Pattern selection and multiscale behaviour in metrically discontinuous non-Euclidean plates

Elastic theory of unconstrained non-Euclidean plates

Non-Euclidean plates are a subset of the class of elastic bodies having no stress-free configuration. Such bodies exhibit residual stress when relaxed from all external constraints, and may assume complicated equilibrium shapes even in the absence of external forces. In this work we present a mathematical framework for such bodies in terms of a covariant theory of linear elasticity, valid for l...

Buckling transition and boundary layer in non-Euclidean plates.

Non-Euclidean plates are thin elastic bodies having no stress-free configuration, hence exhibiting residual stresses in the absence of external constraints. These bodies are endowed with a three-dimensional reference metric, which may not necessarily be immersible in physical space. Here, based on a recently developed theory for such bodies, we characterize the transition from flat to buckled e...

Non-Euclidean dissimilarity data in pattern recognition

This thesis addresses problems in dissimilarity (proximity) learning, particularly focusing on identifying the sources and rectifying the non-Euclidean dissimilarity in pattern recognition. We aim to develop a framework for analyzing the non-Euclidean dissimilarity by combining the methods from differential geometry and manifold learning theory. The algorithms are applied to objects represented...

Pattern Recognition with Non-Euclidean Similarities

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...