Fractal behavior has been observed in both ion-channel gating and neuronal spiking patterns, but a causal relationship between the two has not yet been established. Here, we examine the effects of fractal ion-channel activity in modifications of two classical neuronal models: Fitzhugh-Nagumo (FHN) and Hodgkin-Huxley (HH). For the modified FHN model, the recovery variable was represented as a po...

analysis of food surfaces is of interest because many processes depend on their complexity. food surfaces show several textural characteristics related to their nature, composition and processing. food surface images and their microscopic details need to be translated into numerical data before engineering analysis. fractal geometry is a novel concept to describe the complexity of natural shape...

One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dime...

The forecasting slope deformation potential is required to evaluate slope safety during open-pit mining, allowing us to formulate and promote effective emergency strategies in advance to prevent slope failure disasters. Although fractal models have been used to predict slope deformation, such limitations as low prediction accuracy, poor stability and the requirement for large amounts of data mu...

We introduce fractal liquids by generalizing classical liquids of integer dimensions d = 1, 2, 3 to a fractal dimension df . The particles composing the liquid are fractal objects and their configuration space is also fractal, with the same non-integer dimension. Realizations of our generic model system include microphase separated binary liquids in porous media, and highly branched liquid drop...

We describe Hi-C, a method that probes the three-dimensional architecture of whole genomes by coupling proximity-based ligation with massively parallel sequencing. We constructed spatial proximity maps of the human genome with Hi-C at a resolution of 1 megabase. These maps confirm the presence of chromosome territories and the spatial proximity of small, gene-rich chromosomes. We identified an ...

In his groundbreaking work, ‘The Fractal Geometry of Nature’ (Mandelbrot, 1982), Benoit Mandelbrot described how fractals could account for a long list of natural forms ranging from trees to coastlines. Two recent studies in Science and The EMBO Journal have suggested that chromatin and the nucleoplasmic space surrounding it should be added to the fractal list. Fractals are ‘self-similar’, mean...

In this paper, the optical properties of one dimensional fractal structures are investigated. We consider six typical fractal photonic structures: the symmetric dual cantor-like fractal structure, the asymmetric dual cantor-like fractal structure, the single cantor-like fractal structure, the symmetric dual golden-section fractal structure, the asymmetric dual golden-section fractal structure a...