Theory and phenomenology for a variety of classical and quantum phase transitions

In this review, we first introduce recent progress in the mathematical structure of the three-dimensional Ising model, from the points of view of topologic, algebraic and geometric aspects. Then we discuss in turn Anderson localization due to disorder and then first- and second-order metal-insulator transitions, depending on electron correlation, with and without a magnetic field. Finally, we make intimate contact with the phase diagram showing the equilibrium between low temperature regimes of the magnetically induced Wigner electron solid and the so-called Laughlin electron liquid in the two-dimensional case.     

Constraining spacetime torsion with LAGEOS

We compute the corrections to the orbital Lense-Thirring effect (or frame-dragging) in the presence of spacetime torsion. We analyze the motion of a test body in the gravitational field of a rotating axisymmetric massive body, using the parametrized framework of Mao, Tegmark, Guth and Cabi. In the cases of autoparallel and extremal trajectories, we derive the specific approximate expression of the corresponding system of ordinary differential equations, which are then solved with methods of Celestial Mechanics. We calculate the secular variations of the longitudes of the node and of the pericenter. We also show how the LAser GEOdynamics Satellites (LAGEOS) can be used to constrain torsion parameters. We report the experimental constraints obtained using both the nodes and perigee measurements of the orbital Lense-Thirring effect. This makes LAGEOS and Gravity Probe B complementary frame-dragging and torsion experiments, since they constrain three different combinations of torsion parameters.     

Discrimination between Olfactory Receptor Agonists and Non‐agonists

A joint approach combining free‐energy calculations and calcium‐imaging assays on the broadly tuned human 1G1 olfactory receptor is reported. The free energy of binding of ten odorants was computed by means of molecular‐dynamics simulations. This state function allows separating the experimentally determined eight agonists from the two non‐agonists. This study constitutes a proof‐of‐principle for the computational deorphanization of olfactory receptors.     

Formal Verification of Numerical Programs: From C Annotated Programs to Mechanical Proofs

Numerical programs may require a high level of guarantee. This can be achieved by applying formal methods, such as machine-checked proofs. But these tools handle mathematical theorems while we are interested in C code, in which numerical computations are performed using floating-point arithmetic, whereas proof tools typically handle exact real arithmetic. To achieve this high level of confidence on C programs, we use a chain of tools: Frama-C, its Jessie plugin, Why and provers among Coq, Gappa, Alt-Ergo, CVC3 and Z3. This approach requires the C program to be annotated: each function must be precisely specified, and we prove the correctness of the program by proving both that it meets its specifications and that no runtime error may occur. The purpose of this paper is to illustrate, on various examples, the features of this approach.