Optimisation of on-line principal component analysis

Different techniques, used to optimise on-line principal component analysis, are investigated by methods of statistical mechanics. These include local and global optimisation of node-dependent learning-rates which are shown to be very efficient in speeding up the learning process. They are investigated further for gaining insight into the learning rates' time-dependence, which is then employed for devising simple practical methods to improve training performance. Simulations demonstrate the benefit gained from using the new methods.Comment: 10 pages, 5 figure

Modelling sublimation and atomic layer epitaxy in the presence of competing surface reconstructions

We present a solid-on-solid model of a binary AB compound, where atoms of type A in the topmost layer interact via anisotropic interactions different from those inside the bulk. Depending on temperature and particle flux, this model displays surface reconstructions similar to those of (001) surfaces of II-VI semiconductors. We show, that our model qualitatively reproduces mamy of the characteristic features of these materials which have been observed during sublimation and atomic layer epitaxy. We predict some previously unknown effects which might be observed experimentally.Comment: 4 pages, 2 figures. New title, additional figures, minor changes in the text. See http://theorie.physik.uni-wuerzburg.de/~ahr/AB/ for surface images and MPEG movie

Functional Optimisation of Online Algorithms in Multilayer Neural Networks

We study the online dynamics of learning in fully connected soft committee machines in the student-teacher scenario. The locally optimal modulation function, which determines the learning algorithm, is obtained from a variational argument in such a manner as to maximise the average generalisation error decay per example. Simulations results for the resulting algorithm are presented for a few cases. The symmetric phase plateaux are found to be vastly reduced in comparison to those found when online backpropagation algorithms are used. A discussion of the implementation of these ideas as practical algorithms is given

Modelling (001) surfaces of II-VI semiconductors

First, we present a two-dimensional lattice gas model with anisotropic interactions which explains the experimentally observed transition from a dominant c(2x2) ordering of the CdTe(001) surface to a local (2x1) arrangement of the Cd atoms as an equilibrium phase transition. Its analysis by means of transfer-matrix and Monte Carlo techniques shows that the small energy difference of the competing reconstructions determines to a large extent the nature of the different phases. Then, this lattice gas is extended to a model of a three-dimensional crystal which qualitatively reproduces many of the characteristic features of CdTe which have been observed during sublimation and atomic layer epitaxy.Comment: 5 pages, 3 figure

The Taxpayer Relief Act of 1997 and Homeownership: Is Smaller Now Better?

Prior to 1997, homeowners under 55 were allowed to defer capital gains taxes from a home sale if they bought another house at least as expensive, while those over 55 received a capital gains exclusion regardless of the cost of their new home. The Taxpayer Relief Act of 1997 (TRA97) eliminated this differential tax treatment. We exploit the differential treatment before 1997 to uncover TRA97’s effects. Comparing homeowners under 55 before and after 1997, we find that those who moved after 1997 are twice as likely as to list “seeking less expensive housing” as a reason for moving, 8 percent less likely to own their residences and 9 percent less likely to live in a single family home.

Phase Transitions of Neural Networks

The cooperative behaviour of interacting neurons and synapses is studied using models and methods from statistical physics. The competition between training error and entropy may lead to discontinuous properties of the neural network. This is demonstrated for a few examples: Perceptron, associative memory, learning from examples, generalization, multilayer networks, structure recognition, Bayesian estimate, on-line training, noise estimation and time series generation.Comment: Plenary talk for MINERVA workshop on mesoscopics, fractals and neural networks, Eilat, March 1997 Postscript Fil

Evaporation and Step Edge Diffusion in MBE

Using kinetic Monte-Carlo simulations of a Solid-on-Solid model we investigate the influence of step edge diffusion (SED) and evaporation on Molecular Beam Epitaxy (MBE). Based on these investigations we propose two strategies to optimize MBE-growth. The strategies are applicable in different growth regimes: during layer-by-layer growth one can reduce the desorption rate using a pulsed flux. In three-dimensional (3D) growth the SED can help to grow large, smooth structures. For this purpose the flux has to be reduced with time according to a power law.Comment: 5 pages, 2 figures, latex2e (packages: elsevier,psfig,latexsym

Phase transitions in soft-committee machines

Equilibrium statistical physics is applied to layered neural networks with differentiable activation functions. A first analysis of off-line learning in soft-committee machines with a finite number (K) of hidden units learning a perfectly matching rule is performed. Our results are exact in the limit of high training temperatures. For K=2 we find a second order phase transition from unspecialized to specialized student configurations at a critical size P of the training set, whereas for K > 2 the transition is first order. Monte Carlo simulations indicate that our results are also valid for moderately low temperatures qualitatively. The limit K to infinity can be performed analytically, the transition occurs after presenting on the order of N K examples. However, an unspecialized metastable state persists up to P= O (N K^2).Comment: 8 pages, 4 figure

Binary Neutron Star Merger Remnants as Sources of Cosmic Rays Below the "Ankle"

We investigate non-thermal electron and nuclei energy losses within the binary neutron star merger remnant produced by the event GW170817. The lack of a cooling feature within the detected synchrotron emission from the source is used to constrain the magnetic field at the mG level, assuming that this emission is electron synchrotron in origin, and that the accelerated spectrum in the electrons follows the form $dN/dE_e \propto E_e^{-2}$. The level of subsequent gamma-ray emission from the source is demonstrated to provide a further constraint on the source magnetic field strength. We also put forward alternative strong ($\sim$G) magnetic field scenarios able to support this emission. For such stronger fields, the photo-disintegration of non-thermal nuclei within the source is considered, and a bottleneck period of $\sim$5-30 days is found when this process peaks. We find that this class of source is in principle able to support the population of cosmic rays detected at Earth below the "ankle".Comment: Accepted for publication in Astropart. Phy