Game-theoretic versions of strong law of large numbers for unbounded variables

We consider strong law of large numbers (SLLN) in the framework of game-theoretic probability of Shafer and Vovk (2001). We prove several versions of SLLN for the case that Reality's moves are unbounded. Our game-theoretic versions of SLLN largely correspond to standard measure-theoretic results. However game-theoretic proofs are different from measure-theoretic ones in the explicit consideration of various hedges. In measure-theoretic proofs existence of moments are assumed, whereas in our game-theoretic proofs we assume availability of various hedges to Skeptic for finite prices

Information criteria for efficient quantum state estimation

Recently several more efficient versions of quantum state tomography have been proposed, with the purpose of making tomography feasible even for many-qubit states. The number of state parameters to be estimated is reduced by tentatively introducing certain simplifying assumptions on the form of the quantum state, and subsequently using the data to rigorously verify these assumptions. The simplifying assumptions considered so far were (i) the state can be well approximated to be of low rank, or (ii) the state can be well approximated as a matrix product state. We add one more method in that same spirit: we allow in principle any model for the state, using any (small) number of parameters (which can, e.g., be chosen to have a clear physical meaning), and the data are used to verify the model. The proof that this method is valid cannot be as strict as in above-mentioned cases, but is based on well-established statistical methods that go under the name of "information criteria." We exploit here, in particular, the Akaike Information Criterion (AIC). We illustrate the method by simulating experiments on (noisy) Dicke states

Star formation and dust extinction properties of local galaxies from AKARI-GALEX All-Sky Surveys: First results from most secure multiband sample from FUV to FIR

The AKARI All-Sky Survey provided the first bright point source catalog detected at 90um. Starting from this catalog, we selected galaxies by matching AKARI sources with those in the IRAS PSCz. Next, we have measured total GALEX FUV and NUV flux densities. Then, we have matched this sample with SDSS and 2MASS galaxies. By this procedure, we obtained the final sample which consists of 607 galaxies. If we sort the sample with respect to 90um, their average SED shows a coherent trend: the more luminous at 90um, the redder the global SED becomes. The M_r--NUV-r color-magnitude relation of our sample does not show bimodality, and the distribution is centered on the green valley between the blue cloud and red sequence seen in optical surveys. We have established formulae to convert FIR luminosity from AKARI bands to the total infrared (IR) luminosity L_TIR. With these formulae, we calculated the star formation directly visible with FUV and hidden by dust. The luminosity related to star formation activity (L_SF) is dominated by L_TIR even if we take into account the far-infrared (FIR) emission from dust heated by old stars. At high star formation rate (SFR) (> 20 Msun yr^-1), the fraction of directly visible SFR, SFR_FUV, decreases. We also estimated the FUV attenuation A_FUV from FUV-to-total IR (TIR) luminosity ratio. We also examined the L_TIR/L_FUV-UV slope (FUV- NUV) relation. The majority of the sample has L_TIR/L_FUV ratios 5 to 10 times lower than expected from the local starburst relation, while some LIRGs and all the ULIRGs of this sample have higher L_TIR/L_FUV ratios. We found that the attenuation indicator L_TIR/L_FUV is correlated to the stellar mass of galaxies, M*, but there is no correlation with specific SFR (SSFR), SFR/M*, and dust attenuation L_TIR/L_FUV. (abridged)Comment: 13 pages, 18 figures, accepted for publication in A&

Locking Local Oscillator Phase to the Atomic Phase via Weak Measurement

We propose a new method to reduce the frequency noise of a Local Oscillator (LO) to the level of white phase noise by maintaining (not destroying by projective measurement) the coherence of the ensemble pseudo-spin of atoms over many measurement cycles. This scheme uses weak measurement to monitor the phase in Ramsey method and repeat the cycle without initialization of phase and we call, "atomic phase lock (APL)" in this paper. APL will achieve white phase noise as long as the noise accumulated during dead time and the decoherence are smaller than the measurement noise. A numerical simulation confirms that with APL, Allan deviation is averaged down at a maximum rate that is proportional to the inverse of total measurement time, tau^-1. In contrast, the current atomic clocks that use projection measurement suppress the noise only down to the level of white frequency, in which case Allan deviation scales as tau^-1/2. Faraday rotation is one of the possible ways to realize weak measurement for APL. We evaluate the strength of Faraday rotation with 171Yb+ ions trapped in a linear rf-trap and discuss the performance of APL. The main source of the decoherence is a spontaneous emission induced by the probe beam for Faraday rotation measurement. One can repeat the Faraday rotation measurement until the decoherence become comparable to the SNR of measurement. We estimate this number of cycles to be ~100 cycles for a realistic experimental parameter.Comment: 18 pages, 7 figures, submitted to New Journal of Physic

Superconductivity Under Pressure in FeSe1-xTex Studied by DC Magnetic Measurements

AbstractSuperconductivity under pressure in FeSe1−xTex with x=0.7 (TC∽14K) has been investigated by the measurements of DC magnetization using high quality single crystal specimens. It has been found that TC increases and makes a maximum of ∽15K at 1GPa but rapidly decreases above 1GPa under hydrostatic pressure using liquid Ar as pressure transmitting media (PTM). In contrast, TC is found to increase up to 18K at 2.5GPa then decrease gradually under nearly uniaxial pressure along c-axis using NaCl as PTM. It is also found that TC reaches a maximum of 16K at 1GPa but is nearly pressure independent above 1GPa under nearly uniaxial pressure along a-axis. These behaviors suggest that the superconductivity is suppressed by the isotropic compression but is enhanced (not changed) by the uniaxial compression along c-axis (a-axis)