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

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 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

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

Extremal Optimization for Graph Partitioning

Extremal optimization is a new general-purpose method for approximating solutions to hard optimization problems. We study the method in detail by way of the NP-hard graph partitioning problem. We discuss the scaling behavior of extremal optimization, focusing on the convergence of the average run as a function of runtime and system size. The method has a single free parameter, which we determine numerically and justify using a simple argument. Our numerical results demonstrate that on random graphs, extremal optimization maintains consistent accuracy for increasing system sizes, with an approximation error decreasing over runtime roughly as a power law t^(-0.4). On geometrically structured graphs, the scaling of results from the average run suggests that these are far from optimal, with large fluctuations between individual trials. But when only the best runs are considered, results consistent with theoretical arguments are recovered.Comment: 34 pages, RevTex4, 1 table and 20 ps-figures included, related papers available at http://www.physics.emory.edu/faculty/boettcher

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

Radial versus femoral access in patients with acute coronary syndromes undergoing invasive management: a randomised multicentre trial.

Summary Background It is unclear whether radial compared with femoral access improves outcomes in unselected patients with acute coronary syndromes undergoing invasive management. Methods We did a randomised, multicentre, superiority trial comparing transradial against transfemoral access in patients with acute coronary syndrome with or without ST-segment elevation myocardial infarction who were about to undergo coronary angiography and percutaneous coronary intervention. Patients were randomly allocated (1:1) to radial or femoral access with a web-based system. The randomisation sequence was computer generated, blocked, and stratified by use of ticagrelor or prasugrel, type of acute coronary syndrome (ST-segment elevation myocardial infarction, troponin positive or negative, non-ST-segment elevation acute coronary syndrome), and anticipated use of immediate percutaneous coronary intervention. Outcome assessors were masked to treatment allocation. The 30-day coprimary outcomes were major adverse cardiovascular events, defined as death, myocardial infarction, or stroke, and net adverse clinical events, defined as major adverse cardiovascular events or Bleeding Academic Research Consortium (BARC) major bleeding unrelated to coronary artery bypass graft surgery. The analysis was by intention to treat. The two-sided α was prespecified at 0·025. The trial is registered at ClinicalTrials.gov, number NCT01433627. Findings We randomly assigned 8404 patients with acute coronary syndrome, with or without ST-segment elevation, to radial (4197) or femoral (4207) access for coronary angiography and percutaneous coronary intervention. 369 (8·8%) patients with radial access had major adverse cardiovascular events, compared with 429 (10·3%) patients with femoral access (rate ratio [RR] 0·85, 95% CI 0·74-0·99; p=0·0307), non-significant at α of 0·025. 410 (9·8%) patients with radial access had net adverse clinical events compared with 486 (11·7%) patients with femoral access (0·83, 95% CI 0·73-0·96; p=0·0092). The difference was driven by BARC major bleeding unrelated to coronary artery bypass graft surgery (1·6% vs 2·3%, RR 0·67, 95% CI 0·49-0·92; p=0·013) and all-cause mortality (1·6% vs 2·2%, RR 0·72, 95% CI 0·53-0·99; p=0·045). Interpretation In patients with acute coronary syndrome undergoing invasive management, radial as compared with femoral access reduces net adverse clinical events, through a reduction in major bleeding and all-cause mortality. Funding The Medicines Company and Terumo. © 2015 Elsevier Ltd

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