Properties of Random Graphs via Boltzmann Samplers

This work is devoted to the understanding of properties of random graphs from graph classes with structural constraints. We propose a method that is based on the analysis of the behaviour of Boltzmann sampler algorithms, and may be used to obtain precise estimates for the maximum degree and maximum size of a biconnected block of a “typical” member of the class in question. We illustrate how our method works on several graph classes, namely dissections and triangulations of convex polygons, embedded trees, and block and cactus graphs

Properties of Random Graphs via Boltzmann Samplers

This work is devoted to the understanding of properties of random graphs from graph classes with structural constraints. We propose a method that is based on the analysis of the behaviour of Boltzmann sampler algorithms, and may be used to obtain precise estimates for the maximum degree and maximum size of a biconnected block of a "typical'' member of the class in question. We illustrate how our method works on several graph classes, namely dissections and triangulations of convex polygons, embedded trees, and block and cactus graphs

On Euclidean Vehicle Routing with Allocation

The (Euclidean) Vehicle Routing Allocation Problem (VRAP) is a generalization of Euclidean TSP. We do not require that all points lie on the salesman tour. However, points that do not lie on the tour are allocated, i.e., they are directly connected to the nearest tour point, paying a higher (per-unit) cost. More formally, the input is a set of n points P ⊂ Rd and functions α: P → [0, ∞) and β: P → [1, ∞). We wish to compute a subset T ⊆ P and a salesman tour π through T such that the total length of the tour plus the total allocation cost is minimum. The allocation cost for a single point p ∈ P \ T is α(p) + β(p) · d(p, ( q), where q ∈ T is the nearest point on the tour. We give a PTAS with complexity O n log d+3) n for this problem. Moreover, we propose an O (n polylog (n))-time PTAS for the Steiner variant of this problem. This dramatically improves a recent result of Armon et al. [3]

Technische Universität München Fakultät für Informatik Assignment Problem with Constraints

ii Ich versichere, dass ich diese Diplomarbeit selbständig verfasst und nur die angegebe-nen Quellen und Hilfsmittel verwendet habe

Cellulose carbamate derived cellulose thin films

Cellulose carbamate (CC) was employed as a water-soluble precursor in the manufacturing of cellulose based thin films using the spin coating technique. An intriguing observation was that during spin coating of CC from alkaline aqueous solutions, regeneration to cellulose was accomplished without the addition of any further chemicals. After rinsing, homogeneous thin films with tunable layer thickness in a range between 20 and 80 nm were obtained. Further, CC was blended with cellulose xanthate in different ratios (3:1, 1:1, 1:3) and after regeneration the properties of the resulting all-cellulose blend thin films were investigated. We could observe some slight indications of phase separation by means of atomic force microscopy. The layer thickness of the blend thin films was nearly independent of the ratio of the components, with values between 50 and 60 nm for the chosen conditions. The water uptake capability (80–90% relative to the film mass) determined by H2O/D2O exchange in a quartz crystal microbalance was independent of the blend ratio.Peer reviewe

Unraveling the Mechanics of a Repeat-Protein Nanospring: From Folding of Individual Repeats to Fluctuations of the Superhelix.

Tandem-repeat proteins comprise small secondary structure motifs that stack to form one-dimensional arrays with distinctive mechanical properties that are proposed to direct their cellular functions. Here, we use single-molecule optical tweezers to study the folding of consensus-designed tetratricopeptide repeats (CTPRs), superhelical arrays of short helix-turn-helix motifs. We find that CTPRs display a spring-like mechanical response in which individual repeats undergo rapid equilibrium fluctuations between partially folded and unfolded conformations. We rationalize the force response using Ising models and dissect the folding pathway of CTPRs under mechanical load, revealing how the repeat arrays form from the center toward both termini simultaneously. Most strikingly, we also directly observe the protein's superhelical tertiary structure in the force signal. Using protein engineering, crystallography, and single-molecule experiments, we show that the superhelical geometry can be altered by carefully placed amino acid substitutions, and we examine how these sequence changes affect intrinsic repeat stability and inter-repeat coupling. Our findings provide the means to dissect and modulate repeat-protein stability and dynamics, which will be essential for researchers to understand the function of natural repeat proteins and to exploit artificial repeats proteins in nanotechnology and biomedical applications.Eric Reid Fund for Methodology from the British Biochemical Society AstraZenec

Multiplexing molecular tension sensors reveals piconewton force gradient across talin-1

Förster resonance energy transfer (FRET)-based tension sensor modules (TSMs) are available for investigating how distinct proteins bear mechanical forces in cells. Yet, forces in the single piconewton (pN) regime remain difficult to resolve, and tools for multiplexed tension sensing are lacking. Here, we report the generation and calibration of a genetically encoded, FRET-based biosensor called FL-TSM, which is characterized by a near-digital force response and increased sensitivity at 3–5 pN. In addition, we present a method allowing the simultaneous evaluation of coexpressed tension sensor constructs using two-color fluorescence lifetime microscopy. Finally, we introduce a procedure to calculate the fraction of mechanically engaged molecules within cells. Application of these techniques to new talin biosensors reveals an intramolecular tension gradient across talin-1 that is established upon integrin-mediated cell adhesion. The tension gradient is actomyosin- and vinculin-dependent and sensitive to the rigidity of the extracellular environment