To see the issues that arise when studying incidence problems in higher dimensions, we consider one of the simplest cases: Incidences between m points and n planes in R. To see that this problem is not interesting, we consider the following point-plane configuration. Let l ⊂ R be a line, let P be a set of m points on l, and let H be a set of n planes that contain l (e.g., see Figure 1). This co...

Assumption for 1 sample T test: Data are normally distributed. We have discussed in the last article on how to check the normality assumption of a quantitative data. One issue being highlighted was that these formal normality tests are very sensitive to the sample size of the variable concerned. As seen here, table II shows that the normality assumptions for both the systolic and diastolic bloo...

Changes in children’s family income over the 1990’s The authors find that children’s family income increased at virtually all income levels over the 1990’s, with slightly higher increases among poor families than non-poor families. (See Figure 1) This was true both for poor children generally and for poor children living in families without both parents present (this is predominantly singlepare...

Repeats or Transposable Elements (TEs) are highly repeated sequence stretches, present in virtually all eukaryotic genomes. We explore the distribution of representative TEs from all major classes in entire chromosomes across various organisms. We employ two complementary approaches, the scaling of block entropy and box-counting. Both converge to the conclusion that well-developed fractality is...

This study calls attention to the difference between traditional box-counting method and its modification. The appropriate scaling factor, influence on image size and resolution, and image rotation, as well as different image presentation, are showed on the sample of asymmetrical neurons from the monkey dentate nucleus. The standard BC method and its modification were evaluated on the sample of...

A systematic evaluation of various fractal analysis methods is essential for studying morphologies of finite and noisy experimental patterns such as domains of long chain alkanes at SiO(2)/air interfaces. The derivation of trustworthy fractal dimensions crucially relies on the definition of confidence intervals for the assumed scaling range. We demonstrate that the determination of the interval...

Our Goal • Found that Fractal Features effectively have texture recognition ability using statistical, soft computing, data mining and machine learning methods. • Six texture descriptors introduced in [Chaudhuri and Sarkar, 95] are based on the Fractal Dimension of the original and derived images. The studied features were the FDs of: • the original image (F_1), • the high gray-valued image (F_...

The scale-invariant behavior of air pollutant concentration (APC) time structure was investigated by applying the box counting method to APC time series. One-year series of hourly average APC observations, including O3, CO, SO2, NO, NO2, and PM10 which were obtained from urban, traffic, and national park air monitoring station at Taipei (Taiwan), were transferred into a useful compact form thro...