Detection of signals corrupted by the combination of Gaussian and Non-Gaussian noise

The detection of signals in the presence of noise is one of the most basic and important problems encountered by communication engineers. Although the literature abounds with analyses of communications in Gaussian noise, relatively little work has appeared dealing with communications in non-Gaussian noise. In this thesis several digital communication systems disturbed by non-Gaussian noise are analysed. The thesis is divided into two main parts. In the first part, a filtered-Poisson impulse noise model is utilized to calulate error probability characteristics of a linear receiver operating in additive impulsive noise. Firstly the effect that non-Gaussian interference has on the performance of a receiver that has been optimized for Gaussian noise is determined. The factors affecting the choice of modulation scheme so as to minimize the deterimental effects of non-Gaussian noise are then discussed. In the second part, a new theoretical model of impulsive noise that fits well with the observed statistics of noise in radio channels below 100 MHz has been developed. This empirical noise model is applied to the detection of known signals in the presence of noise to determine the optimal receiver structure. The performance of such a detector has been assessed and is found to depend on the signal shape, the time-bandwidth product, as well as the signal-to-noise ratio. The optimal signal to minimize the probability of error of; the detector is determined. Attention is then turned to the problem of threshold detection. Detector structure, large sample performance and robustness against errors in the detector parameters are examined. Finally, estimators of such parameters as. the occurrence of an impulse and the parameters in an empirical noise model are developed for the case of an adaptive system with slowly varying conditions.

A new randomization assay reveals Unexpected elements of sequence bias in model 'randomized' gene libraries:Implications for biopanning

Although techniques such as biopanning rely heavily upon the screening of randomized gene libraries, there is surprisingly little information available on the construction of those libraries. In general, it is based on the cloning of 'randomized' synthetic oligonucleotides, in which given position(s) contain an equal mixture of all four bases. Yet, many supposedly 'randomized' libraries contain significant elements of bias and/or omission. Here, we report the development and validation of a new, PCR-based assay that enables rapid examination of library composition both prior to and after cloning. By using our assay to analyse model libraries, we demonstrate that the cloning of a given distribution of sequences does not necessarily result in a similarly composed library of clones. Thus, while bias in randomized synthetic oligonucleotide mixtures can be virtually eliminated by using unequal ratios of the four phosphoramidites, the use of such mixtures does not ensure retrieval of a truly randomized library. We propose that in the absence of a technique to control cloning frequencies, the ability to analyse the composition of libraries after cloning will enhance significantly the quality of information derived from those libraries. (C) 2000 Published by Elsevier Science B.V. All rights reserved.

Response normalization and blur adaptation:data and multi-scale model

Adapting to blurred or sharpened images alters perceived blur of a focused image (M. A. Webster, M. A. Georgeson, & S. M. Webster, 2002). We asked whether blur adaptation results in (a) renormalization of perceived focus or (b) a repulsion aftereffect. Images were checkerboards or 2-D Gaussian noise, whose amplitude spectra had (log-log) slopes from -2 (strongly blurred) to 0 (strongly sharpened). Observers adjusted the spectral slope of a comparison image to match different test slopes after adaptation to blurred or sharpened images. Results did not show repulsion effects but were consistent with some renormalization. Test blur levels at and near a blurred or sharpened adaptation level were matched by more focused slopes (closer to 1/f) but with little or no change in appearance after adaptation to focused (1/f) images. A model of contrast adaptation and blur coding by multiple-scale spatial filters predicts these blur aftereffects and those of Webster et al. (2002). A key proposal is that observers are pre-adapted to natural spectra, and blurred or sharpened spectra induce changes in the state of adaptation. The model illustrates how norms might be encoded and recalibrated in the visual system even when they are represented only implicitly by the distribution of responses across multiple channels.

Sun and sky:does human vision assume a mixture of point and diffuse illumination when interpreting shape-from-shading?

People readily perceive smooth luminance variations as being due to the shading produced by undulations of a 3-D surface (shape-from-shading). In doing so, the visual system must simultaneously estimate the shape of the surface and the nature of the illumination. Remarkably, shape-from-shading operates even when both these properties are unknown and neither can be estimated directly from the image. In such circumstances humans are thought to adopt a default illumination model. A widely held view is that the default illuminant is a point source located above the observer's head. However, some have argued instead that the default illuminant is a diffuse source. We now present evidence that humans may adopt a flexible illumination model that includes both diffuse and point source elements. Our model estimates a direction for the point source and then weights the contribution of this source according to a bias function. For most people the preferred illuminant direction is overhead with a strong diffuse component.

Managing uncertainty in complex stochastic models: design and emulation of a Rabies model

In this paper we present a novel method for emulating a stochastic, or random output, computer model and show its application to a complex rabies model. The method is evaluated both in terms of accuracy and computational efficiency on synthetic data and the rabies model. We address the issue of experimental design and provide empirical evidence on the effectiveness of utilizing replicate model evaluations compared to a space-filling design. We employ the Mahalanobis error measure to validate the heteroscedastic Gaussian process based emulator predictions for both the mean and (co)variance. The emulator allows efficient screening to identify important model inputs and better understanding of the complex behaviour of the rabies model.

Projected sequential Gaussian processes: flexible interpolation for large data sets

Recently within the machine learning and spatial statistics communities many papers have explored the potential of reduced rank representations of the covariance matrix, often referred to as projected or fixed rank approaches. In such methods the covariance function of the posterior process is represented by a reduced rank approximation which is chosen such that there is minimal information loss. In this paper a sequential framework for inference in such projected processes is presented, where the observations are considered one at a time. We introduce a C++ library for carrying out such projected, sequential estimation which adds several novel features. In particular we have incorporated the ability to use a generic observation operator, or sensor model, to permit data fusion. We can also cope with a range of observation error characteristics, including non-Gaussian observation errors. Inference for the variogram parameters is based on maximum likelihood estimation. We illustrate the projected sequential method in application to synthetic and real data sets. We discuss the software implementation and suggest possible future extensions.

A pragmatic Bayesian approach to wind field retrieval

The ERS-1 Satellite was launched in July 1991 by the European Space Agency into a polar orbit at about 800 km, carrying a C-band scatterometer. A scatterometer measures the amount of backscatter microwave radiation reflected by small ripples on the ocean surface induced by sea-surface winds, and so provides instantaneous snap-shots of wind flow over large areas of the ocean surface, known as wind fields. Inherent in the physics of the observation process is an ambiguity in wind direction; the scatterometer cannot distinguish if the wind is blowing toward or away from the sensor device. This ambiguity implies that there is a one-to-many mapping between scatterometer data and wind direction. Current operational methods for wind field retrieval are based on the retrieval of wind vectors from satellite scatterometer data, followed by a disambiguation and filtering process that is reliant on numerical weather prediction models. The wind vectors are retrieved by the local inversion of a forward model, mapping scatterometer observations to wind vectors, and minimising a cost function in scatterometer measurement space. This thesis applies a pragmatic Bayesian solution to the problem. The likelihood is a combination of conditional probability distributions for the local wind vectors given the scatterometer data. The prior distribution is a vector Gaussian process that provides the geophysical consistency for the wind field. The wind vectors are retrieved directly from the scatterometer data by using mixture density networks, a principled method to model multi-modal conditional probability density functions. The complexity of the mapping and the structure of the conditional probability density function are investigated. A hybrid mixture density network, that incorporates the knowledge that the conditional probability distribution of the observation process is predominantly bi-modal, is developed. The optimal model, which generalises across a swathe of scatterometer readings, is better on key performance measures than the current operational model. Wind field retrieval is approached from three perspectives. The first is a non-autonomous method that confirms the validity of the model by retrieving the correct wind field 99% of the time from a test set of 575 wind fields. The second technique takes the maximum a posteriori probability wind field retrieved from the posterior distribution as the prediction. For the third technique, Markov Chain Monte Carlo (MCMC) techniques were employed to estimate the mass associated with significant modes of the posterior distribution, and make predictions based on the mode with the greatest mass associated with it. General methods for sampling from multi-modal distributions were benchmarked against a specific MCMC transition kernel designed for this problem. It was shown that the general methods were unsuitable for this application due to computational expense. On a test set of 100 wind fields the MAP estimate correctly retrieved 72 wind fields, whilst the sampling method correctly retrieved 73 wind fields.

The development and stability analysis of a nonlinear growth model for microorganisms

A nonlinear dynamic model of microbial growth is established based on the theories of the diffusion response of thermodynamics and the chemotactic response of biology. Except for the two traditional variables, i.e. the density of bacteria and the concentration of attractant, the pH value, a crucial influencing factor to the microbial growth, is also considered in this model. The pH effect on the microbial growth is taken as a Gaussian function G0e-(f- fc)2/G1, where G0, G1 and fc are constants, f represents the pH value and fc represents the critical pH value that best fits for microbial growth. To study the effects of the reproduction rate of the bacteria and the pH value on the stability of the system, three parameters a, G0 and G1 are studied in detail, where a denotes the reproduction rate of the bacteria, G0 denotes the impacting intensity of the pH value to microbial growth and G1 denotes the bacterial adaptability to the pH value. When the effect of the pH value of the solution which microorganisms live in is ignored in the governing equations of the model, the microbial system is more stable with larger a. When the effect of the bacterial chemotaxis is ignored, the microbial system is more stable with the larger G1 and more unstable with the larger G0 for f0 > fc. However, the stability of the microbial system is almost unaffected by the variation G0 and G1 and it is always stable for f0 < fc under the assumed conditions in this paper. In the whole system model, it is more unstable with larger G1 and more stable with larger G0 for f0 < fc. The system is more stable with larger G1 and more unstable with larger G0 for f0 > fc. However, the system is more unstable with larger a for f0 < fc and the stability of the system is almost unaffected by a for f0 > fc. The results obtained in this study provide a biophysical insight into the understanding of the growth and stability behavior of microorganisms.

Estimating the SCAN*PRO model of store sales: HB, FM or just OLS?

In this paper we investigate whether consideration of store-level heterogeneity in marketing mix effects improves the accuracy of the marketing mix elasticities, fit, and forecasting accuracy of the widely-applied SCAN*PRO model of store sales. Models with continuous and discrete representations of heterogeneity, estimated using hierarchical Bayes (HB) and finite mixture (FM) techniques, respectively, are empirically compared to the original model, which does not account for store-level heterogeneity in marketing mix effects, and is estimated using ordinary least squares (OLS). The empirical comparisons are conducted in two contexts: Dutch store-level scanner data for the shampoo product category, and an extensive simulation experiment. The simulation investigates how between- and within-segment variance in marketing mix effects, error variance, the number of weeks of data, and the number of stores impact the accuracy of marketing mix elasticities, model fit, and forecasting accuracy. Contrary to expectations, accommodating store-level heterogeneity does not improve the accuracy of marketing mix elasticities relative to the homogeneous SCAN*PRO model, suggesting that little may be lost by employing the original homogeneous SCAN*PRO model estimated using ordinary least squares. Improvements in fit and forecasting accuracy are also fairly modest. We pursue an explanation for this result since research in other contexts has shown clear advantages from assuming some type of heterogeneity in market response models. In an Afterthought section, we comment on the controversial nature of our result, distinguishing factors inherent to household-level data and associated models vs. general store-level data and associated models vs. the unique SCAN*PRO model specification.

Matrix-assisted diffusion-ordered spectroscopy:mixture resolution by NMR using SDSmicelles

Diffusion-ordered spectroscopy (DOSY) is a powerful technique for mixture analysis, but in its basic form it cannot separate the component spectra for species with very similar diffusion coefficients. It has been recently demonstrated that the component spectra of a mixture of isomers with nearly identical diffusion coefficients (the three dihydroxybenzenes) can be resolved using matrix-assisted DOSY (MAD), in which diffusion is perturbed by the addition of a co-solute such as a surfactant [R. Evans, S. Haiber, M. Nilsson, G. A. Morris, Anal. Chem. 2009, 81, 4548-4550]. However, little is known about the conditions required for such a separation, for example, the concentrations and concentration ratios of surfactant and solutes. The aim of this study was to explore the concentration range over whichmatrix-assisted DOSY using the surfactant SDS can achieve diffusion resolution of a simple model set of isomers, the monomethoxyphenols. The results show that the separation is remarkably robust with respect to both the concentrations and the concentration ratios of surfactant and solutes, supporting the idea that MAD may become a valuable tool formixture analysis. © 2010 John Wiley & Sons, Ltd.

Non-Gaussian error probability in optical soliton transmission

We find the probability distribution of the fluctuating parameters of a soliton propagating through a medium with additive noise. Our method is a modification of the instanton formalism (method of optimal fluctuation) based on a saddle-point approximation in the path integral. We first solve consistently a fundamental problem of soliton propagation within the framework of noisy nonlinear Schrödinger equation. We then consider model modifications due to in-line (filtering, amplitude and phase modulation) control. It is examined how control elements change the error probability in optical soliton transmission. Even though a weak noise is considered, we are interested here in probabilities of error-causing large fluctuations which are beyond perturbation theory. We describe in detail a new phenomenon of soliton collapse that occurs under the combined action of noise, filtering and amplitude modulation. © 2004 Elsevier B.V. All rights reserved.

NLSE-based model of a random distributed feedback fiber laser

In this work we propose a NLSE-based model of power and spectral properties of the random distributed feedback (DFB) fiber laser. The model is based on coupled set of non-linear Schrödinger equations for pump and Stokes waves with the distributed feedback due to Rayleigh scattering. The model considers random backscattering via its average strength, i.e. we assume that the feedback is incoherent. In addition, this allows us to speed up simulations sufficiently (up to several orders of magnitude). We found that the model of the incoherent feedback predicts the smooth and narrow (comparing with the gain spectral profile) generation spectrum in the random DFB fiber laser. The model allows one to optimize the random laser generation spectrum width varying the dispersion and nonlinearity values: we found, that the high dispersion and low nonlinearity results in narrower spectrum that could be interpreted as four-wave mixing between different spectral components in the quasi-mode-less spectrum of the random laser under study could play an important role in the spectrum formation. Note that the physical mechanism of the random DFB fiber laser formation and broadening is not identified yet. We investigate temporal and statistical properties of the random DFB fiber laser dynamics. Interestingly, we found that the intensity statistics is not Gaussian. The intensity auto-correlation function also reveals that correlations do exist. The possibility to optimize the system parameters to enhance the observed intrinsic spectral correlations to further potentially achieved pulsed (mode-locked) operation of the mode-less random distributed feedback fiber laser is discussed.

Wind power forecasts using Gaussian processes and numerical weather prediction

Since wind at the earth's surface has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safe and economic use of wind energy. In this paper, we investigated a combination of numeric and probabilistic models: a Gaussian process (GP) combined with a numerical weather prediction (NWP) model was applied to wind-power forecasting up to one day ahead. First, the wind-speed data from NWP was corrected by a GP, then, as there is always a defined limit on power generated in a wind turbine due to the turbine controlling strategy, wind power forecasts were realized by modeling the relationship between the corrected wind speed and power output using a censored GP. To validate the proposed approach, three real-world datasets were used for model training and testing. The empirical results were compared with several classical wind forecast models, and based on the mean absolute error (MAE), the proposed model provides around 9% to 14% improvement in forecasting accuracy compared to an artificial neural network (ANN) model, and nearly 17% improvement on a third dataset which is from a newly-built wind farm for which there is a limited amount of training data. © 2013 IEEE.

Short-term wind power forecasting using Gaussian processes

Since wind has an intrinsically complex and stochastic nature, accurate wind power forecasts are necessary for the safety and economics of wind energy utilization. In this paper, we investigate a combination of numeric and probabilistic models: one-day-ahead wind power forecasts were made with Gaussian Processes (GPs) applied to the outputs of a Numerical Weather Prediction (NWP) model. Firstly the wind speed data from NWP was corrected by a GP. Then, as there is always a defined limit on power generated in a wind turbine due the turbine controlling strategy, a Censored GP was used to model the relationship between the corrected wind speed and power output. To validate the proposed approach, two real world datasets were used for model construction and testing. The simulation results were compared with the persistence method and Artificial Neural Networks (ANNs); the proposed model achieves about 11% improvement in forecasting accuracy (Mean Absolute Error) compared to the ANN model on one dataset, and nearly 5% improvement on another.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.