Probing Diffusive Dynamics of Natural Tubule Nanoclays with Machine Learning.

Reproducibility of the experimental results and object of study itself is one of the basic principles in science. But what if the object characterized by technologically important properties is natural and cannot be artificially reproduced one-to-one in the laboratory? The situation becomes even more complicated when we are interested in exploring stochastic properties of a natural system and only a limited set of noisy experimental data is available. In this paper we address these problems by exploring diffusive motion of some natural clays, halloysite and sepiolite, in a liquid environment. By using a combination of dark-field microscopy and machine learning algorithms, a quantitative theoretical characterization of the nanotubes' rotational diffusive dynamics is performed. Scanning the experimental video with the gradient boosting tree method, we can trace time dependence of the diffusion coefficient and probe different regimes of nonequilibrium rotational dynamics that are due to contacts with surfaces and other experimental imperfections. The method we propose is of general nature and can be applied to explore diffusive dynamics of various biological systems in real time.

Multiscale structural complexity of natural patterns.

Complexity of patterns is key information for human brain to differ objects of about the same size and shape. Like other innate human senses, the complexity perception cannot be easily quantified. We propose a transparent and universal machine method for estimating structural (effective) complexity of two-dimensional and three-dimensional patterns that can be straightforwardly generalized onto other classes of objects. It is based on multistep renormalization of the pattern of interest and computing the overlap between neighboring renormalized layers. This way, we can define a single number characterizing the structural complexity of an object. We apply this definition to quantify complexity of various magnetic patterns and demonstrate that not only does it reflect the intuitive feeling of what is "complex" and what is "simple" but also, can be used to accurately detect different phase transitions and gain information about dynamics of nonequilibrium systems. When employed for that, the proposed scheme is much simpler and numerically cheaper than the standard methods based on computing correlation functions or using machine learning techniques.