Learning by a nerual net in a noisy environment - The pseudo-inverse solution revisited

A recurrent neural net is described that learns a set of patterns in the presence of noise. The learning rule is of Hebbian type, and, if noise would be absent during the learning process, the resulting final values of the weights would correspond to the pseudo-inverse solution of the fixed point equation in question. For a non-vanishing noise parameter, an explicit expression for the expectation value of the weights is obtained. This result turns out to be unequal to the pseudo-inverse solution. Furthermore, the stability properties of the system are discussed.Comment: 16 pages, 3 figure

Combining Hebbian and reinforcement learning in a minibrain model

A toy model of a neural network in which both Hebbian learning and reinforcement learning occur is studied. The problem of `path interference', which makes that the neural net quickly forgets previously learned input-output relations is tackled by adding a Hebbian term (proportional to the learning rate $\eta$) to the reinforcement term (proportional to $\rho$) in the learning rule. It is shown that the number of learning steps is reduced considerably if $1/4 < \eta/\rho < 1/2$, i.e., if the Hebbian term is neither too small nor too large compared to the reinforcement term

Comments on "The long-period Galactic Cepheid RS Puppis. I. A geometric distance from its light echoes"

The luminous Galactic Cepheid RS Puppis is unique in being surrounded by a dust nebula illuminated by the variable light of the Cepheid. In a recent paper in this journal, Kervella et al. (2008) report a very precise geometric distance to RS Pup, based on measured phase lags of the light variations of individual knots in the reflection nebula. In this commentary, we examine the validity of the distance measurement, as well as the reality of the spatial structure of the nebula determined by Feast (2008) based upon the phase lags of the knots. {Kervella et al. assumed that the illuminated dust knots lie, on average, in the plane of the sky (otherwise it is not possible to derive a geometric distance from direct imaging of light echoes). We consider the biasing introduced by the high efficiency of forward scattering. We conclude that most of the knots are in fact likely to lie in front of the plane of the sky, thus invalidating the Kervella et al. result. We also show that the flat equatorial disk structure determined by Feast is unlikely; instead, the morphology of the nebula is more probably bipolar, with a significant tilt of its axis with respect to the plane of the sky. Although the Kervella et al. distance result is invalidated, we show that high-resolution polarimetric imaging has the potential to yield a valid geometric distance to this important Cepheid.Comment: 10 pages, 5 figures, 1 table; accepted by Astronomy & Astrophysic

Evidence for nonhadronic degrees of freedom in the transverse mass spectra of kaons from relativistic nucleus-nucleus collisions?

We investigate transverse hadron spectra from relativistic nucleus-nucleus collisions which reflect important aspects of the dynamics - such as the generation of pressure - in the hot and dense zone formed in the early phase of the reaction. Our analysis is performed within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. Both transport models show their reliability for elementary $pp$ as well as light-ion (C+C, Si+Si) reactions. However, for central Au+Au (Pb+Pb) collisions at bombarding energies above $\sim$ 5 A$\cdot$GeV the measured $K^{\pm}$ transverse mass spectra have a larger inverse slope parameter than expected from the calculation. Thus the pressure generated by hadronic interactions in the transport models above $\sim$ 5 A$\cdot$GeV is lower than observed in the experimental data. This finding shows that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - is generated by strong partonic interactions in the early phase of central Au+Au (Pb+Pb) collisions.Comment: 4 pages, 3 figures,discussions extended, references added, to be published in Phys. Rev. Let

Middle to Late Holocene vegetation history of the Upper Engadine (Swiss Alps): the role of man and fire

To reconstruct the vegetation and fire history of the Upper Engadine, two continuous sediment cores from Lej da Champfèr and Lej da San Murezzan (Upper Engadine Valley, southeastern Switzerland) were analysed for pollen, plant macrofossils, charcoal and kerogen. The chronologies of the cores are based on 38 radiocarbon dates. Pollen and macrofossil data suggest a rapid afforestation with Betula, Pinus sylvestris, Pinus cembra, and Larix decidua after the retreat of the glaciers from the lake catchments 11,000cal years ago. This vegetation type persisted until ca. 7300cal b.p. (5350b.c.) when Picea replaced Pinus cembra. Pollen indicative of human impact suggests that in this high-mountain region of the central Alps strong anthropogenic activities began during the Early Bronze Age (3900cal b.p., 1950b.c.). Local human settlements led to vegetational changes, promoting the expansion of Larix decidua and Alnus viridis. In the case of Larix, continuing land use and especially grazing after fire led to the formation of Larix meadows. The expansion of Alnus viridis was directly induced by fire, as evidenced by time-series analysis. Subsequently, the process of forest conversion into open landscapes continued for millennia and reached its maximum at the end of the Middle Ages at around 500cal b.p. (a.d.1450