Dynamics of on-line gradient descent learning for multilayer neural networks

We consider the problem of on-line gradient descent learning for general two-layer neural networks. An analytic solution is presented and used to investigate the role of the learning rate in controlling the evolution and convergence of the learning process.

Transients and asymptotics of natural gradient learning

We analyse natural gradient learning in a two-layer feed-forward neural network using a statistical mechanics framework which is appropriate for large input dimension. We find significant improvement over standard gradient descent in both the transient and asymptotic phases of learning.

Natural gradient matrix momentum

Natural gradient learning is an efficient and principled method for improving on-line learning. In practical applications there will be an increased cost required in estimating and inverting the Fisher information matrix. We propose to use the matrix momentum algorithm in order to carry out efficient inversion and study the efficacy of a single step estimation of the Fisher information matrix. We analyse the proposed algorithm in a two-layer network, using a statistical mechanics framework which allows us to describe analytically the learning dynamics, and compare performance with true natural gradient learning and standard gradient descent.

Blurred edges look faint, and faint edges look sharp:The effect of a gradient threshold in a multi-scale edge coding model

A multi-scale model of edge coding based on normalized Gaussian derivative filters successfully predicts perceived scale (blur) for a wide variety of edge profiles [Georgeson, M. A., May, K. A., Freeman, T. C. A., & Hesse, G. S. (in press). From filters to features: Scale-space analysis of edge and blur coding in human vision. Journal of Vision]. Our model spatially differentiates the luminance profile, half-wave rectifies the 1st derivative, and then differentiates twice more, to give the 3rd derivative of all regions with a positive gradient. This process is implemented by a set of Gaussian derivative filters with a range of scales. Peaks in the inverted normalized 3rd derivative across space and scale indicate the positions and scales of the edges. The edge contrast can be estimated from the height of the peak. The model provides a veridical estimate of the scale and contrast of edges that have a Gaussian integral profile. Therefore, since scale and contrast are independent stimulus parameters, the model predicts that the perceived value of either of these parameters should be unaffected by changes in the other. This prediction was found to be incorrect: reducing the contrast of an edge made it look sharper, and increasing its scale led to a decrease in the perceived contrast. Our model can account for these effects when the simple half-wave rectifier after the 1st derivative is replaced by a smoothed threshold function described by two parameters. For each subject, one pair of parameters provided a satisfactory fit to the data from all the experiments presented here and in the accompanying paper [May, K. A. & Georgeson, M. A. (2007). Added luminance ramp alters perceived edge blur and contrast: A critical test for derivative-based models of edge coding. Vision Research, 47, 1721-1731]. Thus, when we allow for the visual system's insensitivity to very shallow luminance gradients, our multi-scale model can be extended to edge coding over a wide range of contrasts and blurs. © 2007 Elsevier Ltd. All rights reserved.

Resonant gradient force on atom interacting with laser field

The gradient force, as a function of position and velocity, is derived for a two-level atom interacting with a standing-wave laser field. Basing on optical Bloch equations, the numerical solutions for the gradient force f_(|_;n) (n = 0, 1, 2, 3, 4, ...) pointing in the direction of the transverse of the laser beam are given. It is shown the higher order gradient force plays important role at strong intensity (G = 64), the contribution of them can not be neglected.

The investigation of the sensitivity gradient of the visual field, as a function of stimulus dynamic range, in the normal and abnormal eye

The study utilized the advanced technology provided by automated perimeters to investigate the hypothesis that patients with retinitis pigmentosa behave atypically over the dynamic range and to concurrently determine the influence of extraneous factors on the format of the normal perimetric sensitivity profile. The perimetric processing of some patients with retinitis pigmentosa was considered to be abnormal in either the temporal and/or the spatial domain. The standard size III stimulus saturated the central regions and was thus ineffective in detecting early depressions in sensitivity in these areas. When stimulus size was scaled in inverse proportion to the square root of ganglion cell receptive field density (M-scaled), isosensitive profiles did not result, although cortical representation was theoretically equivalent across the visual field. It was conjectured that this was due to variations in the ganglion cell characteristics with increasing peripheral angle, most notably spatial summation. It was concluded that the development of perimetric routines incorporating stimulus sizes adjusted in proportion to the coverage factor of retinal ganglion cells would enhance the diagnostic capacity of perimetry. Good general and local correspondence was found between perimetric sensitivity and the available retinal cell counts. Intraocular light scatter arising both from simulations and media opacities depressed perimetric sensitivity. Attenuation was greater centrally for the smaller LED stimuli, whereas the reverse was true for the larger projected stimuli. Prior perimetric experience and pupil size also demonstrated eccentricity-dependent effect on sensitivity. Practice improved perimetric sensitivity for projected stimuli at eccentricities greater than or equal to 30o; particularly in the superior region. Increase in pupil size for LED stimuli enhanced sensitivity at eccentricities greater than 10o. Conversely, microfluctuation in the accommodative response during perimetric examination and the correction of peripheral refractive error had no significant influence on perimetric sensitivity.

A solar-powered reverse osmosis system for high recovery of freshwater from saline groundwater

Desalination of groundwater is essential in arid regions that are remote from both seawater and freshwater resources. Desirable features of a groundwater desalination system include a high recovery ratio, operation from a sustainable energy source such as solar, and high water output per unit of energy and land. Here we propose a new system that uses a solar-Rankine cycle to drive reverse osmosis (RO). The working fluid such as steam is expanded against a power piston that actuates a pump piston which in turn pressurises the saline water thus passing it through RO membranes. A reciprocating crank mechanism is used to equalise the forces between the two pistons. The choice of batch mode in preference to continuous flow permits maximum energy recovery and minimal concentration polarisation in the vicinity of the RO membrane. This study analyses the sizing and efficiency of the crank mechanism, quantifies energy losses in the RO separation and predicts the overall performance. For example, a system using a field of linear Fresnel collectors occupying 1000 m2 of land and raising steam at 200 °C and 15.5 bar could desalinate 350 m3/day from saline water containing 5000 ppm of sodium chloride with a recovery ratio of 0.7.

Computationally efficient natural gradient descent

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Microarray-formatted clinical biomarker assay development using peptide aptamers to anterior gradient-2

Anterior gradient-2 protein was identified using proteomic technologies as a p53 inhibitor which is overexpressed in human cancers, and this protein presents a novel pro-oncogenic target with which to develop diagnostic assays for biomarker detection in clinical tissue. Combinatorial phage-peptide libraries were used to select 12 amino acid polypeptide aptamers toward anterior gradient-2 to determine whether methods can be developed to affinity purify the protein from clinical biopsies. Selecting phage aptamers through four rounds of screening on recombinant human anterior gradient-2 protein identified two classes of peptide ligand that bind to distinct epitopes on anterior gradient-2 protein in an immunoblot. Synthetic biotinylated peptide aptamers bound in an ELISA format to anterior gradient-2, and substitution mutagenesis further minimized one polypeptide aptamer to a hexapeptide core. Aptamers containing this latter consensus sequence could be used to affinity purify to homogeneity human anterior gradient-2 protein from a single clinical biopsy. The spotting of a panel of peptide aptamers onto a protein microarray matrix could be used to quantify anterior gradient-2 protein from crude clinical biopsy lysates, providing a format for quantitative screening. These data highlight the utility of peptide combinatorial libraries to acquire rapidly a high-affinity ligand that can selectively bind a target protein from a clinical biopsy and provide a technological approach for clinical biomarker assay development in an aptamer microarray format.

A variational conjugate gradient method for determining the fluid velocity of a slow viscous flow

The problem considered is that of determining the fluid velocity for linear hydrostatics Stokes flow of slow viscous fluids from measured velocity and fluid stress force on a part of the boundary of a bounded domain. A variational conjugate gradient iterative procedure is proposed based on solving a series of mixed well-posed boundary value problems for the Stokes operator and its adjoint. In order to stabilize the Cauchy problem, the iterations are ceased according to an optimal order discrepancy principle stopping criterion. Numerical results obtained using the boundary element method confirm that the procedure produces a convergent and stable numerical solution.

Effects of recombinant human DNase and hypertonic saline on airway inflammation in children with cystic fibrosis

Recombinant human DNase (rhDNase) is an established treatment in cystic fibrosis (CF), but it may liberate cationic mediators bound to DNA in the airways. An alternative mucolytic therapy is hypertonic saline (HS); however, HS may potentiate neutrophilic inflammation. We compared the effect of rhDNase and HS on cationic proinflammatory mediators in CF sputum. In a randomized, crossover trial, 48 children with CF were allocated consecutively to 12 weeks of once-daily 2.5 mg rhDNase, alternate-day 2.5 mg rhDNase, and twice-daily 7% HS. Sputum levels of total interleukin-8 (IL-8), free IL-8, myeloperoxidase, eosinophil cationic protein, and neutrophil elastase (NE) activity were measured before and after each treatment. The change in mediator levels from baseline with daily rhDNase and HS was not significant; however, with alternate-day rhDNase, there was an increase in free IL-8. When changes in mediator levels with daily rhDNase were compared with alternate-day rhDNase and HS, no significant differences were detected. Only changes in NE activity were associated with changes in lung function. In summary, we were unable to show that rhDNase or HS promote airway inflammation in CF.

Self-powered desalination of geothermal saline groundwater:technical feasibility

This theoretical study shows the technical feasibility of self-powered geothermal desalination of groundwater sources at <100 °C. A general method and framework are developed and then applied to specific case studies. First, the analysis considers an ideal limit to performance based on exergy analysis using generalised idealised assumptions. This thermodynamic limit applies to any type of process technology. Then, the analysis focuses specifically on the Organic Rankine Cycle (ORC) driving Reverse Osmosis (RO), as these are among the most mature and efficient applicable technologies. Important dimensionless parameters are calculated for the ideal case of the self-powered arrangement and semi-ideal case where only essential losses dependent on the RO system configuration are considered. These parameters are used to compare the performance of desalination systems using ORC-RO under ideal, semi-ideal and real assumptions for four case studies relating to geothermal sources located in India, Saudi Arabia, Tunisia and Turkey. The overall system recovery ratio (the key performance measure for the self-powered process) depends strongly on the geothermal source temperature. It can be as high as 91.5% for a hot spring emerging at 96 °C with a salinity of 1830 mg/kg.

Hydrothermal saline promoted grafting:a route to sulfonic acid SBA-15 silica with ultra-high acid site loading for biodiesel synthesis

A simple grafting protocol is reported which affords a ten-fold enhancement in acid site density of mesoporous sulfonic acid silicas compared to conventional syntheses, offering improved process efficiency and new opportunities for tailored supported solid acids in sustainable chemistry. This journal is