1,122 research outputs found
Dynamics of Learning with Restricted Training Sets I: General Theory
We study the dynamics of supervised learning in layered neural networks, in
the regime where the size of the training set is proportional to the number
of inputs. Here the local fields are no longer described by Gaussian
probability distributions and the learning dynamics is of a spin-glass nature,
with the composition of the training set playing the role of quenched disorder.
We show how dynamical replica theory can be used to predict the evolution of
macroscopic observables, including the two relevant performance measures
(training error and generalization error), incorporating the old formalism
developed for complete training sets in the limit as a
special case. For simplicity we restrict ourselves in this paper to
single-layer networks and realizable tasks.Comment: 39 pages, LaTe
Ancient Egypt 1921 Part 1
Part 1 of the 1921 Ancient Egypt books. Contents include the alphabet in the XIIth dynasty, the Lahun caskets, burial rites of West Africa, a Negro captive, and Queen Tetisheri.https://knowledge.e.southern.edu/kweeks_coll/1014/thumbnail.jp
Magnetic moment non-conservation in magnetohydrodynamic turbulence models
The fundamental assumptions of the adiabatic theory do not apply in presence
of sharp field gradients as well as in presence of well developed
magnetohydrodynamic turbulence. For this reason in such conditions the magnetic
moment is no longer expected to be constant. This can influence particle
acceleration and have considerable implications in many astrophysical problems.
Starting with the resonant interaction between ions and a single parallel
propagating electromagnetic wave, we derive expressions for the magnetic moment
trapping width (defined as the half peak-to-peak difference in the
particle magnetic moment) and the bounce frequency . We perform
test-particle simulations to investigate magnetic moment behavior when
resonances overlapping occurs and during the interaction of a ring-beam
particle distribution with a broad-band slab spectrum.
We find that magnetic moment dynamics is strictly related to pitch angle
for a low level of magnetic fluctuation, , where is the constant and uniform background magnetic field.
Stochasticity arises for intermediate fluctuation values and its effect on
pitch angle is the isotropization of the distribution function .
This is a transient regime during which magnetic moment distribution
exhibits a characteristic one-sided long tail and starts to be influenced by
the onset of spatial parallel diffusion, i.e., the variance
grows linearly in time as in normal diffusion. With strong fluctuations
isotropizes completely, spatial diffusion sets in and
behavior is closely related to the sampling of the varying magnetic field
associated with that spatial diffusion.Comment: 13 pages, 10 figures, submitted to PR
Detection of Coulomb Charging around an Antidot in the Quantum Hall Regime
We have detected oscillations of the charge around a potential hill (antidot)
in a two-dimensional electron gas as a function of a large magnetic field B.
The field confines electrons around the antidot in closed orbits, the areas of
which are quantised through the Aharonov-Bohm effect. Increasing B reduces each
state's area, pushing electrons closer to the centre, until enough charge
builds up for an electron to tunnel out. This is a new form of the Coulomb
blockade seen in electrostatically confined dots. Addition and excitation
spectra in DC bias confirm the Coulomb blockade of tunnelling.Comment: 4 pages, 4 Postscript figure
Shock waves in transonic channel flows at moderate Reynolds numbers
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/76375/1/AIAA-9312-844.pd
Gradient descent learning in and out of equilibrium
Relations between the off thermal equilibrium dynamical process of on-line
learning and the thermally equilibrated off-line learning are studied for
potential gradient descent learning. The approach of Opper to study on-line
Bayesian algorithms is extended to potential based or maximum likelihood
learning. We look at the on-line learning algorithm that best approximates the
off-line algorithm in the sense of least Kullback-Leibler information loss. It
works by updating the weights along the gradient of an effective potential
different from the parent off-line potential. The interpretation of this off
equilibrium dynamics holds some similarities to the cavity approach of
Griniasty. We are able to analyze networks with non-smooth transfer functions
and transfer the smoothness requirement to the potential.Comment: 08 pages, submitted to the Journal of Physics
Coulomb blockade of tunnelling through compressible rings formed around an antidot: an explanation for Aharonov-Bohm oscillations
We consider single-electron tunnelling through antidot states using a
Coulomb-blockade model, and give an explanation for h/2e Aharonov-Bohm
oscillations, which are observed experimentally when the two spins of the
lowest Landau level form bound states. We show that the edge channels may
contain compressible regions, and using simple electrostatics, that the
resonance through the outer spin states should occur twice per h/e period. An
antidot may be a powerful tool for investigating quantum Hall edge states in
general, and the interplay of spin and charging effects that occurs in quantum
dots.Comment: 5 pages, 4 Postscript figure
The evolution of menopause in cetaceans and humans: the role of demography
Human females stop reproducing long before they die. Among other mammals, only pilot and killer whales exhibit a comparable period of post-reproductive life. The grandmother hypothesis suggests that kin selection can favour post-reproductive survival when older females help their relatives to reproduce. But although there is an evidence that grandmothers can provide such assistance, it is puzzling why menopause should have evolved only among the great apes and toothed whales. We have previously suggested (Cant & Johnstone 2008 Proc. Natl Acad. Sci. USA 105, 5332–5336 (doi:10.1073/pnas.0711911105)) that relatedness asymmetries owing to female-biased dispersal in ancestral humans would have favoured younger females in reproductive competition with older females, predisposing our species to the evolution of menopause. But this argument appears inapplicable to menopausal cetaceans, which exhibit philopatry of both sexes combined with extra-group mating. Here, we derive general formulae for ‘kinship dynamics’, the age-related changes in local relatedness that occur in long-lived social organisms as a consequence of dispersal and mortality. We show that the very different social structures of great apes and menopausal whales both give rise to an increase in local relatedness with female age, favouring late-life helping. Our analysis can therefore help to explain why, of all long-lived, social mammals, it is specifically among the great apes and toothed whales that menopause and post-reproductive helping have evolved
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