Between Treewidth and Clique-width

Many hard graph problems can be solved efficiently when restricted to graphs of bounded treewidth, and more generally to graphs of bounded clique-width. But there is a price to be paid for this generality, exemplified by the four problems MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set that are all FPT parameterized by treewidth but none of which can be FPT parameterized by clique-width unless FPT = W[1], as shown by Fomin et al [7, 8]. We therefore seek a structural graph parameter that shares some of the generality of clique-width without paying this price. Based on splits, branch decompositions and the work of Vatshelle [18] on Maximum Matching-width, we consider the graph parameter sm-width which lies between treewidth and clique-width. Some graph classes of unbounded treewidth, like distance-hereditary graphs, have bounded sm-width. We show that MaxCut, Graph Coloring, Hamiltonian Cycle and Edge Dominating Set are all FPT parameterized by sm-width

Investigating the evolution of major Northern Hemisphere ice sheets during the last glacial-interglacial cycle

A 2.5-dimensional climate model of intermediate complexity, CLIMBER-2, fully coupled with the GREMLINS 3-D thermo-mechanical ice sheet model is used to simulate the evolution of major Northern Hemisphere ice sheets during the last glacial-interglacial cycle and to investigate the ice sheets responses to both insolation and atmospheric CO<sub>2</sub> concentration. This model reproduces the main phases of advance and retreat of Northern Hemisphere ice sheets during the last glacial cycle, although the amplitude of these variations is less pronounced than those based on sea level reconstructions. At the last glacial maximum, the simulated ice volume is 52.5×10<sup>15</sup> m<sup>3</sup> and the spatial distribution of both the American and Eurasian ice complexes is in reasonable agreement with observations, with the exception of the marine parts of these former ice sheets. <br> A set of sensitivity studies has also been performed to assess the sensitivity of the Northern Hemisphere ice sheets to both insolation and atmospheric CO<sub>2</sub>. Our results suggest that the decrease of summer insolation is the main factor responsible for the early build up of the North American ice sheet around 120 kyr BP, in agreement with benthic foraminifera δ<sup>18</sup>O signals. In contrast, low insolation and low atmospheric CO<sub>2</sub> concentration are both necessary to trigger a long-lasting glaciation over Eurasia

Nanopores: maltoporin channel as a sensor for maltodextrin and lambda-phage

BACKGROUND: To harvest nutrition from the outside bacteria e.g. E. coli developed in the outer cell wall a number of sophisticated channels called porins. One of them, maltoporin, is a passive specific channel for the maltodextrin uptake. This channel was also named LamB as the bacterial virus phage Lambda mis-uses this channel to recognise the bacteria. The first step is a reversible binding followed after a lag phase by DNA injection. To date little is known about the binding capacity and less on the DNA injection mechanism. To elucidate the mechanism and to show the sensitivity of our method we reconstituted maltoporin in planar lipid membranes. Application of an external transmembrane electric field causes an ion current across the channel. Maltoporin channel diameter is around a few Angstroem. At this size the ion current is extremely sensitive to any modification of the channels surface. Protein conformational changes, substrate binding etc will cause fluctuations reflecting the molecular interactions with the channel wall. The recent improvement in ion current fluctuation analysis allows now studying the interaction of solutes with the channel on a single molecular level. RESULTS: We could demonstrate the asymmetry of the bacterial phage Lambda binding to its natural receptor maltoporin. CONCLUSION: We suggest that this type of measurement can be used as a new type of biosensors

Mixed quantum state detection with inconclusive results

We consider the problem of designing an optimal quantum detector with a fixed rate of inconclusive results that maximizes the probability of correct detection, when distinguishing between a collection of mixed quantum states. We develop a sufficient condition for the scaled inverse measurement to maximize the probability of correct detection for the case in which the rate of inconclusive results exceeds a certain threshold. Using this condition we derive the optimal measurement for linearly independent pure-state sets, and for mixed-state sets with a broad class of symmetries. Specifically, we consider geometrically uniform (GU) state sets and compound geometrically uniform (CGU) state sets with generators that satisfy a certain constraint. We then show that the optimal measurements corresponding to GU and CGU state sets with arbitrary generators are also GU and CGU respectively, with generators that can be computed very efficiently in polynomial time within any desired accuracy by solving a semidefinite programming problem.Comment: Submitted to Phys. Rev.

Corrigendum to "Influence of ablation-related processes in the build-up of simulated Northern Hemisphere ice sheets during the last glacial cycle" published in The Cryosphere, 7, 681–698, 2013

No abstract available

Last interglacial temperature evolution – a model inter-comparison

Abstract. There is a growing number of proxy-based reconstructions detailing the climatic changes during the Last Interglacial period. This period is of special interest because large parts of the globe were characterized by a warmer-than-present-day climate, making this period an interesting test bed for climate models in the light of projected global warming. However, mainly because synchronizing the different records is difficult, there is no consensus on a global picture of Last Interglacial temperature changes. Here we present the first model inter-comparison of transient simulations covering the Last Interglacial period. By comparing the different simulations we aim at investigating the robustness of the simulated surface air temperature evolution. The model inter-comparison shows a robust Northern Hemisphere July temperature evolution characterized by a maximum between 130–122 ka BP with temperatures 0.4 to 6.8 K above pre-industrial values. This temperature evolution is in line with the changes in June insolation and greenhouse-gas concentrations. For the evolution of July temperatures in the Southern Hemisphere, the picture emerging from the inter-comparison is less clear. However, it does show that including greenhouse-gas concentration changes is critical. The simulations that include this forcing show an early, 128 ka BP July temperature anomaly maximum of 0.5 to 2.6 K. The robustness of simulated January temperatures is large in the Southern Hemisphere and the mid-latitudes of the Northern Hemisphere. In these latitudes maximum January temperature anomalies of respectively −2.5 to 2 K and 0 to 2 K are simulated for the period after 118 ka BP. The inter-comparison is inconclusive on the evolution of January temperatures in the high-latitudes of the Northern Hemisphere. Further investigation of regional anomalous patterns and inter-model differences indicate that in specific regions, feedbacks within the climate system are important for the simulated temperature evolution. Firstly in the Arctic region, changes in the summer sea-ice cover control the evolution of Last Interglacial winter temperatures. Secondly, for the Atlantic region, the Southern Ocean and the North Pacific, possible changes in the characteristics of the Atlantic meridional overturning circulation are critical. The third important feedback, having an impact on the temperature evolution of the Northern Hemisphere, is shown to be the presence of remnant continental ice from the preceding glacial period. Another important feedback are changes in the monsoon regime which controls the evolution of temperatures over parts of Africa and India. Finally, the simulations reveal an important land-sea contrast, with temperature changes over the oceans lagging continental temperatures by up to several thousand years. The aforementioned feedback mechanisms tend to be highly model-dependent, indicating that specific proxy-data is needed to constrain future climate simulations and to further enhance our understanding of the evolution of the climate during the Last Interglacial period

ENU Mutagenesis Reveals a Novel Phenotype of Reduced Limb Strength in Mice Lacking Fibrillin 2

Background: Fibrillins 1 (FBN1) and 2 (FBN2) are components of microfibrils, microfilaments that are present in many connective tissues, either alone or in association with elastin. Marfan's syndrome and congenital contractural arachnodactyly (CCA) result from dominant mutations in the genes FBN1 and FBN2 respectively. Patients with both conditions often present with specific muscle atrophy or weakness, yet this has not been reported in the mouse models. In the case of Fbn1, this is due to perinatal lethality of the homozygous null mice making measurements of strength difficult. In the case of Fbn2, four different mutant alleles have been described in the mouse and in all cases syndactyly was reported as the defining phenotypic feature of homozygotes.Methodology/Principal Findings: As part of a large-scale N-ethyl-N-nitrosourea (ENU) mutagenesis screen, we identified a mouse mutant, Mariusz, which exhibited muscle weakness along with hindlimb syndactyly. We identified an amber nonsense mutation in Fbn2 in this mouse mutant. Examination of a previously characterised Fbn2-null mutant, Fbn2(fp), identified a similar muscle weakness phenotype. The two Fbn2 mutant alleles complement each other confirming that the weakness is the result of a lack of Fbn2 activity. Skeletal muscle from mutants proved to be abnormal with higher than average numbers of fibres with centrally placed nuclei, an indicator that there are some regenerating muscle fibres. Physiological tests indicated that the mutant muscle produces significantly less maximal force, possibly as a result of the muscles being relatively smaller in Mariusz mice.Conclusions: These findings indicate that Fbn2 is involved in integrity of structures required for strength in limb movement. As human patients with mutations in the fibrillin genes FBN1 and FBN2 often present with muscle weakness and atrophy as a symptom, Fbn2-null mice will be a useful model for examining this aspect of the disease process further

Effects of deletion of the Streptococcus pneumoniae lipoprotein diacylglyceryl transferase gene lgt on ABC transporter function and on growth in vivo

Lipoproteins are an important class of surface associated proteins that have diverse roles and frequently are involved in the virulence of bacterial pathogens. As prolipoproteins are attached to the cell membrane by a single enzyme, prolipoprotein diacylglyceryl transferase (Lgt), deletion of the corresponding gene potentially allows the characterisation of the overall importance of lipoproteins for specific bacterial functions. We have used a Δlgt mutant strain of Streptococcus pneumoniae to investigate the effects of loss of lipoprotein attachment on cation acquisition, growth in media containing specific carbon sources, and virulence in different infection models. Immunoblots of triton X-114 extracts, flow cytometry and immuno-fluorescence microscopy confirmed the Δlgt mutant had markedly reduced lipoprotein expression on the cell surface. The Δlgt mutant had reduced growth in cation depleted medium, increased sensitivity to oxidative stress, reduced zinc uptake, and reduced intracellular levels of several cations. Doubling time of the Δlgt mutant was also increased slightly when grown in medium with glucose, raffinose and maltotriose as sole carbon sources. These multiple defects in cation and sugar ABC transporter function for the Δlgt mutant were associated with only slightly delayed growth in complete medium. However the Δlgt mutant had significantly reduced growth in blood or bronchoalveolar lavage fluid and a marked impairment in virulence in mouse models of nasopharyngeal colonisation, sepsis and pneumonia. These data suggest that for S. pneumoniae loss of surface localisation of lipoproteins has widespread effects on ABC transporter functions that collectively prevent the Δlgt mutant from establishing invasive infection

EPTAS and Subexponential Algorithm for Maximum Clique on Disk and Unit Ball Graphs

A (unit) disk graph is the intersection graph of closed (unit) disks in the plane. Almost three decades ago, an elegant polynomial-time algorithm was found for Maximum Cliqe on unit disk graphs [Clark, Colbourn, Johnson; Discrete Mathematics ’90]. Since then, it has been an intriguing open question whether or not tractability can be extended to general disk graphs. We show that the disjoint union of two odd cycles is never the complement of a disk graph nor of a unit (3-dimensional) ball graph. From that fact and existing results, we derive a simple QPTAS and a subexponential algorithm running in time 2O˜(n2/3) for Maximum Cliqe on disk and unit ball graphs. We then obtain a randomized EPTAS for computing the independence number on graphs having no disjoint union of two odd cycles as an induced subgraph, bounded VC-dimension, and linear independence number. This, in combination with our structural results, yields a randomized EPTAS for Max Cliqe on disk and unit ball graphs. Max Cliqe on unit ball graphs is equivalent to finding, given a collection of points in R3, a maximum subset of points with diameter at most some fixed value. In stark contrast, Maximum Cliqe on ball graphs and unit 4-dimensional ball graphs, as well as intersection graphs of filled ellipses (even close to unit disks) or filled triangles is unlikely to have such algorithms. Indeed, we show that, for all those problems, there is a constant ratio of approximation which cannot be attained even in time 2n1−ε, unless the Exponential Time Hypothesis fails

Binets: fundamental building blocks for phylogenetic networks

Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph having a unique root in which the leaves are labelled by a given set of species. Recently, some approaches have been developed to construct phylogenetic networks from collections of networks on 2- and 3-leaved networks, which are known as binets and trinets, respectively. Here we study in more depth properties of collections of binets, one of the simplest possible types of networks into which a phylogenetic network can be decomposed. More speci_cally, we show that if a collection of level-1 binets is compatible with some binary network, then it is also compatible with a binary level-1 network. Our proofs are based on useful structural results concerning lowest stable ancestors in networks. In addition, we show that, although the binets do not determine the topology of the network, they do determine the number of reticulations in the network, which is one of its most important parameters. We also consider algorithmic questions concerning binets. We show that deciding whether an arbitrary set of binets is compatible with some network is at least as hard as the well-known Graph Isomorphism problem. However, if we restrict to level-1 binets, it is possible to decide in polynomial time whether there exists a binary network that displays all the binets. We also show that to _nd a network that displays a maximum number of the binets is NP-hard, but that there exists a simple polynomial-time 1/3-approximation algorithm for this problem. It is hoped that these results will eventually assist in the development of new methods for constructing phylogenetic networks from collections of smaller networks