The Combinatorics of Alternating Tangles: from theory to computerized enumeration

We study the enumeration of alternating links and tangles, considered up to topological (flype) equivalences. A weight $n$ is given to each connected component, and in particular the limit $n\to 0$ yields information about (alternating) knots. Using a finite renormalization scheme for an associated matrix model, we first reduce the task to that of enumerating planar tetravalent diagrams with two types of vertices (self-intersections and tangencies), where now the subtle issue of topological equivalences has been eliminated. The number of such diagrams with $p$ vertices scales as $12^p$ for $p\to\infty$. We next show how to efficiently enumerate these diagrams (in time $\sim 2.7^p$) by using a transfer matrix method. We give results for various generating functions up to 22 crossings. We then comment on their large-order asymptotic behavior.Comment: proceedings European Summer School St-Petersburg 200

Cytological identification and quantification of testicular cell types using fine needle aspiration in horses

Fifteen stallions of different breeds, age 3-11 years, had their right testicles evaluated by fine needle aspiration cytology (FNAC). Cytological analysis showed the following spermatogenic cell types: spermatogonia (1.6% +/- 1.1); spermatocyte I (3.4% +/- 2.2); spermatocyte II (0.8% +/- 0.7); early spermatids (25.5% +/- 9.5); late spermatids (37.0% +/- 9.3). Spermatozoal numbers were expressed as the spermatic index (SI = 31.5% +/- 8.5) and Sertoli cells mere expressed as the Sertoli cell index (SEI = 20.9% +/- 17.0) (means +/- s.d). Identification of cell types was relatively easy and no immediate adverse effects of aspiration were noted. The results suggest that FNAC of testis may assist clinical diagnosis in the study of male equine infertility

The critical role of wavelength in the UV-activated grafting of 1-alkene onto silicon and silicon nitride Si x N 4 surfaces

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In situ monitoring of the electronic properties and the pH stability of grafted Si 111

Photoluminescence, surface photovoltage, interface capacitance and vibrational infrared spectroscopy measurements have been used to monitor the electronic properties of silicon surfaces protected by covalently grafted organic monolayers. The grafted surfaces present electronic properties equivalent to those of freshly prepared H terminated surfaces. Moreover, the organic layers are found to improve the lifetime of the surface passivation in ambient atmosphere by orders of magnitude, as compared to a hydrogenated surface. In liquid water, the interfaces are stable up to pH 9. Above that value, and though silicon oxidation is barely detectable, one observes a marked decrease in the photoluminescence intensity, a sharp change in the value of the surface photovoltage, and a strong increase in the capacitance peak associated with surface states. These changes are not fully reversible when pH is brought back to acidic values. Complementary experiments on the wetting properties of paraffin films as a function of pH suggest that the abrupt degradation of electronic properties above pH 9 is triggered by interactions between molecular water and the aliphatic chains, which leads to permeation of water at structural defects of the organic monolayer and to localized oxidation of silicon at the interface. This sets an upper limit to the pH range where sensors based on silicon grafted with an organic layer can be use

Thermal decomposition of alkoxy monolayers grafted on silicon: A mechanistic model

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