Scaling Laws in Human Language

Zipf's law on word frequency is observed in English, French, Spanish, Italian, and so on, yet it does not hold for Chinese, Japanese or Korean characters. A model for writing process is proposed to explain the above difference, which takes into account the effects of finite vocabulary size. Experiments, simulations and analytical solution agree well with each other. The results show that the frequency distribution follows a power law with exponent being equal to 1, at which the corresponding Zipf's exponent diverges. Actually, the distribution obeys exponential form in the Zipf's plot. Deviating from the Heaps' law, the number of distinct words grows with the text length in three stages: It grows linearly in the beginning, then turns to a logarithmical form, and eventually saturates. This work refines previous understanding about Zipf's law and Heaps' law in language systems.Comment: 6 pages, 4 figure

The Battle of the Water Calibration Networks (BWCN)

Calibration is a process of comparing model results with field data and making the appropriate adjustments so that both results agree. Calibration methods can involve formal optimization methods or manual methods where the modeler informally examines alternative model parameters. The development of a calibration framework typically involves: (1) definition of the model variables, coefficients, and equations, (2) selection of an objective function to measure the quality of the calibration, (3) selection of the set of data to be used for the calibration process, and (4) selection of an optimization/manual scheme for altering the coefficient values in the direction of reducing the objective function. Hydraulic calibration usually involves the modification of system demands, fine-tuning the roughness values of pipes, altering pump operation characteristics, and adjusting other model attributes that affect simulation results, and in particular those that have significant uncertainty associated with their values. From the above steps it is clear that model calibration is neither unique nor a straightforward technical task. The success of a calibration process depends on the modeler's experience and intuition, as well as on the mathematical model and procedures adopted for the calibration process. This paper provides a summary of the Battle of the Water Calibration Networks (BWCN), the goal of which was to objectively compare the solutions of different approaches to the calibration of water distribution systems through application to a real water distribution system. Fourteen teams from academia, water utilities, and private consultants participated. The BWCN outcomes were presented and assessed at the 12th Water Distribution Systems Analysis (WDSA 2010) conference in Tucson, Arizona, September 2010. This manuscript summarizes the BWCN exercise and suggests future research directions for water distribution systems calibration