Australian National University

About: Australian National University is a education organization based out in Canberra, Australian Capital Territory, Australia. It is known for research contribution in the topics: Population & Galaxy. The organization has 34419 authors who have published 109261 publications receiving 4315448 citations. The organization is also known as: The Australian National University & ANU.

The sample complexity of pattern classification with neural networks: the size of the weights is more important than the size of the network

Abstract: Sample complexity results from computational learning theory, when applied to neural network learning for pattern classification problems, suggest that for good generalization performance the number of training examples should grow at least linearly with the number of adjustable parameters in the network. Results in this paper show that if a large neural network is used for a pattern classification problem and the learning algorithm finds a network with small weights that has small squared error on the training patterns, then the generalization performance depends on the size of the weights rather than the number of weights. For example, consider a two-layer feedforward network of sigmoid units, in which the sum of the magnitudes of the weights associated with each unit is bounded by A and the input dimension is n. We show that the misclassification probability is no more than a certain error estimate (that is related to squared error on the training set) plus A/sup 3/ /spl radic/((log n)/m) (ignoring log A and log m factors), where m is the number of training patterns. This may explain the generalization performance of neural networks, particularly when the number of training examples is considerably smaller than the number of weights. It also supports heuristics (such as weight decay and early stopping) that attempt to keep the weights small during training. The proof techniques appear to be useful for the analysis of other pattern classifiers: when the input domain is a totally bounded metric space, we use the same approach to give upper bounds on misclassification probability for classifiers with decision boundaries that are far from the training examples.

Fano resonances in photonics

Abstract: The importance of the Fano resonance concept is recognized across multiple fields of physics. In this Review, Fano resonance is explored in the context of optics, with particular emphasis on dielectric nanostructures and metasurfaces. Rapid progress in photonics and nanotechnology brings many examples of resonant optical phenomena associated with the physics of Fano resonances, with applications in optical switching and sensing. For successful design of photonic devices, it is important to gain deep insight into different resonant phenomena and understand their connection. Here, we review a broad range of resonant electromagnetic effects by using two effective coupled oscillators, including the Fano resonance, electromagnetically induced transparency, Kerker and Borrmann effects, and parity–time symmetry breaking. We discuss how to introduce the Fano parameter for describing a transition between two seemingly different spectroscopic signatures associated with asymmetric Fano and symmetric Lorentzian shapes. We also review the recent results on Fano resonances in dielectric nanostructures and metasurfaces.

Remnants of ≥3800 Ma crust in the Chinese part of the Sino-Korean craton

Abstract: Ion microprobe U-Pb analyses of zircons from the Sino-Korean craton have identified remnants of ≥3800 Ma crust at two localities—near Caozhuang east of Beijing, and near Anshan, northeast China. Near Caozhuang, the detrital zircons in an Archean metaquartzite are 3550 Ma or older; about one-fourth have ages between 3800 and 3850 Ma. The ages for detrital zircons with concordant U-Pb ages form a polymodal distribution, interpreted to show that the detritus that formed the quartzite was derived from a terrane containing early Archean rocks of several ages. Near Anshan, sheared gneiss is present in a complex containing ca. 3300 and 3000 Ma granites. Some of the zircons in this gneiss are concordant with a weighted mean 207 Pb/ 206 Pb age of 3804 ±5 Ma (2 σ), interpreted to be the age of the protolith of the gneiss.

Global Mapping Function (GMF): A new empirical mapping function based on numerical weather model data

Abstract: [1] Troposphere mapping functions are used in the analyses of Global Positioning System and Very Long Baseline Interferometry observations to map a priori zenith hydrostatic and wet delays to any elevation angle. Most analysts use the Niell Mapping Function (NMF) whose coefficients are determined from site coordinates and the day of year. Here we present the Global Mapping Function (GMF), based on data from the global ECMWF numerical weather model. The coefficients of the GMF were obtained from an expansion of the Vienna Mapping Function (VMF1) parameters into spherical harmonics on a global grid. Similar to NMF, the values of the coefficients require only the station coordinates and the day of year as input parameters. Compared to the 6-hourly values of the VMF1 a slight degradation in short-term precision occurs using the empirical GMF. However, the regional height biases and annual errors of NMF are significantly reduced with GMF.

The Amount of Recycled Crust in Sources of Mantle-Derived Melts

Abstract: Plate tectonic processes introduce basaltic crust (as eclogite) into the peridotitic mantle. The proportions of these two sources in mantle melts are poorly understood. Silica-rich melts formed from eclogite react with peridotite, converting it to olivine-free pyroxenite. Partial melts of this hybrid pyroxenite are higher in nickel and silicon but poorer in manganese, calcium, and magnesium than melts of peridotite. Olivine phenocrysts' compositions record these differences and were used to quantify the contributions of pyroxenite-derived melts in mid-ocean ridge basalts (10 to 30%), ocean island and continental basalts (many >60%), and komatiites (20 to 30%). These results imply involvement of 2 to 20% (up to 28%) of recycled crust in mantle melting.