Power law and entropy analysis of catastrophic phenomena

Catastrophic events, such as wars and terrorist attacks, tornadoes and hurricanes, earthquakes, tsunamis, floods and landslides, are always accompanied by a large number of casualties. The size distribution of these casualties has separately been shown to follow approximate power law (PL) distributions. In this paper, we analyze the statistical distributions of the number of victims of catastrophic phenomena, in particular, terrorism, and find double PL behavior. This means that the data sets are better approximated by two PLs instead of a single one. We plot the PL parameters, corresponding to several events, and observe an interesting pattern in the charts, where the lines that connect each pair of points defining the double PLs are almost parallel to each other. A complementary data analysis is performed by means of the computation of the entropy. The results reveal relationships hidden in the data that may trigger a future comprehensive explanation of this type of phenomena.

Forest fires in Northern region of Portugal: impact on PM levels

Every year European citizens become victims of devastating fires, which are especially disastrous for Southern European countries. Apart from the numerous health and economic consequences, fires generate hazardous pollutants that are introduced into the environment, thus representing serious risks for public health. In that regard, particulate matter (PM) is of amajor concern. Thus, the objectives of thisworkwere to characterize the trend of forest fire occurrences and burnt area during the period of 2005 and 2010 and to study the influence of forest fires on levels of particulatematter PM10 and PM2.5. In 2010, 22,026 forest fires occurred in Portugal. The northern region was the most affected by forest fires, with 27% of occurrences in Oporto district. The annual means of PM10 and PM2.5 concentrations at two urban background sites were 25±14 μg m−3 and 8.2±4.9 μg m−3, and 17±13 μg m−3 and 7.3±5.9 μg m−3, respectively. At both sites the highest levels of PMfractionswere observed during July and August of 2010, corresponding to the periods when majority (66%) of forest fires occurred. Furthermore, PM10 daily limit at the two sites was exceeded during 20 and 5 days, respectively; 56%, and respectively 60% of those exceedances occurred during the forest fire season. Considering that the risks of forest fire ignition and severity are enhanced with elevated temperatures, the climate change might increase the environmental impacts of forest fires.

A Review on the Characterization of Signals and Systems by Power Law Distributions

Power laws, also known as Pareto-like laws or Zipf-like laws, are commonly used to explain a variety of real world distinct phenomena, often described merely by the produced signals. In this paper, we study twelve cases, namely worldwide technological accidents, the annual revenue of America׳s largest private companies, the number of inhabitants in America׳s largest cities, the magnitude of earthquakes with minimum moment magnitude equal to 4, the total burned area in forest fires occurred in Portugal, the net worth of the richer people in America, the frequency of occurrence of words in the novel Ulysses, by James Joyce, the total number of deaths in worldwide terrorist attacks, the number of linking root domains of the top internet domains, the number of linking root domains of the top internet pages, the total number of human victims of tornadoes occurred in the U.S., and the number of inhabitants in the 60 most populated countries. The results demonstrate the emergence of statistical characteristics, very close to a power law behavior. Furthermore, the parametric characterization reveals complex relationships present at higher level of description.