Reoptimization of Some Maximum Weight Induced Hereditary Subgraph Problems

The reoptimization issue studied in this paper can be described as follows: given an instance I of some problem Π, an optimal solution OPT for Π in I and an instance I′ resulting from a local perturbation of I that consists of insertions or removals of a small number of data, we wish to use OPT in order to solve Π in I', either optimally or by guaranteeing an approximation ratio better than that guaranteed by an ex nihilo computation and with running time better than that needed for such a computation. We use this setting in order to study weighted versions of several representatives of a broad class of problems known in the literature as maximum induced hereditary subgraph problems. The main problems studied are max independent set, max k-colorable subgraph and max split subgraph under vertex insertions and deletion

Tropical Dominating Sets in Vertex-Coloured Graphs

Given a vertex-coloured graph, a dominating set is said to be tropical if every colour of the graph appears at least once in the set. Here, we study minimum tropical dominating sets from structural and algorithmic points of view. First, we prove that the tropical dominating set problem is NP-complete even when restricted to a simple path. Then, we establish upper bounds related to various parameters of the graph such as minimum degree and number of edges. We also give upper bounds for random graphs. Last, we give approximability and inapproximability results for general and restricted classes of graphs, and establish a FPT algorithm for interval graphs.Comment: 19 pages, 4 figure

The Use of Premixed Calcium Silicate Bioceramic Sealer with Warm Carrier-Based Technique: A 2-Year Study for Patients Treated in a Master Program

Background: Recently several calcium silicate flowable sealers have been introduced as endodontic materials for the root canal. This clinical study tested the use of a new premixed calcium silicate bioceramic sealer in association with the Thermafil warm carrier-based technique (TF). Epoxy-resin-based sealer with the warm carrier-based technique was the control group. Methodology: Healthy consecutive patients (n = 85) requiring 94 root canal treatments were enrolled in this study and assigned to one filling group (Ceraseal-TF n = 47, AH Plus-TF n = 47) in accordance with operator training and best clinical practice. Periapical X-rays were taken preoperatively, after root canal filling and after 6, 12 and 24 months. Two evaluators blindly assessed the periapical index (PAI) and sealer extrusion in the groups (k = 0.90). Healing rate and survival rate were also evaluated. Chi-square tests was used to analyze significant differences between the groups. Multilevel analysis was performed to evaluate the factors associated with healing status. Results: A total of 89 root canal treatments in 82 patients were analyzed at the end-line (24 months). The total drop-out was 3.6% (3 patients; 5 teeth). A total of 91.1% of healed teeth (PAI 1-2) was observed in Ceraseal-TF, with 88.6% in AH Plus-TF. No significant difference was observed on healing outcome and survival among the two filling groups (p > 0.05). Apical extrusion of the sealers occurred in 17 cases (19.0%). Of these, 6 occurred in Ceraseal-TF (13.3%) and 11 in AH Plus-TF (25.0%). Three Ceraseal extrusions were radiographically undetectable after 24 months. All the AH Plus extrusions did not change during the evaluation time. Conclusions: The combined use of the carrier-based technique and premixed CaSi-based bioceramic sealer showed clinical results comparable with carrier-based technique and epoxy-resin-based sealer. The radiographical disappearance of apically extruded Ceraseal is a possible event in the first 24 months

Optimal Vertex Cover for the Small-World Hanoi Networks

The vertex-cover problem on the Hanoi networks HN3 and HN5 is analyzed with an exact renormalization group and parallel-tempering Monte Carlo simulations. The grand canonical partition function of the equivalent hard-core repulsive lattice-gas problem is recast first as an Ising-like canonical partition function, which allows for a closed set of renormalization group equations. The flow of these equations is analyzed for the limit of infinite chemical potential, at which the vertex-cover problem is attained. The relevant fixed point and its neighborhood are analyzed, and non-trivial results are obtained both, for the coverage as well as for the ground state entropy density, which indicates the complex structure of the solution space. Using special hierarchy-dependent operators in the renormalization group and Monte-Carlo simulations, structural details of optimal configurations are revealed. These studies indicate that the optimal coverages (or packings) are not related by a simple symmetry. Using a clustering analysis of the solutions obtained in the Monte Carlo simulations, a complex solution space structure is revealed for each system size. Nevertheless, in the thermodynamic limit, the solution landscape is dominated by one huge set of very similar solutions.Comment: RevTex, 24 pages; many corrections in text and figures; final version; for related information, see http://www.physics.emory.edu/faculty/boettcher

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