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

Loopy belief propagation and probabilistic image processing

Estimation of hyperparameters by maximization of the marginal likelihood in probabilistic image processing is investigated by using the cluster variation method. The algorithms are substantially equivalent to generalized loopy belief propagation

Giant Intrinsic Spin and Orbital Hall Effects in Sr2MO4 (M=Ru,Rh,Mo)

We investigate the intrinsic spin Hall conductivity (SHC) and the d-orbital Hall conductivity (OHC) in metallic d-electron systems, by focusing on the t_{2g}-orbital tight-binding model for Sr2MO4 (M=Ru,Rh,Mo). The conductivities obtained are one or two orders of magnitude larger than predicted values for p-type semiconductors with 5% hole doping. The origin of these giant Hall effects is the ``effective Aharonov-Bohm phase'' that is induced by the d-atomic angular momentum in connection with the spin-orbit interaction and the inter-orbital hopping integrals. The huge SHC and OHC generated by this mechanism are expected to be ubiquitous in multiorbital transition metal complexes, which pens the possibility of realizing spintronics as well as orbitronics devices.Comment: 5 pages, accepted for publication in PR

Tunnel magnetoresistance and interfacial electronic state

We study the relation between tunnel magnetoresistance (TMR) and interfacial electronic states modified by magnetic impurities introduced at the interface of the ferromagnetic tunnel junctions, by making use of the periodic Anderson model and the linear response theory. It is indicated that the TMR ratio is strongly reduced depending on the position of the $d$-levels of impurities, based on reduction in the spin-dependent $s$-electron tunneling in the majority spin state. The results are compared with experimental results for Cr-dusted ferromagnetic tunnel junctions, and also with results for metallic multilayers for which similar reduction in giant magnetoresistance has been reported.Comment: 5 pages, 4 figures, 2 column revtex4 format, ICMFS 2002 (Kyoto

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

Electronic structure of Ca1−x_{1-x}Srx_xVO3_3: a tale of two energy-scales

We investigate the electronic structure of Ca$_{1-x}$Sr$_x$VO$_3$ using photoemission spectroscopy. Core level spectra establish an electronic phase separation at the surface, leading to distinctly different surface electronic structure compared to the bulk. Analysis of the photoemission spectra of this system allowed us to separate the surface and bulk contributions. These results help us to understand properties related to two vastly differing energy-scales, namely the low energy-scale of thermal excitations (~$k_{B}T$) and the high-energy scale related to Coulomb and other electronic interactions.Comment: 4 pages and 3 figures. Europhysics Letters (appearing