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Several measures of volatility have been developed in order to quantify the degree of uncertainty of an energy price series, which include historical volatility and price velocities, among others. This paper suggests using the permutation entropy, topological entropy and the modified permutation entropy as alternatives to measure volatility in energy markets. Simulated data show that these measures are more appropriate to quantify the uncertainty associated to a time series than those based on the standard deviation or other measures of dispersion. Finally, the proposed method is applied to some typical electricity markets: Nord Pool, Ontario, Omel and four Australian markets. [ABSTRACT FROM AUTHOR]

It is critically meaningful to accurately predict the ionospheric F2 layer critical frequency (foF2), which greatly limits the efficiency of communications, radar, and navigation systems. This paper introduced the entropy weight method to develop the combination prediction model (CPM) for long-term foF2 at Darwin (12.4° S, 131.5° E) in Australia. The weight coefficient of each individual model in the CPM is determined by using the entropy weight method after completing the simulation of the individual model in the calibration period. We analyzed two sets of data to validate the method used in this study: One set is from 2000 and 2009, which are included in the calibration period (1998–2016), and the other set is outside the calibration cycle (from 1997 and 2017). To examine the performance, the root mean square error (RMSE) of the observed monthly median foF2 value, the proposed CPM, the Union Radio Scientifique Internationale (URSI), and the International Radio Consultative Committee (CCIR) are compared. The yearly RMSE average values calculated from CPM were less than those calculated from URSI and CCIR in 1997, 2000, 2009, and 2017. In 2000 and 2009, the average percentage improvement between CPM and URSI is 9.01%, and the average percentage improvement between CPM and CCIR is 13.04%. Beyond the calibration period, the average percentage improvement between CPM and URSI is 13.2%, and the average percentage improvement between CPM and CCIR is 12.6%. The prediction results demonstrated that the proposed CPM has higher precision of prediction and stability than that of the URSI and CCIR, both within the calibration period and outside the calibration period. [ABSTRACT FROM AUTHOR]

Quantifying the urbanization level is an essential yet challenging task in urban studies because of the high complexity of this phenomenon. The urbanization degree has been estimated using a variety of social, economic, and spatial measures. Among the spatial characteristics, the Shannon entropy of the landscape pattern has recently been intensively explored as one of the most effective urbanization indexes. Here, we introduce a new measure of the spatial entropy of land that characterizes its parcel mosaic, the structure resulting from the division of land into cadastral parcels. We calculate the entropies of the parcel areas' distribution function in different portions of the urban systems. We have established that the Shannon and Renyi entropies R 0 and R 1 / 2 are most effective at differentiating the degree of a spatial organization of the land. Our studies are based on 30 urban systems located in the USA, Australia, and Poland, and three desert areas from Australia. In all the cities, the entropies behave the same as functions of the distance from the center. They attain the lowest values in the city core and reach substantially higher values in suburban areas. Thus, the parcel mosaic entropies provide a spatial characterization of land to measure its urbanization level effectively. [ABSTRACT FROM AUTHOR]