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

Reliability and tolerance comparison in water supply networks

The final publication is available at Springer via http://dx.doi.org/10.1007/s11269-010-9753-2Urban water supply is a high priority service and so looped networks are extensively used in order to considerably reduce the number of consumers affected by a failure. Looped networks may be redundant in connectivity and capacity. The concept of reliability has been introduced in an attempt to quantitatively measure the possibility of maintaining an adequate service for a given period. Numerous researchers have considered reliability as a measure of redundancy. This concept is usually implicit, but some researchers have even stated it explicitly. This paper shows why reliability cannot be considered a measure of redundancy given that branched networks can achieve high values of reliability and this would deny the fact that a looped network is more reliable than a branched network with a similar layout and size. To this end the paper discusses two quantitative indices for measuring expected network behavior: reliability and tolerance. These indices are calculated and a comparison is made between looped, branched, and mixed networks. © 2011 Springer Science+Business Media B.V.The authors wish to acknowledge the support received from project IDAWAS, DPI2009-11591, of the Directorate-General of Research at the Spanish Ministry of Education, the grant PAID-02-09 for a stay at the Universidad Politecnica de Valencia by the first author, and a grant MAEC-AECI 0000202066 awarded to the second author by the Ministerio de Asuntos Exteriores y Cooperacion of Spain. The use of English in this paper was revised by John Rawlins; and the revision was funded by the Universidad Politecnica de Valencia, Spain.Martínez-Rodríguez, JB.; Montalvo Arango, I.; Izquierdo Sebastián, J.; Pérez García, R. (2011). Reliability and tolerance comparison in water supply networks. 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J Water Resour Plan Manage ASCE 117(5):588–605Jowitt P, Xu C (1993) Predicting pipe failure effects in water distribution networks. J Water Resour Plan Manage ASCE 119(l):18–31Kalungi P, Tanyimboh TT (2003) Redundancy model for water distribution systems. Rel Eng Syst Safety 82(3):275–286Khomsi D, Walters GA, Thorley ARD, Ouazar D (1996) Reliability tester for water-distribution networks. J Comput Civ Eng ASCE 10(l):10–9Lansey K, Duan N, Mays LW, Tung YK (1989) Water distribution system design under uncertainty. J Water Resour Plan Manage ASCE 115(5):630–645Loganathan GV, Shah MP, Sherali HP (1990) A two-phase network design heuristic for minimum cost water distribution systems under a reliability constraint. Eng Optim 15(4):311–336Martínez JB (2007) Quantifying the economy of water supply looped networks. J Hydraul Eng ASCE 133(1):88–97Martínez JB (2010) Cost and reliability comparison between branched and looped water supply networks. 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Determining pipe groupings for water distribution networks

Mathematical modeling of a water distribution system allows comparisons between design and operation alternatives. However, to make meaningful comparisons, the true field system must be represented within the model. Water distribution systems contain a large number of pipes with unknown roughness coefficients. Even with an extensive data collection effort, pipe roughnesses for all links cannot be determined exactly. Therefore, the system is simplified by assuming sets of pipes have the same roughness coefficient. The impacts of such simplification have not been examined in quantitative manner. This work develops a methodology to quantify impacts introduced by system simplification and identify the best number of pipe groupings for a network

New Methodologies for the Reliability-Based Analysis and Design of Water Distribution Systems

National Science Foundation Grant No. ECE-8511399Center for Water and the Environmen

New Methodologies for the Reliability-Based Analysis and Design of Water Distribution Systems

National Science Foundation Grant No. ECE-8511399Center for Water and the Environmen

Detecting Pipe Bursts Using Heuristic and CUSUM Methods

Pipe bursts in a drinking water distribution system lead to water losses, interruption of supply, and damage to streets and houses due to the uncontrolled water flow. To minimize the negative consequences of pipe bursts, an early detection is necessary. This paper describes a heuristic burst detection method, which continuously compares forecasted and measured values of the water demand. The forecasts of the water demand were generated by an adaptive water demand forecasting model. To test the method, a dataset of five years of water demand data in a supply area in the Western part of the Netherlands was collected. The method was tested on a subset of the data (only the winter months) in which 9 (larger) burst events were reported. The detection probability for the reported bursts was 44.4%, at an acceptable rate of false alarms of 5.0%. The results were compared with the CUSUM method, which is a general statistical process control (SPC) method to identify anomalies in time series. The heuristic and CUSUM methods generated comparable results, although rate of false alarm for the heuristic method was lower at the same detection probability.QN/Quantum NanoscienceApplied Science