Fractal Analysis of River Flow Fluctuations (with Erratum)

We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at $s_{1\times}\sim12$ and $s_{2\times}\sim130$ months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second ones is approximately equal to the well known cycle of sun activity. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The value of Hurst exponent of the runoff water of rivers without the sinusoidal trend shows a long range correlation behavior. For the Daugava river the value of Hurst exponent is $0.52\pm0.01$ and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.Comment: 13 pages, 10 figures, V2: Added comments, references and one more figure, improved numerical calculations with new version of data, accepted for publication in Physica A: Statistical Mechanics and its Applications. The version with Erratum contains some notes concerning Ref. [58

Segmentation of Fault Networks Determined from Spatial Clustering of Earthquakes

We present a new method of data clustering applied to earthquake catalogs, with the goal of reconstructing the seismically active part of fault networks. We first use an original method to separate clustered events from uncorrelated seismicity using the distribution of volumes of tetrahedra defined by closest neighbor events in the original and randomized seismic catalogs. The spatial disorder of the complex geometry of fault networks is then taken into account by defining faults as probabilistic anisotropic kernels, whose structures are motivated by properties of discontinuous tectonic deformation and previous empirical observations of the geometry of faults and of earthquake clusters at many spatial and temporal scales. Combining this a priori knowledge with information theoretical arguments, we propose the Gaussian mixture approach implemented in an Expectation-Maximization (EM) procedure. A cross-validation scheme is then used and allows the determination of the number of kernels that should be used to provide an optimal data clustering of the catalog. This three-steps approach is applied to a high quality relocated catalog of the seismicity following the 1986 Mount Lewis ($M_l=5.7$) event in California and reveals that events cluster along planar patches of about 2 km$^2$, i.e. comparable to the size of the main event. The finite thickness of those clusters (about 290 m) suggests that events do not occur on well-defined euclidean fault core surfaces, but rather that the damage zone surrounding faults may be seismically active at depth. Finally, we propose a connection between our methodology and multi-scale spatial analysis, based on the derivation of spatial fractal dimension of about 1.8 for the set of hypocenters in the Mnt Lewis area, consistent with recent observations on relocated catalogs

Automated Assessment of Facial Wrinkling: a case study on the effect of smoking

Facial wrinkle is one of the most prominent biological changes that accompanying the natural aging process. However, there are some external factors contributing to premature wrinkles development, such as sun exposure and smoking. Clinical studies have shown that heavy smoking causes premature wrinkles development. However, there is no computerised system that can automatically assess the facial wrinkles on the whole face. This study investigates the effect of smoking on facial wrinkling using a social habit face dataset and an automated computerised computer vision algorithm. The wrinkles pattern represented in the intensity of 0-255 was first extracted using a modified Hybrid Hessian Filter. The face was divided into ten predefined regions, where the wrinkles in each region was extracted. Then the statistical analysis was performed to analyse which region is effected mainly by smoking. The result showed that the density of wrinkles for smokers in two regions around the mouth was significantly higher than the non-smokers, at p-value of 0.05. Other regions are inconclusive due to lack of large scale dataset. Finally, the wrinkle was visually compared between smoker and non-smoker faces by generating a generic 3D face model.Comment: 6 pages, 8 figures, Accepted in 2017 IEEE SMC International Conferenc

Texting and tapping : a dynamical approach to multitasking.

Jobs in various work fields (e.g., flying airplanes; Helmreich, 2000) require a high ability to successfully handle more than one task at a time, or to multitask. Researchers usually explain multitasking by having priorities in which individuals either attend to one task at a time, or one task receives more time processing than the other task. The current study approaches multitasking from a dynamical systems perspective. Fourteen general psychology students participated in the study by pressing a pedal attempting to maintain a steady beat and text messaging. Researchers recorded behavior over time (2 min. for each task and multitasking). The inputs to the data analysis were the X-Y coordinates of thumb movement (in pixels) over time and the recorded beat's deviation (in sec) from the metronome's beat over time. The patterns of behavior were recorded. Nonlinear analyses (Iterated Function Systems and a MANOVA on Hurst exponents for monofractality, and Wavelet Modulus Transform Maxima for multifractality) tested for fractal patterns which characterized both tasks in both conditions (single task or multitasking). Thumb movement's patterns during texting were not significantly different for single task and multitasking conditions, both displaying short-term correlations (brown noise). Patterns in tapping deviations were significantly different between the two conditions. Structure of deviations while only tapping was characterized by strong long-term correlations (pink noise); the structure while multitasking was also positively long-term correlated, but less strong. Results showed that texting and tapping behavior, as single tasks or during multitasking, are fractal