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Cellulose is the most abundant biopolymer on earth and the main load-bearing structure in plant cell walls. Cellulose microfibrils are laid down in a tight parallel array, surrounding plant cells like a corset. Orientation of microfibrils determines the direction of growth by directing turgor pressure to points of expansion (Somerville et al., 2004). Hence, cellulose deficient mutants usually show cell and organ swelling due to disturbed anisotropic cell expansion (reviewed in Endler and Persson, 2011). How do cellulose microfibrils gain their parallel orientation? First experiments in the 1960s suggested, that cortical microtubules aid the cellulose synthases on their way around the cell (Green, 1962; Ledbetter and Porter, 1963). This was proofed in 2006 through life cell imaging (Paredez et al., 2006). However, how this guidance was facilitated, remained unknown. Through a combinatory approach, including forward and reverse genetics together with advanced co-expression analysis, we identified pom2 as a cellulose deficient mutant. Map- based cloning revealed that the gene locus of POM2 corresponded to CELLULOSE SYNTHASE INTERACTING 1 (CSI1). Intriguingly, we previously found the CSI1 protein to interact with the putative cytosolic part of the primary cellulose synthases in a yeast-two-hybrid screen (Gu et al., 2010). Exhaustive cell biological analysis of the POM2/CSI1 protein allowed to determine its cellular function. Using spinning disc confocal microscopy, we could show that in the absence of POM2/CSI1, cellulose synthase complexes lose their microtubule-dependent trajectories in the plasma membrane. The loss of POM2/CSI1, however does not influence microtubule- dependent delivery of cellulose synthases (Bringmann et al., 2012). Consequently, POM2/CSI1 acts as a bridging protein between active cellulose synthases and cortical microtubules. This thesis summarizes three publications of the author, regarding the identification of proteins that connect cellulose synthases to the cytoskeleton. This involves the development of bioinformatics tools allowing candidate gene prediction through co-expression studies (Mutwil et al., 2009), identification of candidate genes through interaction studies (Gu et al., 2010), and determination of the cellular function of the candidate gene (Bringmann et al., 2012).

This work describes the synthesis and characterization of stimuli-responsive polymers made by reversible addition-fragmentation chain transfer (RAFT) polymerization and the investigation of their self-assembly into “smart” hydrogels. In particular the hydrogels were designed to swell at low temperature and could be reversibly switched to a collapsed hydrophobic state by rising the temperature. Starting from two constituents, a short permanently hydrophobic polystyrene (PS) block and a thermo-responsive poly(methoxy diethylene glycol acrylate) (PMDEGA) block, various gelation behaviors and switching temperatures were achieved. New RAFT agents bearing tert-butyl benzoate or benzoic acid groups, were developed for the synthesis of diblock, symmetrical triblock and 3-arm star block copolymers. Thus, specific end groups were attached to the polymers that facilitate efficient macromolecular characterization, e.g by routine 1H-NMR spectroscopy. Further, the carboxyl end-groups allowed functionalizing the various polymers by a fluorophore. Because reports on PMDEGA have been extremely rare, at first, the thermo-responsive behavior of the polymer was investigated and the influence of factors such as molar mass, nature of the end-groups, and architecture, was studied. The use of special RAFT agents enabled the design of polymer with specific hydrophobic and hydrophilic end-groups. Cloud points (CP) of the polymers proved to be sensitive to all molecular variables studied, namely molar mass, nature and number of the end-groups, up to relatively high molar masses. Thus, by changing molecular parameters, CPs of the PMDEGA could be easily adjusted within the physiological interesting range of 20 to 40°C. A second responsivity, namely to light, was added to the PMDEGA system via random copolymerization of MDEGA with a specifically designed photo-switchable azobenzene acrylate. The composition of the copolymers was varied in order to determine the optimal conditions for an isothermal cloud point variation triggered by light. Though reversible light-induced solubility changes were achieved, the differences between the cloud points before and after the irradiation were small. Remarkably, the response to light differed from common observations for azobenzene-based systems, as CPs decreased after UV-irradiation, i.e with increasing content of cis-azobenzene units. The viscosifying and gelling abilities of the various block copolymers made from PS and PMDEGA blocks were studied by rheology. Important differences were observed between diblock copolymers, containing one hydrophobic PS block only, the telechelic symmetrical triblock copolymers made of two associating PS termini, and the star block copolymers having three associating end blocks. Regardless of their hydrophilic block length, diblock copolymers PS11 PMDEGAn were freely flowing even at concentrations as high as 40 wt. %. In contrast, all studied symmetrical triblock copolymers PS8-PMDEGAn-PS8 formed gels at low temperatures and at concentrations as low as 3.5 wt. % at best. When heated, these gels underwent a gel-sol transition at intermediate temperatures, well below the cloud point where phase separation occurs. The gel-sol transition shifted to markedly higher transition temperatures with increasing length of the hydrophilic inner block. This effect increased also with the number of arms, and with the length of the hydrophobic end blocks. The mechanical properties of the gels were significantly altered at the cloud point and liquid-like dispersions were formed. These could be reversibly transformed into hydrogels by cooling. This thesis demonstrates that high molar mass PMDEGA is an easily accessible, presumably also biocompatible and at ambient temperature well water-soluble, non-ionic thermo-responsive polymer. PMDEGA can be easily molecularly engineered via the RAFT method, implementing defined end-groups, and producing different, also complex, architectures, such as amphiphilic triblock and star block copolymers, having an analogous structure to associative telechelics. With appropriate design, such amphiphilic copolymers give way to efficient, “smart” viscosifiers and gelators displaying tunable gelling and mechanical properties.

We introduce a theoretical framework for performing statistical hypothesis testing simultaneously over a fairly general, possibly uncountably infinite, set of null hypotheses. This extends the standard statistical setting for multiple hypotheses testing, which is restricted to a finite set. This work is motivated by numerous modern applications where the observed signal is modeled by a stochastic process over a continuum. As a measure of type I error, we extend the concept of false discovery rate (FDR) to this setting. The FDR is defined as the average ratio of the measure of two random sets, so that its study presents some challenge and is of some intrinsic mathematical interest. Our main result shows how to use the p-value process to control the FDR at a nominal level, either under arbitrary dependence of p-values, or under the assumption that the finite dimensional distributions of the p-value process have positive correlations of a specific type (weak PRDS). Both cases generalize existing results established in the finite setting, the latter one leading to a less conservative procedure. The interest of this approach is demonstrated in several non-parametric examples: testing the mean/signal in a Gaussian white noise model, testing the intensity of a Poisson process and testing the c.d.f. of i.i.d. random variables. Conceptually, an interesting feature of the setting advocated here is that it focuses directly on the intrinsic hypothesis space associated with a testing model on a random process, without referring to an arbitrary discretization.

For a sequence of Hilbert spaces and continuous linear operators the curvature is defined to be the composition of any two consecutive operators. This is modeled on the de Rham resolution of a connection on a module over an algebra. Of particular interest are those sequences for which the curvature is "small" at each step, e.g., belongs to a fixed operator ideal. In this context we elaborate the theory of Fredholm sequences and show how to introduce the Lefschetz number.

We say that (weak/strong) time duality holds for continuous time quasi-birth-and-death-processes if, starting from a fixed level, the first hitting time of the next upper level and the first hitting time of the next lower level have the same distribution. We present here a criterion for time duality in the case where transitions from one level to another have to pass through a given single state, the so-called bottleneck property. We also prove that a weaker form of reversibility called balanced under permutation is sufficient for the time duality to hold. We then discuss the general case.

We analyze a general class of difference operators containing a multi-well potential and a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we treat the eigenvalue problem as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix similar to the analysis for the Schrödinger operator, and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.

In the limit we analyze the generators of families of reversible jump processes in the n-dimensional space associated with a class of symmetric non-local Dirichlet forms and show exponential decay of the eigenfunctions. The exponential rate function is a Finsler distance, given as solution of certain eikonal equation. Fine results are sensitive to the rate functions being twice differentiable or just Lipschitz. Our estimates are similar to the semiclassical Agmon estimates for differential operators of second order. They generalize and strengthen previous results on the lattice.

The authors discuss the use of the discrepancy principle for statistical inverse problems, when the underlying operator is of trace class. Under this assumption the discrepancy principle is well defined, however a plain use of it may occasionally fail and it will yield sub-optimal rates. Therefore, a modification of the discrepancy is introduced, which takes into account both of the above deficiencies. For a variety of linear regularization schemes as well as for conjugate gradient iteration this modification is shown to yield order optimal a priori error bounds under general smoothness assumptions. A posteriori error control is also possible, however at a sub-optimal rate, in general. This study uses and complements previous results for bounded deterministic noise.

We study maximal subsemigroups of the monoid T(X) of all full transformations on the set X = N of natural numbers containing a given subsemigroup W of T(X), where each element of a given set U is a generator of T(X) modulo W. This note continues the study of maximal subsemigroups of the monoid of all full transformations on an infinite set.