Exact Computation of Influence Spread by Binary Decision Diagrams

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.Comment: WWW'1

Computing NP-Hard Repetitiveness Measures via MAX-SAT

Repetitiveness measures reveal profound characteristics of datasets, and give rise to compressed data structures and algorithms working in compressed space. Alas, the computation of some of these measures is NP-hard, and straight-forward computation is infeasible for datasets of even small sizes. Three such measures are the smallest size of a string attractor, the smallest size of a bidirectional macro scheme, and the smallest size of a straight-line program. While a vast variety of implementations for heuristically computing approximations exist, exact computation of these measures has received little to no attention. In this paper, we present MAX-SAT formulations that provide the first non-trivial implementations for exact computation of smallest string attractors, smallest bidirectional macro schemes, and smallest straight-line programs. Computational experiments show that our implementations work for texts of length up to a few hundred for straight-line programs and bidirectional macro schemes, and texts even over a million for string attractors

In vitro dentin permeability after application of Gluma® desensitizer as aqueous solution or aqueous fumed silica dispersion

OBJECTIVES: To assess and to compare the effects of Gluma® Desensitizer (GDL) with an experimental glutaraldehyde and HEMA containing fumed silica dispersion (GDG) on dentin permeability using a chemiluminous tracer penetration test. MATERIAL AND METHODS: Twenty disc-shaped dentin specimens were dissected from extracted human third molars. The dentin specimens were mounted in a split chamber device for determination of permeability under liquid pressure using a photochemical method. Ten specimens were randomly selected and allocated to the evaluation groups Gluma® Desensitizer as aqueous solution and glutaraldehyde/HEMA as fumed silica dispersion, respectively. Dentin disc permeability was determined at two pressure levels after removal of smear with EDTA, after albumin soaking, and after application of the desensitizing agents. Two desensitizer-treated and rinsed specimens of each group were examined by scanning electron microscopy (SEM) for surface remnants. RESULTS: Comparatively large standard deviations of the mean EDTA reference and albumin soaked samples permeability values refected the differences of the dentin substrates. The mean chemiluminescence values of specimen treated with GDL and GDG, respectively, were signifcantly reduced after topical application of the desensitizing agents on albumin-soaked dentin. The effects of GDL and GDG on permeability were not signifcantly different. Treated specimens showed no surface remnants after rinsing. CONCLUSIONS: The experimental desensitizer gel formulation reduced dentin permeability as effectively as the original Gluma® Desensitizer solution

Effect of two desensitizing agents on dentin permeability in vitro

Objective The aim of this in vitro study was to investigate the effect of two desensitizing agents and water on hydraulic conductance in human dentin. Material and Methods GLUMA Desensitizer PowerGel (GLU) contains glutaraldehyde (GA) and 2-hydroxyethyl methacrylate (HEMA), and Teethmate Desensitizer (TD) is a powder comprising tetracalcium phosphate (TTCP) and dicalcium phosphate anhydrous (DCPA) that is mixed with water. Deionized water was used as a negative control (CTR). Thirty discs with a thickness of 1.2 mm were cut from the coronal dentin of the third molars and cleaned with 0.5 M EDTA (pH 7.4). After being mounted in a split-chamber device, the discs were pressurized with water at 1 kPa and 3 kPa in order to measure flow rates with a highly sensitive micro-flow sensor and to calculate hydraulic conductance as a baseline value (BL). Following the application of GLU, TD, and CTR (n=10), hydraulic conductance was remeasured with intermittent storage in water after 15 min, 1 d, 1 w, and 1 m. Reduction in permeability (PR%) was calculated from hydraulic conductance. Data were statistically analyzed using nonparametric methods (