Automated Reasoning and Presentation Support for Formalizing Mathematics in Mizar

This paper presents a combination of several automated reasoning and proof presentation tools with the Mizar system for formalization of mathematics. The combination forms an online service called MizAR, similar to the SystemOnTPTP service for first-order automated reasoning. The main differences to SystemOnTPTP are the use of the Mizar language that is oriented towards human mathematicians (rather than the pure first-order logic used in SystemOnTPTP), and setting the service in the context of the large Mizar Mathematical Library of previous theorems,definitions, and proofs (rather than the isolated problems that are solved in SystemOnTPTP). These differences poses new challenges and new opportunities for automated reasoning and for proof presentation tools. This paper describes the overall structure of MizAR, and presents the automated reasoning systems and proof presentation tools that are combined to make MizAR a useful mathematical service.Comment: To appear in 10th International Conference on. Artificial Intelligence and Symbolic Computation AISC 201

Dynamics of a trapped Fermi gas in the BCS phase

We derive semiclassical transport equations for a trapped atomic Fermi gas in the BCS phase at temperatures between zero and the superfluid transition temperature. These equations interpolate between the two well-known limiting cases of superfluid hydrodynamics at zero temperature and the Vlasov equation at the critical one. The linearized version of these equations, valid for small deviations from equilibrium, is worked out and applied to two simple examples where analytical solutions can be found: a sound wave in a uniform medium and the quadrupole excitation in a spherical harmonic trap. In spite of some simplifying approximations, the main qualitative results of quantum mechanical calculations are reproduced, which are the different frequencies of the quadrupole mode at zero and the critical temperature and strong Landau damping at intermediate temperatures. In addition we suggest a numerical method for solving the semiclassical equations without further approximations.Comment: 15 pages, 4 figures; v2: discussion and references adde

M2000 : an astrometric catalog in the Bordeaux Carte du Ciel zone +11 degrees < {delta} < +18 degrees

During four years, systematic observations have been conducted in drift scan mode with the Bordeaux automated meridian circle in the declination band [+11 ; +18]. The resulting astrometric catalog includes about 2 300 000 stars down to the magnitude limit V_M=16.3. Nearly all stars (96%) have been observed at least 6 times, the catalog being complete down to V_M=15.4. The median internal standard error in position is about 35 mas in the V_M magnitude range [11 ; 15], which degrades to about 50 mas when the faintest stars are considered. M2000 provides also one band photometry with a median internal standard error of 0.04 mag. Comparisons with the Hipparcos and bright part of Tycho-2 catalogs have enabled to estimate external errors in position to be lower than 40 mas. In this zone and at epoch 1998, the faint part of Tycho-2 is found to have an accuracy of 116 mas in alpha instead of 82 mas deduced from the model-based standard errors given in the catalog.Comment: The catalogue can be fetched directly from: ftp://cdsarc.u-strasbg.fr/cats/I/272 or queried from: http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=I/272 More information at : http://www.observ.u-bordeaux.fr/~soubiran/m2000.ht

3D bioprinting for orthopaedic applications: Current advances, challenges and regulatory considerations

In the era of personalised medicine, novel therapeutic approaches raise increasing hopes to address currently unmet medical needs by developing patient-customised treatments. Three-dimensional (3D) bioprinting is rapidly evolving and has the potential to obtain personalised tissue constructs and overcome some limitations of standard tissue engineering approaches. Bioprinting could support a wide range of biomedical applications, such as drug testing, tissue repair or organ transplantation. There is a growing interest for 3D bioprinting in the orthopaedic field, with remarkable scientific and technical advances. However, the full exploitation of 3D bioprinting in medical applications still requires efforts to anticipate the upcoming challenges in translating bioprinted products from bench to bedside. In this review we summarised current trends, advances and challenges in the application of 3D bioprinting for bone and cartilage tissue engineering. Moreover, we provided a detailed analysis of the applicable regulations through the 3D bioprinting process and an overview of available standards covering bioprinting and additive manufacturing

Is pretreatment with Beta-blockers beneficial in patients with acute coronary syndrome?

OBJECTIVES: The role of beta-blockers in the treatment of hypertension is discussed controversially and the data showing a clear benefit in acute coronary syndromes (ACS) were obtained in the thrombolysis era. The goal of this study was to analyze the role of pretreatment with beta-blockers in patients with ACS. METHODS: Using data from the Acute Myocardial Infarction in Switzerland (AMIS Plus) registry, we analyzed outcomes of patients with beta-blocker pretreatment in whom they were continued during hospitalization (group A), those without beta-blocker pretreatment but with administration after admission (group B) and those who never received them (group C). Major adverse cardiac events defined as composed endpoint of re-infarction and stroke (during hospitalization) and/or in-hospital death were compared between the groups. RESULTS: A total of 24,709 patients were included in the study (6,234 in group A, 12,344 in group B, 6,131 in group C). Patients of group B were younger compared to patients of group A and C (62.5, 67.6 and 68.4, respectively). In the multivariate analysis, odds ratio for major adverse cardiac events was 0.59 (CI 0.47-0.74) for group A and 0.66 (CI 0.55-0.83) for group B, while group C was taken as a reference. CONCLUSIONS: beta-Blocker therapy is beneficial in ACS and they should be started in those who are not pretreated and continued in stable patients who had been on chronic beta-blocker therapy before

Parametrization of the octupole degrees of freedom

A simple parametrization for the octupole collective variables is proposed and the symmetries of the wave functions are discussed in terms of the solutions corresponding to the vibrational limit. [PACS: 21.60Ev, 21.60.Fw, 21.10.Re]Comment: 14 page

Theory of solvation in polar nematics

We develop a linear response theory of solvation of ionic and dipolar solutes in anisotropic, axially symmetric polar solvents. The theory is applied to solvation in polar nematic liquid crystals. The formal theory constructs the solvation response function from projections of the solvent dipolar susceptibility on rotational invariants. These projections are obtained from Monte Carlo simulations of a fluid of dipolar spherocylinders which can exist both in the isotropic and nematic phase. Based on the properties of the solvent susceptibility from simulations and the formal solution, we have obtained a formula for the solvation free energy which incorporates experimentally available properties of nematics and the length of correlation between the dipoles in the liquid crystal. Illustrative calculations are presented for the Stokes shift and Stokes shift correlation function of coumarin-153 in 4-n-pentyl-4'-cyanobiphenyl (5CB) and 4,4-n-heptyl-cyanopiphenyl (7CB) solvents as a function of temperature in both the nematic and isotropic phase.Comment: 19 pages, 9 figure