The Origin of Magnetism in Mn‐Doped SrTiO3

An analysis of Mn substitution in SrTiO₃ is performed in order to understand the origin of reported spin coupling in lightly Mn‐doped SrTiO₃. The spin glass state magnetoelectrically coupled to the dipolar glass state has previously been reported for SrTiO₃ substituted with only 2% of Mn on the B‐site. An analysis of the substitution mechanism for A‐ and B‐site doping shows a strong influence of processing conditions, such as processing temperature, oxygen partial pressure, and off‐stoichiometry. The required conditions for a site‐selective substitution are defined, which yield a single‐phase and almost defect‐free perovskite. Magnetic measurements show no magnetic anomalies resulting from spin coupling and only a simple paramagnetic behavior. Magnetic anomalies are observed only for the samples in which Mn is misplaced within the cation sublattice of the SrTiO₃ perovskite. This occurs due to improper material processing, which causes initially unpredicted changes in the valence state of the Mn and results in the formation of structural defects and irregularities associated with segregation and nucleation of the magnetic species. Previously reported spin coupling in Mn‐doped SrTiO₃ is not an intrinsic phenomenon and cannot be treated as a spin glass.     

Fault-diameter of Cartesian graph bundles

Cartesian graph bundles is a class of graphs that is a generalization of the Cartesian graph products. Let G be a kG-connected graph and Dc(G) denote the diameter of G after deleting any of its c<kG vertices. We prove that Da+b+1(G)?Da(F)+Db(B)+1 if G is a graph bundle with fibre F over base B, a<kF, and b<kB.     

Grammatical evolution as a hyper-heuristic to evolve deterministic real-valued optimization algorithms

Hyper-heuristic methodologies have been extensively and successfully used to generate combinatorial optimization heuristics. On the other hand, there have been almost no attempts to build a hyper-heuristic to evolve an algorithm for solving real-valued optimization problems. In our previous research, we succeeded to evolve a Nelder–Mead-like real function minimization heuristic using genetic programming and the primitives extracted from the original Nelder–Mead algorithm. The resulting heuristic was better than the original Nelder–Mead method in the number of solved test problems but it was slower in that it needed considerably more cost function evaluations to solve the problems also solved by the original method. In this paper we exploit grammatical evolution as a hyper-heuristic to evolve heuristics that outperform the original Nelder–Mead method in all aspects. However, the main goal of the paper is not to build yet another real function optimization algorithm but to shed some light on the influence of different factors on the behavior of the evolution process as well as on the quality of the obtained heuristics. In particular, we investigate through extensive evolution runs the influence of the shape and dimensionality of the training function, and the impact of the size limit set to the evolving algorithms. At the end of this research we succeeded to evolve a number of heuristics that solved more test problems and in fewer cost function evaluations than the original Nelder–Mead method. Our solvers are also highly competitive with the improvements made to the original method based on rigorous mathematical convergence proofs found in the literature. Even more importantly, we identified some directions in which to continue the work in order to be able to construct a productive hyper-heuristic capable of evolving real function optimization heuristics that would outperform a human designer in all aspects.