Heavy-tailed distributions in fatal traffic accidents: role of human activities

Human activities can play a crucial role in the statistical properties of observables in many complex systems such as social, technological and economic systems. We demonstrate this by looking into the heavy-tailed distributions of observables in fatal plane and car accidents. Their origin is examined and can be understood as stochastic processes that are related to human activities. Simple mathematical models are proposed to illustrate such processes and compared with empirical results obtained from existing databanks.Comment: 10 pages, 5 figure

Scaling and correlations in the dynamics of forest-fire occurrence

Forest-fire waiting times, defined as the time between successive events above a certain size in a given region, are calculated for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact that the distribution of fire sizes is not a power law. The meaning of such behavior in terms of the possible self-similarity of the process in a nonstationary system is discussed. We find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a non-trivial ``instantaneous'' scaling law, sustained by the correlations of the process.Comment: Not a long paper, but many figures (but no large size in kb

Inverse spectral problems for Dirac operators with summable matrix-valued potentials

We consider the direct and inverse spectral problems for Dirac operators on $(0,1)$ with matrix-valued potentials whose entries belong to $L_p(0,1)$, $p\in[1,\infty)$. We give a complete description of the spectral data (eigenvalues and suitably introduced norming matrices) for the operators under consideration and suggest a method for reconstructing the potential from the corresponding spectral data.Comment: 32 page

Analytic approach to stochastic cellular automata: exponential and inverse power distributions out of Random Domino Automaton

Inspired by extremely simplified view of the earthquakes we propose the stochastic domino cellular automaton model exhibiting avalanches. From elementary combinatorial arguments we derive a set of nonlinear equations describing the automaton. Exact relations between the average parameters of the model are presented. Depending on imposed triggering, the model reproduces both exponential and inverse power statistics of clusters.Comment: improved, new material added; 9 pages, 3 figures, 2 table

Stock mechanics: predicting recession in S&P500, DJIA, and NASDAQ

An original method, assuming potential and kinetic energy for prices and conservation of their sum is developed for forecasting exchanges. Connections with power law are shown. Semiempirical applications on S&P500, DJIA, and NASDAQ predict a coming recession in them. An emerging market, Istanbul Stock Exchange index ISE-100 is found involving a potential to continue to rise.Comment: 14 pages, 4 figure

Non-characteristic Half-lives in Radioactive Decay

Half-lives of radionuclides span more than 50 orders of magnitude. We characterize the probability distribution of this broad-range data set at the same time that explore a method for fitting power-laws and testing goodness-of-fit. It is found that the procedure proposed recently by Clauset et al. [SIAM Rev. 51, 661 (2009)] does not perform well as it rejects the power-law hypothesis even for power-law synthetic data. In contrast, we establish the existence of a power-law exponent with a value around 1.1 for the half-life density, which can be explained by the sharp relationship between decay rate and released energy, for different disintegration types. For the case of alpha emission, this relationship constitutes an original mechanism of power-law generation