20,387 research outputs found
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 of
patterns are embedded via asymmetric Hebbian connections, namely,
for the number of neuron ('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
Ambipolar Diffusion-Mediated Thermal Fronts in the Neutral ISM
In a thermally bistable medium, cold, dense gas is separated from warm,
rareified gas by thin phase transition layers, or fronts, in which heating,
radiative cooling, thermal conduction, and convection of material are balanced.
We calculate the steady-state structure of such fronts in the presence of
magnetic fields, including the processes of ion-neutral drift and ion-neutral
frictional heating. We find that ambipolar diffusion efficiently transports the
magnetic field across the fronts, leading to a flat magnetic field strength
profile. The thermal profiles of such fronts are not significantly different
from those of unmagnetized fronts. The near uniformity of the magnetic field
strength across a front is consistent with the flat field strength-gas density
relation that is observed in diffuse interstellar gas.Comment: 17 pages, 12 figures, 1 table, accepted for publication in Ap
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
Prompt GeV-TeV Emission of Gamma-Ray Bursts Due to High-Energy Protons, Muons and Electron-Positron Pairs
In the framework of the internal shock scenario, we model the broadband
prompt emission of gamma-ray bursts (GRBs) with emphasis on the GeV-TeV bands,
utilizing Monte Carlo simulations that include various processes associated
with electrons and protons accelerated to high energies. While inverse Compton
emission from primary electrons is often dominant, different proton-induced
mechanisms can also give rise to distinct high-energy components, such as
synchrotron emission from protons, muons or secondary electrons/positrons
injected via photomeson interactions. In some cases, they give rise to double
spectral breaks that can serve as unique signatures of ultra-high-energy
protons. We discuss the conditions favorable for such emission, and how they
are related to the production of ultra-high-energy cosmic rays and neutrinos in
internal shocks. Ongoing and upcoming observations by {\it GLAST}, atmospheric
Cerenkov telescopes and other facilities will test these expectations and
provide important information on the physical conditions in GRB outflows.Comment: 11 pages, 8 figures and 14 appendix figures, accepted for publication
in ApJ vol. 671 with minor revision
Possible Magnetic Chirality in Optically Chiral Magnet [Cr(CN)][Mn()-pnH(HO)](HO) Probed by Muon Spin Rotation and Relaxation
Local magnetic fields in a molecule-based optically chiral magnet
[Cr(CN)][Mn()-pnH(HO)](HO) (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
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
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