Advances in large margin classifiers

We apply methods of Statistical Mechanics to study the generalization performance of Support vector Machines in large data spaces.

Learning curves for Gaussian processes models: fluctuations and universality

Based on a statistical mechanics approach, we develop a method for approximately computing average case learning curves and their sample fluctuations for Gaussian process regression models. We give examples for the Wiener process and show that universal relations (that are independent of the input distribution) between error measures can be derived.

Typical performance of low-density parity-check codes over general symmetric channels

Typical performance of low-density parity-check (LDPC) codes over a general binary-input output-symmetric memoryless channel is investigated using methods of statistical mechanics. The binary-input additive-white-Gaussian-noise channel and the binary-input Laplace channel are considered as specific channel noise models.

Probability distribution modelling to improve stability in nonlinear MIMO control

We consider the direct adaptive inverse control of nonlinear multivariable systems with different delays between every input-output pair. In direct adaptive inverse control, the inverse mapping is learned from examples of input-output pairs. This makes the obtained controller sub optimal, since the network may have to learn the response of the plant over a larger operational range than necessary. Moreover, in certain applications, the control problem can be redundant, implying that the inverse problem is ill posed. In this paper we propose a new algorithm which allows estimating and exploiting uncertainty in nonlinear multivariable control systems. This approach allows us to model strongly non-Gaussian distribution of control signals as well as processes with hysteresis. The proposed algorithm circumvents the dynamic programming problem by using the predicted neural network uncertainty to localise the possible control solutions to consider.

The relationship between self-awareness of attentional status, behavioral performance and oscillatory brain rhythms

High-level cognitive factors, including self-awareness, are believed to play an important role in human visual perception. The principal aim of this study was to determine whether oscillatory brain rhythms play a role in the neural processes involved in self-monitoring attentional status. To do so we measured cortical activity using magnetoencephalography (MEG) and functional magnetic resonance imaging (fMRI) while participants were asked to self-monitor their internal status, only initiating the presentation of a stimulus when they perceived their attentional focus to be maximal. We employed a hierarchical Bayesian method that uses fMRI results as soft-constrained spatial information to solve the MEG inverse problem, allowing us to estimate cortical currents in the order of millimeters and milliseconds. Our results show that, during self-monitoring of internal status, there was a sustained decrease in power within the 7-13 Hz (alpha) range in the rostral cingulate motor area (rCMA) on the human medial wall, beginning approximately 430 msec after the trial start (p < 0.05, FDR corrected). We also show that gamma-band power (41-47 Hz) within this area was positively correlated with task performance from 40-640 msec after the trial start (r = 0.71, p < 0.05). We conclude: (1) the rCMA is involved in processes governing self-monitoring of internal status; and (2) the qualitative differences between alpha and gamma activity are reflective of their different roles in self-monitoring internal states. We suggest that alpha suppression may reflect a strengthening of top-down interareal connections, while a positive correlation between gamma activity and task performance indicates that gamma may play an important role in guiding visuomotor behavior. © 2013 Yamagishi et al.

The topographic distribution of the magnetic P100M to full- and half-field stimulation

Visual evoked magnetic responses were recorded to full-field and left and right half-field stimulation with three check sizes (70′, 34′ and 22′) in five normal subjects. Recordings were made sequentially on a 20-position grid (4 × 5) based on the inion, by means of a single-channel direct current-Superconducting Quantum Interference Device second-order gradiometer. The topographic maps were consistent on the same subjects recorded 2 months apart. The half-field responses produced the strongest signals in the contralateral hemisphere and were consistent with the cruciform model of the calcarine fissure. Right half fields produced upper-left-quadrant outgoing fields and lower-left-quadrant ingoing fields, while the left half field produced the opposite response. The topographic maps also varied with check size, with the larger checks producing positive or negative maximum position more anteriorly than small checks. In addition, with large checks the full-field responses could be explained as the summation of the two half fields, whereas full-field responses to smaller checks were more unpredictable and may be due to sources located at the occipital pole or lateral surface. In addition, dipole sources were located as appropriate with the use of inverse problem solutions. Topographic data will be vital to the clinical use of the visual evoked field but, in addition, provides complementary information to visual evoked potentials, allowing detailed studies of the visual cortex. © 1992 Kluwer Academic Publishers.

Typical behavior of relays in communication channels

The typical behavior of the relay-without-delay channel under low-density parity-check coding and its multiple-unit generalization, termed the relay array, is studied using methods of statistical mechanics. A demodulate-and- forward strategy is analytically solved using the replica symmetric ansatz which is exact in the system studied at Nishimori's temperature. In particular, the typical level of improvement in communication performance by relaying messages is shown in the case of a small and a large number of relay units. © 2007 The American Physical Society.

Properties of sparse random matrices over finite fields

Typical properties of sparse random matrices over finite (Galois) fields are studied, in the limit of large matrices, using techniques from the physics of disordered systems. For the case of a finite field GF(q) with prime order q, we present results for the average kernel dimension, average dimension of the eigenvector spaces and the distribution of the eigenvalues. The number of matrices for a given distribution of entries is also calculated for the general case. The significance of these results to error-correcting codes and random graphs is also discussed.

Functional source separation applied to induced visual gamma activity

Objective of this work was to explore the performance of a recently introduced source extraction method, FSS (Functional Source Separation), in recovering induced oscillatory change responses from extra-cephalic magnetoencephalographic (MEG) signals. Unlike algorithms used to solve the inverse problem, FSS does not make any assumption about the underlying biophysical source model; instead, it makes use of task-related features (functional constraints) to estimate source/s of interest. FSS was compared with blind source separation (BSS) approaches such as Principal and Independent Component Analysis, PCA and ICA, which are not subject to any explicit forward solution or functional constraint, but require source uncorrelatedness (PCA), or independence (ICA). A visual MEG experiment with signals recorded from six subjects viewing a set of static horizontal black/white square-wave grating patterns at different spatial frequencies was analyzed. The beamforming technique Synthetic Aperture Magnetometry (SAM) was applied to localize task-related sources; obtained spatial filters were used to automatically select BSS and FSS components in the spatial area of interest. Source spectral properties were investigated by using Morlet-wavelet time-frequency representations and significant task-induced changes were evaluated by means of a resampling technique; the resulting spectral behaviours in the gamma frequency band of interest (20-70 Hz), as well as the spatial frequency-dependent gamma reactivity, were quantified and compared among methods. Among the tested approaches, only FSS was able to estimate the expected sustained gamma activity enhancement in primary visual cortex, throughout the whole duration of the stimulus presentation for all subjects, and to obtain sources comparable to invasively recorded data.

Computing with noise: phase transitions in Boolean formulas

Computing circuits composed of noisy logical gates and their ability to represent arbitrary Boolean functions with a given level of error are investigated within a statistical mechanics setting. Existing bounds on their performance are straightforwardly retrieved, generalized, and identified as the corresponding typical-case phase transitions. Results on error rates, function depth, and sensitivity, and their dependence on the gate-type and noise model used are also obtained.

The development of constrained source localisation algorithms for human brain imaging

This work sets out to evaluate the potential benefits and pit-falls in using a priori information to help solve the Magnetoencephalographic (MEG) inverse problem. In chapter one the forward problem in MEG is introduced, together with a scheme that demonstrates how a priori information can be incorporated into the inverse problem. Chapter two contains a literature review of techniques currently used to solve the inverse problem. Emphasis is put on the kind of a priori information that is used by each of these techniques and the ease with which additional constraints can be applied. The formalism of the FOCUSS algorithm is shown to allow for the incorporation of a priori information in an insightful and straightforward manner. In chapter three it is described how anatomical constraints, in the form of a realistically shaped source space, can be extracted from a subject’s Magnetic Resonance Image (MRI). The use of such constraints relies on accurate co-registration of the MEG and MRI co-ordinate systems. Variations of the two main co-registration approaches, based on fiducial markers or on surface matching, are described and the accuracy and robustness of a surface matching algorithm is evaluated. Figures of merit introduced in chapter four are shown to given insight into the limitations of a typical measurement set-up and potential value of a priori information. It is shown in chapter five that constrained dipole fitting and FOCUSS outperform unconstrained dipole fitting when data with low SNR is used. However, the effect of errors in the constraints can reduce this advantage. Finally, it is demonstrated in chapter six that the results of different localisation techniques give corroborative evidence about the location and activation sequence of the human visual cortical areas underlying the first 125ms of the visual magnetic evoked response recorded with a whole head neuromagnetometer.

Magnetoencephalography:technical improvements in image co-registration and studies of visual cortical oscillations

The work presented in this thesis is divided into two distinct sections. In the first, the functional neuroimaging technique of Magnetoencephalography (MEG) is described and a new technique is introduced for accurate combination of MEG and MRI co-ordinate systems. In the second part of this thesis, MEG and the analysis technique of SAM are used to investigate responses of the visual system in the context of functional specialisation within the visual cortex. In chapter one, the sources of MEG signals are described, followed by a brief description of the necessary instrumentation for accurate MEG recordings. This chapter is concluded by introducing the forward and inverse problems of MEG, techniques to solve the inverse problem, and a comparison of MEG with other neuroimaging techniques. Chapter two provides an important contribution to the field of research with MEG. Firstly, it is described how MEG and MRI co-ordinate systems are combined for localisation and visualisation of activated brain regions. A previously used co-registration methods is then described, and a new technique is introduced. In a series of experiments, it is demonstrated that using fixed fiducial points provides a considerable improvement in the accuracy and reliability of co-registration. Chapter three introduces the visual system starting from the retina and ending with the higher visual rates. The functions of the magnocellular and the parvocellular pathways are described and it is shown how the parallel visual pathways remain segregated throughout the visual system. The structural and functional organisation of the visual cortex is then described. Chapter four presents strong evidence in favour of the link between conscious experience and synchronised brain activity. The spatiotemporal responses of the visual cortex are measured in response to specific gratings. It is shown that stimuli that induce visual discomfort and visual illusions share their physical properties with those that induce highly synchronised gamma frequency oscillations in the primary visual cortex. Finally chapter five is concerned with localization of colour in the visual cortex. In this first ever use of Synthetic Aperture Magnetometry to investigate colour processing in the visual cortex, it is shown that in response to isoluminant chromatic gratings, the highest magnitude of cortical activity arise from area V2.

Uptake of dental services

Previous research has indicated that the majority of the UK dentate population suffers from dental disease. This problem was examined in terms of the supply of, and demand for, dental treatment: how might the uptake of dental services be increased and dental health improved? The target population for the main survey was adolescents among whom demand for dental treatment has decreased. In 524 adolescents surveyed, fear of pain was the major deterrent to regular dental visits. The theoretical literature was explored for illuminating and practical approaches to the problem. The theory of reasoned action developed by Fishbein seemed the most promising. This theory was tested and validated on the adolescent sample identifying clear differences between regular and irregular dental attenders which could be usefully exploited by dental health education. A repertory grid analysis study further illuminated perceptions of dental treatment. A survey of a random sample of 716 dentists revealed that most dentists were in favour of delegating work to auxiliary help but few could do so. Auxiliary help would increase supply of services: data revealed an encouraging trend for younger dentists to be more in favour of delegation than older dentists. A survey was carried out of computer systems available for dentists suggesting that this might reduce the need for clerical assistance but would not ususally affect the supply of treatment. However in some dental practices computerisation might increase demand. For example a personalised reminder was developed and evaluated in a controlled study of 938 appointments demonstrating an uptake in dental services. Conclusions are that demand for treatment can be increased in various ways especially by teaching dentists' behavioural strategies to deal with fear and pain. Various recommendations on this are made. If demand were to outstrip supply increased delegation to auxiliary help could provide a viable way of increasing supply.

Neuro-electromagnetic imaging of the human visual cortex

Methods of solving the neuro-electromagnetic inverse problem are examined and developed, with specific reference to the human visual cortex. The anatomy, physiology and function of the human visual system are first reviewed. Mechanisms by which the visual cortex gives rise to external electric and magnetic fields are then discussed, and the forward problem is described mathematically for the case of an isotropic, piecewise homogeneous volume conductor, and then for an anisotropic, concentric, spherical volume conductor. Methods of solving the inverse problem are reviewed, before a new technique is presented. This technique combines prior anatomical information gained from stereotaxic studies, with a probabilistic distributed-source algorithm to yield accurate, realistic inverse solutions. The solution accuracy is enhanced by using both visual evoked electric and magnetic responses simultaneously. The numerical algorithm is then modified to perform equivalent current dipole fitting and minimum norm estimation, and these three techniques are implemented on a transputer array for fast computation. Due to the linear nature of the techniques, they can be executed on up to 22 transputers with close to linear speedup. The latter part of the thesis describes the application of the inverse methods to the analysis of visual evoked electric and magnetic responses. The CIIm peak of the pattern onset evoked magnetic response is deduced to be a product of current flowing away from the surface areas 17, 18 and 19, while the pattern reversal P100m response originates in the same areas, but from oppositely directed current. Cortical retinotopy is examined using sectorial stimuli, the CI and CIm ;peaks of the pattern onset electric and magnetic responses are found to originate from areas V1 and V2 simultaneously, and they therefore do not conform to a simple cruciform model of primary visual cortex.

Effective electromagnetic noise cancellation with beamformers and synthetic gradiometry in shielded and partly shielded environments

The major challenge of MEG, the inverse problem, is to estimate the very weak primary neuronal currents from the measurements of extracranial magnetic fields. The non-uniqueness of this inverse solution is compounded by the fact that MEG signals contain large environmental and physiological noise that further complicates the problem. In this paper, we evaluate the effectiveness of magnetic noise cancellation by synthetic gradiometers and the beamformer analysis method of synthetic aperture magnetometry (SAM) for source localisation in the presence of large stimulus-generated noise. We demonstrate that activation of primary somatosensory cortex can be accurately identified using SAM despite the presence of significant stimulus-related magnetic interference. This interference was generated by a contact heat evoked potential stimulator (CHEPS), recently developed for thermal pain research, but which to date has not been used in a MEG environment. We also show that in a reduced shielding environment the use of higher order synthetic gradiometry is sufficient to obtain signal-to-noise ratios (SNRs) that allow for accurate localisation of cortical sensory function.