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

Heinrich event 1: an example of dynamical ice-sheet reaction to oceanic changes

Heinrich events, identified as enhanced ice-rafted detritus (IRD) in North Atlantic deep sea sediments (Heinrich, 1988; Hemming, 2004) have classically been attributed to Laurentide ice-sheet (LIS) instabilities (MacAyeal, 1993; Calov et al., 2002; Hulbe et al., 2004) and assumed to lead to important disruptions of the Atlantic meridional overturning circulation (AMOC) and North Atlantic deep water (NADW) formation. However, recent paleoclimate data have revealed that most of these events probably occurred after the AMOC had already slowed down or/and NADW largely collapsed, within about a thousand years (Hall et al., 2006; Hemming, 2004; Jonkers et al., 2010; Roche et al., 2004), implying that the initial AMOC reduction could not have been caused by the Heinrich events themselves. Here we propose an alternative driving mechanism, specifically for Heinrich event 1 (H1; 18 to 15 ka BP), by which North Atlantic ocean circulation changes are found to have strong impacts on LIS dynamics. By combining simulations with a coupled climate model and a three-dimensional ice sheet model, our study illustrates how reduced NADW and AMOC weakening lead to a subsurface warming in the Nordic and Labrador Seas resulting in rapid melting of the Hudson Strait and Labrador ice shelves. Lack of buttressing by the ice shelves implies a substantial ice-stream acceleration, enhanced ice-discharge and sea level rise, with peak values 500–1500 yr after the initial AMOC reduction. Our scenario modifies the previous paradigm of H1 by solving the paradox of its occurrence during a cold surface period, and highlights the importance of taking into account the effects of oceanic circulation on ice-sheets dynamics in order to elucidate the triggering mechanism of Heinrich events.Peer reviewe

The relative contribution of orbital forcing and greenhouse gases to the North American deglaciation

Understanding what drove Northern Hemisphere ice sheet melt during the last deglaciation (21–7 ka) can help constrain how sensitive contemporary ice sheets are to greenhouse gas (GHGs) changes. The roles of orbital forcing and GHGs in the deglaciation have previously been modelled, but not yet quantified. Here, for the first time we calculate the relative effect of these forcings on the North American deglaciation by driving a dynamical ice sheet model (GLIMMER-CISM) with a set of un-accelerated transient deglacial simulations with a full primitive equation based ocean atmosphere general circulation model (FAMOUS). We find that by 9 ka, orbital forcing has caused 50% of the deglaciation, GHG 30% and the interaction between the two 20%. Orbital forcing starts affecting the ice volume at 19 ka, 2,000 years before CO2 starts increasing in our experiments, a delay which partly controls their relative effect

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.

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

Molecular control of sucrose utilization in Escherichia coli W, an efficient sucrose-utilizing strain

Sucrose is an industrially important carbon source for microbial fermentation. Sucrose utilization in Escherichia coli, however, is poorly understood, and most industrial strains cannot utilize sucrose. The roles of the chromosomally encoded sucrose catabolism (csc) genes in E. coli W were examined by knockout and overexpression experiments. At low sucrose concentrations, the csc genes are repressed and cells cannot grow. Removal of either the repressor protein (cscR) or the fructokinase (cscK) gene facilitated derepression. Furthermore, combinatorial knockout of cscR and cscK conferred an improved growth rate on low sucrose. The invertase (cscA) and sucrose transporter (cscB) genes are essential for sucrose catabolism in E. coli W, demonstrating that no other genes can provide sucrose transport or inversion activities. However, cscK is not essential for sucrose utilization. Fructose is excreted into the medium by the cscK-knockout strain in the presence of high sucrose, whereas at low sucrose (when carbon availability is limiting), fructose is utilized by the cell. Overexpression of cscA, cscAK, or cscAB could complement the W Delta cscRKAB knockout mutant or confer growth on a K-12 strain which could not naturally utilize sucrose. However, phenotypic stability and relatively good growth rates were observed in the K-12 strain only when overexpressing cscAB, and full growth rate complementation in W Delta cscRKA Balso required cscAB. Our understanding of sucrose utilization can be used to improve E. coli Wand engineer sucrose utilization in strains which do not naturally utilize sucrose, allowing substitution of sucrose for other, less desirable carbon sources in industrial fermentations

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

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

Directed evolution of a biterminal bacterial display scaffold enhances the display of diverse peptides

Bacterial cell-surface display systems coupled with quantitative screening methods offer the potential to expand protein engineering capabilities. To more fully exploit this potential, a unique bacterial surface display scaffold was engineered to display peptides more efficiently from the surface exposed C- and N-termini of a circularly permuted outer membrane protein. Using directed evolution, efficient membrane localization of a circularly permuted OmpX (CPX) display scaffold was rescued, thereby improving the presentation of diverse passenger peptides on the cell surface. Random and targeted mutagenesis directed towards linkers joining the native N- and C-termini of OmpX coupled with screening by FACS yielded an enhanced CPX (eCPX) variant which localized to the outer membrane as efficiently as the non-permuted parent. Interestingly, enhancing substitutions coincided with a C-terminal motif conserved in outer membrane proteins. Surface localization of various passenger peptides and mini-proteins was expedited using eCPX relative to that achieved with the parent scaffold. The new variant also permitted simultaneous display and labeling of distinct peptides on structurally adjacent C- and N-termini, thus enabling display level normalization during library screening and the display of bidentate or dimeric peptides. Consequently, the evolved scaffold, eCPX, expands the range of applications for bacterial display. Finally, this approach provides a route to improve the performance of cell-surface display vectors for protein engineering and design