framing was selected to ensure structural stability during construction. The highcapacity concrete piles were socketed into the rock, driven to refusal, and anchored to the rock. The effects of pile slenderness on axial and bending capacity under berthing, mooring, and seismic conditions were thoroughly examined in the deepwater dolphins. Seismic effects were evaluated to ensure adequate deformation capacity and strength in piles and pile-deck connections. Pier construction was further complicated by the intrinsic offshore nature of the project and exposure to ocean swells. This translated into extensive and careful construction planning, spanning from the transportation, handling, and erection of precast piles and girders, some of which were as long as 42.5 meters, to the casting and curing of the concrete dolphin caps and the installation of surface features. 1891 Ports 2013
Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a variety of fields. More recently, data availability has allowed us to study rank dynamics: how elements of a ranking change in time. Here, we study the rank distributions and rank dynamics of 12 datasets from different sports and games. To study rank dynamics, we consider measures that we have defined previously: rank diversity, change probability, rank entropy, and rank complexity. We also introduce a new measure that we call “system closure” that reflects how many elements enter or leave the rankings in time. We use a random walk model to reproduce the observed rank dynamics, showing that a simple mechanism can generate similar statistical properties as the ones observed in the datasets. Our results show that while rank distributions vary considerably for different rankings, rank dynamics have similar behaviors, independently of the nature and competitiveness of the sport or game and its ranking method. Our results also suggest that our measures of rank dynamics are general and applicable for complex systems of different natures.
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