On Split-Coloring Problems

We study a new coloring concept which generalizes the classical vertex coloring problem in a graph by extending the notion of stable sets to split graphs. First of all, we propose the packing problem of finding the split graph of maximum size where a split graph is a graph G = (V,E) in which the vertex set V can be partitioned into a clique K and a stable set S. No condition is imposed on the edges linking vertices in S to the vertices in K. This maximum split graph problem gives rise to an associated partitioning problem that we call the split-coloring problem. Given a graph, the objective is to cover all his vertices by a least number of split graphs. Definitions related to this new problem are introduced. We mention some polynomially solvable cases and describe open questions on this are

On the minimum and maximum selective graph coloring problems in some graph classes

Given a graph together with a partition of its vertex set, the minimum selective coloring problem consists of selecting one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is minimum. The contribution of this paper is twofold. First, we investigate the complexity status of the minimum selective coloring problem in some specific graph classes motivated by some models described in Demange et al. (2015). Second, we introduce a new problem that corresponds to the worst situation in the minimum selective coloring; the maximum selective coloring problem aims to select one vertex per partition set such that the chromatic number of the subgraph induced by the selected vertices is maximum. We motivat

Integer Programming Formulations and Cutting Plane Algorithms for the Maximum Selective Tree Problem

This paper considers the Maximum Selective Tree Problem (MSelTP) as a generalization of the Maximum Induced Tree problem. Given an undirected graph with a partition of its vertex set into clusters, MSelTP aims to choose the maximum number of vertices such that at most one vertex per cluster is selected and the graph induced by the selected vertices is a tree. To the best of our knowledge, MSelTP has not been studied before although several related optimization problems have been investigated in the literature. We propose two mixed integer programming formulations for MSelTP; one based on connectivity constraints, the other based on cycle elimination constraints. In addition, we develop two exact cutting plane procedures to solve the problem to optimality. On graphs with up to 25 clusters, up to 250 vertices, and varying densities, we conduct computational experiments to compare the results of two solution procedures with solving a compact integer programming formulation of MSelTP. Our experiments indicate that the algorithm CPAXnY outperforms the other procedures overall except for graphs with low density and large cluster size, and that the algorithm CPAX yields better results in terms of the average time of instances optimally solved and the overall average time

Hardness and approximation for the geodetic set problem in some graph classes

In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of vertices from $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum cardinality. In this paper, we prove that solving the \textsc{MGS} problem is NP-hard on planar graphs with a maximum degree six and line graphs. We also show that unless $P=NP$, there is no polynomial time algorithm to solve the \textsc{MGS} problem with sublogarithmic approximation factor (in terms of the number of vertices) even on graphs with diameter $2$. On the positive side, we give an $O\left(\sqrt[3]{n}\log n\right)$-approximation algorithm for the \textsc{MGS} problem on general graphs of order $n$. We also give a $3$-approximation algorithm for the \textsc{MGS} problem on the family of solid grid graphs which is a subclass of planar graphs

Clonal exhaustion as a mechanism to protect against severe immunopathology and death from an overwhelming CD8 T cell response

The balance between protective immunity and immunopathology often determines the fate of the virus-infected host. How rapidly virus is cleared is a function of initial viral load, viral replication rate, and efficiency of the immune response. Here, we demonstrate, with three different inocula of lymphocytic choriomeningitis virus (LCMV), how the race between virus replication and T cell responses can result in different disease outcomes. A low dose of LCMV generated efficient CD8 T effector cells, which cleared the virus with minimal lung and liver pathology. A high dose of LCMV resulted in clonal exhaustion of T cell responses, viral persistence, and little immunopathology. An intermediate dose only partially exhausted the T cell responses and resulted in significant mortality, and the surviving mice developed viral persistence and massive immunopathology, including necrosis of the lungs and liver. This suggests that for non-cytopathic viruses like LCMV, hepatitis C virus, and hepatitis B virus, clonal exhaustion may be a protective mechanism preventing severe immunopathology and death

Diel metabolomics analysis of a hot spring chlorophototrophic microbial mat leads to new hypotheses of community member metabolisms

© 2015 Kim, Nowack, Olsen, Becraft, Wood, Thiel, Klapper, Kühl, Fredrickson, Bryant, Ward and Metz. Dynamic environmental factors such as light, nutrients, salt, and temperature continuously affect chlorophototrophic microbial mats, requiring adaptive and acclimative responses to stabilize composition and function. Quantitative metabolomics analysis can provide insights into metabolite dynamics for understanding community response to such changing environmental conditions. In this study, we quantified volatile organic acids, polar metabolites (amino acids, glycolytic and citric acid cycle intermediates, nucleobases, nucleosides, and sugars), wax esters, and polyhydroxyalkanoates, resulting in the identification of 104 metabolites and related molecules in thermal chlorophototrophic microbial mat cores collected over a diel cycle in Mushroom Spring, Yellowstone National Park. A limited number of predominant taxa inhabit this community and their functional potentials have been previously identified through metagenomic and metatranscriptomic analyses and in situ metabolisms, and metabolic interactions among these taxa have been hypothesized. Our metabolomics results confirmed the diel cycling of photorespiration (e.g. glycolate) and fermentation (e.g. acetate, propionate, and lactate) products, the carbon storage polymers polyhydroxyalkanoates, and dissolved gases (e.g. H2 and CO2) in the waters overlying the mat, which were hypothesized to occur in major mat chlorophototrophic community members. In addition, we have formulated the following new hypotheses: 1) the morning hours are a time of biosynthesis of amino acids, DNA, and RNA; 2) photo-inhibited cells may also produce lactate via fermentation as an alternate metabolism; 3) glycolate and lactate are exchanged among Synechococcus and Roseiflexus spp.; and 4) fluctuations in many metabolite pools (e.g. wax esters) at different times of day result from species found at different depths within the mat responding to temporal differences in their niches

Management of children with congenital nephrotic syndrome: challenging treatment paradigms

Background: Management of children with congenital nephrotic syndrome (CNS) is challenging. Bilateral nephrectomies followed by dialysis and transplantation are practiced in most centres, but conservative treatment may also be effective. / Methods: We conducted a 6-year review across members of the European Society for Paediatric Nephrology Dialysis Working Group to compare management strategies and their outcomes in children with CNS. / Results: Eighty children (50% male) across 17 tertiary nephrology units in Europe were included (mutations in NPHS1, n = 55; NPHS2, n = 1; WT1, n = 9; others, n = 15). Excluding patients with mutations in WT1, antiproteinuric treatment was given in 42 (59%) with an increase in S-albumin in 70% by median 6 (interquartile range: 3–8) g/L (P < 0.001). Following unilateral nephrectomy, S-albumin increased by 4 (1–8) g/L (P = 0.03) with a reduction in albumin infusion dose by 5 (2–9) g/kg/week (P = 0.02). Median age at bilateral nephrectomies (n = 29) was 9 (7–16) months. Outcomes were compared between two groups of NPHS1 patients: those who underwent bilateral nephrectomies (n = 25) versus those on conservative management (n = 17). The number of septic or thrombotic episodes and growth were comparable between the groups. The response to antiproteinuric treatment, as well as renal and patient survival, was independent of NPHS1 mutation type. At final follow-up (median age 34 months) 20 (80%) children in the nephrectomy group were transplanted and 1 died. In the conservative group, 9 (53%) remained without dialysis, 4 (24%; P < 0.001) were transplanted and 2 died. / Conclusion: An individualized, stepwise approach with prolonged conservative management may be a reasonable alternative to early bilateral nephrectomies and dialysis in children with CNS and NPHS1 mutations. Further prospective studies are needed to define indications for unilateral nephrectomy

Cold atoms in space: community workshop summary and proposed road-map

We summarise the discussions at a virtual Community Workshop on Cold Atoms in Space concerning the status of cold atom technologies, the prospective scientific and societal opportunities offered by their deployment in space, and the developments needed before cold atoms could be operated in space. The cold atom technologies discussed include atomic clocks, quantum gravimeters and accelerometers, and atom interferometers. Prospective applications include metrology, geodesy and measurement of terrestrial mass change due to, e.g., climate change, and fundamental science experiments such as tests of the equivalence principle, searches for dark matter, measurements of gravitational waves and tests of quantum mechanics. We review the current status of cold atom technologies and outline the requirements for their space qualification, including the development paths and the corresponding technical milestones, and identifying possible pathfinder missions to pave the way for missions to exploit the full potential of cold atoms in space. Finally, we present a first draft of a possible road-map for achieving these goals, that we propose for discussion by the interested cold atom, Earth Observation, fundamental physics and other prospective scientific user communities, together with the European Space Agency (ESA) and national space and research funding agencies