Mathematical Models of Video-Sequences of Digital Half-Tone Images

This chapter is devoted to Mathematical Models (MM) of Digital Half-Tone Images (DHTI) and their video-sequences presented as causal multi-dimensional Markov Processes (MP) on discrete meshes. The difficulties of MM development for DHTI video-sequences of Markov type are shown. These difficulties are related to the enormous volume of computational operations required for their realization. The method of MM-DHTI construction and their statistically correlated video-sequences on the basis of the causal multi-dimensional multi-value MM is described in detail. Realization of such operations is not computationally intensive; Markov models from the second to fourth order demonstrate this. The proposed method is especially effective when DHTI is represented by low-bit (4-8 bits) binary numbers

Mathematical models in physiology

Computational modelling of biological processes and systems has witnessed a remarkable development in recent years. The search-term (modelling OR modeling) yields over 58000 entries in PubMed, with more than 34000 since the year 2000: thus, almost two-thirds of papers appeared in the last 5–6 years, compared to only about one-third in the preceding 5–6 decades.\ud \ud The development is fuelled both by the continuously improving tools and techniques available for bio-mathematical modelling and by the increasing demand in quantitative assessment of element inter-relations in complex biological systems. This has given rise to a worldwide public domain effort to build a computational framework that provides a comprehensive theoretical representation of integrated biological function—the Physiome.\ud \ud The current and next issues of this journal are devoted to a small sub-set of this initiative and address biocomputation and modelling in physiology, illustrating the breadth and depth of experimental data-based model development in biological research from sub-cellular events to whole organ simulations

Mathematical models of martensitic microstructure

Martensitic microstructures are studied using variational models based on nonlinear elasticity. Some relevant mathematical tools from nonlinear analysis are described, and applications given to austenite-martensite interfaces and related topics