Conway polynomials of two-bridge links

We give necessary conditions for a polynomial to be the Conway polynomial of a two-bridge link. As a consequence, we obtain simple proofs of the classical theorems of Murasugi and Hartley. We give a modulo 2 congruence for links, which implies the classical modulo 2 Murasugi congruence for knots. We also give sharp bounds for the coefficients of the Conway and Alexander polynomials of a two-bridge link. These bounds improve and generalize those of Nakanishi and Suketa.Comment: 15

Observation and Spectroscopy of a Two-Electron Wigner Molecule in an Ultra-Clean Carbon Nanotube

Coulomb interactions can have a decisive effect on the ground state of electronic systems. The simplest system in which interactions can play an interesting role is that of two electrons on a string. In the presence of strong interactions the two electrons are predicted to form a Wigner molecule, separating to the ends of the string due to their mutual repulsion. This spatial structure is believed to be clearly imprinted on the energy spectrum, yet to date a direct measurement of such a spectrum in a controllable one-dimensional setting is still missing. Here we use an ultra-clean suspended carbon nanotube to realize this system in a tunable potential. Using tunneling spectroscopy we measure the excitation spectra of two interacting carriers, electrons or holes, and identify seven low-energy states characterized by their spin and isospin quantum numbers. These states fall into two multiplets according to their exchange symmetries. The formation of a strongly-interacting Wigner molecule is evident from the small energy splitting measured between the two multiplets, that is quenched by an order of magnitude compared to the non-interacting value. Our ability to tune the two-electron state in space and to study it for both electrons and holes provides an unambiguous demonstration of the fundamental Wigner molecule state.Comment: SP and FK contributed equally to this wor

Scale relativity and fractal space-time: theory and applications

In the first part of this contribution, we review the development of the theory of scale relativity and its geometric framework constructed in terms of a fractal and nondifferentiable continuous space-time. This theory leads (i) to a generalization of possible physically relevant fractal laws, written as partial differential equation acting in the space of scales, and (ii) to a new geometric foundation of quantum mechanics and gauge field theories and their possible generalisations. In the second part, we discuss some examples of application of the theory to various sciences, in particular in cases when the theoretical predictions have been validated by new or updated observational and experimental data. This includes predictions in physics and cosmology (value of the QCD coupling and of the cosmological constant), to astrophysics and gravitational structure formation (distances of extrasolar planets to their stars, of Kuiper belt objects, value of solar and solar-like star cycles), to sciences of life (log-periodic law for species punctuated evolution, human development and society evolution), to Earth sciences (log-periodic deceleration of the rate of California earthquakes and of Sichuan earthquake replicas, critical law for the arctic sea ice extent) and tentative applications to system biology.Comment: 63 pages, 14 figures. In : First International Conference on the Evolution and Development of the Universe,8th - 9th October 2008, Paris, Franc

Glutathione Deficiency in Cardiac Patients Is Related to the Functional Status and Structural Cardiac Abnormalities

International audienceBACKGROUND: The tripeptide glutathione (L-gamma-glutamyl-cysteinyl-glycine) is essential to cell survival, and deficiency in cardiac and systemic glutathione relates to heart failure progression and cardiac remodelling in animal models. Accordingly, we investigated cardiac and blood glutathione levels in patients of different functional classes and with different structural heart diseases. METHODS: Glutathione was measured using standard enzymatic recycling method in venous blood samples obtained from 91 individuals, including 15 healthy volunteers and 76 patients of New York Heart Association (NYHA) functional class I to IV, undergoing cardiac surgery for coronary artery disease, aortic stenosis or terminal cardiomyopathy. Glutathione was also quantified in right atrial appendages obtained at the time of surgery. RESULTS: In atrial tissue, glutathione was severely depleted (-58%) in NYHA class IV patients compared to NYHA class I patients (P = 0.002). In patients with coronary artery disease, this depletion was related to the severity of left ventricular dysfunction (P = 0.006). Compared to healthy controls, blood glutathione was decreased by 21% in NYHA class I patients with structural cardiac disease (P<0.01), and by 40% in symptomatic patients of NYHA class II to IV (P<0.0001). According to the functional NYHA class, significant depletion in blood glutathione occurred before detectable elevation in blood sTNFR1, a marker of symptomatic heart failure severity, as shown by the exponential relationship between these two parameters in the whole cohort of patients (r = 0.88). CONCLUSIONS: This study provides evidence that cardiac and systemic glutathione deficiency is related to the functional status and structural cardiac abnormalities of patients with cardiac diseases. These data also suggest that blood glutathione test may be an interesting new biomarker to detect asymptomatic patients with structural cardiac abnormalities