On the (non-)existence of polynomial kernels for Pl-free edge modification problems

Given a graph G = (V,E) and an integer k, an edge modification problem for a graph property P consists in deciding whether there exists a set of edges F of size at most k such that the graph H = (V,E \vartriangle F) satisfies the property P. In the P edge-completion problem, the set F of edges is constrained to be disjoint from E; in the P edge-deletion problem, F is a subset of E; no constraint is imposed on F in the P edge-edition problem. A number of optimization problems can be expressed in terms of graph modification problems which have been extensively studied in the context of parameterized complexity. When parameterized by the size k of the edge set F, it has been proved that if P is an hereditary property characterized by a finite set of forbidden induced subgraphs, then the three P edge-modification problems are FPT. It was then natural to ask whether these problems also admit a polynomial size kernel. Using recent lower bound techniques, Kratsch and Wahlstrom answered this question negatively. However, the problem remains open on many natural graph classes characterized by forbidden induced subgraphs. Kratsch and Wahlstrom asked whether the result holds when the forbidden subgraphs are paths or cycles and pointed out that the problem is already open in the case of P4-free graphs (i.e. cographs). This paper provides positive and negative results in that line of research. We prove that parameterized cograph edge modification problems have cubic vertex kernels whereas polynomial kernels are unlikely to exist for the Pl-free and Cl-free edge-deletion problems for large enough l

Cell wall characteristics during sexual reproduction of Mougeotia sp. (Zygnematophyceae) revealed by electron microscopy, glycan microarrays and RAMAN spectroscopy

Mougeotia spp. collected from field samples were investigated for their conjugation morphology by light-, fluorescence-, scanning- and transmission electron microscopy. During a scalarifom conjugation, the extragametangial zygospores were initially surrounded by a thin cell wall that developed into a multi-layered zygospore wall. Maturing zygospores turned dark brown and were filled with storage compounds such as lipids and starch. While M. parvula had a smooth surface, M. disjuncta had a punctated surface structure and a prominent suture. The zygospore wall consisted of a polysaccharide rich endospore, followed by a thin layer with a lipid-like appaerance, a massive electron dense mesospore and a very thin exospore composed of polysaccharides. Glycan microarray analysis of zygospores of different developmental stages revealed the occurrence of pectins and hemicelluloses, mostly composed of homogalacturonan (HG), xyloglucans, xylans, arabino-galactan proteins and extensins. In situ localization by the probe OG7-13AF 488 labelled HG in young zygospore walls, vegetative filaments and most prominently in conjugation tubes and cross walls. Raman imaging showed the distribution of proteins, lipids, carbohydrates and aromatic components of the mature zygospore with a spatial resolution of ~ 250 nm. The carbohydrate nature of the endo- and exospore was confirmed and in-between an enrichment of lipids and aromatic components, probably algaenan or a sporopollenin-like material. Taken together, these results indicate that during zygospore formation, reorganizations of the cell walls occured, leading to a resistant and protective structure

Results and recommendations from an intercomparison of six Hygroscopicity-TDMA systems

The performance of six custom-built Hygrocopicity-Tandem Differential Mobility Analyser (H-TDMA) systems was investigated in the frame of an international calibration and intercomparison workshop held in Leipzig, February 2006. The goal of the workshop was to harmonise H-TDMA measurements and develop recommendations for atmospheric measurements and their data evaluation. The H-TDMA systems were compared in terms of the sizing of dry particles, relative humidity (RH) uncertainty, and consistency in determination of number fractions of different hygroscopic particle groups. The experiments were performed in an air-conditioned laboratory using ammonium sulphate particles or an external mixture of ammonium sulphate and soot particles. The sizing of dry particles of the six H-TDMA systems was within 0.2 to 4.2% of the selected particle diameter depending on investigated size and individual system. Measurements of ammonium sulphate aerosol found deviations equivalent to 4.5% RH from the set point of 90% RH compared to results from previous experiments in the literature. Evaluation of the number fraction of particles within the clearly separated growth factor modes of a laboratory generated externally mixed aerosol was done. The data from the H-TDMAs was analysed with a single fitting routine to investigate differences caused by the different data evaluation procedures used for each H-TDMA. The differences between the H-TDMAs were reduced from +12/-13% to +8/-6% when the same analysis routine was applied. We conclude that a common data evaluation procedure to determine number fractions of externally mixed aerosols will improve the comparability of H-TDMA measurements. It is recommended to ensure proper calibration of all flow, temperature and RH sensors in the systems. It is most important to thermally insulate the aerosol humidification unit and the second DMA and to monitor these temperatures to an accuracy of 0.2 degrees C. For the correct determination of external mixtures, it is necessary to take into account size-dependent losses due to diffusion in the plumbing between the DMAs and in the aerosol humidification unit.Peer reviewe

Prevalence of Mental Health Problems and Factors Associated with Psychological Distress in Mountain Exercisers: A Cross-Sectional Study in Austria

Knowledge about potential protective factors against mental health problems is highly needed. Regular physical activity (PA) in an outdoor environment, like mountain exercising, might reduce psychological distress. Therefore, the aims of the present study were to assess the prevalence of mental health problems in mountain exercisers and to detect factors associated with psychological distress. In a cross-sectional design, we collected self-reported data of 1,536 Austrian mountain exercisers. The prevalence of mental health problems and psychological distress (Kessler Psychological Distress Scale), the level of PA International Physical Activity Questionnaire, and affective valence during PA (Feeling Scale) were obtained. Stepwise multiple linear regression analysis was conducted to assess factors influencing psychological distress. The prevalence of mental health problems in Austrian mountain exercisers was 14%. Health-enhancing PA level and higher affective valence during PA were significantly associated with lower psychological distress. Minimal PA level was not significantly associated with lower psychological distress compared to inactive PA level. Marital status, education, alpine association membership, and body mass index did not show a significant influence on psychological distress. The prevalence of mental health problems seems to be lower in Austrian mountain exercisers compared to the European population. A health-enhancing PA level and affective valence increasing forms of PA were shown to be associated with lower psychological distress. Results might lead to interventional studies focusing on the potential of outdoor PA, e.g., mountain exercise, as an adjunct treatment in people at risk or with mental health problems.(VLID)2157397Version of recor

Vertex Cover Kernelization Revisited: Upper and Lower Bounds for a Refined Parameter

An important result in the study of polynomial-time preprocessing shows that there is an algorithm which given an instance (G,k) of Vertex Cover outputs an equivalent instance (G',k') in polynomial time with the guarantee that G' has at most 2k' vertices (and thus O((k')^2) edges) with k' <= k. Using the terminology of parameterized complexity we say that k-Vertex Cover has a kernel with 2k vertices. There is complexity-theoretic evidence that both 2k vertices and Theta(k^2) edges are optimal for the kernel size. In this paper we consider the Vertex Cover problem with a different parameter, the size fvs(G) of a minimum feedback vertex set for G. This refined parameter is structurally smaller than the parameter k associated to the vertex covering number vc(G) since fvs(G) <= vc(G) and the difference can be arbitrarily large. We give a kernel for Vertex Cover with a number of vertices that is cubic in fvs(G): an instance (G,X,k) of Vertex Cover, where X is a feedback vertex set for G, can be transformed in polynomial time into an equivalent instance (G',X',k') such that |V(G')| <= 2k and |V(G')| <= O(|X'|^3). A similar result holds when the feedback vertex set X is not given along with the input. In sharp contrast we show that the Weighted Vertex Cover problem does not have a polynomial kernel when parameterized by the cardinality of a given vertex cover of the graph unless NP is in coNP/poly and the polynomial hierarchy collapses to the third level.Comment: Published in "Theory of Computing Systems" as an Open Access publicatio

Radiative corrections to deeply virtual Compton scattering

We discuss possibilities of measurement of deeply virtual Compton scattering amplitudes via different asymmetries in order to access the underlying skewed parton distributions. Perturbative one-loop coefficient functions and two-loop evolution kernels, calculated recently by a tentative use of residual conformal symmetry of QCD, are used for a model dependent numerical estimation of scattering amplitudes.Comment: 9 pages LaTeX, 3 figures, czjphyse.cls required Talk given by D. M\"uller at Inter. Workshop ``PRAHA-Spin99'', Prague, Sept. 6-11, 199

Parameterized bounded-depth Frege is not optimal

A general framework for parameterized proof complexity was introduced by Dantchev, Martin, and Szeider [9]. There the authors concentrate on tree-like Parameterized Resolution-a parameterized version of classical Resolution-and their gap complexity theorem implies lower bounds for that system. The main result of the present paper significantly improves upon this by showing optimal lower bounds for a parameterized version of bounded-depth Frege. More precisely, we prove that the pigeonhole principle requires proofs of size n in parameterized bounded-depth Frege, and, as a special case, in dag-like Parameterized Resolution. This answers an open question posed in [9]. In the opposite direction, we interpret a well-known technique for FPT algorithms as a DPLL procedure for Parameterized Resolution. Its generalization leads to a proof search algorithm for Parameterized Resolution that in particular shows that tree-like Parameterized Resolution allows short refutations of all parameterized contradictions given as bounded-width CNF's

The immersion mode ice nucleation behavior of mineral dusts: A comparison of different pure and surface modified dusts

In this study we present results from immersion freezing experiments with size-segregated mineral dust particles. Besides two already existing data sets for Arizona Test Dust (ATD), and Fluka kaolinite, we show two new data sets for illite-NX, which consists mainly of illite, a clay mineral, and feldspar, a common crustal material. The experiments were carried out with the Leipzig Aerosol Cloud Interaction Simulator. After comparing the different dust samples, it became obvious that the freezing ability was positively correlated with the K-feldspar content. Furthermore, a comparison of the composition of the ATD, illite-NX, and feldspar samples suggests that within the K-feldspars, microcline is more ice nucleation active than orthoclase. A coating with sulfuric acid leads to a decrease in the ice nucleation ability of all mineral dusts, with the effect being more pronounced for the feldspar sample. Key Points The freezing ability of mineral dusts correlated with the K-feldspar contentAmong feldspars, microcline shows a better ice nucleation ability than orthoclaseAfter coating, all investigated dusts feature a similar ice nucleation abilit

Solving Problems on Graphs of High Rank-Width

A modulator of a graph G to a specified graph class H is a set of vertices whose deletion puts G into H. The cardinality of a modulator to various tractable graph classes has long been used as a structural parameter which can be exploited to obtain FPT algorithms for a range of hard problems. Here we investigate what happens when a graph contains a modulator which is large but "well-structured" (in the sense of having bounded rank-width). Can such modulators still be exploited to obtain efficient algorithms? And is it even possible to find such modulators efficiently? We first show that the parameters derived from such well-structured modulators are strictly more general than the cardinality of modulators and rank-width itself. Then, we develop an FPT algorithm for finding such well-structured modulators to any graph class which can be characterized by a finite set of forbidden induced subgraphs. We proceed by showing how well-structured modulators can be used to obtain efficient parameterized algorithms for Minimum Vertex Cover and Maximum Clique. Finally, we use well-structured modulators to develop an algorithmic meta-theorem for deciding problems expressible in Monadic Second Order (MSO) logic, and prove that this result is tight in the sense that it cannot be generalized to LinEMSO problems.Comment: Accepted at WADS 201