Search

Eukaryotic transcription factors (TFs) are proteins that bind short DNA motifs and regulate gene transcription. Because genomic DNA is organised into nucleosomes via binding histone octamers, TFs compete with histones for binding DNA. Also, the functions of a TF are mainly defined by its domains; therefore, a TF gene can vary the characteristics of its protein product through the expression of alternative isoforms with different domains. However, the mechanisms of TF-nucleosome interactions and the functional importance of alternative TF isoforms are not fully understood. Here, I address these two problems computationally via the integrative analysis of publicly available in vivo human sequencing data. First, I evaluated a novel, gyre-spanning, mode of TF-nucleosome binding proposed recently by another lab based on in vitro evidence. Analysing the nucleosome occupancy and TF binding in the human genome, I found no evidence of such binding and concluded that it must be extremely rare, if at all present. Secondly, I studied the alternative isoforms of human TFs genome-wide. I found that independently of the gene length and the number of exons, TF genes more efficiently sample the set of possible alternative isoforms than non-TF genes, suggesting the particular importance of alternative isoforms for TFs. Also, I found that TF isoforms without a DNA-binding domain (DBD) are produced by almost a third of all human TFs, tend to be tissue-specific and likely reverse the transcription regulation effect of DBD-containing isoforms. Moreover, I demonstrated that the switches of the highest-expressed TF isoforms across human adult tissues may represent a widespread functional mechanism. Finally, I collected a compendium of human TFs with experimentally characterised alternative isoforms which will hopefully serve as a resource for future studies. In summary, my analysis further developed the fundamental knowledge about the TF-nucleosome interactions and the alternative isoforms of TFs in humans.

Finally, a novel application of 3D appearance modelling is proposed: a faster than real-time algorithm for statistically constrained quasi-mechanical simulation. Experiments demonstrate superior realism, achieved in the proposed method by employing statistical appearance models to drive the simulation, in comparison with the comparable state-of-the-art quasi-mechanical approaches.

The study of open dynamical systems is the study of systems with holes. This thesis focuses on the sets of orbits that avoid these holes, called the survivor sets, and on the families of open strictly monotonic functions with one discontinuity, all restricted to their survivor set. Such functions have applications in electricity (switching systems) and mechanics (oscillators with multiple impacts). The aim of this thesis is to find and describe the transition to chaos from zero to positive topological entropy for these families. The literature uses two different approaches for open maps: combinatorics on words and piecewise monotone maps without holes. Combinatorics on words have led to a full description, on the parameter space, of the transition to chaos for one family: the doubling map with a hole. Studies on piecewise monotone maps have proved more detailed results on entropy for maps without holes and described the main tool of our method: renormalisation. This thesis combines these two approaches to describe the transition to chaos for the tent map and two other similar functions with a hole. It also describes the route to chaos, i.e. the evolution of the functions' dynamics as parameters continuously move across the boundary of chaos. Our method uses a set of sub-regions of the parameter space that contains the boundary of chaos. Each of these sub-regions is called a renormalisation box and is associated with one specific renormalisation. The results of this thesis are stated in four theorems. The first theorem describes the possible dynamics of a function for its parameters in one renormalisation box. This allows to create a simple network of renormalisations to define sub-regions within sub-regions, and create an induction process. The second theorem proves that at each step of this process the set of sub-regions contains the boundary of chaos. The third theorem proves that the limit of our process is the full transition to chaos, which is a connected curve. Finally, the last theorem computes the speed of convergence of our method for a new kind of route to chaos which does not exist for the doubling map with a hole. These four theorems describe the transition and routes to chaos for the tent map and two other similar functions with holes. Our work is a first full description of the transition to chaos for these families of open strictly monotonic functions with one discontinuity.

Due to limited experimental data and a lack of understanding of the underlying microstructural deformation mechanisms involved, modeling of material behavior of biomechanical tissues presents a rather formidable task. In this dissertation, a nonlinear multi-mechanism inelastic material model is introduced for modeling vascular tissue, collagen recruitment and elastin degradation. The model is implemented into the commercial finite element software package ANSYS with user programmable features. Although the idea of using several deformation mechanisms in the same material model is by no means novel, it is the first time such model is being implemented in a commercial finite element package and applied to a numerical study of physiological processes taking place inside the vascular walls. Two numerical examples are presented: a simulation of angioplasty procedure, and a finite element analysis of fusiform aneurysm development and growth. This is by far not the exhaustive list of possible applications of the developed material model; implementation in a commercial finite element code will help facilitate innovative developments, including new ways to surgically treat vascular disorders.

We have measured the temperature-dependent thermal conductivity, K(T) of single walled carbon nanotubes from 300 K to 8 K by 3w methods. K(T) exhibits linear temperature dependence in the entire temperature range. Our results are in good agreement with the results obtained by Hone et al. using a standard steady state technique. Also we measured the temperature-dependent thermal conductivity K(T) of quartz and SiO2 in the same temperature range (300 K to 8 K) as a standardization tool. Our technique shows promise for the thermal conductivity measurements of many nanostructures with slight modifications.

We study the combinatorial properties of beta expansions. In particular we study those bases which admit points with finitely many or countably many expansions. This leads to interesting questions, such as what is the smallest base admitting a points with finitely many or countably many expansions. We also consider the dimension theory of the set of expansions for a typical point within a "natural" parameter space.

This work motivates the study of open dynamical systems corresponding to the doubling map. In particular, the dynamical properties of the attractor of the doubling map when a symmetric, centred open interval is removed are studied. Using the arithmetical properties of the binary expansion of the points on the boundary of the removed interval, we study properties such as topological transitivity, the specification property and intrinsic ergodicity. The properties of the function that associates to each hole $(a,b)$ the topological entropy of the attractor of the considered dynamical system are also shown. For these purposes, a subshift corresponding to an element of the lexicographic world is associated to each attractor and the mentioned properties are studied symbolically.