On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J-test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications need to be introduced. The example also reveals that empirical and parametric likelihood may have non-negligible differences for the types of properties we consider, even in models in which they are first-order asymptotically equivalent. Second, under stronger assumptions than those in Kitamura (2001), we establish the following optimality result: (i) empirical likelihood controls the rate at which the probability of a Type I error tends to zero and (ii) among all procedures for which the probability of a Type I error tends to zero at least as fast, empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for "most" alternatives. This result further implies that empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their Type I error probabilities.Empirical likelihood, Large deviations, Hoeffding optimality, Moment restrictions

Switching Dynamics in Reaction Networks Induced by Molecular Discreteness

To study the fluctuations and dynamics in chemical reaction processes, stochastic differential equations based on the rate equation involving chemical concentrations are often adopted. When the number of molecules is very small, however, the discreteness in the number of molecules cannot be neglected since the number of molecules must be an integer. This discreteness can be important in biochemical reactions, where the total number of molecules is not significantly larger than the number of chemical species. To elucidate the effects of such discreteness, we study autocatalytic reaction systems comprising several chemical species through stochastic particle simulations. The generation of novel states is observed; it is caused by the extinction of some molecular species due to the discreteness in their number. We demonstrate that the reaction dynamics are switched by a single molecule, which leads to the reconstruction of the acting network structure. We also show the strong dependence of the chemical concentrations on the system size, which is caused by transitions to discreteness-induced novel states.Comment: 11 pages, 5 figure

On the Asymptotic Optimality of Empirical Likelihood for Testing Moment Restrictions

In this paper we make two contributions. First, we show by example that empirical likelihood and other commonly used tests for parametric moment restrictions, including the GMM-based J -test of Hansen (1982), are unable to control the rate at which the probability of a Type I error tends to zero. From this it follows that, for the optimality claim for empirical likelihood in Kitamura (2001) to hold, additional assumptions and qualifications need to be introduced. The example also reveals that empirical and parametric likelihood may have non-negligible differences for the types of properties we consider, even in models in which they are first-order asymptotically equivalent. Second, under stronger assumptions than those in Kitamura (2001), we establish the following optimality result: (i) empirical likelihood controls the rate at which the probability of a Type I error tends to zero and (ii) among all procedures for which the probability of a Type I error tends to zero at least as fast, empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for “most” alternatives. This result further implies that empirical likelihood maximizes the rate at which probability of a Type II error tends to zero for all alternatives among a class of tests that satisfy a weaker criterion for their Type I error probabilities

Chandra Snapshot Observations of Low-Luminosity AGNs with a Compact Radio Source

The results of Chandra snapshot observations of 11 LINERs (Low-Ionization Nuclear Emission-line Regions), three low-luminosity Seyfert galaxies, and one HII-LINER transition object are presented. Our sample consists of all the objects with a flat or inverted spectrum compact radio core in the VLA survey of 48 low-luminosity AGNs (LLAGNs) by Nagar et al. (2000). An X-ray nucleus is detected in all galaxies except one and their X-ray luminosities are in the range 5x10^38 to 8x10^41 erg/s. The X-ray spectra are generally steeper than expected from thermal bremsstrahlung emission from an advection-dominated accretion flow (ADAF). The X-ray to Halpha luminosity ratios for 11 out of 14 objects are in good agreement with the value characteristic of LLAGNs and more luminous AGNs, and indicate that their optical emission lines are predominantly powered by a LLAGN. For three objects, this ratio is less than expected. Comparing with properties in other wavelengths, we find that these three galaxies are most likely to be heavily obscured AGN. We use the ratio RX = \nu L\nu (5 GHz)/LX, where LX is the luminosity in the 2-10 keV band, as a measure of radio loudness. In contrast to the usual definition of radio loudness (RO = L\nu(5 GHz)/L\nu(B)), RX can be used for heavily obscured (NH >~ 10^23 cm^-2, AV>50 mag) nuclei. Further, with the high spatial resolution of Chandra, the nuclear X-ray emission of LLAGNs is often easier to measure than the nuclear optical emission. We investigate the values of RX for LLAGNs, luminous Seyfert galaxies, quasars and radio galaxies and confirm the suggestion that a large fraction of LLAGNs are radio loud.Comment: 15 pages, accepted for publication in Ap

Mapping the Polarization of the Radio-Loud Lyα\alpha Nebula B3 J2330+3927

Lya nebulae, or "Lya blobs", are extended (up to ~100 kpc), bright (L[Lya] > 10^43 erg/s) clouds of Lya emitting gas that tend to lie in overdense regions at z ~ 2--5. The origin of the Lya emission remains unknown, but recent theoretical work suggests that measuring the polarization might discriminate among powering mechanisms. Here we present the first narrowband, imaging polarimetry of a radio-loud Lya nebula, B3 J2330+3927 at z=3.09, with an embedded active galactic nucleus (AGN). The AGN lies near the blob's Lya emission peak and its radio lobes align roughly with the blob's major axis. With the SPOL polarimeter on the 6.5m MMT telescope, we map the total (Lya + continuum) polarization in a grid of circular apertures of radius 0.6" (4.4kpc), detecting a significant (>2sigma) polarization fraction P in nine apertures and achieving strong upper-limits (as low as 2%) elsewhere. P increases from <2% at ~5kpc from the blob center to ~17% at ~15-25kpc. The detections are distributed asymmetrically, roughly along the nebula's major axis. The polarization angles theta are mostly perpendicular to this axis. Comparing the Lya flux to that of the continuum, and conservatively assuming that the continuum is highly polarized (20-100%) and aligned with the total polarization, we place lower limits on the polarization of the Lya emission P(Lya) ranging from no significant polarization at ~5 kpc from the blob center to ~ 3--17% at 10--25kpc. Like the total polarization, the Lya polarization detections occur more often along the blob's major axis.Comment: 9 pages, 7 figures, accepted for publication in Ap

A Chandra Observation of M51: Active Nucleus and Nuclear Outflows

We present a Chandra ACIS-S observation of the nuclear region of the nearby spiral galaxy M51 (NGC 5194), which has a low-luminosity Seyfert 2 nucleus. The X-ray image shows the nucleus, southern extranuclear cloud, and northern loop, the morphology of the extended emission being very similar to those seen in radio continuum and optical emission line images. The X-ray spectrum of the nucleus is well represented by a model consisting of soft thermal plasma with kT ~0.5 keV, a very hard continuum, and an Fe Kalpha emission line at 6.45 keV with an equivalent width of >2 keV. The very strong Fe line and the flat continuum indicate that the nucleus is obscured by a column density in excess of 10^24 cm^-2 and the spectrum is dominated by reflected emission from cold matter near the nucleus. The X-ray spectra of the extranuclear clouds are well fitted by a thermal plasma model with kT ~0.5 keV. This spectral shape and morphology strongly suggest that the clouds are shock heated by the bi-polar outflow from the nucleus. The shock velocities of the extranuclear cloud and northern loop inferred from the temperatures of the X-ray gas are 690 km/s and 660 km/s, respectively. By assuming a steady-state situation in which the emission of the extranuclear clouds is powered by the jets, the mechanical energy in the jets is found to be comparable to the bolometric luminosity of the nucleus.Comment: 7 pages, 5 figures, Accepted for publication in the Astrophyscal Jouna

Hox gene and development of the auditory circuit

Sound vibration is sensed by hair cells in the inner ear. The information is transmitted to the cochlear nucleus in the brainstem via spiral ganglion neurons. The information is further transmitted to higher relaying centers in the brain such as superior olivary complex and inferior colliculus. The connectivity between these components is topographically organized in a frequency-specific manner. It is known that the organization is well-established from the beginning of the circuit development. However, little is still known about the molecular mechanisms underlying the development of connectivity in the auditory circuit. Homeobox transcription factors of the Hox gene family are known for their involvement in early anterior-posterior axis patterning of neuronal progenitors in the hindbrain. Recent evidence indicates that they also play important roles in late aspects of neuronal development and establishment of topographic circuitry. Moreover, a mutation in the HOXA2 gene has been recently shown to be responsible for hearing deficits in humans. By means of spatiotemporally controlled Hoxa2 and Hoxb2 conditional mutations in the mouse we analyzed the involvement of these factors in auditory circuit development and connectivity

The Coffee Market in Japan

This publication presents information on Japan in the world coffee market. It includes distribution channels in Japan and consumer profiles and perceptions

Magnetic-Field-Independent Ultrasonic Dispersions in the Magnetically Robust Heavy Fermion System SmOs4Sb12

Elastic properties of the filled skutterudite compound SmOs$_4$Sb$_{12}$ have been investigated by ultrasonic measurements. The elastic constant $C_{11}(\omega)$ shows two ultrasonic dispersions at $\sim$15 K and $\sim$53 K for frequencies $\omega$ between 33 and 316 MHz, which follow a Debye-type formula with Arrhenius-type temperature-dependent relaxation times, and remain unchanged even with applied magnetic fields up to 10 T. The corresponding activation energies were estimated to be $E_2$ = 105 K and $E_1$ = 409 K, respectively. The latter, $E_1$, is the highest value reported so far in the Sb-based filled skutterudites. The presence of magnetically robust ultrasonic dispersions in SmOs$_4$Sb$_{12}$ implies a possibility that an emergence of a magnetically insensitive heavy fermion state in this system is associated with a novel local charge degree of freedom which causes the ultrasonic dispersion.Comment: 5 pages, 4 figure