Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

Rhythmic Motion of a Droplet under a DC Electric Field

The effect of a stationary electric field on a water droplet with a diameter of several tens micrometers in oil was examined. Such a droplet exhibits repetitive translational motion between the electrodes in a spontaneous manner. The state diagram of this oscillatory motion was deduced; at 0-20 V the droplet is fixed at the surface of the electrode, at 20-70 V the droplet exhibits small-amplitude oscillatory motion between the electrodes, and at 70-100 V the droplet shows large-amplitude periodic motion between the electrodes. The observed rhythmic motion is explained in a semi-quantitative manner by using differential equations, which includes the effect of charging the droplet under an electric field. We also found that twin droplets exhibit synchronized rhythmic motion between the electrodes

Entanglement Purification of Any Stabilizer State

We present a method for multipartite entanglement purification of any stabilizer state shared by several parties. In our protocol each party measures the stabilizer operators of a quantum error-correcting code on his or her qubits. The parties exchange their measurement results, detect or correct errors, and decode the desired purified state. We give sufficient conditions on the stabilizer codes that may be used in this procedure and find that Steane's seven-qubit code is the smallest error-correcting code sufficient to purify any stabilizer state. An error-detecting code that encodes two qubits in six can also be used to purify any stabilizer state. We further specify which classes of stabilizer codes can purify which classes of stabilizer states.Comment: 11 pages, 0 figures, comments welcome, submitting to Physical Review

Picosecond Nonlinear Relaxation of Photoinjected Carriers in a Single GaAs/AlGaAs Quantum Dot

Photoemission from a single self-organized GaAs/AlGaAs quantum dot (QD) is temporally resolved with picosecond time resolution. The emission spectra consisting of the multiexciton structures are observed to depend on the delay time and the excitation intensity. Quantitative agreement is found between the experimental data and the calculation based on a model which characterizes the successive relaxation of multiexcitons. Through the analysis we can determine the carrier relaxation time as a function of population of photoinjected carriers. Enhancement of the intra-dot carrier relaxation is demonstrated to be due to the carrier-carrier scattering inside a single QD.Comment: 4 pages, 4 figures, to be published in Phys. Rev. B, Rapid