Hae

Given a finite set of square tiles, the domino problem is the question of whether is it possible to tile the plane using these tiles. This problem is known to be undecidable in the planar case, and is strongly linked to ...

This thesis introduces a new, algebraic method to study multidimensional configurations, also sometimes called words, which have low pattern complexity. This is the setting of several open problems, most notably Nivat’s ...

This thesis studies properties of minimizers of variational integrals and solutions of partial differential equations with generalized Orlicz growth (also known as Musielak– Orlicz growth). This is continuation of regularity ...

Practical applications usually have multiobjective nature rather than having only one objective to optimize. A multiobjective problem cannot be solved with a single-objective solver as such. On the other hand, optimization ...

This thesis is devoted to the so-called k-abelian equivalence relation of sequences of symbols, that is, words. This equivalence relation is a generalization of the abelian equivalence of words. Two words are abelian ...

In this thesis we present four applications in bioinformatics with Markov models. That is, we extend the use of such models in the mathematical and statistical analysis of biological data. The data we consider are drawn ...

A subshift is a collection of bi-infinite sequences (configurations) of symbols where some finite patterns of symbols are forbidden to occur. A cellular automaton is a transformation that changes each configuration of a ...

Due to the complexity of many practical applications, we encounter optimization problems with nonsmooth functions, that is, functions which are not continuously differentiable everywhere. Classical gradient-based methods ...

Organotypic cancer cell cultures combined with modern imaging technology have greatly expanded the possibilities of in vitro cancer research and drug development. In fact, imaging and subsequent image analyses have become ...

The main goal of this thesis work has been to develop tools to recover hidden structures, latent variables, or latent subspaces for multivariate and dependent time series data. The secondary goal has been to write ...