Different Approaches to Proof Systems

The classical approach to proof complexity perceives proof systems as deterministic, uniform, surjective, polynomial-time computable functions that map strings to (propositional) tautologies. This approach has been intensively studied since the late 70’s and a lot of progress has been made. During the last years research was started investigating alternative notions of proof systems. There are interesting results stemming from dropping the uniformity requirement, allowing oracle access, using quantum computations, or employing probabilism. These lead to different notions of proof systems for which we survey recent results in this paper

Bounded Representations of Interval and Proper Interval Graphs

Klavik et al. [arXiv:1207.6960] recently introduced a generalization of recognition called the bounded representation problem which we study for the classes of interval and proper interval graphs. The input gives a graph G and in addition for each vertex v two intervals L_v and R_v called bounds. We ask whether there exists a bounded representation in which each interval I_v has its left endpoint in L_v and its right endpoint in R_v. We show that the problem can be solved in linear time for interval graphs and in quadratic time for proper interval graphs. Robert's Theorem states that the classes of proper interval graphs and unit interval graphs are equal. Surprisingly the bounded representation problem is polynomially solvable for proper interval graphs and NP-complete for unit interval graphs [Klav\'{\i}k et al., arxiv:1207.6960]. So unless P = NP, the proper and unit interval representations behave very differently. The bounded representation problem belongs to a wider class of restricted representation problems. These problems are generalizations of the well-understood recognition problem, and they ask whether there exists a representation of G satisfying some additional constraints. The bounded representation problems generalize many of these problems

An animal model for the juvenile non-alcoholic fatty liver disease and non-alcoholic steatohepatitis

11Non Alcoholic Fatty Liver Disease (NAFLD) and Non-Alcoholic Steatohepatitis (NASH) are the hepatic manifestations of the metabolic syndrome; worrisome is the booming increase in pediatric age. To recreate the full spectrum of juvenile liver pathology and investigate the gender impact, male and female C57Bl/6 mice were fed with high fat diet plus fructose in the drinking water (HFHC) immediately after weaning (equal to 3-years old human), and disease progression followed for 16 weeks, until adults (equal to 30-years old human). 100% of subjects of both genders on HFHC diet developed steatosis in 4weeks, and some degree of fibrosis in 8weeks, with the 86% of males and 15% of females presenting a stage 2 fibrosis at 16weeks. Despite a similar final liver damage both groups, a sex difference in the pathology progression was observed. Alterations in glucose homeostasis, dyslipidemia, hepatomegaly and obese phenotype were evident from the very beginning in males with an increased hepatic inflammatory activity. Conversely, such alterations were present in females only at the end of the HFHC diet (with the exception of insulin resistance and the hepatic inflammatory state). Interestingly, only females showed an altered hepatic redox state. This juvenile model appears a good platform to unravel the underlying gender dependent mechanisms in the progression from NAFLD to NASH, and to characterize novel therapeutic approaches.openopenMarin, Veronica; Rosso, Natalia; Dal Ben, Matteo; Raseni, Alan; Boschelle, Manuela; Degrassi, Cristina; Nemeckova, Ivana; Nachtigal, Petr; Avellini, Claudio; Tiribelli, Claudio; Gazzin, SilviaMarin, Veronica; Rosso, NATALIA CAROLINA; DAL BEN, Matteo; Raseni, Alan; Boschelle, Manuela; Degrassi, Cristina; Nemeckova, Ivana; Nachtigal, Petr; Avellini, Claudio; Tiribelli, Claudio; Gazzin, Silvi

Parameterized complexity of coloring problems: Treewidth versus vertex cover

AbstractWe compare the fixed parameter complexity of various variants of coloring problems (including List Coloring, Precoloring Extension, Equitable Coloring, L(p,1)-Labeling and Channel Assignment) when parameterized by treewidth and by vertex cover number. In most (but not all) cases we conclude that parametrization by the vertex cover number provides a significant drop in the complexity of the problems