Pattern-recalling processes in quantum Hopfield networks far from saturation

As a mathematical model of associative memories, the Hopfield model was now well-established and a lot of studies to reveal the pattern-recalling process have been done from various different approaches. As well-known, a single neuron is itself an uncertain, noisy unit with a finite unnegligible error in the input-output relation. To model the situation artificially, a kind of 'heat bath' that surrounds neurons is introduced. The heat bath, which is a source of noise, is specified by the 'temperature'. Several studies concerning the pattern-recalling processes of the Hopfield model governed by the Glauber-dynamics at finite temperature were already reported. However, we might extend the 'thermal noise' to the quantum-mechanical variant. In this paper, in terms of the stochastic process of quantum-mechanical Markov chain Monte Carlo method (the quantum MCMC), we analytically derive macroscopically deterministic equations of order parameters such as 'overlap' in a quantum-mechanical variant of the Hopfield neural networks (let us call "quantum Hopfield model" or "quantum Hopfield networks"). For the case in which non-extensive number $p$ of patterns are embedded via asymmetric Hebbian connections, namely, $p/N \to 0$ for the number of neuron $N \to \infty$ ('far from saturation'), we evaluate the recalling processes for one of the built-in patterns under the influence of quantum-mechanical noise.Comment: 10 pages, 3 figures, using jpconf.cls, Proc. of Statphys-Kolkata VI

Exact Computation of Influence Spread by Binary Decision Diagrams

Evaluating influence spread in social networks is a fundamental procedure to estimate the word-of-mouth effect in viral marketing. There are enormous studies about this topic; however, under the standard stochastic cascade models, the exact computation of influence spread is known to be #P-hard. Thus, the existing studies have used Monte-Carlo simulation-based approximations to avoid exact computation. We propose the first algorithm to compute influence spread exactly under the independent cascade model. The algorithm first constructs binary decision diagrams (BDDs) for all possible realizations of influence spread, then computes influence spread by dynamic programming on the constructed BDDs. To construct the BDDs efficiently, we designed a new frontier-based search-type procedure. The constructed BDDs can also be used to solve other influence-spread related problems, such as random sampling without rejection, conditional influence spread evaluation, dynamic probability update, and gradient computation for probability optimization problems. We conducted computational experiments to evaluate the proposed algorithm. The algorithm successfully computed influence spread on real-world networks with a hundred edges in a reasonable time, which is quite impossible by the naive algorithm. We also conducted an experiment to evaluate the accuracy of the Monte-Carlo simulation-based approximation by comparing exact influence spread obtained by the proposed algorithm.Comment: WWW'1

Non-equilibrium spin accumulation in ferromagnetic single-electron transistors

We study transport in ferromagnetic single-electron transistors. The non- equilibrium spin accumulation on the island caused by a finite current through the system is described by a generalized theory of the Coulomb blockade. It enhances the tunnel magnetoresistance and has a drastic effect on the time- dependent transport properties. A transient decay of the spin accumulation may reverse the electric current on time scales of the order of the spin-flip relaxation time. This can be used as an experimental signature of the non- equilibrium spin accumulation.Comment: 9 postscript figures, to appear in The European Physical Journal

Possible Magnetic Chirality in Optically Chiral Magnet [Cr(CN)6_6][Mn(SS)-pnH(H2_2O)](H2_2O) Probed by Muon Spin Rotation and Relaxation

Local magnetic fields in a molecule-based optically chiral magnet [Cr(CN)$_6$][Mn($S$)-pnH(H$_2$O)](H$_2$O) (GN-S) and its enantiomer (GN-R) are studied by means of muon spin rotation and relaxation (muSR). Detailed analysis of muon precession signals under zero field observed below T_c supports the average magnetic structure suggested by neutron powder diffraction. Moreover, comparison of muSR spectra between GN-S and GN-R suggests that they are a pair of complete optical isomers in terms of both crystallographic and magnetic structure. Possibility of magnetic chirality in such a pair is discussed.Comment: 5 pages, 5 figures, submitted to J. Phys. Soc. Jp

A mechanism for unipolar resistance switching in oxide non-volatile memory devices

Building on a recently introduced model for non-volatile resistive switching, we propose a mechanism for unipolar resistance switching in metal-insulator-metal sandwich structures. The commutation from the high to low resistance state and back can be achieved with successive voltage sweeps of the same polarity. Electronic correlation effects at the metal-insulator interface are found to play a key role to produce a resistive commutation effect in qualitative agreement with recent experimental reports on binary transition metal oxide based sandwich structures.Comment: 4 pages, 2 figure

How large is our universe?

We reexamine constraints on the spatial size of closed toroidal models with cold dark matter and the cosmological constant from cosmic microwave background. We carry out Bayesian analyses using the Cosmic Background Explorer (COBE) data properly taking into account the statistically anisotropic correlation, i.e., off-diagonal elements in the covariance. We find that the COBE constraint becomes more stringent in comparison with that using only the angular power spectrum, if the likelihood is marginalized over the orientation of the observer. For some limited choices of orientations, the fit to the COBE data is considerably better than that of the infinite counterpart. The best-fit matter normalization is increased because of large-angle suppression in the power and the global anisotropy of the temperature fluctuations. We also study several deformed closed toroidal models in which the fundamental cell is described by a rectangular box. In contrast to the cubic models, the large-angle power can be enhanced in comparison with the infinite counterparts if the cell is sufficiently squashed in a certain direction. It turns out that constraints on some slightly deformed models are less stringent. We comment on how these results affect our understanding of the global topology of our universe.Comment: 19 pages, 9 figures, version accepted for PRD. More elaborate discussion on the best-fit orientation has been adde

High Resolution VSOP Imaging of a Southern Blazar PKS 1921-293 at 1.6 GHz

We present a high resolution 1.6 GHz VSOP image of the southern blazar PKS 1921-293. The image shows a typical core-jet morphology, consistent with ground-based VLBI images. However, the addition of data from the space antenna has greatly improved the angular resolution (especially along the north-south direction for this source), and thus allowed us to clearly identify the core. Model fitting reveals an inner jet component ~1.5 mas north of the core. This jet feature may be moving on a common curved path connecting the jet within a few parsecs to the 10-parsec-scale jet. The compact core has a brightness temperature of 2.6*10**12 K (in the rest frame of the quasar), an indication of relativistic beaming. We analyzed the source in terms of three models, involving the inverse Compton catastrophe, an inhomogeneous relativistic jet, and the equipartition of energy between the radiating particles and the magnetic field. Our analysis of this gamma-ray-quiet blazar shows no preference to any particular one of these models.Comment: 7 pages including 2 figures and 1 table, PASJLaTeX, accepted for publication in PAS

Fermi Surface of 3d^1 Perovskite CaVO3 Near the Mott Transition

We present a detailed de Haas van Alphen effect study of the perovskite CaVO3, offering an unprecedented test of electronic structure calculations in a 3d transition metal oxide. Our experimental and calculated Fermi surfaces are in good agreement -- but only if we ignore large orthorhombic distortions of the cubic perovskite structure. Subtle discrepancies may shed light on an apparent conflict between the low energy properties of CaVO3, which are those of a simple metal, and high energy probes which reveal strong correlations that place CaVO3 on the verge of a metal-insulator transition.Comment: 4 pages, 4 figures (REVTeX

The Nature of the Hard-X-Ray Emitting Symbiotic Star RT Cru

We describe Chandra High-Energy Transmission Grating Spectrometer observations of RT Cru, the first of a new sub-class of symbiotic stars that appear to contain white dwarfs (WDs) capable of producing hard X-ray emission out to greater than 50 keV. The production of such hard X-ray emission from the objects in this sub-class (which also includes CD -57 3057, T CrB, and CH Cyg) challenges our understanding of accreting WDs. We find that the 0.3 -- 8.0 keV X-ray spectrum of RT Cru emanates from an isobaric cooling flow, as in the optically thin accretion-disk boundary layers of some dwarf novae. The parameters of the spectral fit confirm that the compact accretor is a WD, and they are consistent with the WD being massive. We detect rapid, stochastic variability from the X-ray emission below 4 keV. The combination of flickering variability and a cooling-flow spectrum indicates that RT Cru is likely powered by accretion through a disk. Whereas the cataclysmic variable stars with the hardest X-ray emission are typically magnetic accretors with X-ray flux modulated at the WD spin period, we find that the X-ray emission from RT Cru is not pulsed. RT Cru therefore shows no evidence for magnetically channeled accretion, consistent with our interpretation that the Chandra spectrum arises from an accretion-disk boundary layer.Comment: 3 figures, accepted for publication in Ap

Weak commutation relations of unbounded operators: nonlinear extensions

We continue our analysis of the consequences of the commutation relation [S,T]=\Id, where $S$ and $T$ are two closable unbounded operators. The {\em weak} sense of this commutator is given in terms of the inner product of the Hilbert space \H where the operators act. {We also consider what we call, adopting a physical terminology}, a {\em nonlinear} extension of the above commutation relations