2,388 research outputs found

    Sparse Kneser graphs are Hamiltonian

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    For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words

    Partial Dynamical Symmetry and Mixed Dynamics

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    Partial dynamical symmetry describes a situation in which some eigenstates have a symmetry which the quantum Hamiltonian does not share. This property is shown to have a classical analogue in which some tori in phase space are associated with a symmetry which the classical Hamiltonian does not share. A local analysis in the vicinity of these special tori reveals a neighbourhood of phase space foliated by tori. This clarifies the suppression of classical chaos associated with partial dynamical symmetry. The results are used to divide the states of a mixed system into ``chaotic'' and ``regular'' classes.Comment: 10 pages, Revtex, 3 figures, Phys. Rev. Lett. in pres

    Diffusion and Transport Coefficients in Synthetic Opals

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    Opals are structures composed of the closed packing of spheres in the size range of nano-to-micro meter. They are sintered to create small necks at the points of contact. We have solved the diffusion problem in such structures. The relation between the diffusion coefficient and the termal and electrical conductivity makes possible to estimate the transport coefficients of opal structures. We estimate this changes as function of the neck size and the mean-free path of the carriers. The theory presented is also applicable to the diffusion problem in other periodic structures.Comment: Submitted to PR

    Influence of bone density on implant stability parameters and implant success: a retrospective clinical study

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    <p>Abstract</p> <p>Background</p> <p>The aim of the present clinical study was to determine the local bone density in dental implant recipient sites using computerized tomography (CT) and to investigate the influence of local bone density on implant stability parameters and implant success.</p> <p>Methods</p> <p>A total of 300 implants were placed in 111 patients between 2003 and 2005. The bone density in each implant recipient site was determined using CT. Insertion torque and resonance frequency analysis were used as implant stability parameters. The peak insertion torque values were recorded with OsseoCare machine. The resonance frequency analysis measurements were performed with Osstell instrument immediately after implant placement, 6, and 12 months later.</p> <p>Results</p> <p>Of 300 implants placed, 20 were lost, meaning a survival rate of %. 93.3 after three years (average 3.7 ± 0.7 years). The mean bone density, insertion torque and RFA recordings of all 300 implants were 620 ± 251 HU, 36.1 ± 8 Ncm, and 65.7 ± 9 ISQ at implant placement respectively; which indicated statistically significant correlations between bone density and insertion torque values (p < 0.001), bone density and ISQ values (p < 0.001), and insertion torque and ISQ values (p < 0.001). The mean bone density, insertion torque and RFA values were 645 ± 240 HU, 37.2 ± 7 Ncm, and 67.1 ± 7 ISQ for 280 successful implants at implant placement, while corresponding values were 267 ± 47 HU, 21.8 ± 4 Ncm, and 46.5 ± 4 ISQ for 20 failed implants; which indicated statistically significant differences for each parameter (p < 0.001).</p> <p>Conclusion</p> <p>CT is a useful tool to determine the bone density in the implant recipient sites, and the local bone density has a prevailing influence on primary implant stability, which is an important determinant for implant success.</p

    Environmental and occupational interventions for primary prevention of cancer: A cross-sectorial policy framework

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    Background: Nearly 13 million new cancer cases and 7.6 million cancer deaths occur worldwide each year; 63% of cancer deaths occur in low and middle-income countries. A substantial proportion of all cancers are attributable to carcinogenic exposures in the environment and the workplace. Objective: We aimed to develop an evidence-based global vision and strategy for the primary prevention of environmental and occupational cancer. Methods: We identified relevant studies through PubMed by using combinations of the search terms "environmental," "occupational," "exposure," "cancer," "primary prevention," and "interventions." To supplement the literature review, we convened an international conference titled "Environmental and Occupational Determinants of Cancer: Interventions for Primary Prevention" under the auspices of the World Health Organization, in Asturias, Spain, on 17-18 March 2011. Discussion: Many cancers of environmental and occupational origin could be prevented. Prevention is most effectively achieved through primary prevention policies that reduce or eliminate involuntary exposures to proven and probable carcinogens. Such strategies can be implemented in a straightforward and cost-effective way based on current knowledge, and they have the added benefit of synergistically reducing risks for other noncommunicable diseases by reducing exposures to shared risk factors. Conclusions: Opportunities exist to revitalize comprehensive global cancer control policies by incorporating primary interventions against environmental and occupational carcinogens
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