Hilbert Space Valued Signal Plus Noise Models: Analysis of Structural Breaks under High Dimensionality and Temporal Dependence

This thesis is concerned with change point analysis for time series, i.e. with detection of structural breaks in time-ordered, random data. This long-standing research field regained popularity over the last few years and is still undergoing, as statistical analysis in general, a transformation to high-dimensional problems. We focus on the fundamental »change in the mean« problem and provide extensions of the classical non-parametric Darling-Erdős-type cumulative sum (CUSUM) testing and estimation theory within highdimensional Hilbert space settings. In the first part we contribute to (long run) principal component based testing methods for Hilbert space valued time series under a rather broad (abrupt, epidemic, gradual, multiple) change setting and under dependence. For the dependence structure we consider either traditional m-dependence assumptions or more recently developed m-approximability conditions which cover, e.g., MA, AR and ARCH models. We derive Gumbel and Brownian bridge type approximations of the distribution of the test statistic under the null hypothesis of no change and consistency conditions under the alternative. A new formulation of the test statistic using projections on subspaces allows us to simplify the standard proof techniques and to weaken common assumptions on the covariance structure. Furthermore, we propose to adjust the principal components by an implicit estimation of a (possible) change direction. This approach adds flexibility to projection based methods, weakens typical technical conditions and provides better consistency properties under the alternative. In the second part we contribute to estimation methods for common changes in the means of panels of Hilbert space valued time series. We analyze weighted CUSUM estimates within a recently proposed »high-dimensional low sample size (HDLSS)« framework, where the sample size is fixed but the number of panels increases. We derive sharp conditions on »pointwise asymptotic accuracy« or »uniform asymptotic accuracy« of those estimates in terms of the weighting function. Particularly, we prove that a covariance-based correction of Darling-Erdős-type CUSUM estimates is required to guarantee uniform asymptotic accuracy under moderate dependence conditions within panels and that these conditions are fulfilled, e.g., by any MA(1) time series. As a counterexample we show that for AR(1) time series, close to the non-stationary case, the dependence is too strong and uniform asymptotic accuracy cannot be ensured. Finally, we conduct simulations to demonstrate that our results are practically applicable and that our methodological suggestions are advantageous.

Effect of temperature and mixing conditions on quality and consistency of poly(methyl methacrylate) bone cement

The mixing of poly(methyl methacrylate) (PMMA) bone cement has been studied to develop methods for preparing a consistently high quality cement. A novel droplet test experimental procedure was developed that characterised the wetting characteristics involved in bone cement mixing. Using this technique it was established that increased wetting occurred by mixing bone cement at a lower temperature (-28 degreesC) than normal mixing at room temperature.

Diurnal variation of ocular biometrics under natural and defocused conditions

It is well known that a broad range of ocular anatomical and physiological parameters undergo significant diurnal variation. However, the natural diurnal variations that occur in the length of the human eye (axial length) and their underlying causes have been less well studied. Improvements in optical methods for the measurement of ocular biometrics now allow more precise and comprehensive measurements of axial length to be performed than has previously been possible. Research from animal models also suggests a link between diurnal axial length variations and longer term myopic eye growth, and that retinal image defocus can disrupt these diurnal rhythms in axial length. This research programme has examined the diurnal variations in axial length in young normal eyes, the contributing components and the influence of optical stimuli on these changes. In the first experiment, the normal pattern and consistency of the diurnal variations in axial length were examined at 10 different times (5 measurements each day, at ~ 3-hour intervals from ~ 9 am to ~ 9 pm) over 2 consecutive days on 30 young adult subjects (15 myopes, 15 emmetropes). Additionally, variations in a range of other ocular biometric measurements such as choroidal thickness, intraocular pressure, and other ocular biometrics were also explored as potential factors that may be associated with the observed variations in axial length. To investigate the potential influence of refractive error on diurnal axial length variations, the differences in the magnitude and pattern of diurnal variations in axial length between the myopic and emmetropic subjects were examined. Axial length underwent significant diurnal variation that was consistently observed over the 2 consecutive days of measurements, with the longest axial length typically occurring during the day, and the shortest at night. Significant diurnal variations were also observed in choroidal thickness, IOP and other ocular biometrics (such as central corneal thickness, anterior chamber depth and vitreous chamber depth) of the eye. Diurnal variations in vitreous chamber depth, IOP (positive associations) and choroidal thickness (negative association) were all significantly correlated with the diurnal changes in axial length. Choroidal thickness was found to fluctuate approximately in antiphase to the axial length changes, with the average timing of the longest axial length coinciding with the thinnest choroid and vice versa. There were no significant differences in the ocular diurnal variations associated with refractive error. Given that the diurnal changes in axial length could be associated with the changes in the eye’s optical quality, whether the optical quality of the eye also undergoes diurnal variation in the same cohort of young adult myopes and emmetropes over 2 consecutive days was also examined. Significant diurnal variations were observed only in the best sphere refraction (power vector M) and in the spherical aberration of the eye over two consecutive days of testing. The changes in the eyes lower and higher order ocular optics were not significantly associated with the diurnal variations in axial length and the other measured ocular biometric parameters. No significant differences were observed in the magnitude and timing of diurnal variations in lower-order and higher-order optics associated with refractive error. Since the small natural fluctuations in the eye’s optical quality did not appear to be sufficient to influence the natural diurnal fluctuations in ocular biometric parameters, in the next experiment, the influence of monocular myopic defocus (+1.50 DS) upon the normal diurnal variations in axial length and choroidal thickness of young adult emmetropic human subjects (n=13) imposed over a 12 hour period was examined. A series of axial length and choroidal thickness measurements (collected at ~3 hourly intervals, with the first measurement at ~9 am and the final measurement at ~9 pm) were obtained over three consecutive days. The natural diurnal rhythms (Day 1, no defocus), diurnal rhythms with monocular myopic defocus (Day 2, +1.50 DS spectacle lens over the right eye), and the recovery from any defocus induced changes (Day 3, no defocus) were examined. Significant diurnal variations over the course of the day were observed in both axial length and choroidal thickness on each of the three measurement days. The introduction of monocular myopic defocus led to significant reductions in the mean amplitude of diurnal change, and phase shifts in the peak timing of the diurnal rhythms in axial length and choroidal thickness. These defocus induced changes were found to be transient in nature and returned to normal the day following removal of the defocus. To further investigate the influence of optical stimuli on human diurnal rhythms, in the final experiment, the influence of monocular hyperopic defocus on the normal diurnal rhythms in axial length and choroidal thickness was examined in young adult emmetropic subjects (n=15). Similar to the previous experiment, the natural diurnal rhythms (Day 1, no defocus), diurnal rhythms with monocular hyperopic defocus (Day 2, -2.00 DS spectacle lens over the right eye), and the recovery from any defocus induced changes (Day 3, no defocus) were examined over three consecutive days. Both axial length and choroidal thickness underwent significant diurnal variations on each of the three days. The introduction of monocular hyperopic defocus resulted in a significant increase in the amplitude of diurnal change, but no change in the peak timing of diurnal rhythms in both parameters. The ocular changes associated with hyperopic defocus returned to normal, the day following removal of the defocus. This research has shown that axial length undergoes significant diurnal variation in young adult human eyes, and has shown that the natural diurnal variations in choroidal thickness and IOP are significantly associated, and may underlie these diurnal fluctuations in axial length. This work also demonstrated for the first time that exposing young human eyes to monocular myopic and hyperopic defocus leads to a significant disruption in the normal diurnal rhythms of axial length and choroidal thickness. These changes in axial length with defocus may reflect underlying mechanisms in the human eye that are involved in the regulation of longer term eye growth.

Laser-to-radar sensing redundancy for resilient perception in adverse environmental conditions

This paper presents an approach to promote the integrity of perception systems for outdoor unmanned ground vehicles (UGV) operating in challenging environmental conditions (presence of dust or smoke). The proposed technique automatically evaluates the consistency of the data provided by two sensing modalities: a 2D laser range finder and a millimetre-wave radar, allowing for perceptual failure mitigation. Experimental results, obtained with a UGV operating in rural environments, and an error analysis validate the approach.

Non-parametric consistency test for multiple-sensing-modality data fusion

Fusing data from multiple sensing modalities, e.g. laser and radar, is a promising approach to achieve resilient perception in challenging environmental conditions. However, this may lead to \emph{catastrophic fusion} in the presence of inconsistent data, i.e. when the sensors do not detect the same target due to distinct attenuation properties. It is often difficult to discriminate consistent from inconsistent data across sensing modalities using local spatial information alone. In this paper we present a novel consistency test based on the log marginal likelihood of a Gaussian process model that evaluates data from range sensors in a relative manner. A new data point is deemed to be consistent if the model statistically improves as a result of its fusion. This approach avoids the need for absolute spatial distance threshold parameters as required by previous work. We report results from object reconstruction with both synthetic and experimental data that demonstrate an improvement in reconstruction quality, particularly in cases where data points are inconsistent yet spatially proximal.

Thermodynamic consistency of the ternary functions

A ternary thermodynamic function has been developed based on statistico-thermodynamic considerations, with a particular emphasis on the higher-order terms indicating the effects of truncation at the various stages of the treatment. Although the truncation of a series involved in the equation introduces inconsistency, the latter may be removed by imposing various thermodynamic boundary conditions. These conditions are discussed in the paper. The present equation with higher-order terms shows that the α function of a component reduces to a quadratic function of composition at constant compositional paths involving the other two components in the system. The form of the function has been found to be representative of various experimental observations.

Derivation and consistency of the partial functions of the ternary system involving interaction coefficients

The logarithm of activity coefficients of the components of the ternary system is derived based on the Maclaurin infinite series, which is expressed in terms of the integral property of the system and subjected to appropriate boundary conditions. The derivation of the functions involves extensive summation of various infinite series pertaining to the first-order interaction coefficients that have been shown completely to remove any truncational error. Since the conventional equations involving interaction coefficients are internally inconsistent, a consistent form of the partial functions is developed in the article using the technique just described. The thermodynamic consistency of the functions based on the Maxwell and the Gibbs-Duhem relations has been established. The derived values of the logarithmic activity coefficients of the components have been found to be in agreement with the thermodynamic data of the Fe-Cr-Ni system at 1873 K and have been found to be independent of the compositional paths.

Boundary conditions in the simplest model of linear and second harmonic magneto-optical effects

This paper is concerned with linear and nonlinear magneto- optical effects in multilayered magnetic systems when treated by the simplest phenomenological model that allows their response to be represented in terms of electric polarization, The problem is addressed by formulating a set of boundary conditions at infinitely thin interfaces, taking into account the existence of surface polarizations. Essential details are given that describe how the formalism of distributions (generalized functions) allows these conditions to be derived directly from the differential form of Maxwell's equations. Using the same formalism we show the origin of alternative boundary conditions that exist in the literature. The boundary value problem for the wave equation is formulated, with an emphasis on the analysis of second harmonic magneto-optical effects in ferromagnetically ordered multilayers. An associated problem of conventions in setting up relationships between the nonlinear surface polarization and the fundamental electric field at the interfaces separating anisotropic layers through surface susceptibility tensors is discussed. A problem of self- consistency of the model is highlighted, relating to the existence of resealing procedures connecting the different conventions. The linear approximation with respect to magnetization is pursued, allowing rotational anisotropy of magneto-optical effects to be easily analyzed owing to the invariance of the corresponding polar and axial tensors under ordinary point groups. Required representations of the tensors are given for the groups infinitym, 4mm, mm2, and 3m, With regard to centrosymmetric multilayers, nonlinear volume polarization is also considered. A concise expression is given for its magnetic part, governed by an axial fifth-rank susceptibility tensor being invariant under the Curie group infinityinfinitym.

Quantifying consistency of Event Related Potentials across subjects based on single-trial topographic analysis

Introduction: Non-invasive brain imaging techniques often contrast experimental conditions across a cohort of participants, obfuscating distinctions in individual performance and brain mechanisms that are better characterised by the inter-trial variability. To overcome such limitations, we developed topographic analysis methods for single-trial EEG data [1]. So far this was typically based on time-frequency analysis of single-electrode data or single independent components. The method's efficacy is demonstrated for event-related responses to environmental sounds, hitherto studied at an average event-related potential (ERP) level. Methods: Nine healthy subjects participated to the experiment. Auditory meaningful sounds of common objects were used for a target detection task [2]. On each block, subjects were asked to discriminate target sounds, which were living or man-made auditory objects. Continuous 64-channel EEG was acquired during the task. Two datasets were considered for each subject including single-trial of the two conditions, living and man-made. The analysis comprised two steps. In the first part, a mixture of Gaussians analysis [3] provided representative topographies for each subject. In the second step, conditional probabilities for each Gaussian provided statistical inference on the structure of these topographies across trials, time, and experimental conditions. Similar analysis was conducted at group-level. Results: Results show that the occurrence of each map is structured in time and consistent across trials both at the single-subject and at group level. Conducting separate analyses of ERPs at single-subject and group levels, we could quantify the consistency of identified topographies and their time course of activation within and across participants as well as experimental conditions. A general agreement was found with previous analysis at average ERP level. Conclusions: This novel approach to single-trial analysis promises to have impact on several domains. In clinical research, it gives the possibility to statistically evaluate single-subject data, an essential tool for analysing patients with specific deficits and impairments and their deviation from normative standards. In cognitive neuroscience, it provides a novel tool for understanding behaviour and brain activity interdependencies at both single-subject and at group levels. In basic neurophysiology, it provides a new representation of ERPs and promises to cast light on the mechanisms of its generation and inter-individual variability.

The effects of consistency and inconsistency between attentional focus and task objective in learning a golf putting task

Converging evidence has demonstrated learning advantages when an individual is instructed to focus their attention externally. However, many of the motor tasks utilized in past research had clear external objectives (i.e., putting accuracy), creating a compatible relationship between an external focus of attention (i.e., outcome) and an external task objective (i.e., putting accuracy). The present study examined whether or not the consistency of instructions and task objective would differentially impact the acquisition of a golf putting task. Participants performed a putting task in a control condition or in one of four experimental conditions resulting from the factorial interaction of task instructions (internal or external) and task objective (internal or external). The retention and transfer data revealed that participants who received an external task objective demonstrated superior outcome scores. Participants who received technique information paired with outcome information demonstrated superior technique scores.

Assessment of the consistency of H2O line intensities over the near-infrared using sun-pointing ground-based Fourier transform spectroscopy

We report on the consistency of water vapour line intensities in selected spectral regions between 800–12,000 cm−1 under atmospheric conditions using sun-pointing Fourier transform infrared spectroscopy. Measurements were made across a number of days at both a low and high altitude field site, sampling a relatively moist and relatively dry atmosphere. Our data suggests that across most of the 800–12,000 cm−1 spectral region water vapour line intensities in recent spectral line databases are generally consistent with what was observed. However, we find that HITRAN-2008 water vapour line intensities are systematically lower by up to 20% in the 8000–9200 cm−1 spectral interval relative to other spectral regions. This discrepancy is essentially removed when two new linelists (UCL08, a compilation of linelists and ab-initio calculations, and one based on recent laboratory measurements by Oudot et al. (2010) [10] in the 8000–9200 cm−1 spectral region) are used. This strongly suggests that the H2O line strengths in the HITRAN-2008 database are indeed underestimated in this spectral region and in need of revision. The calculated global-mean clear-sky absorption of solar radiation is increased by about 0.3 W m−2 when using either the UCL08 or Oudot line parameters in the 8000–9200 cm−1 region, instead of HITRAN-2008. We also found that the effect of isotopic fractionation of HDO is evident in the 2500–2900 cm−1 region in the observations.

Sequential hydrocarbon biodegradation of a soil from arid coastal Australia oil-treated under laboratory controlled conditions

A general consistency in the sequential order of petroleum hydrocarbon reduction in previous biodegradation studies has led to the proposal of several molecularly based biodegradation scales. Few studies have investigated the biodegradation susceptibility of petroleum hydrocarbon products in soil media, however, and metabolic preferences can change with habitat type. A laboratory based study comprising gas chromatography–mass spectrometry (GC–MS) analysis of extracts of oil-treated soil samples incubated for up to 161 days was conducted to investigate the biodegradation of crude oil exposed to sandy soils of Barrow Island, home to both a Class ‘‘A” nature reserve and Australia’s largest on-shore oil field. Biodegradation trends of the hydrocarbon-treated soils were largely consistent with previous reports but some unusual behaviour was recognised both between and within hydrocarbon classes. For example, the n-alkanes persisted at trace levels from day 86 to 161 following the removal of typically more stable dimethyl naphthalenes and methyl phenanthrenes. The relative susceptibility to biodegradation of different di- tri- and tetramethylnaphthalene isomers also showed several features distinct from previous reports. The unique biodegradation behaviour of Barrow Is. soil likely reflects difference in microbial functioning with physiochemical variation in the environment. Correlation of molecular parameters, reduction rates of selected alkyl naphthalene isomers and CO2 respiration values with a delayed (61 d) oil-treated soil identified a slowing of biodegradation with microcosm incubation; a reduced function or population of incubated soil flora might also influence the biodegradation patterns observed.

The consistency of welfare judgements with a representative consumer

This paper is about economies with a representative consumer. In general a representative consumer need not exist, although there are several well known sets of sufficient conditions under which Qne will. It is common practice, however, to use the representative consumer hypothesis without specifically assuming any of these. We show, firstly, that it is possible for the utility of the representative consumer to increase when every actual consumer is made worse off. This shows a serious shortcoming of welfare judgements based on the representatíve consumer. Secondly, in economies where this does not occur, there exists a social welfare function, which we construct, which is consistent with welfare judgements based on the utility of the representative consumer. Finally we provide a converse to Samuelson' s 1956 representative consumer result, which relates it to Scitovsky's community indifference curves.

Consistency of superspace low energy equations of motion of 4D Type II superstring with Type II sigma model at tree-level

We derive the torsion constraints and show the consistency of equations of motion of four-dimensional Type II supergravity in superspace. with Type II sigma model. This is achieved by coupling the four-dimensional compactified Type II Berkovits' superstring to an N = 2 curved background and requiring that the sigma-model has superconformal invariance at tree-level. We compute this in a manifestly 4D N = 2 supersymmetric way. The constraints break the target conformal and SU(2) invariances and the dilaton will be a conformal, SU(2) x U(1) compensator. For Type II superstring in four dimensions, worldsheet supersymmetry requires two different compensators. One type is described by chiral and anti-chiral superfields. This compensator can be identified with a vector multiplet. The other Type II compensator is described by twist-chiral and twist-anti-chiral superfields and can be identified with a tensor hypermultiplet. Also, the superconformal invariance at tree-level selects a particular gauge, where the matter is fixed, but not the compensators. After imposing the reality conditions, we show that the Type II sigma model at tree-level is consistent with the equations of motion for Type II supergravity in the string gauge. (C) 2003 Elsevier B.V All rights reserved.