Faster Existential FO Model Checking on Posets

We prove that the model checking problem for the existential fragment of first-order (FO) logic on partially ordered sets is fixed-parameter tractable (FPT) with respect to the formula and the width of a poset (the maximum size of an antichain). While there is a long line of research into FO model checking on graphs, the study of this problem on posets has been initiated just recently by Bova, Ganian and Szeider (CSL-LICS 2014), who proved that the existential fragment of FO has an FPT algorithm for a poset of fixed width. We improve upon their result in two ways: (1) the runtime of our algorithm is O(f(|{\phi}|,w).n^2) on n-element posets of width w, compared to O(g(|{\phi}|). n^{h(w)}) of Bova et al., and (2) our proofs are simpler and easier to follow. We complement this result by showing that, under a certain complexity-theoretical assumption, the existential FO model checking problem does not have a polynomial kernel.Comment: Paper as accepted to the LMCS journal. An extended abstract of an earlier version of this paper has appeared at ISAAC'14. Main changes to the previous version are improvements in the Multicoloured Clique part (Section 4

Solving order constraints in logarithmic space.

We combine methods of order theory, finite model theory, and universal algebra to study, within the constraint satisfaction framework, the complexity of some well-known combinatorial problems connected with a finite poset. We identify some conditions on a poset which guarantee solvability of the problems in (deterministic, symmetric, or non-deterministic) logarithmic space. On the example of order constraints we study how a certain algebraic invariance property is related to solvability of a constraint satisfaction problem in non-deterministic logarithmic space

Tropically convex constraint satisfaction

A semilinear relation S is max-closed if it is preserved by taking the componentwise maximum. The constraint satisfaction problem for max-closed semilinear constraints is at least as hard as determining the winner in Mean Payoff Games, a notorious problem of open computational complexity. Mean Payoff Games are known to be in the intersection of NP and co-NP, which is not known for max-closed semilinear constraints. Semilinear relations that are max-closed and additionally closed under translations have been called tropically convex in the literature. One of our main results is a new duality for open tropically convex relations, which puts the CSP for tropically convex semilinaer constraints in general into NP intersected co-NP. This extends the corresponding complexity result for scheduling under and-or precedence constraints, or equivalently the max-atoms problem. To this end, we present a characterization of max-closed semilinear relations in terms of syntactically restricted first-order logic, and another characterization in terms of a finite set of relations L that allow primitive positive definitions of all other relations in the class. We also present a subclass of max-closed constraints where the CSP is in P; this class generalizes the class of max-closed constraints over finite domains, and the feasibility problem for max-closed linear inequalities. Finally, we show that the class of max-closed semilinear constraints is maximal in the sense that as soon as a single relation that is not max-closed is added to L, the CSP becomes NP-hard.Comment: 29 pages, 2 figure

Intake of dairy foods and oral health: review of epidemiological data

Introduction: The relationship between diet and oral health is intriguing. Various components of milk have been suggested to be protective against oral health problems, although specific mechanisms linking dairy components to the pathogenesis of certain diseases are still unclear. Purpose: To provide an overview of the associations between intake of milk and dairy products and dental plaque, periodontal disease and tooth loss based on currently available literature. Methods: We performed a review of relevant literature with critical appraisal of those human epidemiological studies evaluating the association between intake of milk or dairy products and periodontal disease, plaque score or tooth loss among adults and elderly. Results: Nine studies were included in the review, eight of which were cross-sectional and only one applied a longitudinal design. None of the studies included institutionalised participants. Overall, reported studies suggested an inverse association between dairy intake and plaque score and periodontal disease. Results related to tooth loss were inclusive. Conclusion: The methodological quality of reviewed studies was moderate to low with only one longitudinal design. Therefore, well-designed, confounding-controlled, longitudinal studies are warranted to be able to conclude on the potential protective effect of dairy intake on periodontal disease, dental plaque and tooth loss

On Backdoors to Tractable Constraint Languages

International audienceIn the context of CSPs, a strong backdoor is a subset of variables such that every complete assignment yields a residual instance guaranteed to have a specified property. If the property allows efficient solving, then a small strong backdoor provides a reasonable decomposition of the original instance into easy instances. An important challenge is the design of algorithms that can find quickly a small strong backdoor if one exists. We present a systematic study of the parameterized complexity of backdoor detection when the target property is a restricted type of constraint language defined by means of a family of polymor-phisms. In particular, we show that under the weak assumption that the polymorphisms are idempotent, the problem is unlikely to be FPT when the parameter is either r (the constraint arity) or k (the size of the backdoor) unless P = NP or FPT = W[2]. When the parameter is k + r, however, we are able to identify large classes of languages for which the problem of finding a small backdoor is FPT

GRS 1915+105 : High-energy Insights with SPI/INTEGRAL

We report on results of two years of INTEGRAL/SPI monitoring of the Galactic microquasar GRS 1915+105. From September 2004 to May 2006, the source has been observed twenty times with long (approx 100 ks) exposures. We present an analysis of the SPI data and focus on the description of the high-energy (> 20 keV) output of the source. We found that the 20 - 500 keV spectral emission of GRS 1915+105 was bound between two states. It seems that these high-energy states are not correlated with the temporal behavior of the source, suggesting that there is no direct link between the macroscopic characteristics of the coronal plasma and the the variability of the accretion flow. All spectra are well fitted by a thermal comptonization component plus an extra high-energy powerlaw. This confirms the presence of thermal and non-thermal electrons around the black hole.Comment: 7 pages, 8 figures, 2 tables; accepted (09/11/2008) for publication in A&

On the reduction of the CSP dichotomy conjecture to digraphs

It is well known that the constraint satisfaction problem over general relational structures can be reduced in polynomial time to digraphs. We present a simple variant of such a reduction and use it to show that the algebraic dichotomy conjecture is equivalent to its restriction to digraphs and that the polynomial reduction can be made in logspace. We also show that our reduction preserves the bounded width property, i.e., solvability by local consistency methods. We discuss further algorithmic properties that are preserved and related open problems.Comment: 34 pages. Article is to appear in CP2013. This version includes two appendices with proofs of claims omitted from the main articl

Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps

What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called fixed-template constraint satisfaction problems (CSPs) -- it has turned out that their complexity is captured by a certain specific form of symmetry. This paper explains an extension of this theory to a much broader class of computational problems, the promise CSPs, which includes relaxed versions of CSPs such as the problem of finding a 137-coloring of a 3-colorable graph

The effect of vitamin D and/or Calcium supplementation on periodontitis

Objective: To perform a systematic review and assess whether the use of vitamin D and calcium supplements can benefit the prevention of periodontitis and tooth loss among adults and elderly. Method: Research of MEDLINE, LILACS, Cochrane Library, Scopus and ClinicalTrials.gov and reference lists of relevant papers to identify experimental and observational studies on the effect of vitamin D and/or calcium supplementation on clinical parameters of periodontitis. Primary outcomes were clinical attachment loss (CAL), probing depth (PD) and tooth loss. Results: Four studies were included. Meta-analysis across studies showed a standardized mean difference (SMD) of –0.194 (95% CI: –0.777 to 0.389) and –0.168 (95% CI: –0.736 to 0.400) for CAL and PD, respectively. Conclusion: Vitamin D and calcium supplementation seem to have some beneficial effect on clinical parameters of periodontitis as a complementary therapy. However, these findings need to be confirmed before being used in clinical practice