Domino Tatami Covering is NP-complete

A covering with dominoes of a rectilinear region is called \emph{tatami} if no four dominoes meet at any point. We describe a reduction from planar 3SAT to Domino Tatami Covering. As a consequence it is NP-complete to decide whether there is a perfect matching of a graph that meets every 4-cycle, even if the graph is restricted to be an induced subgraph of the grid-graph. The gadgets used in the reduction were discovered with the help of a SAT-solver.Comment: 10 pages, accepted at The International Workshop on Combinatorial Algorithms (IWOCA) 201

Effects of zinc and fluoride on the remineralisation of artificial carious lesions under simulated plaque fluid conditions.

The aim was to study the effects of zinc (Zn) and fluoride (F) on remineralisation at plaque fluid concentrations. Artificial carious lesions were created in 2 acid-gel demineralising systems (initially infinitely undersaturated and partially saturated with respect to enamel) giving lesions with different mineral distribution characteristics (high and low R values, respectively) but similar integrated mineral loss values. Lesions of both types were assigned to 1 of 4 groups and remineralised for 5 days at 37°C. Zn and F were added, based on plaque fluid concentrations 1 h after application, to give 4 treatments: 231 μmol/l Zn, 10.5 μmol/l F, Zn/F combined and an unmodified control solution (non-F/non-Zn). Subsequently remineralisation was measured using microradiography. High-R lesions were analysed for calcium, phosphorus, F and Zn using electron probe micro-analysis. All lesions underwent statistically significant remineralisation. For low-R lesions, remineralisation was in the order F(a) < non-F/non-Zn(a) < Zn(a, b) < Zn/F(b), and for high-R lesions F(a) < non-F/non-Zn(b) < Zn(b) < Zn/F(c) (treatments with the same superscript letter not significantly different, at p < 0.05). Qualitatively, remineralisation occurred throughout non-F/non-Zn and Zn groups, predominantly at the surface zone (F) and within the lesion body (Zn/F). Electron probe micro-analysis revealed Zn in relatively large amounts in the outer regions (Zn, Zn/F). F was abundant not only at the surface (F), but also in the lesion body (Zn/F). Calcium:phosphate ratios were similar to hydroxyapatite (all). To conclude, under static remineralising conditions simulating plaque fluid, Zn/F treatment gave significantly greater remineralisation than did F treatment, possibly because Zn in the Zn/F group maintained greater surface zone porosity compared with F, facilitating greater lesion body remineralisation

Poly(alkyl methacrylate) tooth coatings for dental care: evaluation of the demineralisation-protection benefit using a time-resolved in vitro method

An in vitro method for the time-resolved quantification of acid-mediated tooth demineralisation has been developed and evaluated against putative non-permanent protective formulations based on a series of poly(alkyl methacrylate)s. Using a thermostatted carousel, dentally relevant substrates consisting of hydroxyapatite discs or sections of bovine teeth have been exposed to aqueous citric acid under controlled conditions, before and after being treated with the polymeric coatings. The dissolution of phosphate was monitored by the determination of 31P by Inductively Coupled Plasma—Mass Spectrometry and by the spectrophotometric phosphovanadomolybdate method. Dose-response plots constructed for both groups of treated substrates have revealed that the coatings significantly reduce erosion rates but are less effective at inhibiting tooth demineralisation than the standard fluoride treatment. The approach has enabled an evaluation of the erosion-protection efficiency of each coating

Bacteria-instructed synthesis of polymers for self-selective microbial binding and labelling

The detection and inactivation of pathogenic strains of bacteria continues to be an important therapeutic goal. Hence, there is a need for materials that can bind selectively to specific microorganisms, for diagnostic or anti-infective applications, but which can be formed from simple and inexpensive building blocks. Here, we exploit bacterial redox systems to induce a copper-mediated radical polymerisation of synthetic monomers at cell surfaces, generating polymers in situ that bind strongly to the microorganisms which produced them. This ‘bacteria-instructed synthesis’ can be carried out with a variety of microbial strains, and we show that the polymers produced are self-selective binding agents for the ‘instructing’ cell types. We further expand on the bacterial redox chemistries to ‘click’ fluorescent reporters onto polymers directly at the surfaces of a range of clinical isolate strains, allowing rapid, facile and simultaneous binding and visualisation of pathogens

Surfing the spectrum - what is on the horizon?

Diagnostic imaging techniques have evolved with technological advancements - but how far? The objective of this article was to explore the electromagnetic spectrum to find imaging techniques which may deliver diagnostic information of equal, or improved, standing to conventional radiographs and to explore any developments within radiography which may yield improved diagnostic data. A comprehensive literature search was performed using Medline, Web of Knowledge, Science Direct and PubMed Databases. Boolean Operators were used and key-terms included (not exclusively): terahertz, X-ray, ultraviolet, visible, infra-red, magnetic resonance, dental, diagnostic, caries and periodontal. Radiographic techniques are primarily used for diagnostic imaging in dentistry, and continued developments in X-ray imaging include: phase contrast, darkfield and spectral imaging. Other modalities have potential application, for example, terahertz, laser doppler and optical techniques, but require further development. In particular, infra-red imaging has regenerated interest with caries detection in vitro, due to improved quality and accessibility of cameras. Non-ionising imaging techniques, for example, infra-red, are becoming more commensurate with traditional radiographic techniques for caries detection. Nevertheless, X-rays continue to be the leading diagnostic image for dentists, with improved diagnostic potential for lower radiation dose becoming a reality