Refinement Type Inference via Horn Constraint Optimization

We propose a novel method for inferring refinement types of higher-order functional programs. The main advantage of the proposed method is that it can infer maximally preferred (i.e., Pareto optimal) refinement types with respect to a user-specified preference order. The flexible optimization of refinement types enabled by the proposed method paves the way for interesting applications, such as inferring most-general characterization of inputs for which a given program satisfies (or violates) a given safety (or termination) property. Our method reduces such a type optimization problem to a Horn constraint optimization problem by using a new refinement type system that can flexibly reason about non-determinism in programs. Our method then solves the constraint optimization problem by repeatedly improving a current solution until convergence via template-based invariant generation. We have implemented a prototype inference system based on our method, and obtained promising results in preliminary experiments.Comment: 19 page

Maximization of thermal entanglement of arbitrarily interacting two qubits

We investigate the thermal entanglement of interacting two qubits. We maximize it by tuning a local Hamiltonian under a given interaction Hamiltonian. We prove that the optimizing local Hamiltonian takes a simple form which dose not depend on the temperature and that the corresponding optimized thermal entanglement decays as $1/(T log T)$ at high temperatures. We also find that at low temperatures the thermal entanglement is maximum without any local Hamiltonians and that the second derivative of the maximized thermal entanglement changes discontinuously at the boundary between the high- and low-temperature phases.Comment: 23 pages, 4 figure

Cr-doping effect on the orbital fluctuation of heavily doped Nd1-xSrxMnO3 (x ~ 0.625)

We have investigated the Cr-doping effect of Nd0.375Sr0.625MnO3 near the phase boundary between the x2-y2 and 3z2-r2 orbital ordered states, where a ferromagnetic correlation and concomitant large magnetoresistance are observed owing to orbital fluctuation. Cr-doping steeply suppresses the ferromagnetic correlation and magnetoresistance in Nd0.375Sr0.625Mn1-yCryO3 with 0 < y < 0.05, while they reappear in 0.05 < y < 0.10. Such a reentrant behavior implies that a phase boundary is located at y = 0.05, or a phase crossover occurs across y = 0.05.Comment: 3 pages, 3 figures, to be published in Journal of Applied Physic

Enhancement of the anomalous Hall effect and spin glass behavior in the bilayered manganite La(2-2x)Sr(1+2x)Mn2O7

The Hall resistivity and magnetization have been investigated in the ferromagnetic state of the bilayered manganite La(2-2x)Sr(1+2x)Mn2O7 (x=0.36). The Hall resistivity shows an increase in both the ordinary and anomalous Hall coefficients at low temperatures below 50K, a region in which experimental evidence for the spin glass state has been found in a low magnetic field of 1mT. The origin of the anomalous behavior of the Hall resistivity relevant to magnetic states may lie in the intrinsic microscopic inhomogeneity in a quasi-two-dimensional electron system.Comment: 7 pages, 4 figures, Solid State Communications (in press

Transport and structural study of pressure-induced magnetic states in Nd0.55Sr0.45MnO3 and Nd0.5Sr0.5MnO3

Pressure effects on the electron transport and structure of Nd1-xSrxMnO3 (x = 0.45, 0.5) were investigated in the range from ambient to ~6 GPa. In Nd0.55Sr0.45MnO3, the low-temperature ferromagnetic metallic state is suppressed and a low temperature insulating state is induced by pressure. In Nd0.5Sr0.5MnO3, the CE-type antiferromagnetic charge-ordering state is suppressed by pressure. Under pressure, both samples have a similar electron transport behavior although their ambient ground states are much different. It is surmised that pressure induces an A-type antiferromagnetic state at low temperature in both compounds

Thermal relaxation in charge ordered Pr0.63_{0.63} Ca0.37_{0.37} MnO3_3 in presence of a magnetic field

We report observation of substantial thermal relaxation in single crystal of charge ordered system Pr$_{0.63}$Ca$_{0.37}$MnO$_3$ in an applied magnetic field of H = 8T. The relaxation is observed when the temperature is scanned in presence of a magnetic field in the temperature interval $T_{MH}<T<T_{CO}$ where $T_{CO}$ is the charge ordering temperature and $T_{MH}$ is charge melting temperature in a field. In this temperature range the system has coexisting charged ordered insulator (COI) and ferromagnetic metallic (FMM) phases. No such relaxation is observed in the COI state in H = 0T or in the FMM phase at $T < T_{MH}$ in presence of a magnetic field. We conclude that the thermal relaxation is due to two coexisting phases with nearly same free energies but separated by a potential barrier. This barrier makes the transformation from one phase to the other time-dependent in the scale of the specific heat experiment and gives rise to the thermal relaxation.Comment: 4 pages LaTEX, 3 eps figure