Influence of the generated power, measurement bandwidth, and noise level on intensity statistics of a quasi-CW Raman fiber laser

In the present paper we numerically study instrumental impact on statistical properties of quasi-CW Raman fiber laser using a simple model of multimode laser radiation. Effects, that have the most influence, are limited electrical bandwidth of measurement equipment and noise. To check this influence, we developed a simple model of the multimode quasi- CW generation with exponential statistics (i.e. uncorrelated modes). We found that the area near zero intensity in probability density function (PDF) is strongly affected by both factors, for example both lead to formation of a negative wing of intensity distribution. But far wing slope of PDF is not affected by noise and, for moderate mismatch between optical and electrical bandwidth, is only slightly affected by bandwidth limitation. The generation spectrum often becomes broader at higher power in experiments, so the spectral/electrical bandwidth mismatch factor increases over the power that can lead to artificial dependence of the PDF slope over the power. It was also found that both effects influence the ACF background level: noise impact decreases it, while limited bandwidth leads to its increase. © (2014) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.

Noise, regularizers, and unrealizable scenarios in online learning from restricted training sets

We study the dynamics of on-line learning in multilayer neural networks where training examples are sampled with repetition and where the number of examples scales with the number of network weights. The analysis is carried out using the dynamical replica method aimed at obtaining a closed set of coupled equations for a set of macroscopic variables from which both training and generalization errors can be calculated. We focus on scenarios whereby training examples are corrupted by additive Gaussian output noise and regularizers are introduced to improve the network performance. The dependence of the dynamics on the noise level, with and without regularizers, is examined, as well as that of the asymptotic values obtained for both training and generalization errors. We also demonstrate the ability of the method to approximate the learning dynamics in structurally unrealizable scenarios. The theoretical results show good agreement with those obtained by computer simulations.

Critical noise levels for LDPC decoding

We determine the critical noise level for decoding low density parity check error correcting codes based on the magnetization enumerator , rather than on the weight enumerator employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Contrast discrimination and pattern masking: contrast gain control with fixed additive noise

We studied the visual mechanisms that serve to encode spatial contrast at threshold and supra-threshold levels. In a 2AFC contrast-discrimination task, observers had to detect the presence of a vertical 1 cycle deg-1 test grating (of contrast dc) that was superimposed on a similar vertical 1 cycle deg-1 pedestal grating, whereas in pattern masking the test grating was accompanied by a very different masking grating (horizontal 1 cycle deg-1, or oblique 3 cycles deg-1). When expressed as threshold contrast (dc at 75% correct) versus mask contrast (c) our results confirm previous ones in showing a characteristic 'dipper function' for contrast discrimination but a smoothly increasing threshold for pattern masking. However, fresh insight is gained by analysing and modelling performance (p; percent correct) as a joint function of (c, dc) - the performance surface. In contrast discrimination, psychometric functions (p versus logdc) are markedly less steep when c is above threshold, but in pattern masking this reduction of slope did not occur. We explored a standard gain-control model with six free parameters. Three parameters control the contrast response of the detection mechanism and one parameter weights the mask contrast in the cross-channel suppression effect. We assume that signal-detection performance (d') is limited by additive noise of constant variance. Noise level and lapse rate are also fitted parameters of the model. We show that this model accounts very accurately for the whole performance surface in both types of masking, and thus explains the threshold functions and the pattern of variation in psychometric slopes. The cross-channel weight is about 0.20. The model shows that the mechanism response to contrast increment (dc) is linearised by the presence of pedestal contrasts but remains nonlinear in pattern masking.

Reduction of noise levels in vaccum cleaners

The work described in this thesis is directed towards the reduction of noise levels in the Hoover Turbopower upright vacuum cleaner. The experimental work embodies a study of such factors as the application of noise source identification techniques, investigation of the noise generating principles for each major source and evaluation of the noise reducing treatments. It was found that the design of the vacuum cleaner had not been optimised from the standpoint of noise emission. Important factors such as noise `windows', isolation of vibration at the source, panel rattle, resonances and critical speeds had not been considered. Therefore, a number of experimentally validated treatments are proposed. Their noise reduction benefit together with material and tooling costs are presented. The solutions to the noise problems were evaluated on a standard Turbopower and the sound power level of the cleaner was reduced from 87.5 dB(A) to 80.4 db(A) at a cost of 93.6 pence per cleaner.The designers' lack of experience in noise reduction was identified as one of the factors for the low priority given to noise during design of the cleaner. Consequently, the fundamentals of acoustics, principles of noise prediction and absorption and guidelines for good acoustical design were collated into a Handbook and circulated at Hoover plc.Mechanical variations during production of the motor and the cleaner were found to be important. These caused a vast spread in the noise levels of the cleaners. Subsequently, the manufacturing processes were briefly studied to identify their source and recommendations for improvement are made.Noise of a product is quality related and a high level of noise is considered to be a bad feature. This project suggested that the noise level be used constructively both as a test on the production line to identify cleaners above a certain noise level and also to promote the product by `designing' the characteristics of the sound so that the appliance is pleasant to the user. This project showed that good noise control principles should be implemented early in the design stage.As yet there are no mandatory noise limits or noise-labelling requirements for household appliances. However, the literature suggests that noise-labelling is likely in the near future and the requirement will be to display the A-weighted sound power level. However, the `noys' scale of perceived noisiness was found more appropriate to the rating of appliance noise both as it is linear and therefore, a sound level that seems twice as loud is twice the value in noys and also takes into consideration the presence of pure tones, which even in the absence of a high noise level can lead to annoyance.

Critical noise levels for low-density parity check decoding

We determine the critical noise level for decoding low-density parity check error-correcting codes based on the magnetization enumerator (M), rather than on the weight enumerator (W) employed in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. In addition, our analysis provides an explanation for the difference in performance between MN and Gallager codes. Our results are more optimistic than those derived using the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Upper and lower bounds on the learning curve for Gaussian processes

In this paper we introduce and illustrate non-trivial upper and lower bounds on the learning curves for one-dimensional Gaussian Processes. The analysis is carried out emphasising the effects induced on the bounds by the smoothness of the random process described by the Modified Bessel and the Squared Exponential covariance functions. We present an explanation of the early, linearly-decreasing behavior of the learning curves and the bounds as well as a study of the asymptotic behavior of the curves. The effects of the noise level and the lengthscale on the tightness of the bounds are also discussed.

Finite-size effects and error-free communication in Gaussian channels

The efficacy of a specially constructed Gallager-type error-correcting code to communication in a Gaussian channel is examined. The construction is based on the introduction of complex matrices, used in both encoding and decoding, which comprise sub-matrices of cascading connection values. The finite-size effects are estimated for comparing the results with the bounds set by Shannon. The critical noise level achieved for certain code rates and infinitely large systems nearly saturates the bounds set by Shannon even when the connectivity used is low.

Tighter decoding reliability bound for Gallager's error-correcting code

Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average decoding error rate, but invoke the replica method to reproduce the tightest general bound to date, and to improve on the most accurate zero-error noise level threshold reported in the literature. The relation between the methods used and those presented in the information theory literature are explored.

Weight vs magnetization enumerator for Gallager codes

We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator (¸M), rather than on the weight enumerator (¸W) presented recently in the information theory literature. The interpretation of our method is appealingly simple, and the relation between the different decoding schemes such as typical pairs decoding, MAP, and finite temperature decoding (MPM) becomes clear. Our results are more optimistic than those derived via the methods of information theory and are in excellent agreement with recent results from another statistical physics approach.

Magnetization enumerator for LDPC codes - a statistical physics approach

We propose a method based on the magnetization enumerator to determine the critical noise level for Gallager type low density parity check error correcting codes (LDPC). Our method provides an appealingly simple interpretation to the relation between different decoding schemes, and provides more optimistic critical noise levels than those reported in the information theory literature.

Feasibility studies of an on-line identification technique

This thesis is concerned with the study of a non-sequential identification technique, so that it may be applied to the identification of process plant mathematical models from process measurements with the greatest degree of accuracy and reliability. In order to study the accuracy of the technique under differing conditions, simple mathematical models were set up on a parallel hybrid. computer and these models identified from input/output measurements by a small on-line digital computer. Initially, the simulated models were identified on-line. However, this method of operation was found not suitable for a thorough study of the technique due to equipment limitations. Further analysis was carried out in a large off-line computer using data generated by the small on-line computer. Hence identification was not strictly on-line. Results of the work have shovm that the identification technique may be successfully applied in practice. An optimum sampling period is suggested, together with noise level limitations for maximum accuracy. A description of a double-effect evaporator is included in this thesis. It is proposed that the next stage in the work will be the identification of a mathematical model of this evaporator using the teclmique described.

Experimental and theoretical characterisation of tunable fibre gratings

This thesis presents details on both theoretical and experimental aspects of UV written fibre gratings. The main body of the thesis deals with the design, fabrication and testing of telecommunication optical fibre grating devices, but also an accurate theoretical analysis of intra-core fibre gratings is presented. Since more than a decade, fibre gratings have been extensively used in the telecommunication field (as filters, dispersion compensators, and add/drop multiplexers for instance). Gratings for telecommunication should conform to very high fabrication standards as the presence of any imperfection raises the noise level in the transmission system compromising its ability of transmitting intelligible sequence of bits to the receiver. Strong side lobes suppression and high and sharp reflection profile are then necessary characteristics. A fundamental part of the theoretical and experimental work reported in this thesis is about apodisation. The physical principle of apodisation is introduced and a number of apodisation techniques, experimental results and numerical optimisation of the shading functions and all the practical parameters involved in the fabrication are detailed. The measurement of chromatic dispersion in fibres and FBGs is detailed and an estimation of its accuracy is given. An overview on the possible methods that can be implemented for the fabrication of tunable fibre gratings is given before detailing a new dispersion compensator device based on the action of a distributed strain onto a linearly chirped FBG. It is shown that tuning of second and third order dispersion of the grating can be obtained by the use of a specially designed multipoint bending rig. Experiments on the recompression of optical pulses travelling long distances are detailed for 10 Gb/s and 40 Gb/s. The characterisation of a new kind of double section LPG fabricated on a metal-clad coated fibre is reported. The fabrication of the device is made easier by directly writing the grating through the metal coating. This device may be used to overcome the recoating problems associated with standard LPGs written in step-index fibre. Also, it can be used as a sensor for simultaneous measurements of temperature and surrounding medium refractive index.

Effects of inducer continuity on auditory stream segregation:comparison of physical and perceived continuity in different contexts

The factors influencing the stream segregation of discrete tones and the perceived continuity of discrete tones as continuing through an interrupting masker are well understood as separate phenomena. Two experiments tested whether perceived continuity can influence the build-up of stream segregation by manipulating the perception of continuity during an induction sequence and measuring streaming in a subsequent test sequence comprising three triplets of low and high frequency tones (LHL-…). For experiment 1, a 1.2-s standard induction sequence comprising six 100-ms L-tones strongly promoted segregation, whereas a single extended L-inducer (1.1 s plus 100-ms silence) did not. Segregation was similar to that following the single extended inducer when perceived continuity was evoked by inserting noise bursts between the individual tones. Reported segregation increased when the noise level was reduced such that perceived continuity no longer occurred. Experiment 2 presented a 1.3-s continuous inducer created by bridging the 100-ms silence between an extended L-inducer and the first test-sequence tone. This configuration strongly promoted segregation. Segregation was also increased by filling the silence after the extended inducer with noise, such that it was perceived like a bridging inducer. Like physical continuity, perceived continuity can promote or reduce test-sequence streaming, depending on stimulus context.

The role of stochasticity in an information-optimal neural population code

In this paper we consider the optimisation of Shannon mutual information (MI) in the context of two model neural systems The first is a stochastic pooling network (population) of McCulloch-Pitts (MP) type neurons (logical threshold units) subject to stochastic forcing; the second is (in a rate coding paradigm) a population of neurons that each displays Poisson statistics (the so called 'Poisson neuron'). The mutual information is optimised as a function of a parameter that characterises the 'noise level'-in the MP array this parameter is the standard deviation of the noise, in the population of Poisson neurons it is the window length used to determine the spike count. In both systems we find that the emergent neural architecture and; hence, code that maximises the MI is strongly influenced by the noise level. Low noise levels leads to a heterogeneous distribution of neural parameters (diversity), whereas, medium to high noise levels result in the clustering of neural parameters into distinct groups that can be interpreted as subpopulations In both cases the number of subpopulations increases with a decrease in noise level. Our results suggest that subpopulations are a generic feature of an information optimal neural population.