On the complexity of strongly connected components in directed hypergraphs

We study the complexity of some algorithmic problems on directed hypergraphs and their strongly connected components (SCCs). The main contribution is an almost linear time algorithm computing the terminal strongly connected components (i.e. SCCs which do not reach any components but themselves). "Almost linear" here means that the complexity of the algorithm is linear in the size of the hypergraph up to a factor alpha(n), where alpha is the inverse of Ackermann function, and n is the number of vertices. Our motivation to study this problem arises from a recent application of directed hypergraphs to computational tropical geometry. We also discuss the problem of computing all SCCs. We establish a superlinear lower bound on the size of the transitive reduction of the reachability relation in directed hypergraphs, showing that it is combinatorially more complex than in directed graphs. Besides, we prove a linear time reduction from the well-studied problem of finding all minimal sets among a given family to the problem of computing the SCCs. Only subquadratic time algorithms are known for the former problem. These results strongly suggest that the problem of computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure

The use of different adhesive filling material and mass combinations to restore class II cavities under loading and shrinkage effects: a 3D-FEA

3D tooth models were virtually restored: flowable composite resin + bulk-fill composite (A), glass ionomer cement + bulk-fill composite (B) or adhesive + bulk-fill composite (C). Polymerization shrinkage and masticatory loads were simulated. All models exhibited the highest stress concentration at the enamel–restoration interfaces. A and C showed similar pattern with lower magnitude in A in comparison to C. B showed lower stress in dentine and C the highest cusps displacement. The use of glass ionomer cement or flowable composite resin in combination with a bulk-fill composite improved the biomechanical behavior of deep class II MO cavities

The use of different adhesive filling material and mass combinations to restore class II cavities under loading and shrinkage effects: a 3D-FEA

3D tooth models were virtually restored: flowable composite resin + bulk-fill composite (A), glass ionomer cement + bulk-fill composite (B) or adhesive + bulk-fill composite (C). Polymerization shrinkage and masticatory loads were simulated. All models exhibited the highest stress concentration at the enamel-restoration interfaces. A and C showed similar pattern with lower magnitude in A in comparison to C. B showed lower stress in dentine and C the highest cusps displacement. The use of glass ionomer cement or flowable composite resin in combination with a bulk-fill composite improved the biomechanical behavior of deep class II MO cavities

A heterotrimeric G protein, G alpha i-3, on Golgi membranes regulates the secretion of a heparan sulfate proteoglycan in LLC-PK1 epithelial cells

A heterotrimeric G-alpha-i subunit, alpha-i-3, is localized on Golgi membranes in LLC-PK1 and NRK epithelial cells where it colocalizes with mannosidase II by immunofluorescence. The alpha-i-3 was found to be localized on the cytoplasmic face of Golgi cisternae and it was distributed across the whole Golgi stack. The alpha-i-3 subunit is found on isolated rat liver Golgi membranes by Western blotting and G-alpha-i-3 on the Golgi apparatus is ADP ribosylated by pertussis toxin. LLC-PK1 cells were stably transfected with G-alpha-i-3 on an MT-1, inducible promoter in order to overexpress alpha-i-3 on Golgi membranes. The intracellular processing and constitutive secretion of the basement membrane heparan sulfate proteoglycan (HSPG) was measured in LLC-PK1 cells. Overexpression of alpha-i-3 on Golgi membranes in transfected cells retarded the secretion of HSPG and accumulated precursors in the medial-trans-Golgi. This effect was reversed by treatment of cells with pertussis toxin which results in ADP-ribosylation and functional uncoupling of G-alpha-i-3 on Golgi membranes. These results provide evidence for a novel role for the pertussis toxin sensitive G-alpha-i-3 protein in Golgi trafficking of a constitutively secreted protein in epithelial cells

Experimental implementation of an adiabatic quantum optimization algorithm

We report the realization of a nuclear magnetic resonance computer with three quantum bits that simulates an adiabatic quantum optimization algorithm. Adiabatic quantum algorithms offer new insight into how quantum resources can be used to solve hard problems. This experiment uses a particularly well suited three quantum bit molecule and was made possible by introducing a technique that encodes general instances of the given optimization problem into an easily applicable Hamiltonian. Our results indicate an optimal run time of the adiabatic algorithm that agrees well with the prediction of a simple decoherence model.Comment: REVTeX, 5 pages, 4 figures, improved lay-out; accepted for publication in Physical Review Letter

A Port Graph Rewriting Approach to Relational Database Modelling

International audienceWe present new algorithms to compute the Syntactic Closure and the Minimal Cover of a set of functional dependencies, using strategic port graph rewriting. We specify a Visual Domain Specific Language to model relational database schemata as port graphs, and provide an extension to port graph rewriting rules. Using these rules we implement strategies to compute a syntactic closure, analyse it and find minimal covers, essential for schema normalisation. The graph program provides a visual description of the computation steps coupled with analysis features not available in other approaches. We prove soundness and completeness of the computed closure. This methodology is implemented in PORGY

Complexity of Discrete Energy Minimization Problems

Discrete energy minimization is widely-used in computer vision and machine learning for problems such as MAP inference in graphical models. The problem, in general, is notoriously intractable, and finding the global optimal solution is known to be NP-hard. However, is it possible to approximate this problem with a reasonable ratio bound on the solution quality in polynomial time? We show in this paper that the answer is no. Specifically, we show that general energy minimization, even in the 2-label pairwise case, and planar energy minimization with three or more labels are exp-APX-complete. This finding rules out the existence of any approximation algorithm with a sub-exponential approximation ratio in the input size for these two problems, including constant factor approximations. Moreover, we collect and review the computational complexity of several subclass problems and arrange them on a complexity scale consisting of three major complexity classes -- PO, APX, and exp-APX, corresponding to problems that are solvable, approximable, and inapproximable in polynomial time. Problems in the first two complexity classes can serve as alternative tractable formulations to the inapproximable ones. This paper can help vision researchers to select an appropriate model for an application or guide them in designing new algorithms.Comment: ECCV'16 accepte

Number partitioning as random energy model

Number partitioning is a classical problem from combinatorial optimisation. In physical terms it corresponds to a long range anti-ferromagnetic Ising spin glass. It has been rigorously proven that the low lying energies of number partitioning behave like uncorrelated random variables. We claim that neighbouring energy levels are uncorrelated almost everywhere on the energy axis, and that energetically adjacent configurations are uncorrelated, too. Apparently there is no relation between geometry (configuration) and energy that could be exploited by an optimization algorithm. This ``local random energy'' picture of number partitioning is corroborated by numerical simulations and heuristic arguments.Comment: 8+2 pages, 9 figures, PDF onl

Structural motifs recurring in different folds recognize the same ligand fragments

<p>Abstract</p> <p>Background</p> <p>The structural analysis of protein ligand binding sites can provide information relevant for assigning functions to unknown proteins, to guide the drug discovery process and to infer relations among distant protein folds. Previous approaches to the comparative analysis of binding pockets have usually been focused either on the ligand or the protein component. Even though several useful observations have been made with these approaches they both have limitations. In the former case the analysis is restricted to binding pockets interacting with similar ligands, while in the latter it is difficult to systematically check whether the observed structural similarities have a functional significance.</p> <p>Results</p> <p>Here we propose a novel methodology that takes into account the structure of both the binding pocket and the ligand. We first look for local similarities in a set of binding pockets and then check whether the bound ligands, even if completely different, share a common fragment that can account for the presence of the structural motif. Thanks to this method we can identify structural motifs whose functional significance is explained by the presence of shared features in the interacting ligands.</p> <p>Conclusion</p> <p>The application of this method to a large dataset of binding pockets allows the identification of recurring protein motifs that bind specific ligand fragments, even in the context of molecules with a different overall structure. In addition some of these motifs are present in a high number of evolutionarily unrelated proteins.</p