Spanners of bounded degree graphs

A k-spanner of a graph G is a spanning subgraph of G in which the distance between any pair of vertices is at most k times the distance in G. We prove that for fixed k,w, the problem of deciding if a given graph has a k-spanner of treewidth w is fixed-parameter tractable on graphs of bounded degree. In particular, this implies that finding a k-spanner that is a tree (a tree k-spanner) is fixed-parameter tractable on graphs of bounded degree. In contrast, we observe that if the graph has only one vertex of unbounded degree, then Treek-Spanner is NP-complete for k?4.     

Implicit branching and parameterized partial cover problems

Covering problems are fundamental classical problems in optimization, computer science and complexity theory. Typically an input to these problems is a family of sets over a finite universe and the goal is to cover the elements of the universe with as few sets of the family as possible. The variations of covering problems include well-known problems like Set Cover, Vertex Cover, Dominating Set and Facility Location to name a few. Recently there has been a lot of study on partial covering problems, a natural generalization of covering problems. Here, the goal is not to cover all the elements but to cover the specified number of elements with the minimum number of sets. In this paper we study partial covering problems in graphs in the realm of parameterized complexity. Classical (non-partial) version of all these problems has been intensively studied in planar graphs and in graphs excluding a fixed graph H as a minor. However, the techniques developed for parameterized version of non-partial covering problems cannot be applied directly to their partial counterparts. The approach we use, to show that various partial covering problems are fixed parameter tractable on planar graphs, graphs of bounded local treewidth and graph excluding some graph as a minor, is quite different from previously known techniques. The main idea behind our approach is the concept of implicit branching. We find implicit branching technique to be interesting on its own and believe that it can be used for some other problems.     

On the Power of Las Vegas for One-Way Communication Complexity, OBDDs, and Finite Automata

The study of the computational power of randomized computations is one of the central tasks of complexity theory. The main goal of this paper is the comparison of the power of Las Vegas computation and deterministic respectively nondeterministic computation. We investigate the power of Las Vegas computation for the complexity measures of one-way communication, ordered binary decision diagrams, and finite automata.(i) For the one-way communication complexity of two-party protocols we show that Las Vegas communication can save at most one half of the deterministic one-way communication complexity. We also present a language for which this gap is tight.(ii) The result (i) is applied to show an at most polynomial gap between determinism and Las Vegas for ordered binary decision diagrams.(iii) For the size (i.e., the number of states) of finite automata we show that the size of Las Vegas finite automata recognizing a language L is at least the square root of the size of the minimal deterministic finite automaton recognizing L. Using a specific language we verify the optimality of this lower bound.     

Fast Minor Testing in Planar Graphs

Minor Containment is a fundamental problem in Algorithmic Graph Theory used as a subroutine in numerous graph algorithms. A model of a graph H in a graph G is a set of disjoint connected subgraphs of G indexed by the vertices of H, such that if {u,v} is an edge of H, then there is an edge of G between components C _u and C _v . A graph H is a minor of G if G contains a model of H as a subgraph. We give an algorithm that, given a planar n-vertex graph G and an h-vertex graph H, either finds in time $\mathcal{O}(2^{\mathcal{O}(h)} \cdot n +n^{2}\cdot\log n)$ a model of H in G, or correctly concludes that G does not contain H as a minor. Our algorithm is the first single-exponential algorithm for this problem and improves all previous minor testing algorithms in planar graphs. Our technique is based on a novel approach called partially embedded dynamic programming.     

DNA Break Mapping Reveals Topoisomerase II Activity Genome-Wide

Genomic DNA is under constant assault by endogenous and exogenous DNA damaging agents. DNA breakage can represent a major threat to genome integrity but can also be necessary for genome function. Here we present approaches to map DNA double-strand breaks (DSBs) and single-strand breaks (SSBs) at the genome-wide scale by two methods called DSB- and SSB-Seq, respectively. We tested these methods in human colon cancer cells and validated the results using the Topoisomerase II (Top2)-poisoning agent etoposide (ETO). Our results show that the combination of ETO treatment with break-mapping techniques is a powerful method to elaborate the pattern of Top2 enzymatic activity across the genome.     

Expanding the Toolbox of R-Selective Amine Transaminases by Identification and Characterization of New Members

Amine transaminases (ATAs) are used to synthesize enantiomerically pure amines, which are building blocks for pharmaceuticals and agrochemicals. R-selective ATAs belong to the fold type IV PLP-dependent enzymes, and different sequence-, structure- and substrate scope-based features have been identified in the past decade. However, our knowledge is still restricted due to the limited number of characterized (R)-ATAs, with additional bias towards fungal origin. We aimed to expand the toolbox of (R)-ATAs and contribute to the understanding of this enzyme subfamily. We identified and characterized four new (R)-ATAs. The ATA from Exophiala sideris contains a motif characteristic for d -ATAs, which was previously believed to be a disqualifying factor for (R)-ATA activity. The crystal structure of the ATA from Shinella is the first from a Gram-negative bacterium. The ATAs from Pseudonocardia acaciae and Tetrasphaera japonica are the first characterized (R)-ATAs with a shortened/missing N-terminal helix. The active-site charges vary significantly between the new and known ATAs, correlating with their diverging substrate scope.     

Production and Emulsifying Effect of Polyglycerol and Fatty Acid Esters with Varying Degrees of Esterification

Esters with acyl groups can be formed by the esterification of polyglycerol. The purpose of the present study was to produce fatty acid esters [hexanoic (caproic), octanoic (caprylic), decanoic (capric), dodecanoic (lauric), tetradecanoic (myristic), hexadecanoic (palmitic), octadecanoic (stearic)] and polyglycerol (average number‐of degrees of polymerization of 5) with varying degrees of esterification and to examine their emulsifying properties. A number of fundamental catalysts of polyglycerol acylation reactions by methyl esters of carboxylic acid were studied, and sodium methoxide was found to be the best choice. The temperature rate of transesterification increased from 180 to 220 °C with the fatty acid chain alkyl residue. Synthesized mono‐, di‐, tri‐, tetra‐, and heptaesters of various fatty acids and polyglycerol provided the highest hydroxyl values from 15 to 815 mg KOH g^?1 and saponification values from 82 to 321 mg KOH g^?1. The emulsifying properties were assessed for all polyglycerol and fatty acid esters, with results showing maximum emulsifying effect for tri‐ and tetraesters of capric, lauric, and caprylic acids. Regardless of the hydrophilic–lipophilic balance value (HLB) of polyglycerol esters and carboxylic acid, a 4:1 ratio of sunflower oil to water formed a water‐in‐oil type emulsion. When mixing oil and water in a 1:1 ratio, mono‐ and diesters of polyglycerol formed an oil‐in‐water type emulsion, heptaesters formed a water‐in‐oil type emulsion, and tri‐ and tetraesters formed both of types of emulsions, depending on the length of the acid hydrocarbon radicals.