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.

The spectral sensitivity of long period gratings fabricated in elliptical core D-shaped optical fibre

Long period gratings (LPGs) were written into a D-shaped optical fibre that has an elliptical core with a W-shaped refractive index profile and the first detailed investigation of such LPGs is presented. The LPGs’ attenuation bands were found to be sensitive to the polarisation of the interrogating light with a spectral separation of about 15 nm between the two orthogonal polarisation states. A finite element method was successfully used to model many of the behavioural features of the LPGs. In addition, two spectrally overlapping attenuation bands corresponding to orthogonal polarisation states were observed; modelling successfully reproduced this spectral feature. The spectral sensitivity of both orthogonal states was experimentally measured with respect to temperature and bending. These LPG devices produced blue and red wavelength shifts depending upon the orientation of the bend with measured maximum sensitivities of -3.56 and +6.51 nm m, suggesting that this type of fibre LPG may be useful as a shape/bend orientation sensor with reduced errors associated with polarisation dependence. The use of neighbouring bands to discriminate between temperature and bending was also demonstrated, leading to an overall curvature error of ±0.14 m-1 and an overall temperature error of ±0.3 °C with a maximum polarisation dependence error of ±8 × 10-2 m-1 for curvature and ±5 × 10-2 °C for temperature.

Analysis of β-amyloid (Aβ) deposition in the temporal lobe in Alzheimer's disease using Fourier (spectral) analysis

To determine the spatial pattern of ß-amyloid (Aß) deposition throughout the temporal lobe in Alzheimer's disease (AD). Methods: Sections of the complete temporal lobe from six cases of sporadic AD were immunolabelled with antibody against Aß. Fourier (spectral) analysis was used to identify sinusoidal patterns in the fluctuation of Aß deposition in a direction parallel to the pia mater or alveus. Results: Significant sinusoidal fluctuations in density were evident in 81/99 (82%) analyses. In 64% of analyses, two frequency components were present with density peaks of Aß deposits repeating every 500–1000 µm and at distances greater than 1000 µm. In 25% of analyses, three or more frequency components were present. The estimated period or wavelength (number of sample units to complete one full cycle) of the first and second frequency components did not vary significantly between gyri of the temporal lobe, but there was evidence that the fluctuations of the classic deposits had longer periods than the diffuse and primitive deposits. Conclusions: (i) Aß deposits exhibit complex sinusoidal fluctuations in density in the temporal lobe in AD; (ii) fluctuations in Aß deposition may reflect the formation of Aß deposits in relation to the modular and vascular structure of the cortex; and (iii) Fourier analysis may be a useful statistical method for studying the patterns of Aß deposition both in AD and in transgenic models of disease.

A projected process kriging algorithm for sensor networks with heterogeneous error characteristics

Large monitoring networks are becoming increasingly common and can generate large datasets from thousands to millions of observations in size, often with high temporal resolution. Processing large datasets using traditional geostatistical methods is prohibitively slow and in real world applications different types of sensor can be found across a monitoring network. Heterogeneities in the error characteristics of different sensors, both in terms of distribution and magnitude, presents problems for generating coherent maps. An assumption in traditional geostatistics is that observations are made directly of the underlying process being studied and that the observations are contaminated with Gaussian errors. Under this assumption, sub–optimal predictions will be obtained if the error characteristics of the sensor are effectively non–Gaussian. One method, model based geostatistics, assumes that a Gaussian process prior is imposed over the (latent) process being studied and that the sensor model forms part of the likelihood term. One problem with this type of approach is that the corresponding posterior distribution will be non–Gaussian and computationally demanding as Monte Carlo methods have to be used. An extension of a sequential, approximate Bayesian inference method enables observations with arbitrary likelihoods to be treated, in a projected process kriging framework which is less computationally intensive. The approach is illustrated using a simulated dataset with a range of sensor models and error characteristics.

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.

The spectral sensitivity of long period gratings fabricated in elliptical core D-shaped optical fibre

Long period gratings (LPGs) were written into a D-shaped optical fibre that has an elliptical core with a W-shaped refractive index profile and the first detailed investigation of such LPGs is presented. The LPGs’ attenuation bands were found to be sensitive to the polarisation of the interrogating light with a spectral separation of about 15 nm between the two orthogonal polarisation states. A finite element method was successfully used to model many of the behavioural features of the LPGs. In addition, two spectrally overlapping attenuation bands corresponding to orthogonal polarisation states were observed; modelling successfully reproduced this spectral feature. The spectral sensitivity of both orthogonal states was experimentally measured with respect to temperature and bending. These LPG devices produced blue and red wavelength shifts depending upon the orientation of the bend with measured maximum sensitivities of -3.56 and +6.51 nm m, suggesting that this type of fibre LPG may be useful as a shape/bend orientation sensor with reduced errors associated with polarisation dependence. The use of neighbouring bands to discriminate between temperature and bending was also demonstrated, leading to an overall curvature error of ±0.14 m-1 and an overall temperature error of ±0.3 °C with a maximum polarisation dependence error of ±8 × 10-2 m-1 for curvature and ±5 × 10-2 °C for temperature.

A simple bioanalytical method for the quantification of antiepileptic drugs in dried blood spots

An increasing number of publications on the dried blood spot (DBS) sampling approach for the quantification of drugs and metabolites have been spurred on by the inherent advantages of this sampling technique. In the present research, a selective and sensitive high-performance liquid chromatography method for the concurrent determination of multiple antiepileptic drugs (AEDs) [levetiracetam (LVT), lamotrigine (LTG), phenobarbital (PHB)], carbamazepine (CBZ) and its active metabolite carbamazepine-10,11 epoxide (CBZE)] in a single DBS has been developed and validated. Whole blood was spotted onto Guthrie cards and dried. Using a standard punch (6 mm diameter), a circular disc was punched from the card and extracted with methanol: acetonitrile (3:1, v/v) containing hexobarbital (Internal Standard) and sonicated prior to evaporation. The extract was then dissolved in water and vortex mixed before undergoing solid phase extraction using HLB cartridges. Chromatographic separation of the AEDs was achieved using Waters XBridge™ C18 column with a gradient system. The developed method was linear over the concentration ranges studied with r ≥ 0.995 for all compounds. The lower limits of quantification (LLOQs) were 2, 1, 2, 0.5 and 1 μg/mL for LVT, LTG, PHB, CBZE and CBZ, respectively. Accuracy (%RE) and precision (%CV) values for within and between day were <20% at the LLOQs and <15% at all other concentrations tested. This method was successfully applied to the analysis of the AEDs in DBS samples taken from children with epilepsy for the assessment of their adherence to prescribed treatments.

Quantitative analysis of multi-spectral fundus images

We have developed a new technique for extracting histological parameters from multi-spectral images of the ocular fundus. The new method uses a Monte Carlo simulation of the reflectance of the fundus to model how the spectral reflectance of the tissue varies with differing tissue histology. The model is parameterised by the concentrations of the five main absorbers found in the fundus: retinal haemoglobins, choroidal haemoglobins, choroidal melanin, RPE melanin and macular pigment. These parameters are shown to give rise to distinct variations in the tissue colouration. We use the results of the Monte Carlo simulations to construct an inverse model which maps tissue colouration onto the model parameters. This allows the concentration and distribution of the five main absorbers to be determined from suitable multi-spectral images. We propose the use of "image quotients" to allow this information to be extracted from uncalibrated image data. The filters used to acquire the images are selected to ensure a one-to-one mapping between model parameters and image quotients. To recover five model parameters uniquely, images must be acquired in six distinct spectral bands. Theoretical investigations suggest that retinal haemoglobins and macular pigment can be recovered with RMS errors of less than 10%. We present parametric maps showing the variation of these parameters across the posterior pole of the fundus. The results are in agreement with known tissue histology for normal healthy subjects. We also present an early result which suggests that, with further development, the technique could be used to successfully detect retinal haemorrhages.

A variational method for identifying a spacewise-dependent heat source

The inverse problem of determining a spacewise-dependent heat source for the parabolic heat equation using the usual conditions of the direct problem and information from one supplementary temperature measurement at a given instant of time is studied. This spacewise-dependent temperature measurement ensures that this inverse problem has a unique solution, but the solution is unstable and hence the problem is ill-posed. We propose a variational conjugate gradient-type iterative algorithm for the stable reconstruction of the heat source based on a sequence of well-posed direct problems for the parabolic heat equation which are solved at each iteration step using the boundary element method. The instability is overcome by stopping the iterative procedure at the first iteration for which the discrepancy principle is satisfied. Numerical results are presented which have the input measured data perturbed by increasing amounts of random noise. The numerical results show that the proposed procedure yields stable and accurate numerical approximations after only a few iterations.

Nonlinear spectral management:linearization of the lossless fiber channel

Using the integrable nonlinear Schrodinger equation (NLSE) as a channel model, we describe the application of nonlinear spectral management for effective mitigation of all nonlinear distortions induced by the fiber Kerr effect. Our approach is a modification and substantial development of the so-called eigenvalue communication idea first presented in A. Hasegawa, T. Nyu, J. Lightwave Technol. 11, 395 (1993). The key feature of the nonlinear Fourier transform (inverse scattering transform) method is that for the NLSE, any input signal can be decomposed into the so-called scattering data (nonlinear spectrum), which evolve in a trivial manner, similar to the evolution of Fourier components in linear equations. We consider here a practically important weakly nonlinear transmission regime and propose a general method of the effective encoding/modulation of the nonlinear spectrum: The machinery of our approach is based on the recursive Fourier-type integration of the input profile and, thus, can be considered for electronic or all-optical implementations. We also present a novel concept of nonlinear spectral pre-compensation, or in other terms, an effective nonlinear spectral pre-equalization. The proposed general technique is then illustrated through particular analytical results available for the transmission of a segment of the orthogonal frequency division multiplexing (OFDM) formatted pattern, and through WDM input based on Gaussian pulses. Finally, the robustness of the method against the amplifier spontaneous emission is demonstrated, and the general numerical complexity of the nonlinear spectrum usage is discussed. © 2013 Optical Society of America.

Simple design method for gain-flattened three-pump Raman amplifiers

A simple and efficient approach to the optimal design of 3-wavelength backward-pumped Raman amplifiers is proposed. Gain flatness of 1.7 dB is demonstrated in a spectral range of 1520-1595 nm using only three pumps with wavelengths within the 1420-1480 nm interval.

High spectral efficiency transmission emulation for non-linear transmission performance estimation for high order modulation formats

We demonstrate a simple method to experimentally evaluate nonlinear transmission performance of high order modulation formats using a low number of channels and channel-like ASE. We verify it's behaviour is consistent with the AWGN model of transmission.

Laser-induced breakdown spectroscopy quantitative analysis method via adaptive analytical line selection and relevance vector machine regression model

Abstract A new LIBS quantitative analysis method based on analytical line adaptive selection and Relevance Vector Machine (RVM) regression model is proposed. First, a scheme of adaptively selecting analytical line is put forward in order to overcome the drawback of high dependency on a priori knowledge. The candidate analytical lines are automatically selected based on the built-in characteristics of spectral lines, such as spectral intensity, wavelength and width at half height. The analytical lines which will be used as input variables of regression model are determined adaptively according to the samples for both training and testing. Second, an LIBS quantitative analysis method based on RVM is presented. The intensities of analytical lines and the elemental concentrations of certified standard samples are used to train the RVM regression model. The predicted elemental concentration analysis results will be given with a form of confidence interval of probabilistic distribution, which is helpful for evaluating the uncertainness contained in the measured spectra. Chromium concentration analysis experiments of 23 certified standard high-alloy steel samples have been carried out. The multiple correlation coefficient of the prediction was up to 98.85%, and the average relative error of the prediction was 4.01%. The experiment results showed that the proposed LIBS quantitative analysis method achieved better prediction accuracy and better modeling robustness compared with the methods based on partial least squares regression, artificial neural network and standard support vector machine.

Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers

In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schrödinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk, effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any modulation formats. Here, we demonstrate numerically the feasibility of merging the NIS technique in a burst mode with high spectral efficiency methods, such as orthogonal frequency division multiplexing and Nyquist pulse shaping with advanced modulation formats (e.g., QPSK, 16QAM, and 64QAM), showing a performance improvement up to 4.5 dB, which is comparable to results achievable with multi-step per span digital back propagation.

Real-time heterodyne-based measurements of fiber laser spectral dynamics

We present a method to measure in real-time the instantaneous generation spectrum of fiber lasers over consecutive cavity round-trips. © 2015 OSA.