Statnote 20: non-linear regression: fitting a general polynomial curve

In some circumstances, there may be no scientific model of the relationship between X and Y that can be specified in advance and indeed the objective of the investigation may be to provide a ‘curve of best fit’ for predictive purposes. In such an example, the fitting of successive polynomials may be the best approach. There are various strategies to decide on the polynomial of best fit depending on the objectives of the investigation.

Assessment of the oculomotor response in human factor environments

The need to measure the response of the oculomotor system, such as ocular accommodation, accurately and in real-world environments is essential. New instruments have been developed over the past 50 years to measure eye focus including the extensively utilised and well validated Canon R-1, but in general these have had limitations such as a closed field-of-view, a poor temporal resolution and the need for extensive instrumentation bulk preventing naturalistic performance of environmental tasks. The use of photoretinoscopy and more specifically the PowerRefractor was examined in this regard due to its remote nature, binocular measurement of accommodation, eye movement and pupil size and its open field-of-view. The accuracy of the PowerRefractor to measure refractive error was on averaging similar, but more variable than subjective refraction and previously validated instrumentation. The PowerRefractor was found to be tolerant to eye movements away from the visual axis, but could not function with small pupil sizes in brighter illumination. The PowerRefractor underestimated the lead of accommodation and overestimated the slope of the accommodation stimulus response curve. The PowerRefractor and the SRW-5000 were used to measure the oculomotor responses in a variety of real-world environment: spectacles compared to single vision contract lenses; the use of multifocal contact lenses by pre-presbyopes (relevant to studies on myopia retardation); and ‘accommodating’ intraocular lenses. Due to the accuracy concerns with the PowerRefractor, a purpose-built photoretinoscope was designed to measure the oculomotor response to a monocular head-mounted display. In conclusion, this thesis has shown the ability of photoretinoscopy to quantify changes in the oculomotor system. However there are some major limitations to the PowerRefractor, such as the need for individual calibration for accurate measures of accommodation and vergence, and the relatively large pupil size necessary for measurement.

The development of calibration and adaptive filtering procedures for neuromagnetic studies of human visual function

This thesis first considers the calibration and signal processing requirements of a neuromagnetometer for the measurement of human visual function. Gradiometer calibration using straight wire grids is examined and optimal grid configurations determined, given realistic constructional tolerances. Simulations show that for gradiometer balance of 1:104 and wire spacing error of 0.25mm the achievable calibration accuracy of gain is 0.3%, of position is 0.3mm and of orientation is 0.6°. Practical results with a 19-channel 2nd-order gradiometer based system exceed this performance. The real-time application of adaptive reference noise cancellation filtering to running-average evoked response data is examined. In the steady state, the filter can be assumed to be driven by a non-stationary step input arising at epoch boundaries. Based on empirical measures of this driving step an optimal progression for the filter time constant is proposed which improves upon fixed time constant filter performance. The incorporation of the time-derivatives of the reference channels was found to improve the performance of the adaptive filtering algorithm by 15-20% for unaveraged data, falling to 5% with averaging. The thesis concludes with a neuromagnetic investigation of evoked cortical responses to chromatic and luminance grating stimuli. The global magnetic field power of evoked responses to the onset of sinusoidal gratings was shown to have distinct chromatic and luminance sensitive components. Analysis of the results, using a single equivalent current dipole model, shows that these components arise from activity within two distinct cortical locations. Co-registration of the resulting current source localisations with MRI shows a chromatically responsive area lying along the midline within the calcarine fissure, possibly extending onto the lingual and cuneal gyri. It is postulated that this area is the human homologue of the primate cortical area V4.

Fabrication of high quality optical coherence tomography (OCT) calibration artefacts using femtosecond inscription

Optical coherence tomography (OCT) is a non-invasive three-dimensional imaging system that is capable of producing high resolution in-vivo images. OCT is approved for use in clinical trials in Japan, USA and Europe. For OCT to be used effectively in a clinical diagnosis, a method of standardisation is required to assess the performance across different systems. This standardisation can be implemented using highly accurate and reproducible artefacts for calibration at both installation and throughout the lifetime of a system. Femtosecond lasers can write highly reproducible and highly localised micro-structured calibration artefacts within a transparent media. We report on the fabrication of high quality OCT calibration artefacts in fused silica using a femtosecond laser. The calibration artefacts were written in fused silica due to its high purity and ability to withstand high energy femtosecond pulses. An Amplitude Systemes s-Pulse Yb:YAG femtosecond laser with an operating wavelength of 1026 nm was used to inscribe three dimensional patterns within the highly optically transmissive substrate. Four unique artefacts have been designed to measure a wide variety of parameters, including the points spread function (PSF), modulation transfer function (MTF), sensitivity, distortion and resolution - key parameters which define the performance of the OCT. The calibration artefacts have been characterised using an optical microscope and tested on a swept source OCT. The results demonstrate that the femtosecond laser inscribed artefacts have the potential of quantitatively and qualitatively validating the performance of any OCT system.

Three-dimensional calibration targets for optical coherence tomography

The recent expansion of clinical applications for optical coherence tomography (OCT) is driving the development of approaches for consistent image acquisition. There is a simultaneous need for time-stable, easy-to-use imaging targets for calibration and standardization of OCT devices. We present calibration targets consisting of three-dimensional structures etched into nanoparticle-embedded resin. Spherical iron oxide nanoparticles with a predominant particle diameter of 400 nm were homogeneously dispersed in a two part polyurethane resin and allowed to harden overnight. These samples were then etched using a precision micromachining femtosecond laser with a center wavelength of 1026 nm, 100kHz repetition rate and 450 fs pulse duration. A series of lines in depth were etched, varying the percentage of inscription energy and speed of the translation stage moving the target with respect to the laser. Samples were imaged with a dual wavelength spectral-domain OCT system and point-spread function of nanoparticles within the target was measured.

Evaluating the environmental Kuznets curve

We examine the empirical evidence for an environmental Kuznets curve using a semiparametric smooth coefficient regression model that allows us to incorporate flexibility in the parameter estimates, while maintaining the basic econometric structure that is typically used to estimate the pollution-income relationship. This allows us to assess the sensitivity to parameter heterogeneity of typical parametric models used to estimate the relationship between pollution and income, as well as identify why the results from such models are seldom found to be robust. Our results confirm that the resulting relationship between pollution and income is fragile; we show that the estimated pollution-income relationship depends substantially on the heterogeneity of the slope coefficients and the parameter values at which the relationship is evaluated. Different sets of parameters obtained from the semiparametric model give rise to many different shapes for the pollution-income relationship that are commonly found in the literature.

Managers' perceptual errors revisited:the role of knowledge calibration

Insights from the stream of research on knowledge calibration, which refers to the correspondence between accuracy and confidence in knowledge, enable a better understanding of consequences of inaccurate perceptions of managers. This paper examines the consequences of inaccurate managerial knowledge through the lens of knowledge calibration. Specifically, the paper examines the antecedent role of miscalibration of knowledge in strategy formation. It is postulated that miscalibrated managers who overestimate external factors and display a high level of confidence in their estimates are likely to enact strategies that are relatively more evolutionary and incremental in nature, whereas miscalibrated managers who overestimate internal factors and display a high level of confidence in their estimates are likely to enact strategies that are relatively more discontinuous and disruptive in nature. Perspectives from social cognitive theory provide support for the underlying processes. The paper, in part, explains the paradox of the prevalence of inaccurate managerial perceptions and efficacious performance. It also advances the literature on strategy formation through the application of the construct of knowledge calibration.

Calibration of consumer knowledge of the web

Calibration of consumer knowledge of the web refers to the correspondence between accuracy and confidence in knowledge of the web. Being well-calibrated means that a person is realistic in his or her assessment of the level of knowledge that he or she possesses. This study finds that involvement leads to better calibration and that calibration is higher for procedural knowledge and common knowledge, as compared to declarative knowledge and specialized knowledge. Neither usage, nor experience, has any effect on calibration of knowledge of the web. No difference in calibration is observed between genders. But, in agreement with previous findings, this study also finds that males are more confident in their knowledge of the web. The results point out that calibration could be more a function of knowledge-specific factors and less that of individual-specific factors. The study also identifies flow and frustration with the web as consequences of calibration of knowledge of the web and draws the attention of future researchers to examine these aspects.

Laminar distribution of the pathological changes in sporadic frontotemporal lobar degeneration with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy:a quantitative study using polynomial curve fitting

Aims: Previous data suggest heterogeneity in laminar distribution of the pathology in the molecular disorder frontotemporal lobar degeneration (FTLD) with transactive response (TAR) DNA-binding protein of 43kDa (TDP-43) proteinopathy (FTLD-TDP). To study this heterogeneity, we quantified the changes in density across the cortical laminae of neuronal cytoplasmic inclusions, glial inclusions, neuronal intranuclear inclusions, dystrophic neurites, surviving neurones, abnormally enlarged neurones, and vacuoles in regions of the frontal and temporal lobe. Methods: Changes in density of histological features across cortical gyri were studied in 10 sporadic cases of FTLD-TDP using quantitative methods and polynomial curve fitting. Results: Our data suggest that laminar neuropathology in sporadic FTLD-TDP is highly variable. Most commonly, neuronal cytoplasmic inclusions, dystrophic neurites and vacuolation were abundant in the upper laminae and glial inclusions, neuronal intranuclear inclusions, abnormally enlarged neurones, and glial cell nuclei in the lower laminae. TDP-43-immunoreactive inclusions affected more of the cortical profile in longer duration cases; their distribution varied with disease subtype, but was unrelated to Braak tangle score. Different TDP-43-immunoreactive inclusions were not spatially correlated. Conclusions: Laminar distribution of pathological features in 10 sporadic cases of FTLD-TDP is heterogeneous and may be accounted for, in part, by disease subtype and disease duration. In addition, the feedforward and feedback cortico-cortical connections may be compromised in FTLD-TDP. © 2012 The Authors. Neuropathology and Applied Neurobiology © 2012 British Neuropathological Society.

Shared action spaces:a basis function framework for social re-calibration of sensorimotor representations supporting joint action

The article explores the possibilities of formalizing and explaining the mechanisms that support spatial and social perspective alignment sustained over the duration of a social interaction. The basic proposed principle is that in social contexts the mechanisms for sensorimotor transformations and multisensory integration (learn to) incorporate information relative to the other actor(s), similar to the "re-calibration" of visual receptive fields in response to repeated tool use. This process aligns or merges the co-actors' spatial representations and creates a "Shared Action Space" (SAS) supporting key computations of social interactions and joint actions; for example, the remapping between the coordinate systems and frames of reference of the co-actors, including perspective taking, the sensorimotor transformations required for lifting jointly an object, and the predictions of the sensory effects of such joint action. The social re-calibration is proposed to be based on common basis function maps (BFMs) and could constitute an optimal solution to sensorimotor transformation and multisensory integration in joint action or more in general social interaction contexts. However, certain situations such as discrepant postural and viewpoint alignment and associated differences in perspectives between the co-actors could constrain the process quite differently. We discuss how alignment is achieved in the first place, and how it is maintained over time, providing a taxonomy of various forms and mechanisms of space alignment and overlap based, for instance, on automaticity vs. control of the transformations between the two agents. Finally, we discuss the link between low-level mechanisms for the sharing of space and high-level mechanisms for the sharing of cognitive representations. © 2013 Pezzulo, Iodice, Ferraina and Kessler.

Three-dimensional calibration targets for optical coherence tomography

The recent expansion of clinical applications for optical coherence tomography (OCT) is driving the development of approaches for consistent image acquisition. There is a simultaneous need for time-stable, easy-to-use imaging targets for calibration and standardization of OCT devices. We present calibration targets consisting of three-dimensional structures etched into nanoparticle-embedded resin. Spherical iron oxide nanoparticles with a predominant particle diameter of 400 nm were homogeneously dispersed in a two part polyurethane resin and allowed to harden overnight. These samples were then etched using a precision micromachining femtosecond laser with a center wavelength of 1026 nm, 100kHz repetition rate and 450 fs pulse duration. A series of lines in depth were etched, varying the percentage of inscription energy and speed of the translation stage moving the target with respect to the laser. Samples were imaged with a dual wavelength spectral-domain OCT system and point-spread function of nanoparticles within the target was measured.

Neural networks applied to ignition timing calibration

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT

A study of the behaviour of the single phase induction type energy meter and the design of an instrumentation system for its calibration

DUE TO COPYRIGHT RESTRICTIONS ONLY AVAILABLE FOR CONSULTATION AT ASTON UNIVERSITY LIBRARY AND INFORMATION SERVICES WITH PRIOR ARRANGEMENT