Prediction with Gaussian processes: from linear regression to linear prediction and beyond

The main aim of this paper is to provide a tutorial on regression with Gaussian processes. We start from Bayesian linear regression, and show how by a change of viewpoint one can see this method as a Gaussian process predictor based on priors over functions, rather than on priors over parameters. This leads in to a more general discussion of Gaussian processes in section 4. Section 5 deals with further issues, including hierarchical modelling and the setting of the parameters that control the Gaussian process, the covariance functions for neural network models and the use of Gaussian processes in classification problems.

In vivo analysis of ciliary muscle morphologic changes with accommodation and axial ametropia

Purpose. To use anterior segment optical coherence tomography (AS-OCT) to analyze ciliary muscle morphology and changes with accommodation and axial ametropia. Methods. Fifty prepresbyopic volunteers, aged 19 to 34 years were recruited. High-resolution images were acquired of nasal and temporal ciliary muscles in the relaxed state and at stimulus vergence levels of -4 and -8 D. Objective accommodative responses and axial lengths were also recorded. Two-way, mixed-factor analyses of variance (ANOVAs) were used to assess the changes in ciliary muscle parameters with accommodation and determine whether these changes are dependent on the nasal–temporal aspect or axial length, whereas linear regression analysis was used to analyze the relationship between axial length and ciliary muscle length. Results. The ciliary muscle was longer (r = 0.34, P = 0.02), but not significantly thicker (F = 2.84, P = 0.06), in eyes with greater axial length. With accommodation, the ciliary muscle showed a contractile shortening (F = 42.9. P < 0.001), particularly anteriorly (F = 177.2, P < 0.001), and a thickening of the anterior portion (F= 46.2, P < 0.001). The ciliary muscle was thicker (F = 17.8, P < 0.001) and showed a greater contractile response on the temporal side. Conclusions. The accommodative changes observed support an anterior, as well as centripetal, contractile shift of ciliary muscle mass.

Statnote 19: non-linear regression: fitting an exponential curve to data

Non-linear relationships are common in microbiological research and often necessitate the use of the statistical techniques of non-linear regression or curve fitting. In some circumstances, the investigator may wish to fit an exponential model to the data, i.e., to test the hypothesis that a quantity Y either increases or decays exponentially with increasing X. This type of model is straight forward to fit as taking logarithms of the Y variable linearises the relationship which can then be treated by the methods of linear regression.

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.

The relationship between alexithymia and salivary cortisol levels in somatoform disorders

The purpose of this study was to investigate cortisol levels as a function of the hypothalamic-pituitary-adrenal axis (HPA) in relation to alexithymia in patients with somatoform disorders (SFD). Diurnal salivary cortisol was sampled in 32 patients with SFD who also underwent a psychiatric examination and filled in questionnaires (Toronto Alexithymia Scale, TAS scale; Screening for Somatoform Symptoms, SOMS scale; Hamilton Depression Scale, HAMD). The mean TAS total score in the sample was 55.69.6, 32% of patients being classified as alexithymic on the basis of their TAS scores. Depression scores were moderate (HAMD=13.2, Beck Depression Inventory, BDI=16.5). The patients' alexithymia scores (TAS scale Difficulty identifying feelings) correlated significantly positively with their somatization scale scores (Symptom Checklist-90 Revised, SCL-90-R); r=0.3438 (P0.05) and their scores on the Global Severity Index (GSI) on the SCL-90-R; r=0.781 (P0.01). Regression analysis was performed with cortisol variables as the dependent variables. Cortisol levels [measured by the area under the curve-ground (AUC-G), area under the curve-increase (AUC-I) and morning cortisol (MCS)] were best predicted in a multiple linear regression model by lower depressive scores (HAMD) and more psychopathological symptoms (SCL-90-R). No significant correlations were found between the patients' alexithymia scores (TAS) and cortisol levels. The healthy control group (n=25) demonstrated significantly higher cortisol levels than did the patients with SFD; in both tests P0.001 for AUC-G and AUC-I. However, the two groups did not differ in terms of their mean morning cortisol levels (P0.05). The results suggest that pre-existing hypocortisolism might possibly be associated with SFD.

Innovation, networking and globalisation:the role of regional innovation systems in the global innovation process

In the global economy, innovation is one of the most important competitive assets for companies willing to compete in international markets. As competition moves from standardised products to customised ones, depending on each specific market needs, economies of scale are not anymore the only winning strategy. Innovation requires firms to establish processes to acquire and absorb new knowledge, leading to the recent theory of Open Innovation. Knowledge sharing and acquisition happens when firms are embedded in networks with other firms, university, institutions and many other economic actors. Several typologies of innovation and firm networks have been identified, with various geographical spans. One of the first being modelled was the Industrial Cluster (or in Italian Distretto Industriale) which was for long considered the benchmark for innovation and economic development. Other kind of networks have been modelled since the late 1970s; Regional Innovation Systems represent one of the latest and more diffuse model of innovation networks, specifically introduced to combine local networks and the global economy. This model was qualitatively exploited since its introduction, but, together with National Innovation Systems, is among the most inspiring for policy makers and is often cited by them, not always properly. The aim of this research is to setup an econometric model describing Regional Innovation Systems, becoming one the first attempts to test and enhance this theory with a quantitative approach. A dataset of 104 secondary and primary data from European regions was built in order to run a multiple linear regression, testing if Regional Innovation Systems are really correlated to regional innovation and regional innovation in cooperation with foreign partners. Furthermore, an exploratory multiple linear regression was performed to verify which variables, among those describing a Regional Innovation Systems, are the most significant for innovating, alone or with foreign partners. Furthermore, the effectiveness of present innovation policies has been tested based on the findings of the econometric model. The developed model confirmed the role of Regional Innovation Systems for creating innovation even in cooperation with international partners: this represents one of the firsts quantitative confirmation of a theory previously based on qualitative models only. Furthermore the results of this model confirmed a minor influence of National Innovation Systems: comparing the analysis of existing innovation policies, both at regional and national level, to our findings, emerged the need for potential a pivotal change in the direction currently followed by policy makers. Last, while confirming the role of the presence a learning environment in a region and the catalyst role of regional administration, this research offers a potential new perspective for the whole private sector in creating a Regional Innovation System.

Conclusion : on multiple levels of analysis, context, contingency and capital

In this concluding chapter, we bring together the threads and reflections on the chapters contained in this text and show how they relate to multi-level issues. The book has focused on the world of Human Resource Management (HRM) and the systems and practices it must put in place to foster innovation. Many of the contributions argue that in order to bring innovation about, organisations have to think carefully about the way in which they will integrate what is, in practice, organisationally relevant — but socially distributed — knowledge. They need to build a series of knowledge-intensive activities and networks, both within their own boundaries and across other important external inter-relationships. In so doing, they help to co-ordinate important information structures. They have, in effect, to find ways of enabling people to collaborate with each other at lower cost, by reducing both the costs of their co-ordination and the levels of unproductive search activity. They have to engineer these behaviours by reducing the risks for people that might be associated with incorrect ideas and help individuals, teams and business units to advance incomplete ideas that are so often difficult to codify. In short, a range of intangible assets must flow more rapidly throughout the organisation and an appropriate balance must be found between the rewards and incentives associated with creativity, novelty and innovation, versus the risks that innovation may also bring.

The effect of ageing on in vivo human ciliary muscle morphology and contractility

Purpose. To assess the effect of ageing on in vivo human ciliary muscle morphology and contractility during accommodation. Methods. Seventy-nine subjects, aged 19–70 years were recruited. High-resolution images were acquired of nasal and temporal ciliary muscle in the relaxed state, and at stimulus vergence levels of -4 and -8 D, using anterior segment optical coherence tomography (AS-OCT). Objective refractions and axial lengths were also recorded. Linear regression analysis was performed to determine the effect of age on nasal and temporal ciliary muscle morphologic characteristics. Results. Ciliary muscle anterior length decreased significantly with age both nasally (R = 0.461, P = 0.001) and temporally (R = 0.619, P < 0.001) in emmetropic eyes. In a subset of 37 participants, ciliary muscle maximum width increased significantly with age, by 2.8 µm/year nasally (R = 0.54, P < 0.001) and 3.0 µm/year temporally (R = 0.44, P = 0.007), while the distance from the inner apex of the ciliary muscle to the scleral spur decreased significantly with age on both the nasal and temporal aspects (R = 0.47; P = 0.004 and R = 0.43; P = 0.009, respectively). During accommodation, changes to ciliary muscle thickness and length remained constant throughout life. Conclusions. The human ciliary muscle undergoes age-dependent changes in morphology that suggest an antero-inwards displacement of muscle mass, particularly in emmetropic eyes. However, the morphologic changes observed appear not to affect the ability of the muscle to contract during accommodation, even in established presbyopes, thus supporting a lenticular model of presbyopia development.

Role of β3-adrenergic receptors in the action of a tumour lipid mobilizing factor

Induction of lipolysis in murine white adipocytes, and stimulation of adenylate cyclase in adipocyte plasma membranes, by a tumour-produced lipid mobilizing factor, was attenuated by low concentrations (10-7-10-5M) of the specific β3-adrenoceptor antagonist SR59230A. Lipid mobilizing factor (250 nM) produced comparable increases in intracellular cyclic AMP in CHOKI cells transfected with the human β3-adrenoceptor to that obtained with isoprenaline (1 nM). In both cases cyclic AMP production was attenuated by SR59230A confirming that the effect is mediated through a β3-adrenoceptor. A non-linear regression analysis of binding of lipid mobilizing factor to the β3-adrenoceptor showed a high affinity binding site with a Kd value 78±45 nM and a Bmax value (282±1 fmole mg protein-1) comparable with that of other β3-adrenoceptor agonists. These results suggest that lipid mobilizing factor induces lipolysis through binding to a β3-adrenoceptor. © 2002 The Cancer Research Campaign.

The two-dose measles, mumps, and rubella (MMR) immunisation schedule: factors affecting maternal intention to vaccinate

BACKGROUND: In the light of sub-optimal uptake of the measles, mumps, and rubella (MMR) vaccination, we investigated the factors that influence the intentions of mothers to vaccinate. METHOD: A cross-sectional survey of 300 mothers in Birmingham with children approaching a routine MMR vaccination was conducted using a postal questionnaire to measure: intention to vaccinate, psychological variables, knowledge of the vaccine, and socioeconomic status. The vaccination status of the children was obtained from South Birmingham Child Health Surveillance Unit. RESULTS: The response rate was 59%. Fewer mothers approaching the second MMR vaccination (Group 2) intended to take their children for this vaccination than Group 1 (mothers approaching the first MMR vaccination) (Mann-Whitney U = 2180, P < 0.0001). Group 2 expressed more negative beliefs about the outcome of having the MMR vaccine ('vaccine outcome beliefs') (Mann-Whitney U = 2155, P < 0.0001), were more likely to believe it was 'unsafe' (chi 2 = 9.114, P = 0.004) and that it rarely protected (chi 2 = 6.882, P = 0.014) than Group 1. The commonest side-effect cited was general malaise, but 29.8% cited autism. The most trusted source of information was the general practitioner but the most common source of information on side-effects was television (34.6%). Multiple linear regression revealed that, in Group 1, only 'vaccine outcome beliefs' significantly predicted intention (77.1% of the variance). In Group 2 'vaccine outcome beliefs', attitude to the MMR vaccine, and prior MMR status all predicted intention (93% of the variance). CONCLUSION: A major reason for the low uptake of the MMR vaccination is that it is not perceived to be important for children's health, particularly the second dose. Health education from GPs is likely to have a considerable impact.

Formulation of topical non-steroidal anti-inflammatory agents

Reversed-pahse high-performance liquid chromatographic (HPLC) methods were developed for the assay of indomethacin, its decomposition products, ibuprofen and its (tetrahydro-2-furanyl)methyl-, (tetrahydro-2-(2H)pyranyl)methyl- and cyclohexylmethyl esters. The development and application of these HPLC systems were studied. A number of physico-chemical parameters that affect percutaneous absorption were investigated. The pKa values of indomethacin and ibuprofen were determined using the solubility method. Potentiometric titration and the Taft equation were also used for ibuprofen. The incorporation of ethanol or propylene glycol in the solvent resulted in an improvement in the aqueous solubility of these compounds. The partition coefficients were evaluated in order to establish the affinity of these drugs towards the stratum corneum. The stability of indomethacin and of ibuprofen esters were investigated and the effect of temperature and pH on the decomposition rates were studied. The effect of cetyltrimethylammonium bromide on the alkaline degradation of indomethacin was also followed. In the presence of alcohol, indomethacin alcoholysis was observed and the kinetics of decomposition were subjected to non-linear regression analysis and the rate constants for the various pathways were quantified. The non-isothermal, sufactant non-isoconcentration and non-isopH degradation of indomethacin were investigated. The analysis of the data was undertaken using NONISO, a BASIC computer program. The degradation profiles obtained from both non-iso and iso-kinetic studies show that there is close concordance in the results. The metabolic biotransformation of ibuprofen esters was followed using esterases from hog liver and rat skin homogenates. The results showed that the esters were very labile under these conditions. The presence of propylene glycol affected the rates of enzymic hydrolysis of the ester. The hydrolysis is modelled using an equation involving the dielectric constant of the medium. The percutaneous absorption of indomethacin and of ibuprofen and its esters was followed from solutions using an in vitro excised human skin model. The absorption profiles followed first order kinetics. The diffusion process was related to their solubility and to the human skin/solvent partition coefficient. The percutaneous absorption of two ibuprofen esters from suspensions in 20% propylene glycol-water were also followed through rat skin with only ibuprofen being detected in the receiver phase. The sensitivity of ibuprofen esters to enzymic hydrolysis compared to the chemical hydrolysis may prove valuable in the formulation of topical delivery systems.

Premature cardiovascular events and mortality in south Asians with type 2 diabetes in the United Kingdom Asian Diabetes Study - effect of ethnicity on risk

Background/Aim - People of south Asian origin have an excessive risk of morbidity and mortality from cardiovascular disease. We examined the effect of ethnicity on known risk factors and analysed the risk of cardiovascular events and mortality in UK south Asian and white Europeans patients with type 2 diabetes over a 2 year period. Methods - A total of 1486 south Asian (SA) and 492 white European (WE) subjects with type 2 diabetes were recruited from 25 general practices in Coventry and Birmingham, UK. Baseline data included clinical history, anthropometry and measurements of traditional risk factors – blood pressure, total cholesterol, HbA1c. Multiple linear regression models were used to examine ethnicity differences in individual risk factors. Ten-year cardiovascular risk was estimated using the Framingham and UKPDS equations. All subjects were followed up for 2 years. Cardiovascular events (CVD) and mortality between the two groups were compared. Findings - Significant differences were noted in risk profiles between both groups. After adjustment for clustering and confounding a significant ethnicity effect remained only for higher HbA1c (0.50 [0.22 to 0.77]; P?=?0.0004) and lower HDL (-0.09 [-0.17 to -0.01]; P?=?0.0266). Baseline CVD history was predictive of CVD events during follow-up for SA (P?

Ocular biometric correlates of ciliary muscle thickness in human myopia

Purpose - Anterior segment optical coherent tomography (AS-OCT) is used to further examine previous reports that ciliary muscle thickness (CMT) is increased in myopic eyes. With reference to temporal and nasal CMT, interrelationships between biometric and morphological characteristics of anterior and posterior segments are analysed for British-White and British-South-Asian adults with and without myopia. Methods - Data are presented for the right eyes of 62 subjects (British-White n = 39, British-South-Asian n = 23, aged 18–40 years) with a range of refractive error (mean spherical error (MSE (D)) -1.74 ± 3.26; range -10.06 to +4.38) and separated into myopes (MSE (D) <-0.50, range -10.06 to -0.56; n = 30) and non-myopes (MSE (D) =-0.50, -0.50 to +4.38; n = 32). Temporal and nasal ciliary muscle cross-sections were imaged using a Visante AS-OCT. Using Visante software, manual measures of nasal and temporal CMT (NCMT and TCMT respectively) were taken in successive posterior 1 mm steps from the scleral spur over a 3 mm distance (designated NCMT1, TCMT1 et seq). Measures of axial length and anterior chamber depth were taken with an IOLMaster biometer. MSE and corneal curvature (CC) measurements were taken with a Shin-Nippon auto-refractor. Magnetic resonance imaging was used to determine total ocular volume (OV) for 31 of the original subject group. Statistical comparisons and analyses were made using mixed repeated measures anovas, Pearson's correlation coefficient and stepwise forward multiple linear regression. Results - MSE was significantly associated with CMT, with thicker CMT2 and CMT3 being found in the myopic eyes (p = 0.002). In non-myopic eyes TCMT1, TCMT2, NCMT1 and NCMT2 correlated significantly with MSE, AL and OV (p < 0.05). In contrast, myopic eyes failed generally to exhibit a significant correlation between CMT, MSE and axial length but notably retained a significant correlation between OV, TCMT2, TCMT3, NCMT2 and NCMT3 (p < 0.05). OV was found to be a significantly better predictor of TCMT2 and TCMT3 than AL by approximately a factor of two (p < 0.001). Anterior chamber depth was significantly associated with both temporal and nasal CMT2 and CMT3; TCMT1 correlated positively with CC. Ethnicity had no significant effect on differences in CMT. Conclusions - Increased CMT is associated with myopia. We speculate that the lack of correlation in myopic subjects between CMT and axial length, but not between CMT and OV, is evidence that disrupted feedback between the fovea and ciliary apparatus occurs in myopia development.

Regional variation in peripapillary retinal blood flow in primary open angle glaucoma:a follow-up study

Purpose: To investigate whether regional long-term changes in peripapillary retinal flow, measured by scanning laser Doppler flowmetry (SLDF), occur in patients with primary open angle glaucoma (POAG). Methods: 31 healthy volunteers (mean age: 65 8.3 years) and 33 POAG patients (mean age: 71.2 7.6 years) were followed up every 4 months for 16 months. Using SLDF, three images of the superior and inferior optic nerve head were obtained for each subject. A 1010-pixel frame was used to measure blood flow, volume and velocity in the four quadrants of the peripapillary retina. Central 24-2 visual field testing was carried out at each visit. Repeated measures analysis of covariance was used to assess change over time between the normal and POAG groups for the SLDF parameters. Univariate linear regression analysis for mean deviation and glaucoma change probability (GCP) analysis were used to identify visual field progression. Results: Blood volume, flow and velocity measured in the inferior nasal quadrant of the peripapillary retina decreased significantly over time for the POAG group compared to the normal group (p=0.0073, 0.0097, 0.0095 respectively). Overall, 2 glaucoma patients showed a significantly deteriorating MD slope, while 7 patients showed visual field progression with GPA. All of the patients progressing with GPA, showed change in the superior hemifield and, of those, 14% showed change in the inferior hemifield. Conclusion: Glaucoma patients showed a decrease in blood flow, volume and velocity in the inferior nasal peripapillary retina. A regional variation in microvascular retinal capillary blood flow may provide insight into the pathogenesis of glaucomatous optic neuropathy. Keywords: 331 blood supply • 554 retina • 624 visual fields