Superconductivity in higher titanium oxides

Recent renewal of the highest transition temperature in a conventional superconductor of the sulfer hydride attracts much attention to exploring simple compounds with the lighter elements, situated in unconventional conditions. We report the discovery of superconductivity in simple oxides of Ti4O7 and g-Ti3O5 in a thin-film form having deliberately tuned epitaxial structures and off-stoichiometry. These higher titanium oxides join in a class of simple-oxide superconductors, and g-Ti3O5 now holds the highest superconducting transition temperature of 7.1 kelvin among them. The mechanism behind the superconductivity is discussed on the basis of electrical measurements and theoretical predictions. We conclude that superconductivity arises from unstabilized bipolaronic insulating states.Comment: 25 pages, 4 figures in main text, 14 pages, 11 figures in supplemental informatio

Statistical Mechanics of Dictionary Learning

Finding a basis matrix (dictionary) by which objective signals are represented sparsely is of major relevance in various scientific and technological fields. We consider a problem to learn a dictionary from a set of training signals. We employ techniques of statistical mechanics of disordered systems to evaluate the size of the training set necessary to typically succeed in the dictionary learning. The results indicate that the necessary size is much smaller than previously estimated, which theoretically supports and/or encourages the use of dictionary learning in practical situations.Comment: 6 pages, 4 figure

Replica symmetry breaking in an adiabatic spin-glass model of adaptive evolution

We study evolutionary canalization using a spin-glass model with replica theory, where spins and their interactions are dynamic variables whose configurations correspond to phenotypes and genotypes, respectively. The spins are updated under temperature T_S, and the genotypes evolve under temperature T_J, according to the evolutionary fitness. It is found that adaptation occurs at T_S < T_S^{RS}, and a replica symmetric phase emerges at T_S^{RSB} < T_S < T_S^{RS}. The replica symmetric phase implies canalization, and replica symmetry breaking at lower temperatures indicates loss of robustness.Comment: 5pages, 2 figure

The development of air shower in the iron absorber

The iron open-sandwich experiments to observe one dimensional development of individual air showers were carried out at Akeno Observatory. One dimensional energy flow, incident energy and production height of shower is estimated using the data of size and age obtained from the above experiment and simple calculation