Time trials on second-order and variable-learning-rate algorithms

The performance of seven minimization algorithms are compared on five neural network problems. These include a variable-step-size algorithm, conjugate gradient, and several methods with explicit analytic or numerical approximations to the Hessian.

Typical kernel size and number of sparse random matrices over Galois fields: a statistical physics approach

Using methods of statistical physics, we study the average number and kernel size of general sparse random matrices over GF(q), with a given connectivity profile, in the thermodynamical limit of large matrices. We introduce a mapping of GF(q) matrices onto spin systems using the representation of the cyclic group of order q as the q-th complex roots of unity. This representation facilitates the derivation of the average kernel size of random matrices using the replica approach, under the replica symmetric ansatz, resulting in saddle point equations for general connectivity distributions. Numerical solutions are then obtained for particular cases by population dynamics. Similar techniques also allow us to obtain an expression for the exact and average number of random matrices for any general connectivity profile. We present numerical results for particular distributions.

Femtosecond inscription of the first order Bragg gratings in pure fused silica

The fabrication of sub-micron periodic structures beyond diffraction limit is a major motivation for the present paper. We describe the fabrication of the periodic structure of 25 mm long with a pitch size of 260 nm which is less than a third of the wavelength used. This is the smallest reported period of the periodic structure inscribed by direct point-by-point method. A prototype of the add-drop filter, which utilizes such gratings, was demonstrated in one stage fabrication process of femtosecond inscription, in the bulk fused silica.

Influence of check and field size on the visual evoked magnetic response to a pattern shift stimulus

A decrease in the check size of a pattern shift stimulus increases the latency and amplitude of the visual evoked potential (VEP) P100. In addition, for a given check size, decreasing the size of the stimulus field increases the latency and amplitude of the P100. These results imply that the central regions of the retina make a significant contribution to the generation of the electrical P100. However, the corresponding magnetic P100m may have a different origin. We have studied the effects of check and field size on the P100m in five normal subjects using a DC-Squid, second-order gradiometer. Magnetic responses were recorded at the positive maximum of the P100m over the occipital scalp to six check sizes (10-100') presented in a large (13 degrees 34') and small (5 degrees 14') field and to a large check (100') presented in seven field sizes (1 degree 45' - 15 degrees 10'). No responses were recorded to any check size with a small field. Decreasing the check size presented in a large field increased latency of the P100m by approx. 30 ms while the amplitude of the response decreased with the largest reduction occurring between 70' and 12' checks. Using a large check, latency increased and amplitude decreased as the field size was reduced. The latency changes in response to check and field size were similar to those described for the VEP although the magnitudes of the magnetic changes were greater. Unlike the VEP, amplitude responses were maximal when large checks were presented in a large stimulus field. This suggests that regions outside the central retina make a more significant contribution to the visual evoked magnetic response than they do to the VEP, and that the P100m may be useful clinically in the study of diseases that affect the more peripheral regions of the retina.

Femtosecond inscription of the first order Bragg gratings in pure fused silica

The fabrication of sub-micron periodic structures beyond diffraction limit is a major motivation for the present paper. We describe the fabrication of the periodic structure of 25 mm long with a pitch size of 260 nm which is less than a third of the wavelength used. This is the smallest reported period of the periodic structure inscribed by direct point-by-point method. A prototype of the add-drop filter, which utilizes such gratings, was demonstrated in one stage fabrication process of femtosecond inscription, in the bulk fused silica.

Sample size estimation and statistical power analyses

The concept of sample size and statistical power estimation is now something that Optometrists that want to perform research, whether it be in practice or in an academic institution, cannot simply hide away from. Ethics committees, journal editors and grant awarding bodies are now increasingly requesting that all research be backed up with sample size and statistical power estimation in order to justify any study and its findings. This article presents a step-by-step guide of the process for determining sample sizeand statistical power. It builds on statistical concepts presented in earlier articles in Optometry Today by Richard Armstrong and Frank Eperjesi.

Energy efficient radio access architectures for green radio:large versus small cell size deployment

In this paper new architectural approaches that improve the energy efficiency of a cellular radio access network (RAN) are investigated. The aim of the paper is to characterize both the energy consumption ratio (ECR) and the energy consumption gain (ECG) of a cellular RAN when the cell size is reduced for a given user density and service area. The paper affirms that reducing the cell size reduces the cell ECR as desired while increasing the capacity density but the overall RAN energy consumption remains unchanged. In order to trade the increase in capacity density with RAN energy consumption, without degrading the cell capacity provision, a sleep mode is introduced. In sleep mode, cells without active users are powered-off, thereby saving energy. By combining a sleep mode with a small-cell deployment architecture, the paper shows that the ECG can be increased by the factor n = (R/R) while the cell ECR continues to decrease with decreasing cell size.

Exploring the optimum step size for defocus curves

Purpose: To evaluate the effect of reducing the number of visual acuity measurements made in a defocus curve on the quality of data quantified. Setting: Midland Eye, Solihull, United Kingdom. Design: Evaluation of a technique. Methods: Defocus curves were constructed by measuring visual acuity on a distance logMAR letter chart, randomizing the test letters between lens presentations. The lens powers evaluated ranged between +1.50 diopters (D) and -5.00 D in 0.50 D steps, which were also presented in a randomized order. Defocus curves were measured binocularly with the Tecnis diffractive, Rezoom refractive, Lentis rotationally asymmetric segmented (+3.00 D addition [add]), and Finevision trifocal multifocal intraocular lenses (IOLs) implanted bilaterally, and also for the diffractive IOL and refractive or rotationally asymmetric segmented (+3.00 D and +1.50 D adds) multifocal IOLs implanted contralaterally. Relative and absolute range of clear-focus metrics and area metrics were calculated for curves fitted using 0.50 D, 1.00 D, and 1.50 D steps and a near add-specific profile (ie, distance, half the near add, and the full near-add powers). Results: A significant difference in simulated results was found in at least 1 of the relative or absolute range of clear-focus or area metrics for each of the multifocal designs examined when the defocus-curve step size was increased (P<.05). Conclusion: Faster methods of capturing defocus curves from multifocal IOL designs appear to distort the metric results and are therefore not valid. Financial Disclosure: No author has a financial or proprietary interest in any material or method mentioned. © 2013 ASCRS and ESCRS.

Pd/C catalysts based on synthetic carbons with bi- and tri-modal pore-size distribution:applications in flow chemistry

Two new types of phenolic resin-derived synthetic carbons with bi-modal and tri-modal pore-size distributions were used as supports for Pd catalysts. The catalysts were tested in chemoselective hydrogenation and hydrodehalogenation reactions in a compact multichannel flow reactor. Bi-modal and tri-modal micro-mesoporous structures of the synthetic carbons were characterised by N2 adsorption. HR-TEM, PXRD and XPS analyses were performed for characterising the synthesised catalysts. N2 adsorption revealed that tri-modal synthetic carbon possesses a well-developed hierarchical mesoporous structure (with 6.5 nm and 42 nm pores), contributing to a larger mesopore volume than the bi-modal carbon (1.57 cm3 g-1versus 1.23 cm3 g-1). It was found that the tri-modal carbon promotes a better size distribution of Pd nanoparticles than the bi-modal carbon due to presence of hierarchical mesopore limitting the growth of Pd nanoparticles. For all the model reactions investigated, the Pd catalyst based on tri-modal synthetic carbon (Pd/triC) show high activity as well as high stability and reproducibility. The trend in reactivities of different functional groups over the Pd/triC catalyst follows a general order alkyne ≫ nitro > bromo ≫ aldehyde.