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...

The existing recognition methods of radiation source signal are extremely sensitive to the change of signal-to-noise ratio (SNR). In order to solve this problem, in this paper, it proposes a radar signal recognition method based on fractal box dimension and neural network under the condition of unstable SNR. Firstly, it extracts box counting dimension features of four different radiation source...

We calculate the box-counting dimension of the limit set of a general geometrically finite Kleinian group. Using the “global measure formula” for the Patterson measure and using an estimate on the horoball counting function we show that the Hausdorff dimension of the limit set is equal to both: the box-counting dimension and packing dimension of the limit set. Thus, by a result of Sullivan, we ...

The paper deals with an algorithm for Hausdorff dimension estimation based on box-counting dimension calculation. The main goal of the paper is to propose a new approach to box-counting dimension calculation with less computational demands. Streszczenie. W artykule opisano algorytm estymacji wymiaru Hausdorffa oparty o wyznaczanie wymiaru pudełkowego. Głównym celem pracy jest zaproponowanie now...

Since the end of the Seventies, following work of the French mathematician Mandelbrot, We are witnessing the true exploitation of the interest expressed by the scientific community for the fractals objects. The aim of this paper is to introduce the fractal theory by the calculation of the fractal dimension in the radiographic images. We implement for that, the box counting method for the segmen...

OBJECTIVE Mathematical morphology and box counting were used to extract trabecular pattern and to evaluate changes of reactive bone following root canal treatment. STUDY DESIGN Periapical radiographs were digitized and processed with mathematical morphology operations known as skeletonization. The trabecular patterns resulting from this skeletonization process were further analyzed with fract...

In this paper we consider the relationship between the Assouad and box-counting dimension and how both behave under the operation of taking products. We introduce the notion of ‘equi-homogeneity’ of a set, which requires a uniformity in the size of local covers at all lengths and at all points We prove that the Assouad and box-counting dimensions coincide for sets that have equal upper and lowe...