14,261 research outputs found
Storage capacity of correlated perceptrons
We consider an ensemble of single-layer perceptrons exposed to random
inputs and investigate the conditions under which the couplings of these
perceptrons can be chosen such that prescribed correlations between the outputs
occur. A general formalism is introduced using a multi-perceptron costfunction
that allows to determine the maximal number of random inputs as a function of
the desired values of the correlations. Replica-symmetric results for and
are compared with properties of two-layer networks of tree-structure and
fixed Boolean function between hidden units and output. The results show which
correlations in the hidden layer of multi-layer neural networks are crucial for
the value of the storage capacity.Comment: 16 pages, Latex2
Correlations between hidden units in multilayer neural networks and replica symmetry breaking
We consider feed-forward neural networks with one hidden layer, tree
architecture and a fixed hidden-to-output Boolean function. Focusing on the
saturation limit of the storage problem the influence of replica symmetry
breaking on the distribution of local fields at the hidden units is
investigated. These field distributions determine the probability for finding a
specific activation pattern of the hidden units as well as the corresponding
correlation coefficients and therefore quantify the division of labor among the
hidden units. We find that although modifying the storage capacity and the
distribution of local fields markedly replica symmetry breaking has only a
minor effect on the correlation coefficients. Detailed numerical results are
provided for the PARITY, COMMITTEE and AND machines with K=3 hidden units and
nonoverlapping receptive fields.Comment: 9 pages, 3 figures, RevTex, accepted for publication in Phys. Rev.
Multilayer neural networks with extensively many hidden units
The information processing abilities of a multilayer neural network with a
number of hidden units scaling as the input dimension are studied using
statistical mechanics methods. The mapping from the input layer to the hidden
units is performed by general symmetric Boolean functions whereas the hidden
layer is connected to the output by either discrete or continuous couplings.
Introducing an overlap in the space of Boolean functions as order parameter the
storage capacity if found to scale with the logarithm of the number of
implementable Boolean functions. The generalization behaviour is smooth for
continuous couplings and shows a discontinuous transition to perfect
generalization for discrete ones.Comment: 4 pages, 2 figure
Side-jumps in the spin-Hall effect: construction of the Boltzmann collision integral
We present a systematic derivation of the side-jump contribution to the
spin-Hall current in systems without band structure spin-orbit interactions,
focusing on the construction of the collision integral for the Boltzmann
equation. Starting from the quantum Liouville equation for the density operator
we derive an equation describing the dynamics of the density matrix in the
first Born approximation and to first order in the driving electric field.
Elastic scattering requires conservation of the total energy, including the
spin-orbit interaction energy with the electric field: this results in a first
correction to the customary collision integral found in the Born approximation.
A second correction is due to the change in the carrier position during
collisions. It stems from the part of the density matrix off-diagonal in wave
vector. The two corrections to the collision integral add up and are
responsible for the total side-jump contribution to the spin-Hall current. The
spin-orbit-induced correction to the velocity operator also contains terms
diagonal and off-diagonal in momentum space, which together involve the total
force acting on the system. This force is explicitly shown to vanish (on the
average) in the steady state: thus the total contribution to the spin-Hall
current due to the additional terms in the velocity operator is zero.Comment: Added references, expanded discussion, revised introductio
Optical injection and terahertz detection of the macroscopic Berry curvature
We propose an experimental scheme to probe the Berry curvature of solids. Our
method is sensitive to arbitrary regions of the Brillouin zone, and employs
only basic optical and terahertz techniques to yield a background free signal.
Using semiconductor quantum wells as a prototypical system, we discuss how to
inject Berry curvature macroscopically, and probe it in a way that provides
information about the underlying microscopic Berry curvature.Comment: 4 pages, accepted in Physical Review Letter
Becke-Johnson-type exchange potential for two-dimensional systems
We extend the Becke-Johnson approximation [J. Chem. Phys. 124, 221101 (2006)]
of the exchange potential to two dimensions. We prove and demonstrate that a
direct extension of the underlying formalism may lead to divergent behavior of
the potential. We derive a cure to the approach by enforcing the gauge
invariance and correct asymptotic behavior of the exchange potential. The
procedure leads to an approximation which is shown, in various
quasi-two-dimensional test systems, to be very accurate in comparison with the
exact exchange potential, and thus a considerable improvement over the commonly
applied local-density approximation.Comment: submitted to Phys. Rev. B on July 9th, 200
Thermal ratchet effects in ferrofluids
Rotational Brownian motion of colloidal magnetic particles in ferrofluids
under the influence of an oscillating external magnetic field is investigated.
It is shown that for a suitable time dependence of the magnetic field, a noise
induced rotation of the ferromagnetic particles due to rectification of thermal
fluctuations takes place. Via viscous coupling, the associated angular momentum
is transferred from the magnetic nano-particles to the carrier liquid and can
then be measured as macroscopic torque on the fluid sample. A thorough
theoretical analysis of the effect in terms of symmetry considerations,
analytical approximations, and numerical solutions is given which is in
accordance with recent experimental findings.Comment: 18 pages, 6 figure
On the violation of a local form of the Lieb-Oxford bound
In the framework of density-functional theory, several popular density
functionals for exchange and correlation have been constructed to satisfy a
local form of the Lieb-Oxford bound. In its original global expression, the
bound represents a rigorous lower limit for the indirect Coulomb interaction
energy. Here we employ exact-exchange calculations for the G2 test set to show
that the local form of the bound is violated in an extensive range of both the
dimensionless gradient and the average electron density. Hence, the results
demonstrate the severity in the usage of the local form of the bound in
functional development. On the other hand, our results suggest alternative ways
to construct accurate density functionals for the exchange energy.Comment: (Submitted on 27 April 2012
Storage of correlated patterns in a perceptron
We calculate the storage capacity of a perceptron for correlated gaussian
patterns. We find that the storage capacity can be less than 2 if
similar patterns are mapped onto different outputs and vice versa. As long as
the patterns are in general position we obtain, in contrast to previous works,
that in agreement with Cover's theorem. Numerical simulations
confirm the results.Comment: 9 pages LaTeX ioplppt style, figures included using eps
Spin-dependent electron-impurity scattering in two-dimensional electron systems
We present a theoretical study of elastic spin-dependent electron scattering
caused by a charged impurity in the vicinity of a two-dimensional electron gas.
We find that the symmetry properties of the spin-dependent differential
scattering cross section are different for an impurity located in the plane of
the electron gas and for one at a finite distance from the plane. We show that
in the latter case asymmetric (`skew') scattering can arise if the polarization
of the incident electron has a finite projection on the plane spanned by the
normal vector of the two-dimensional electron gas and the initial propagation
direction. In specially preparated samples this scattering mechanism may give
rise to a Hall-like effect in the presence of an in-plane magnetic field.Comment: 4.1 pages, 2 figure
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