820 research outputs found
Replica Symmetry Breaking and the Kuhn-Tucker Cavity Method in simple and multilayer Perceptrons
Within a Kuhn-Tucker cavity method introduced in a former paper, we study
optimal stability learning for situations, where in the replica formalism the
replica symmetry may be broken, namely
(i) the case of a simple perceptron above the critical loading, and
(ii) the case of two-layer AND-perceptrons, if one learns with maximal
stability.
We find that the deviation of our cavity solution from the replica symmetric
one in these cases is a clear indication of the necessity of replica symmetry
breaking. In any case the cavity solution tends to underestimate the storage
capabilities of the networks.Comment: 32 pages, LaTex Source with 9 .eps-files enclosed, accepted by J.
Phys I (France
The impact of two-dimensional elastic disk
The impact of a two-dimensional elastic disk with a wall is numerically
studied. It is clarified that the coefficient of restitution (COR) decreases
with the impact velocity. The result is not consistent with the recent
quasi-static theory of inelastic collisions even for very slow impact. The
abrupt drop of COR is found due to the plastic deformation of the disk, which
is assisted by the initial internal motion.(to be published in J. Phys. Soc.
Jpn.)Comment: 6 Pages,2 figure
Statics and dynamics of an Ashkin-Teller neural network with low loading
An Ashkin-Teller neural network, allowing for two types of neurons is
considered in the case of low loading as a function of the strength of the
respective couplings between these neurons. The storage and retrieval of
embedded patterns built from the two types of neurons, with different degrees
of (in)dependence is studied. In particular, thermodynamic properties including
the existence and stability of Mattis states are discussed. Furthermore, the
dynamic behaviour is examined by deriving flow equations for the macroscopic
overlap. It is found that for linked patterns the model shows better retrieval
properties than a corresponding Hopfield model.Comment: 20 pages, 6 figures, Latex with postscript figures in one tar.gz fil
Collision of One-Dimensional Nonlinear Chains
We investigate one-dimensional collisions of unharmonic chains and a rigid
wall. We find that the coefficient of restitution (COR) is strongly dependent
on the velocity of colliding chains and has a minimum value at a certain
velocity. The relationship between COR and collision velocity is derived for
low-velocity collisions using perturbation methods. We found that the velocity
dependence is characterized by the exponent of the lowest unharmonic term of
interparticle potential energy
Development of Slowed Down Beams at the Fragment Separator for FAIR
The feasibility studies of the slowed down beam setup involving deceleration of a 64Ni beam at 250 MeV/u to 13 MeV/u in a thick Al degrader was performed at the FRagment Separator (FRS) at GSI. The experimentally measured energy spread and the nuclear reaction yields in the degrader are in good agreement with simulations
Performance of HPGe Detectors in High Magnetic Fields
A new generation of high-resolution hypernuclear gamma$-spectroscopy
experiments with high-purity germanium detectors (HPGe) are presently designed
at the FINUDA spectrometer at DAPhiNE, the Frascati phi-factory, and at PANDA,
the antiproton proton hadron spectrometer at the future FAIR facility. Both,
the FINUDA and PANDA spectrometers are built around the target region covering
a large solid angle. To maximise the detection efficiency the HPGe detectors
have to be located near the target, and therefore they have to be operated in
strong magnetic fields B ~ 1 T. The performance of HPGe detectors in such an
environment has not been well investigated so far. In the present work VEGA and
EUROBALL Cluster HPGe detectors were tested in the field provided by the ALADiN
magnet at GSI. No significant degradation of the energy resolution was found,
and a change in the rise time distribution of the pulses from preamplifiers was
observed. A correlation between rise time and pulse height was observed and is
used to correct the measured energy, recovering the energy resolution almost
completely. Moreover, no problems in the electronics due to the magnetic field
were observed.Comment: submitted to Nucl. Instrum. Meth. Phys. Res. A, LaTeX, 19 pages, 9
figure
Fission half-lives of super-heavy nuclei in a microscopic approach
A systematic study of 160 heavy and super-heavy nuclei is performed in the
Hartree-Fock-Bogoliubov approach with the finite range and density dependent
Gogny force with the D1S parameter set. We show calculations in several
approximations: with axially symmetric and reflexion symmetric wave functions,
with axially symmetric and non-reflexion symmetric wave functions and finally
some representative examples with triaxial wave functions are also discussed.
Relevant properties of the ground state and along the fission path are
thoroughly analyzed. Fission barriers, Q-factors and lifetimes with
respect to fission and -decay as well as other observables are
discussed. Larger configuration spaces and more general HFB wave functions as
compared to previous studies provide a very good agreement with the
experimental data.Comment: 26 pages, 15 figure
Optimal coloured perceptrons
Ashkin-Teller type perceptron models are introduced. Their maximal capacity
per number of couplings is calculated within a first-step
replica-symmetry-breaking Gardner approach. The results are compared with
extensive numerical simulations using several algorithms.Comment: 8 pages in Latex with 2 eps figures, RSB1 calculations has been adde
Storage capacity of a constructive learning algorithm
Upper and lower bounds for the typical storage capacity of a constructive
algorithm, the Tilinglike Learning Algorithm for the Parity Machine [M. Biehl
and M. Opper, Phys. Rev. A {\bf 44} 6888 (1991)], are determined in the
asymptotic limit of large training set sizes. The properties of a perceptron
with threshold, learning a training set of patterns having a biased
distribution of targets, needed as an intermediate step in the capacity
calculation, are determined analytically. The lower bound for the capacity,
determined with a cavity method, is proportional to the number of hidden units.
The upper bound, obtained with the hypothesis of replica symmetry, is close to
the one predicted by Mitchinson and Durbin [Biol. Cyber. {\bf 60} 345 (1989)].Comment: 13 pages, 1 figur
Hydrodynamics of driven granular gases
Hydrodynamic equations for granular gases driven by the Fokker-Planck
operator are derived. Transport coefficients appeared in Navier-Stokes order
change from the values of a free cooling state to those of a steady state.Comment: 5 pages, 3 figure
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