TY - THES
AB - In this thesis, we consider several of the most classical and fundamental problems in static analysis and formal verification, including invariant generation, reachability analysis, termination analysis of probabilistic programs, data-flow analysis, quantitative analysis of Markov chains and Markov decision processes, and the problem of data packing in cache management.
We use techniques from parameterized complexity theory, polyhedral geometry, and real algebraic geometry to significantly improve the state-of-the-art, in terms of both scalability and completeness guarantees, for the mentioned problems. In some cases, our results are the first theoretical improvements for the respective problems in two or three decades.
AU - Goharshady, Amir Kafshdar
ID - 8934
SN - 2663-337X
TI - Parameterized and algebro-geometric advances in static program analysis
ER -
TY - THES
AB - In this thesis we study certain mathematical aspects of evolution. The two primary forces that drive an evolutionary process are mutation and selection. Mutation generates new variants in a population. Selection chooses among the variants depending on the reproductive rates of individuals. Evolutionary processes are intrinsically random – a new mutation that is initially present in the population at low frequency can go extinct, even if it confers a reproductive advantage. The overall rate of evolution is largely determined by two quantities: the probability that an invading advantageous mutation spreads through the population (called fixation probability) and the time until it does so (called fixation time). Both those quantities crucially depend not only on the strength of the invading mutation but also on the population structure. In this thesis, we aim to understand how the underlying population structure affects the overall rate of evolution. Specifically, we study population structures that increase the fixation probability of advantageous mutants (called amplifiers of selection). Broadly speaking, our results are of three different types: We present various strong amplifiers, we identify regimes under which only limited amplification is feasible, and we propose population structures that provide different tradeoffs between high fixation probability and short fixation time.
AU - Tkadlec, Josef
ID - 7196
TI - A role of graphs in evolutionary processes
ER -
TY - THES
AB - Proteins and their complex dynamic interactions regulate cellular mechanisms from sensing and transducing extracellular signals, to mediating genetic responses, and sustaining or changing cell morphology. To manipulate these protein-protein interactions (PPIs) that govern the behavior and fate of cells, synthetically constructed, genetically encoded tools provide the means to precisely target proteins of interest (POIs), and control their subcellular localization and activity in vitro and in vivo. Ideal synthetic tools react to an orthogonal cue, i.e. a trigger that does not activate any other endogenous process, thereby allowing manipulation of the POI alone.
In optogenetics, naturally occurring photosensory domain from plants, algae and bacteria are re-purposed and genetically fused to POIs. Illumination with light of a specific wavelength triggers a conformational change that can mediate PPIs, such as dimerization or oligomerization. By using light as a trigger, these tools can be activated with high spatial and temporal precision, on subcellular and millisecond scales. Chemogenetic tools consist of protein domains that recognize and bind small molecules. By genetic fusion to POIs, these domains can mediate PPIs upon addition of their specific ligands, which are often synthetically designed to provide highly specific interactions and exhibit good bioavailability.
Most optogenetic tools to mediate PPIs are based on well-studied photoreceptors responding to red, blue or near-UV light, leaving a striking gap in the green band of the visible light spectrum. Among both optogenetic and chemogenetic tools, there is an abundance of methods to induce PPIs, but tools to disrupt them require UV illumination, rely on covalent linkage and subsequent enzymatic cleavage or initially result in protein clustering of unknown stoichiometry.
This work describes how the recently structurally and photochemically characterized green-light responsive cobalamin-binding domains (CBDs) from bacterial transcription factors were re-purposed to function as a green-light responsive optogenetic tool. In contrast to previously engineered optogenetic tools, CBDs do not induce PPI, but rather confer a PPI already upon expression, which can be rapidly disrupted by illumination. This was employed to mimic inhibition of constitutive activity of a growth factor receptor, and successfully implement for cell signalling in mammalian cells and in vivo to rescue development in zebrafish. This work further describes the development and application of a chemically induced de-dimerizer (CDD) based on a recently identified and structurally described bacterial oxyreductase. CDD forms a dimer upon expression in absence of its cofactor, the flavin derivative F420. Safety and of domain expression and ligand exposure are demonstrated in vitro and in vivo in zebrafish. The system is further applied to inhibit cell signalling output from a chimeric receptor upon F420 treatment.
CBDs and CDD expand the repertoire of synthetic tools by providing novel mechanisms of mediating PPIs, and by recognizing previously not utilized cues. In the future, they can readily be combined with existing synthetic tools to functionally manipulate PPIs in vitro and in vivo.
AU - Kainrath, Stephanie
ID - 7680
TI - Synthetic tools for optogenetic and chemogenetic inhibition of cellular signals
ER -
TY - THES
AB - This thesis considers two examples of reconfiguration problems: flipping edges in edge-labelled triangulations of planar point sets and swapping labelled tokens placed on vertices of a graph. In both cases the studied structures – all the triangulations of a given point set or all token placements on a given graph – can be thought of as vertices of the so-called reconfiguration graph, in which two vertices are adjacent if the corresponding structures differ by a single elementary operation – by a flip of a diagonal in a triangulation or by a swap of tokens on adjacent vertices, respectively. We study the reconfiguration of one instance of a structure into another via (shortest) paths in the reconfiguration graph.
For triangulations of point sets in which each edge has a unique label and a flip transfers the label from the removed edge to the new edge, we prove a polynomial-time testable condition, called the Orbit Theorem, that characterizes when two triangulations of the same point set lie in the same connected component of the reconfiguration graph. The condition was first conjectured by Bose, Lubiw, Pathak and Verdonschot. We additionally provide a polynomial time algorithm that computes a reconfiguring flip sequence, if it exists. Our proof of the Orbit Theorem uses topological properties of a certain high-dimensional cell complex that has the usual reconfiguration graph as its 1-skeleton.
In the context of token swapping on a tree graph, we make partial progress on the problem of finding shortest reconfiguration sequences. We disprove the so-called Happy Leaf Conjecture and demonstrate the importance of swapping tokens that are already placed at the correct vertices. We also prove that a generalization of the problem to weighted coloured token swapping is NP-hard on trees but solvable in polynomial time on paths and stars.
AU - Masárová, Zuzana
ID - 7944
KW - reconfiguration
KW - reconfiguration graph
KW - triangulations
KW - flip
KW - constrained triangulations
KW - shellability
KW - piecewise-linear balls
KW - token swapping
KW - trees
KW - coloured weighted token swapping
SN - 978-3-99078-005-3
TI - Reconfiguration problems
ER -
TY - THES
AB - Algorithms in computational 3-manifold topology typically take a triangulation as an input and return topological information about the underlying 3-manifold. However, extracting the desired information from a triangulation (e.g., evaluating an invariant) is often computationally very expensive. In recent years this complexity barrier has been successfully tackled in some cases by importing ideas from the theory of parameterized algorithms into the realm of 3-manifolds. Various computationally hard problems were shown to be efficiently solvable for input triangulations that are sufficiently “tree-like.”
In this thesis we focus on the key combinatorial parameter in the above context: we consider the treewidth of a compact, orientable 3-manifold, i.e., the smallest treewidth of the dual graph of any triangulation thereof. By building on the work of Scharlemann–Thompson and Scharlemann–Schultens–Saito on generalized Heegaard splittings, and on the work of Jaco–Rubinstein on layered triangulations, we establish quantitative relations between the treewidth and classical topological invariants of a 3-manifold. In particular, among other results, we show that the treewidth of a closed, orientable, irreducible, non-Haken 3-manifold is always within a constant factor of its Heegaard genus.
AU - Huszár, Kristóf
ID - 8032
SN - 2663-337X
TI - Combinatorial width parameters for 3-dimensional manifolds
ER -