Revisiting the Two-Filter Formula for Smoothing for State-Space Models

Smoothing algorithms for state-space models, i.e., fixed-interval smoothing, fixed-lag smoothing, and two-filter formula for smoothing, are examined using real examples. For linear and Gaussian state-space models, it is observed that similar posterior distributions can be obtained by properly defining the inverse filter. In the case of linear non-Gaussian state-space models, it is shown that Gaussian-sum smoothing is possible even for relatively high dimensional state-space model with Gaussian-mixture noise inputs by properly setting the inverse filter. The two-filter formula is also applicable for particle filter, but better results are obtained with fixed lag smoothing or with the average of forward and backward fixed lag smoothers.Comment: 27 pages, 2 tables, 12 figure

Crossover from commensurate to incommensurate antiferromagnetism in stoichiometric NaFeAs revealed by single-crystal 23Na,75As-NMR experiments

We report results of 23Na and 75As nuclear magnetic resonance (NMR) experiments on a self-flux grown high-quality single crystal of stoichiometric NaFeAs. The NMR spectra revealed a tetragonal to twinned-orthorhombic structural phase transition at T_O = 57 K and an antiferromagnetic (AF) transition at T_AF = 45 K. The divergent behavior of nuclear relaxation rate near T_AF shows significant anisotropy, indicating that the critical slowing down of stripe-type AF fluctuations are strongly anisotropic in spin space. The NMR spectra at low enough temperatures consist of sharp peaks showing a commensurate stripe AF order with a small moment \sim 0.3 muB. However, the spectra just below T_AF exhibits highly asymmetric broadening pointing to an incommensurate modulation. The commensurate-incommensurate crossover in NaFeAs shows a certain similarity to the behavior of SrFe2As2 under high pressure.Comment: 5 pages, 5 figures, revised version to appear in J. Phys. Soc. Jp

Use of self-referential (ipsative) feedback to motivate and guide distance learners

Distance learners often rely on written feedback for learning and for motivation. But feedback that is 'given' to learners and that relies on praise to motivate does not engage learners in the process of self-development. We propose that an ipsative approach to assessment and feedback based on a comparison with a learner's previous performance motivates distance learners by developing a self-awareness of progress that encourages learners to interact with feedback and apply this to future work. A study of a distance learning Masters programme in Educational Leadership indicated that formal self-referential (ipsative) feedback was largely absent. An ipsative feedback scheme was therefore developed in consultation with the tutors in which students completed a reflection on their progress in implementing past feedback. Tutors provided both an ipsative and a developmental response. Student and tutor evaluations of the scheme indicated that feedback on progress has the potential to motivate distance learners and to encourage them to act on developmental feedback, but can also raise grade expectations. Sustainable methods of applying ipsative feedback to a wide range of distance learning programmes are worth further exploration

Competing Ground States of a Peierls-Hubbard Nanotube

Motivated by iodo platinum complexes assembled within a quadratic-prism lattice, [Pt(C$_2$H$_8$N$_2$)(C$_{10}$H$_8$N$_2$)I]$_4$(NO$_3$)$_8$, we investigate the ground-state properties of a Peierls-Hubbard four-legged tube. Making a group-theoretical analysis, we systematically reveal a variety of valence arrangements, including half-metallic charge-density-wave states. Quantum and thermal phase competition is numerically demonstrated with particular emphasis on doping-induced successive insulator-to-metal transitions with conductivity increasing stepwise.Comment: 6 pages, 4 figures. to be published in Europhys. Lett. 87 (2009) 1700

Non-magnetic pair-breaking effect on La(Fe_{1-x}Zn_{x})AsO_{0.85} studied by NMR and NQR

$^{75}$As and $^{139}$La NMR and nuclear quadrupole resonance (NQR) studies on Zn-substituted LaFeAsO$_{0.85}$ have been performed to investigate the Zn-impurity effects microscopically. Although superconductivity in LaFeAsO$_{0.85}$ disappears by 3% Zn substitution, we found that NMR/NQR spectra and NMR physical quantities in the normal state are hardly changed, indicating that the crystal structure and electronic states are not modified by Zn substitution. Our results suggest that the suppression of superconductivity by Zn substitution is not due to the change of the normal-state properties, but due to strong non-magnetic pair-breaking effect to superconductivity.Comment: 5 pages, 4 figures, This paper was chosen as "Paper of Editors' Suggestion

Development of Ce³⁺ and Li⁺ co-doped magnesium borate glass ceramics for optically stimulated luminescence dosimetry

Magnesium tetraborate, MgB₄O₇, is an attractive host material for dosimetry due to the two characteristics: its low effective atomic number (Zeff = 8.4) and high neutron capture cross-section of the ¹⁰B isotope. Particularly, Ce³⁺ and Li⁺ ions co-doped MgB₄O₇ has shown optically stimulated luminescence (OSL) signal comparable to that of Al₂O₃:C, which is a well-known OSL dosimetry material. In this work, for further improvement of the dosimetric properties, a new synthesis route for MgB₄O₇:Ce³⁺-Li⁺ is described: glass-ceramic (GC) MgB₄O₇: Ce³⁺- Li⁺ samples were prepared by heat treatment of the magnesium borate glass with the composition, 25MgO–72B₂O₃–3Li₂O-0.3Ce³⁺. The prepared GC samples show UV-blue radioluminescence assigned to the Ce³⁺ 5d → 4f transition under X-ray irradiation and two thermoluminescence (TL) glow peaks related to the shallow and deep electron traps. Although fading of the TL and OSL signal was observed due to electron release from the shallow traps, the electrons captured by deep traps were stable at room temperature. Particularly, GC samples annealed at 750 °C and 800 °C, named GC750 and GC800, showed stable OSL up to 10 h following β-ray irradiation, after an initial fading mainly due to the presence of shallow traps in the material. From the viewpoint of this fading ratio, GC750 and GC800 showed potential as a practical OSL dosimeter