Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

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.

A type system with usage aspects

Linear typing schemes can be used to guarantee non-interference and so the soundness of in-place update with respect to a functional semantics. But linear schemes are restrictive in practice, and more restrictive than necessary to guarantee soundness of in-place update. This limitation has prompted research into static analysis and more sophisticated typing disciplines to determine when in-place update may be safely used, or to combine linear and non-linear schemes. Here we contribute to this direction by defining a new typing scheme that better approximates the semantic property of soundness of in-place update for a functional semantics. We begin from the observation that some data are used only in a read-only context, after which it may be safely re-used before being destroyed. Formalising the in-place update interpretation in a machine model semantics allows us to refine this observation, motivating three usage aspects apparent from the semantics that are used to annotate function argument types. The aspects are (1) used destructively, (2), used read-only but shared with result, and (3) used read-only and not shared with the result. The main novelty is aspect (2), which allows a linear value to be safely read and even aliased with a result of a function without being consumed. This novelty makes our type system more expressive than previous systems for functional languages in the literature. The system remains simple and intuitive, but it enjoys a strong soundness property whose proof is non-trivial. Moreover, our analysis features principal types and feasible type reconstruction, as shown in M. Konen'y (In TYPES 2002 workshop, Nijmegen, Proceedings, Springer-Verlag, 2003).

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.

Transition in homogeneously heated inclined plane parallel shear flows

The transition of internally heated inclined plane parallel shear flows is examined numerically for the case of finite values of the Prandtl number Pr. We show that as the strength of the homogeneously distributed heat source is increased the basic flow loses stability to two-dimensional perturbations of the transverse roll type in a Hopf bifurcation for the vertical orientation of the fluid layer, whereas perturbations of the longitudinal roll type are most dangerous for a wide range of the value of the angle of inclination. In the case of the horizontal inclination transverse roll and longitudinal roll perturbations share the responsibility for the prime instability. Following the linear stability analysis for the general inclination of the fluid layer our attention is focused on a numerical study of the finite amplitude secondary travelling-wave solutions (TW) that develop from the perturbations of the transverse roll type for the vertical inclination of the fluid layer. The stability of the secondary TW against three-dimensional perturbations is also examined and our study shows that for Pr=0.71 the secondary instability sets in as a quasi-periodic mode, while for Pr=7 it is phase-locked to the secondary TW. The present study complements and extends the recent study by Nagata and Generalis (2002) in the case of vertical inclination for Pr=0.

Transition in inclined internally heated fluid layers

Non-linear solutions and studies of their stability are presented for flows in a homogeneously heated fluid layer under the influence of a constant pressure gradient or when the mass flux across any lateral cross-section of the channel is required to vanish. The critical Grashof number is determined by a linear stability analysis of the basic state which depends only on the z-coordinate perpendicular to the boundary. Bifurcating longitudinal rolls as well as secondary solutions depending on the streamwise x-coordinate are investigated and their amplitudes are determined as functions of the supercritical Grashof number for various Prandtl numbers and angles of inclination of the layer. Solutions that emerge from a Hopf bifurcation assume the form of propagating waves and can thus be considered as steady flows relative to an appropriately moving frame of reference. The stability of these solutions with respect to three-dimensional disturbances is also analyzed in order to identify possible bifurcation points for evolving tertiary flows.

Entry modes and performance of foreign direct investment in China

How does a firm choose a proper model of foreign direct investment (FDI) for entering a foreign market? Which mode of entry performs better? What are the performance implications of joint venture (JV) ownership structure? These important questions face a multinational enterprise (MNE) that decides to enter a foreign market. However, few studies have been conducted on such issues, and no consistent or conclusive findings are generated, especially with respect to China. It’s composed of five chapters, providing corresponding answers to the questions given above. Specifically, Chapter One is an overall introductory chapter. Chapter Two is about the choice of entry mode of FDI in China. Chapter Three examines the relationship between four main entry modes and performance. Chapter Four explores the performance implications of JV ownership structure. Chapter Five is an overall concluding chapter. These empirical studies are based on the most recent and richest data that has never been explored in previous studies. It contains information on 11,765 foreign-invested enterprises in China in seven manufacturing industries in 2000, 10,757 in 1999, and 10,666 in 1998. The four FDI entry modes examined include wholly-owned enterprises (WOEs), equity joint ventures (EJVs), contractual joint ventures (CJVs), and joint stock companies (JSCs). In Chapter Two, a multinominal logit model is established, and techniques of multiple linear regression analysis are employed in Chapter Three and Four. It was found that MNEs, under the conditions of a good investment environment, large capital commitment and small cultural distance, prefer the WOE strategy. If these conditions are not met, the EJV mode would be of greater use. The relative propensity to pursue the CJV mode increases with a good investment environment, small capital commitment, and small cultural distance. JSCs are not favoured by MNEs when the investment environment improves and when affiliates are located in the coastal areas. MNEs have been found to have a greater preference for an EJV as a mode of entry into the Chinese market in all industries. It is also found that in terms of return on assets (ROA) and asset turnover, WOEs perform the best, followed by EJVs, CJVs, and JSCs. Finally, minority-owned EJVs or JSCs are found to outperform their majority-owned counterparts in terms of ROA and asset turnover.

Characterization of the hairpin vortex solution in plane Couette flow

Quantitative evidence that establishes the existence of the hairpin vortex state (HVS) in plane Couette flow (PCF) is provided in this work. The evidence presented in this paper shows that the HVS can be obtained via homotopy from a flow with a simple geometrical configuration, namely, the laterally heated flow (LHF). Although the early stages of bifurcations of LHF have been previously investigated, our linear stability analysis reveals that the root in the LHF yields multiple branches via symmetry breaking. These branches connect to the PCF manifold as steady nonlinear amplitude solutions. Moreover, we show that the HVS has a direct bifurcation route to the Rayleigh-Bénard convection. © 2010 The American Physical Society.

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.

Transition in plane parallel shear flows heated internally

The stability of internally heated inclined plane parallel shear flows is examined numerically for the case of finite value of the Prandtl number, Pr. The transition in a vertical channel has already been studied for 0≤Pr≤100 with or without the application of an external pressure gradient, where the secondary flow takes the form of travelling waves (TWs) that are spanwise-independent (see works of Nagata and Generalis). In this work, in contrast to work already reported (J. Heat Trans. T. ASME 124 (2002) 635-642), we examine transition where the secondary flow takes the form of longitudinal rolls (LRs), which are independent of the steamwise direction, for Pr=7 and for a specific value of the angle of inclination of the fluid layer without the application of an external pressure gradient. We find possible bifurcation points of the secondary flow by performing a linear stability analysis that determines the neutral curve, where the basic flow, which can have two inflection points, loses stability. The linear stability of the secondary flow against three-dimensional perturbations is also examined numerically for the same value of the angle of inclination by employing Floquet theory. We identify possible bifurcation points for the tertiary flow and show that the bifurcation can be either monotone or oscillatory. © 2003 Académie des sciences. Published by Elsevier SAS. All rights reserved.

Settlement of fill with particular reference to opencast coal mining sites

A study of information available on the settlement characteristics of backfill in restored opencast coal mining sites and other similar earthworks projects has been undertaken. In addition, the methods of opencast mining, compaction controls, monitoring and test methods have been reviewed. To consider and develop the methods of predicting the settlement of fill, three sites in the West Midlands have been examined; at each, the backfill had been placed in a controlled manner. In addition, use has been made of a finite element computer program to compare a simple two-dimensional linear elastic analysis with field observations of surface settlements in the vicinity of buried highwalls. On controlled backfill sites, settlement predictions have been accurately made, based on a linear relationship between settlement (expressed as a percentage of fill height) against logarithm of time. This `creep' settlement was found to be effectively complete within 18 months of restoration. A decrease of this percentage settlement was observed with increasing fill thickness; this is believed to be related to the speed with which the backfill is placed. A rising water table within the backfill is indicated to cause additional gradual settlement. A prediction method, based on settlement monitoring, has been developed and used to determine the pattern of settlement across highwalls and buried highwalls. The zone of appreciable differential settlement was found to be mainly limited to the highwall area, the magnitude was dictated by the highwall inclination. With a backfill cover of about 15 metres over a buried highwall the magnitude of differential settlement was negligible. Use has been made of the proposed settlement prediction method and monitoring to control the re-development of restored opencase sites. The specifications, tests and monitoring techniques developed in recent years have been used to aid this. Such techniques have been valuable in restoring land previously derelict due to past underground mining.

Lateral instability of slender reinforced concrete columns in a fire environment

The research concerns the development and application of an analytical computer program, SAFE-ROC, that models material behaviour and structural behaviour of a slender reinforced concrete column that is part of an overall structure and is subjected to elevated temperatures as a result of exposure to fire. The analysis approach used in SAFE-RCC is non-linear. Computer calculations are used that take account of restraint and continuity, and the interaction of the column with the surrounding structure during the fire. Within a given time step an iterative approach is used to find a deformed shape for the column which results in equilibrium between the forces associated with the external loads and internal stresses and degradation. Non-linear geometric effects are taken into account by updating the geometry of the structure during deformation. The structural response program SAFE-ROC includes a total strain model which takes account of the compatibility of strain due to temperature and loading. The total strain model represents a constitutive law that governs the material behaviour for concrete and steel. The material behaviour models employed for concrete and steel take account of the dimensional changes caused by the temperature differentials and changes in the material mechanical properties with changes in temperature. Non-linear stress-strain laws are used that take account of loading to a strain greater than that corresponding to the peak stress of the concrete stress-strain relation, and model the inelastic deformation associated with unloading of the steel stress-strain relation. The cross section temperatures caused by the fire environment are obtained by a preceding non-linear thermal analysis, a computer program FIRES-T.

When creativity enhances sales effectiveness:the moderating role of leader–member exchange

This study extends research on creativity by exploring the boundary conditions of the creativity-job effectiveness relationship. Building on social exchange theory, we argue that the extent to which employee creativity is related to sales - an objective work effectiveness measure - depends on the quality of leader-member exchange (LMX). We hypothesize that the relationship between creativity and sales is significant and positive when LMX is high, but not when LMX is low. Hierarchical linear modelling analysis provided support for the interaction hypothesis in a sample of 151 sales agents and 26 supervisors drawn from both pharmaceutical and insurance companies. Results showed that sales agents who were more creative generated higher sales only when they had high quality LMX. An ad-hoc qualitative study provided a more detailed understanding of the moderator role played by LMX. Copyright © 2012 John Wiley & Sons, Ltd.

Applying Information Foraging Theory to understand user interaction with content-based image retrieval

The paper proposes an ISE (Information goal, Search strategy, Evaluation threshold) user classification model based on Information Foraging Theory for understanding user interaction with content-based image retrieval (CBIR). The proposed model is verified by a multiple linear regression analysis based on 50 users' interaction features collected from a task-based user study of interactive CBIR systems. To our best knowledge, this is the first principled user classification model in CBIR verified by a formal and systematic qualitative analysis of extensive user interaction data. Copyright 2010 ACM.