A rigorous evaluation of crossover and mutation in genetic programming

The role of crossover and mutation in Genetic Programming (GP) has been the subject of much debate since the emergence of the field. In this paper, we contribute new empirical evidence to this argument using a rigorous and principled experimental method applied to six problems common in the GP literature. The approach tunes the algorithm parameters to enable a fair and objective comparison of two different GP algorithms, the first using a combination of crossover and reproduction, and secondly using a combination of mutation and reproduction. We find that crossover does not significantly outperform mutation on most of the problems examined. In addition, we demonstrate that the use of a straightforward Design of Experiments methodology is effective at tuning GP algorithm parameters

Phenomenology of the superconducting state in Sr2RuO4

The symmetry of the superconducting phase of Sr2RuO4 is identified as the odd-parity pairing state d(k)=\hat{z}(k_x \pm i k_y) based on recent experiments. The experimental evidence for the so-called orbital dependent superconductivity leads to a single-band description of superconductivity based on spin fluctuation mechanism. It is shown that the state \hat{z}(k_x \pm i k_y) can be stabilized by the spin fluctuation feedback mechanism analogous to the A-phase in 3He and by spin-orbit coupling effects.Comment: 7 pages, 1 figure, to be published in Proc. of the conference "Anomalous Complex Superconductors" (Crete, 1998

Micro-Hall Magnetometry Studies of Thermally Assisted and Pure Quantum Tunneling in Single Molecule Magnet Mn12-Acetate

We have studied the crossover between thermally assisted and pure quantum tunneling in single crystals of high spin (S=10) uniaxial single molecule magnet Mn12-acetate using micro-Hall effect magnetometry. Magnetic hysteresis experiments have been used toinvestigate the energy levels that determine the magnetization reversal as a function of magnetic field and temperature. These experiments demonstrate that the crossover occurs in a narrow (~0.1 K) or broad (~1 K) temperature interval depending on the magnitude and direction of the applied field. For low external fields applied parallel to the easy axis, the energy levels that dominate the tunneling shift abruptly with temperature. In the presence of a transverse field and/or large longitudinal field these energy levels change with temperature more gradually. A comparison of our experimental results with model calculations of this crossover suggest that there are additional mechanisms that enhance the tunneling rate of low lying energy levels and broaden the crossover for small transverse fields.Comment: 5 pages, 5 figure

Anisotropy in the Antiferromagnetic Spin Fluctuations of Sr2RuO4

It has been proposed that Sr_2RuO_4 exhibits spin triplet superconductivity mediated by ferromagnetic fluctuations. So far neutron scattering experiments have failed to detect any clear evidence of ferromagnetic spin fluctuations but, instead, this type of experiments has been successful in confirming the existence of incommensurate spin fluctuations near q=(1/3 1/3 0). For this reason there have been many efforts to associate the contributions of such incommensurate fluctuations to the mechanism of its superconductivity. Our unpolarized inelastic neutron scattering measurements revealed that these incommensurate spin fluctuations possess c-axis anisotropy with an anisotropic factor \chi''_{c}/\chi''_{a,b} of \sim 2.8. This result is consistent with some theoretical ideas that the incommensurate spin fluctuations with a c-axis anisotropy can be a origin of p-wave superconductivity of this material.Comment: 5 pages, 3 figures; accepted for publication in PR

Field dependence of the vortex structure in chiral p-wave superconductors

To investigate the different vortex structure between two chiral pairing p_x +(-) i p_y, we calculate the pair potential, the internal field, the local density of states, and free energy in the vortex lattice state based on the quasiclassical Eilenberger theory, and analyze the magnetic field dependence. The induced opposite chiral component of the pair potential plays an important role in the vortex structure. It also produces H^{1/2}-behavior of the zero-energy density of states at higher field. These results are helpful when we understand the vortex states in Sr2RuO4.Comment: 11 pages, 10 figures, to be published in Phys. Rev.

Vortex structure in chiral p-wave superconductors

We investigate the vortex structure in chiral p-wave superconductors by the Bogoliubov-de Gennes theory on a tight-binding model. We calculate the spatial structure of the pair potential and electronic state around a vortex, including the anisotropy of the Fermi surface and superconducting gap structure. The differences of the vortex structure between $\sin p_x + {\rm i} \sin p_y$-wave and $\sin p_x - {\rm i} \sin p_y$-wave superconductors are clarified in the vortex lattice state. We also discuss the winding $\mp 3$ case of the $\sin{(p_x+p_y)} \pm {\rm i} \sin{(-p_x+p_y)}$-wave superconductivity.Comment: 10 pages, 8 figure

Quantum electrodynamics in finite volume and nonrelativistic effective field theories

8 LaTeX pages, 2 figuresInternational audienceElectromagnetic effects are increasingly being accounted for in lattice quantum chromodynamics computations. Because of their long-range nature, they lead to large finite-size effects over which it is important to gain analytical control. Nonrelativistic effective field theories provide an efficient tool to describe these effects. Here we argue that some care has to be taken when applying these methods to quantum electrodynamics in a finite volume