Because Hodrick–Prescott (HP) filtering and ℓ1 trend filtering are expressed as penalized least squares problem, both of them require the specification of their tuning parameter. For HP filtering, we have accumulated knowledge for selecting the value of its tuning parameter. However, we do not have similar knowledge for ℓ1 trend filtering. This paper presents a new method for specifying the tuning parameter of ℓ1 trend filtering so that the sum of squared residuals of HP filtering and that of ℓ1 trend filtering may be equivalent.
The ℓ1 trend filter, which is similar to the popular Hodrick–Prescott (HP) filter, seems to be very promising because it enables us to estimate a piecewise linear trend without specifying the location and number of kink points a priori. Such a trend may be regarded as a result of occasional permanent shocks to the growth rate. Similarly to the HP filter, the value of the tuning parameter needs to be selected in applying this filter. This paper proposes a method for selecting the tuning parameter of the ℓ1 trend filter and its generalization.
By applying the Sherman–Morrison–Woodbury (SMW) formula and a discrete cosine transformation matrix, De Jong and Sakarya [De Jong, R. M., and N. Sakarya. 2016. “The Econometrics of the Hodrick–Prescott Filter.” Review of Economics and Statistics 98 (2): 310–317] recently derived an explicit formula for the smoother weights of the Hodrick–Prescott filter. More recently, by applying the SMW formula and the spectral decomposition of a symmetric tridiagonal Toeplitz matrix, Cornea-Madeira [Cornea-Madeira, A. 2017. “The Explicit Formula for the Hodrick–Prescott Filter in Finite Sample.” Review of Economics and Statistics 99: 314–318] provided a simpler formula. This paper provides an alternative simpler formula for it and explains the reason why our approach leads to a simpler formula.
Li3InBr6 and NaInBr4 have been synthesized and characterized by means of DTA, 81Br NQR, 6Li, 7Li, 23Na, and 115In NMR, and AC conductivity. These measurements revealed the presence of phase transitions and cationic diffusion in both compounds. From the spin-lattice relaxation times of 81Br NQR and the peak widths of 7Li and 23Na NMR spectra, it is deduced that the conduction is due to cationic diffusion. The activity energy for the Li+ diffusion was found to be 24 kJ/mol for Li3InBr6 .
The flagellar autofluorescent substance of the brown alga Scytosiphon lomentaria , which is probably involved in the photoreception of the phototaxis of flagellate cells, was investi gated. 4′,5′-Cyclic FMN (1) was isolated from the extract of whole mature plants for the first time as a natural product. Since the concentration of 4′,5′-cyclic FMN (1) was considerably low in vegetative plants, which do not contain fluorescent flagella, this substance is considered to correspond to the flagellar fluorescent substance.
Influenza A virus (IAV) is one of the most common infectious pathogens in humans. Entry of this virus into cells is primarily determined by host cellular trypsin-type processing proteases, which proteolytically activate viral membrane fusion glycoprotein precursors. Human IAV and murine parainfluenza virus type 1 Sendai virus are exclusively pneumotropic, and the infectious organ tropism of these viruses is determined by the susceptibility of the viral envelope glycoprotein to cleavage by proteases in the airway. Proteases in the upper respiratory tract are suppressed by secretory leukoprotease inhibitor, and those in the lower respiratory tract are suppressed by pulmonary surfactant, which by adsorption inhibits the interaction between the proteases and viral membrane proteins. Although the protease activities are predominant over the activities of inhibitory compounds under normal airway conditions, intranasal administration of inhibitors was able to significantly suppress multi-cycles of viral replication in the airway. In addition, we identified chemical agents that could act as defensive factors by up-regulating the levels of the natural inhibitors and immunoglobulin A (IgA) in airway fluids. One of these compounds, ambroxol, is a mucolytic and anti-oxidant agent that stimulates the release of secretory leukoprotease inhibitor and pulmonary surfactant in the early phase, and IgA in the late phase of infection at an optimal dose, i.e. a dose sufficient to inhibit virus proliferation and increase the survival rate of animals after treatment with a lethal dose of IAV. Another agent, clarithromycin, is a macrolide antibiotic that increases IgA levels through augmentation of interleukin-12 levels and mucosal immunization in the airway. In addition to the sialidase inhibitors, which prevent the release of IAV from infected cells, inhibitors of the processing proteases and chemical agents that augment mucosal immunity and/or levels of the relevant defensive compounds may also ultimately prove to be useful as new anti-influenza agents.