A morphological multiscale method in 3D image and 3D image sequence processing is discussed which identifies edges on level sets and the motion of features in time. Based on these indicator evaluation the image data is processed applying nonlinear diffusion and the theory of geometric evolution problems. The aim is to smooth level sets of a 3D image while simultaneously preserving geometric fea...

The history-dependent behaviors of classical plasticity models are often driven by internal variables evolved according to phenomenological laws. difficulty interpret how these represent a history deformation, the lack direct measurement for calibration and validation, weak physical underpinning those laws have long been criticized as barriers creating realistic models. In this work, geometric ...

We show how the Gaussian min-max theorem provides direct proofs of several famous results in asymptotic geometric analysis, such as, the Dvoretzky theorem, the Johnson-Lindenstrauss Lemma, Gluskin’s theorem on embedding in `1 , and others.

The subject of geometric analysis evolves according to our understanding of geometry and analysis. However, one should say that ideas of algebraic geometry and representation theory have been extremely powerful in both global and local geometry. In fact, the spectacular idea of using geometry to understand Diophantine problem has already widened our concept of space. The desire to find suitable...

A functional composition of the cumulative distribution function of one probability distribution with the inverse cumulative distribution function of another is called the transmutation map. In this article, we will use the quadratic rank transmutation map (QRTM) in order to generate a flexible family of probability distributions taking Lindley-geometric distribution as the base value distribut...

Bernard Jones told you about multiresolution analysis in his wavelet lectures. This is a pretty well formalized and self-contained area of wavelet analysis. Multiscale methods form a wider and less well defined area of tools and approaches; the term is used, e.g., in numerical analysis, but the main range of multiscale methods are based on application of wavelets. In this this lecture I shall e...

We describe a range of powerful multiscale analysis methods. We also focus on the pivotal issue of measurement noise in the physical sciences. From multiscale analysis and noise modeling, we develop a comprehensive methodology for data analysis of 2D images, 1D signals (or spectra), and point pattern data. Noise modeling is based on the following: (i) multiscale transforms, including wavelet tr...

This paper discusses the design goals and the first developments of PROTO-PLASM, a novel computational environment to produce libraries of executable, combinable and customizable computer models of natural and synthetic biosystems, aiming to provide a supporting framework for predictive understanding of structure and behaviour through multiscale geometric modelling and multiphysics simulations....

A morphological multiscale method in 3D image and 3D image sequence processing is discussed which identifies edges on level sets and the motion of features in time. Based on these indicator evaluation the image data is processed applying nonlinear diffusion and the theory of geometric evolution problems. The aim is to smooth level sets of a 3D image while preserving geometric features such as e...

Viruses are infectious agents that can cause epidemics and pandemics. The understanding of virus formation, evolution, stability, and interaction with host cells is of great importance to the scientific community and public health. Typically, a virus complex in association with its aquatic environment poses a fabulous challenge to theoretical description and prediction. In this work, we propose...