Estimation of functional connectivity from electromagnetic signals and the amount of empirical data required

An increasing number of neuroimaging studies are concerned with the identification of interactions or statistical dependencies between brain areas. Dependencies between the activities of different brain regions can be quantified with functional connectivity measures such as the cross-correlation coefficient. An important factor limiting the accuracy of such measures is the amount of empirical data available. For event-related protocols, the amount of data also affects the temporal resolution of the analysis. We use analytical expressions to calculate the amount of empirical data needed to establish whether a certain level of dependency is significant when the time series are autocorrelated, as is the case for biological signals. These analytical results are then contrasted with estimates from simulations based on real data recorded with magnetoencephalography during a resting-state paradigm and during the presentation of visual stimuli. Results indicate that, for broadband signals, 50-100 s of data is required to detect a true underlying cross-correlations coefficient of 0.05. This corresponds to a resolution of a few hundred milliseconds for typical event-related recordings. The required time window increases for narrow band signals as frequency decreases. For instance, approximately 3 times as much data is necessary for signals in the alpha band. Important implications can be derived for the design and interpretation of experiments to characterize weak interactions, which are potentially important for brain processing.

Molecular phase space transport in water:non-stationary random walk model

Molecular transport in phase space is crucial for chemical reactions because it defines how pre-reactive molecular configurations are found during the time evolution of the system. Using Molecular Dynamics (MD) simulated atomistic trajectories we test the assumption of the normal diffusion in the phase space for bulk water at ambient conditions by checking the equivalence of the transport to the random walk model. Contrary to common expectations we have found that some statistical features of the transport in the phase space differ from those of the normal diffusion models. This implies a non-random character of the path search process by the reacting complexes in water solutions. Our further numerical experiments show that a significant long period of non-stationarity in the transition probabilities of the segments of molecular trajectories can account for the observed non-uniform filling of the phase space. Surprisingly, the characteristic periods in the model non-stationarity constitute hundreds of nanoseconds, that is much longer time scales compared to typical lifetime of known liquid water molecular structures (several picoseconds).

Pulse compression applied to the detection of F.S.K. and P.S.K. signals

The matched filter detector is well known as the optimum detector for use in communication, as well as in radar systems for signals corrupted by Additive White Gaussian Noise (A.W.G.N.). Non-coherent F.S.K. and differentially coherent P.S.K. (D.P.S.K.) detection schemes, which employ a new approach in realizing the matched filter processor, are investigated. The new approach utilizes pulse compression techniques, well known in radar systems, to facilitate the implementation of the matched filter in the form of the Pulse Compressor Matched Filter (P.C.M.F.). Both detection schemes feature a mixer- P.C.M.F. Compound as their predetector processor. The Compound is utilized to convert F.S.K. modulation into pulse position modulation, and P.S.K. modulation into pulse polarity modulation. The mechanisms of both detection schemes are studied through examining the properties of the Autocorrelation function (A.C.F.) at the output of the P.C.M.F.. The effects produced by time delay, and carrier interference on the output A.C.F. are determined. Work related to the F.S.K. detection scheme is mostly confined to verifying its validity, whereas the D.P.S.K. detection scheme has not been reported before. Consequently, an experimental system was constructed, which utilized combined hardware and software, and operated under the supervision of a microprocessor system. The experimental system was used to develop error-rate models for both detection schemes under investigation. Performances of both F. S. K. and D.P. S. K. detection schemes were established in the presence of A. W. G. N. , practical imperfections, time delay, and carrier interference. The results highlight the candidacy of both detection schemes for use in the field of digital data communication and, in particular, the D.P.S.K. detection scheme, which performed very close to optimum in a background of A.W.G.N.

The design of a real-time nowcasting system for localised weather

National meteorological offices are largely concerned with synoptic-scale forecasting where weather predictions are produced for a whole country for 24 hours ahead. In practice, many local organisations (such as emergency services, construction industries, forestry, farming, and sports) require only local short-term, bespoke, weather predictions and warnings. This thesis shows that the less-demanding requirements do not require exceptional computing power and can be met by a modern, desk-top system which monitors site-specific ground conditions (such as temperature, pressure, wind speed and direction, etc) augmented with above ground information from satellite images to produce `nowcasts'. The emphasis in this thesis has been towards the design of such a real-time system for nowcasting. Local site-specific conditions are monitored using a custom-built, stand alone, Motorola 6809 based sub-system. Above ground information is received from the METEOSAT 4 geo-stationary satellite using a sub-system based on a commercially available equipment. The information is ephemeral and must be captured in real-time. The real-time nowcasting system for localised weather handles the data as a transparent task using the limited capabilities of the PC system. Ground data produces a time series of measurements at a specific location which represents the past-to-present atmospheric conditions of the particular site from which much information can be extracted. The novel approach adopted in this thesis is one of constructing stochastic models based on the AutoRegressive Integrated Moving Average (ARIMA) technique. The satellite images contain features (such as cloud formations) which evolve dynamically and may be subject to movement, growth, distortion, bifurcation, superposition, or elimination between images. The process of extracting a weather feature, following its motion and predicting its future evolution involves algorithms for normalisation, partitioning, filtering, image enhancement, and correlation of multi-dimensional signals in different domains. To limit the processing requirements, the analysis in this thesis concentrates on an `area of interest'. By this rationale, only a small fraction of the total image needs to be processed, leading to a major saving in time. The thesis also proposes an extention to an existing manual cloud classification technique for its implementation in automatically classifying a cloud feature over the `area of interest' for nowcasting using the multi-dimensional signals.

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.

Identification of nonlinear systems by correlation using pseudorandom signals

This thesis is concerned with the measurement of the characteristics of nonlinear systems by crosscorrelation, using pseudorandom input signals based on m sequences. The systems are characterised by Volterra series, and analytical expressions relating the rth order Volterra kernel to r-dimensional crosscorrelation measurements are derived. It is shown that the two-dimensional crosscorrelation measurements are related to the corresponding second order kernel values by a set of equations which may be structured into a number of independent subsets. The m sequence properties determine how the maximum order of the subsets for off-diagonal values is related to the upper bound of the arguments for nonzero kernel values. The upper bound of the arguments is used as a performance index, and the performance of antisymmetric pseudorandom binary, ternary and quinary signals is investigated. The performance indices obtained above are small in relation to the periods of the corresponding signals. To achieve higher performance with ternary signals, a method is proposed for combining the estimates of the second order kernel values so that the effects of some of the undesirable nonzero values in the fourth order autocorrelation function of the input signal are removed. The identification of the dynamics of two-input, single-output systems with multiplicative nonlinearity is investigated. It is shown that the characteristics of such a system may be determined by crosscorrelation experiments using phase-shifted versions of a common signal as inputs. The effects of nonlinearities on the estimates of system weighting functions obtained by crosscorrelation are also investigated. Results obtained by correlation testing of an industrial process are presented, and the differences between theoretical and experimental results discussed for this case;

Can we observe collective neuronal activity from macroscopic aggregate signals?

The fundamental problem faced by noninvasive neuroimaging techniques such as EEG/MEG1 is to elucidate functionally important aspects of the microscopic neuronal network dynamics from macroscopic aggregate measurements. Due to the mixing of the activities of large neuronal populations in the observed macroscopic aggregate, recovering the underlying network that generates the signal in the absence of any additional information represents a considerable challenge. Recent MEG studies have shown that macroscopic measurements contain sufficient information to allow the differentiation between patterns of activity, which are likely to represent different stimulus-specific collective modes in the underlying network (Hadjipapas, A., Adjamian, P., Swettenham, J.B., Holliday, I.E., Barnes, G.R., 2007. Stimuli of varying spatial scale induce gamma activity with distinct temporal characteristics in human visual cortex. NeuroImage 35, 518–530). The next question arising in this context is whether aspects of collective network activity can be recovered from a macroscopic aggregate signal. We propose that this issue is most appropriately addressed if MEG/EEG signals are to be viewed as macroscopic aggregates arising from networks of coupled systems as opposed to aggregates across a mass of largely independent neural systems. We show that collective modes arising in a network of simulated coupled systems can be indeed recovered from the macroscopic aggregate. Moreover, we show that nonlinear state space methods yield a good approximation of the number of effective degrees of freedom in the network. Importantly, information about hidden variables, which do not directly contribute to the aggregate signal, can also be recovered. Finally, this theoretical framework can be applied to experimental MEG/EEG data in the future, enabling the inference of state dependent changes in the degree of local synchrony in the underlying network.

Stationary scattering from a nonlinear network

Transmission through a complex network of nonlinear one-dimensional leads is discussed by extending the stationary scattering theory on quantum graphs to the nonlinear regime. We show that the existence of cycles inside the graph leads to a large number of sharp resonances that dominate scattering. The latter resonances are then shown to be extremely sensitive to the nonlinearity and display multistability and hysteresis. This work provides a framework for the study of light propagation in complex optical networks.

Determination of muscle fatigue in clinical practices using dynamically embedded signals

This paper explores a new method of analysing muscle fatigue within the muscles predominantly used during microsurgery. The captured electromyographic (EMG) data retrieved from these muscles are analysed for any defining patterns relating to muscle fatigue. The analysis consists of dynamically embedding the EMG signals from a single muscle channel into an embedded matrix. The muscle fatigue is determined by defining its entropy characterized by the singular values of the dynamically embedded (DE) matrix. The paper compares this new method with the traditional method of using mean frequency shifts in the EMG signal's power spectral density. Linear regressions are fitted to the results from both methods, and the coefficients of variation of both their slope and point of intercept are determined. It is shown that the complexity method is slightly more robust in that the coefficient of variation for the DE method has lower variability than the conventional method of mean frequency analysis.

40-Gbaud 16-QAM transmitter using tandem IQ modulators with binary driving electronic signals

We propose a novel 16-quadrature amplitude modulation (QAM) transmitter based on two cascaded IQ modulators driven by four separate binary electrical signals. The proposed 16-QAM transmitter features scalable configuration and stable performance with simple bias-control. Generation of 16-QAM signals at 40 Gbaud is experimentally demonstrated for the first time and visualized with a high speed constellation analyzer. The proposed modulator is also compared to two other schemes. We investigate the modulator bandwidth requirements and tolerance to accumulated chromatic dispersion through numerical simulations, and the minimum theoretical insertion attenuation is calculated analytically.

Novel real-time homodyne coherent receiver using a feed-forward based carrier extraction scheme for phase modulated signals

We report a novel real-time homodyne coherent receiver based on a DPSK optical-electrical-optical (OEO) regenerator used to extract a carrier from carrier-less phase modulated signals based on feed-forward based modulation stripping. The performance of this non-DSP based coherent receiver was evaluated for 10.66Gbit/s BPSK signals. Self-homodyne coherent detection and homodyne detection with an injection-locked local oscillator laser was demonstrated. The performance was evaluated by measuring the electrical signal-to-noise (SNR) and recording the eye diagrams. Using injection-locking for the LO improves the performance and enables homodyne detection with optical injection-locking to operate with carrier-less BPSK signals without the need for polarization multiplexed pilot-tones.

Phase synchronization scheme for a practical phase sensitive amplifier of ASK-NRZ signals

We present a phase locking scheme that enables the demonstration of a practical dual pump degenerate phase sensitive amplifier for 10 Gbit/s non-return to zero amplitude shift keying signals. The scheme makes use of cascaded Mach Zehnder modulators for creating the pump frequencies as well as of injection locking for extracting the signal carrier and synchronizing the local lasers. An in depth optimization study has been performed, based on measured error rate performance, and the main degradation factors have been identified.

Multi-wavelength regeneration of phase encoded signals based on phase sensitive amplifiers

Future high capacity optical links will have to make use of frequent signal regeneration to enable long distance transmission. In this respect, the role of all-optical signal processing becomes increasingly important because of its potential to mitigate signal impairments at low cost and power consumption. More substantial benefits are expected if regeneration is achieved simultaneously on a multiple signal band. Until recently, this had been achieved only for on-off keying modulation formats. However, as in future transmission links the information will be encoded also in the phase for enhancing the spectral efficiency, novel subsystem concepts will be needed for multichannel processing of such advanced signal formats. In this paper we show that phase sensitive amplifiers can be an ideal technology platform for developing such regenerators and we discuss our recent demonstration of the first multi-channel regenerator for phase encoded signals.

Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

Generalized methods and solvers for noise removal from piecewise constant signals. II. New methods

Removing noise from signals which are piecewise constant (PWC) is a challenging signal processing problem that arises in many practical scientific and engineering contexts. In the first paper (part I) of this series of two, we presented background theory building on results from the image processing community to show that the majority of these algorithms, and more proposed in the wider literature, are each associated with a special case of a generalized functional, that, when minimized, solves the PWC denoising problem. It shows how the minimizer can be obtained by a range of computational solver algorithms. In this second paper (part II), using this understanding developed in part I, we introduce several novel PWC denoising methods, which, for example, combine the global behaviour of mean shift clustering with the local smoothing of total variation diffusion, and show example solver algorithms for these new methods. Comparisons between these methods are performed on synthetic and real signals, revealing that our new methods have a useful role to play. Finally, overlaps between the generalized methods of these two papers and others such as wavelet shrinkage, hidden Markov models, and piecewise smooth filtering are touched on.