We propose a general dual ascent framework for Lagrangean decomposition of combinatorial problems. Although methods of this type have shown their efficiency for a number of problems, so far there was no general algorithm applicable to multiple problem types. In this work, we propose such a general algorithm. It depends on several parameters, which can be used to optimize its performance in each particular setting. We demonstrate efficacy of our method on graph matching and multicut problems, where it outperforms state-of-the-art solvers including those based on subgradient optimization and off-the-shelf linear programming solvers.
The competition potential of 14 Rhizobium leguminosarum bv. viciae isolates originating from nodules of Pisum sativum was estimated. Genotypic analyses of the isolates revealed a high level of chromosomal and plasmid content diversity. The isolates tagged with a plasmid-bearing constitutively expressed gusA gene were used to inoculate vetch (Vicia villosa) in competition experiments carried out under laboratory conditions. Soil extract containing autochthonous rhizobial population was used as competitor for gus-tagged strains, and the competition was studied by: (i) estimation of Gus + root nodules on whole root systems, (ii) the pattern of individual nodule colonization by Gus + /Gus − rhizobia, and (iii) the number of Gus + /Gus − bacteria recovered from individual nodules. Several patterns of nodule colonization by Gus + /Gus − bacteria were found. Some nodules identified as Gus + contained gus-tagged bacteria only in the young and saprophytic zones, while the symbiotic zone was occupied by unmarked soil rhizobia. In other Gus + nodules, despite the visible colonization of the entire nodule by gusmarked bacteria, a high number of Gus − soil-derived rhizobia were recovered. The results suggest that rhizobial strains compete with each other also in the late stage of nodule development. Therefore, they may use different strategies to reach the late saprophytic zone of the nodule, which serves as an optimal environment for massive proliferation.
Abstract. We present a novel convex relaxation and a corresponding inference algorithm for the non-binary discrete tomography problem, that is, reconstructing discrete-valued images from few linear measurements. In contrast to state of the art approaches that split the problem into a continuous reconstruction problem for the linear measurement constraints and a discrete labeling problem to enforce discrete-valued reconstructions, we propose a joint formulation that addresses both problems simultaneously, resulting in a tighter convex relaxation. For this purpose a constrained graphical model is set up and evaluated using a novel relaxation optimized by dual decomposition. We evaluate our approach experimentally and show superior solutions both mathematically (tighter relaxation) and experimentally in comparison to previously proposed relaxations.
The recovery of structured signals from a few linear measurements is a central point in both compressed sensing (CS) and discrete tomography. In CS the signal structure is described by means of a low complexity model e.g. co-/sparsity. The CS theory shows that any signal/image can be undersampled at a rate dependent on its intrinsic complexity. Moreover, in such undersampling regimes, the signal can be recovered by sparsity promoting convex regularization like 1 -or total variation (TV-) minimization. Precise relations between many low complexity measures and the sufficient number of random measurements are known for many sparsity promoting norms. However, a precise estimate of the undersampling rate for the TV seminorm is still lacking. We address this issue by: a) providing dual certificates testing uniqueness of a given cosparse signal with bounded signal values, b) approximating the undersampling rates via the statistical dimension of the TV descent cone and c) showing empirically that the provided rates also hold for tomographic measurements.
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