Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples

Resonant Inelastic X-ray Scattering Studies of Elementary Excitations

In the past decade, Resonant Inelastic X-ray Scattering (RIXS) has made remarkable progress as a spectroscopic technique. This is a direct result of the availability of high-brilliance synchrotron X-ray radiation sources and of advanced photon detection instrumentation. The technique's unique capability to probe elementary excitations in complex materials by measuring their energy-, momentum-, and polarization-dependence has brought RIXS to the forefront of experimental photon science. We review both the experimental and theoretical RIXS investigations of the past decade, focusing on those determining the low-energy charge, spin, orbital and lattice excitations of solids. We present the fundamentals of RIXS as an experimental method and then review the theoretical state of affairs, its recent developments and discuss the different (approximate) methods to compute the dynamical RIXS response. The last decade's body of experimental RIXS data and its interpretation is surveyed, with an emphasis on RIXS studies of correlated electron systems, especially transition metal compounds. Finally, we discuss the promise that RIXS holds for the near future, particularly in view of the advent of x-ray laser photon sources.Comment: Review, 67 pages, 44 figure

Dynamics of metallic stripes in cuprates

We study the dynamics of metallic vertical stripes in cuprates within the three-band Hubbard model based on a recently developed time dependent Gutzwiller approximation. As doping increases the optical conductivity shows transfer of spectral weight from the charge transfer band towards i) an incoherent band centered at 1.3eV, {ii} a Drude peak, mainly due to motion along the stripe, {iii} a low energy collective mode which softens with doping and merges with ii} at optimum doping in good agreement with experiment. The softening is related to the quasidegeneracy between Cu centered and O centered mean-field stripe solutions close to optimal doping.Comment: 4 pages, 5 figures, corrections to Fig.

Spin relaxation in (110) and (001) InAs/GaSb superlattices

We report an enhancement of the electron spin relaxation time (T1) in a (110) InAs/GaSb superlattice by more than an order of magnitude (25 times) relative to the corresponding (001) structure. The spin dynamics were measured using polarization sensitive pump probe techniques and a mid-infrared, subpicosecond PPLN OPO. Longer T1 times in (110) superlattices are attributed to the suppression of the native interface asymmetry and bulk inversion asymmetry contributions to the precessional D'yakonov Perel spin relaxation process. Calculations using a nonperturbative 14-band nanostructure model give good agreement with experiment and indicate that possible structural inversion asymmetry contributions to T1 associated with compositional mixing at the superlattice interfaces may limit the observed spin lifetime in (110) superlattices. Our findings have implications for potential spintronics applications using InAs/GaSb heterostructures.Comment: 4 pages, 2 figure

T Lymphocytes Amplify the Anabolic Activity of Parathyroid Hormone through Wnt10b Signaling

SummaryIntermittent administration of parathyroid hormone (iPTH) is used to treat osteoporosis because it improves bone architecture and strength, but the underlying cellular and molecular mechanisms are unclear. Here, we show that iPTH increases the production of Wnt10b by bone marrow CD8+ T cells and induces these lymphocytes to activate canonical Wnt signaling in preosteoblasts. Accordingly, in responses to iPTH, T cell null mice display diminished Wnt signaling in preosteoblasts and blunted osteoblastic commitment, proliferation, differentiation, and life span, which result in decreased trabecular bone anabolism and no increase in strength. Demonstrating the specific role of lymphocytic Wnt10b, iPTH has no anabolic activity in mice lacking T-cell-produced Wnt10b. Therefore, T-cell-mediated activation of Wnt signaling in osteoblastic cells plays a key permissive role in the mechanism by which iPTH increases bone strength, suggesting that T cell osteoblast crosstalk pathways may provide pharmacological targets for bone anabolism

Intersubband spin-density excitations in quantum wells with Rashba spin splitting

In inversion-asymmetric semiconductors, spin-orbit coupling induces a k-dependent spin splitting of valence and conduction bands, which is a well-known cause for spin decoherence in bulk and heterostructures. Manipulating nonequilibrium spin coherence in device applications thus requires understanding how valence and conduction band spin splitting affects carrier spin dynamics. This paper studies the relevance of this decoherence mechanism for collective intersubband spin-density excitations (SDEs) in quantum wells. A density-functional formalism for the linear spin-density matrix response is presented that describes SDEs in the conduction band of quantum wells with subbands that may be non-parabolic and spin-split due to bulk or structural inversion asymmetry (Rashba effect). As an example, we consider a 40 nm GaAs/AlGaAs quantum well, including Rashba spin splitting of the conduction subbands. We find a coupling and wavevector-dependent splitting of the longitudinal and transverse SDEs. However, decoherence of the SDEs is not determined by subband spin splitting, due to collective effects arising from dynamical exchange and correlation.Comment: 10 pages, 4 figure

Resonant X-ray Scattering in Manganites - Study of Orbital Degree of Freedom -

Orbital degree of freedom of electrons and its interplay with spin, charge and lattice degrees of freedom are one of the central issues in colossal magnetoresistive manganites. The orbital degree of freedom has until recently remained hidden, since it does not couple directly to most of experimental probes. Development of synchrotron light sources has changed the situation; by the resonant x-ray scattering (RXS) technique the orbital ordering has successfully been observed . In this article, we review progress in the recent studies of RXS in manganites. We start with a detailed review of the RXS experiments applied to the orbital ordered manganites and other correlated electron systems. We derive the scattering cross section of RXS where the tensor character of the atomic scattering factor (ASF) with respect to the x-ray polarization is stressed. Microscopic mechanisms of the anisotropic tensor character of ASF is introduced and numerical results of ASF and the scattering intensity are presented. The azimuthal angle scan is a unique experimental method to identify RXS from the orbital degree of freedom. A theory of the azimuthal angle and polarization dependence of the RXS intensity is presented. The theoretical results show good agreement with the experiments in manganites. Apart from the microscopic description of ASF, a theoretical framework of RXS to relate directly to the 3d orbital is presented. The scattering cross section is represented by the correlation function of the pseudo-spin operator for the orbital degree of freedom. A theory is extended to the resonant inelastic x-ray scattering and methods to observe excitations of the orbital degree of freedom are proposed.Comment: 47 pages, 24 figures, submitted to Rep. Prog. Phy