Predictive gene lists for breast cancer prognosis: a topographic visualisation study

Background: The controversy surrounding the non-uniqueness of predictive gene lists (PGL) of small selected subsets of genes from very large potential candidates as available in DNA microarray experiments is now widely acknowledged 1. Many of these studies have focused on constructing discriminative semi-parametric models and as such are also subject to the issue of random correlations of sparse model selection in high dimensional spaces. In this work we outline a different approach based around an unsupervised patient-specific nonlinear topographic projection in predictive gene lists. Methods: We construct nonlinear topographic projection maps based on inter-patient gene-list relative dissimilarities. The Neuroscale, the Stochastic Neighbor Embedding(SNE) and the Locally Linear Embedding(LLE) techniques have been used to construct two-dimensional projective visualisation plots of 70 dimensional PGLs per patient, classifiers are also constructed to identify the prognosis indicator of each patient using the resulting projections from those visualisation techniques and investigate whether a-posteriori two prognosis groups are separable on the evidence of the gene lists. A literature-proposed predictive gene list for breast cancer is benchmarked against a separate gene list using the above methods. Generalisation ability is investigated by using the mapping capability of Neuroscale to visualise the follow-up study, but based on the projections derived from the original dataset. Results: The results indicate that small subsets of patient-specific PGLs have insufficient prognostic dissimilarity to permit a distinction between two prognosis patients. Uncertainty and diversity across multiple gene expressions prevents unambiguous or even confident patient grouping. Comparative projections across different PGLs provide similar results. Conclusion: The random correlation effect to an arbitrary outcome induced by small subset selection from very high dimensional interrelated gene expression profiles leads to an outcome with associated uncertainty. This continuum and uncertainty precludes any attempts at constructing discriminative classifiers. However a patient's gene expression profile could possibly be used in treatment planning, based on knowledge of other patients' responses. We conclude that many of the patients involved in such medical studies are intrinsically unclassifiable on the basis of provided PGL evidence. This additional category of 'unclassifiable' should be accommodated within medical decision support systems if serious errors and unnecessary adjuvant therapy are to be avoided.

The correlation of indentation size effect experiments with pyramidal and spherical indenters

Experiments were conducted in annealed iridium using pyramidal and spherical indenters over a wide range of load. For a Berkovich pyramidal indenter, the hardness increased with decreasing depth of penetration. However, for spherical indenters, hardness increased with decreasing sphere radius. Based on the number of geometrically necessary dislocations generated during indentation, a theory that takes into account the work hardening differences between pyramidal and spherical indenters is developed to correlate the indentation size effects measured with the two indenters. The experimental results verify the theoretical correlation.

The correlation of the indentation size effect measured with indenters of various shapes

Experimental results are presented which show that the indentation size effect for pyramidal and spherical indenters can be correlated. For a pyramidal indenter, the hardness measured in crystalline materials usually increases with decreasing depth of penetration, which is known as the indentation size effect. Spherical indentation also shows an indentation size effect. However, for a spherical indenter, hardness is not affected by depth, but increases with decreasing sphere radius. The correlation for pyramidal and spherical indenter shapes is based on geometrically necessary dislocations and work-hardening. The Nix and Gao indentation size effect model (J. Mech. Phys. Solids 46 (1998) 411) for conical indenters is extended to indenters of various shapes and compared to the experimental results. © 2002 Elsevier Science Ltd. All rights reserved.

The effect of corneal thickness and corneal curvature on pneumatonometer measurements

Purpose. The purpose of this study was to investigate the influence of corneal topography and thickness on intraocular pressure (IOP) and pulse amplitude (PA) as measured using the Ocular Blood Flow Analyzer (OBFA) pneumatonometer (Paradigm Medical Industries, Utah, USA). Methods. 47 university students volunteered for this cross-sectional study: mean age 20.4 yrs, range 18 to 28 yrs; 23 male, 24 female. Only the measurements from the right eye of each participant were used. Central corneal thickness and mean corneal radius were measured using Scheimpflug biometry and corneal topographic imaging respectively. IOP and PA measurements were made with the OBFA pneumatonometer. Axial length was measured using A-scan ultrasound, due to its known correlation with these corneal parameters. Stepwise multiple regression analysis was used to identify those components that contributed significant variance to the independent variables of IOP and PA. Results. The mean IOP and PA measurements were 13.1 (SD 3.3) mmHg and 3.0 (SD 1.2) mmHg respectively. IOP measurements made with the OBFA pneumatonometer correlated significantly with central corneal thickness (r = +0.374, p = 0.010), such that a 10 mm change in CCT was equivalent to a 0.30 mmHg change in measured IOP. PA measurements correlated significantly with axial length (part correlate = -0.651, p < 0.001) and mean corneal radius (part correlate = +0.459, p < 0.001) but not corneal thickness. Conclusions. IOP measurements taken with the OBFA pneumatonometer are correlated with corneal thickness, but not axial length or corneal curvature. Conversely, PA measurements are unaffected by corneal thickness, but correlated with axial length and corneal radius. These parameters should be taken into consideration when interpreting IOP and PA measurements made with the OBFA pneumatonometer.

Effect of a protein and energy dense n-3 fatty acid enriched oral supplement on loss of weight and lean tissue in cancer cachexia:A randomised double blind trial

Aim: N-3 fatty acids, especially eicosapentaenoic acid (EPA), may possess anticachectic properties. This trial compared a protein and energy dense supplement enriched with n-3 fatty acids and antioxidants (experimental: E) with an isocaloric isonitrogenous control supplement (C) for their effects on weight, lean body mass (LBM), dietary intake, and quality of life in cachectic patients with advanced pancreatic cancer. Methods: A total of 200 patients (95 E; 105 C) were randomised to consume two cans/day of the E or C supplement (480 ml, 620 kcal, 32 g protein ± 2.2 g EPA) for eight weeks in a multicentre, randomised, double blind trial. Results: At enrolment, patients' mean rate of weight loss was 3.3 kg/month. Intake of the supplements (E or C) was below the recommended dose (2 cans/day) and averaged 1.4 cans/day. Over eight weeks, patients in both groups stopped losing weight (Δweight E: -0.25 kg/month versus C: -0.37 kg/month; p=0.74) and LBM (ΔLBM E: +0.27 kg/month versus C: +0.12 kg/month; p=0.88) to an equal degree (change from baseline E and C, p<0.001). In view of evident non-compliance in both E and C groups, correlation analyses were undertaken to examine for potential dose-response relationships. E patients demonstrated significant correlations between their supplement intake and weight gain (r=0.50, p<0.001) and increase in LBM (r=0.33, p=0.036). Such correlations were not statistically significant in C patients. The relationship of supplement intake with change in LBM was significantly different between E and C patients (p=0.043). Increased plasma EPA levels in the E group were associated with weight and LBM gain (r=0.50, p<0.001; r=0.51, p=0.001). Weight gain was associated with improved quality of life (p<0.01) only in the E group. Conclusion: Intention to treat group comparisons indicated that at the mean dose taken, enrichment with n-3 fatty acids did not provide a therapeutic advantage and that both supplements were equally effective in arresting weight loss. Post hoc dose-response analysis suggests that if taken in sufficient quantity, only the n-3 fatty acid enriched energy and protein dense supplement results in net gain of weight, lean tissue, and improved quality of life. Further trials are required to examine the potential role of n-3 enriched supplements in the treatment of cancer cachexia.

Lipoplexes formulation and optimisation:in vitro transfection studies reveal no correlation with in vivo vaccination studies

The aim of these studies was to compare the effect of liposome composition on physico-chemical characteristics and transfection efficacy of cationic liposomes both in vitro and in vivo. Comparison between 4 popularly used cationic lipids, showed 3b-N-(dimethylaminoethyl)carbamate (DC-Chol) to promote the highest transfect levels in cells in vitro with levels being at least 6 times higher than those of 1,2-di-O-octadecenyl-3-trimethylammonium propane (DOTMA). 1,2-dioleoyl-3-trimethylammonium-propane (DOTAP), and dimethyldioctadecylammonium (DDA) and approximately twice as efficient as dipalmitoyl-trimethylammonium-propane (DPTAP). To establish the role of the helper lipid, DC-Chol liposomes were formulated in combination with either 1,2-dioleoyl-sn-glycero-3-phosphatidylethanolamine (DOPE) or cholesterol (Chol) (1:1 molar ratio) with and without the addition of phosphatidyl choline. The choice of helper lipid incorporated within the bilayer was found to influence the formation of complexes, their resultant structure and their transfection efficiency in vitro, with SUV-DNA complexes containing optimum levels of DOPE giving higher transfection than those containing cholesterol. The inclusion of PC within the formulation also reduced transfection efficiency in vitro. However, when administered in vivo, SUV-DNA complexes composed of PC:Chol:DC-Chol at a molar ratio of 16:8:4 micromole/ml were the most effective at inducing splenocyte proliferation upon exposure to antigen in comparison to control spleens. These results demonstrate that there is no in vitro/in vivo correlation between the transfection efficacy of these liposome formulations and in vitro transfection in the above cell model cannot be taken as a reliable indicator for in vivo efficacy of DNA vaccines.

A study of the effect of harmonics in the system on the performance of residual current-operated circuit-breakers and electromechanical overcurrent relays

Residual current-operated circuit-breakers (RCCBs) have proved useful devices for the protection of both human beings against ventricular fibrillation and installations against fire. Although they work well with sinusoidal waveforms, there is little published information on their characteristics. Due to shunt connected non-linear devices, not the least of which is the use of power electronic equipment, the supply is distorted. Consequently, RCCBs as well as other protection relays are subject to non-sinusoidal current waveforms. Recent studies showed that RCCBs are greatly affected by harmonics, however the reasons for this are not clear. A literature search has also shown that there are inconsistencies in the analysis of the effect of harmonics on protection relays. In this work, the way RCCBs operate is examined, then a model is built with the aim of assessing the effect of non-sinusoidal current on RCCBs. Tests are then carried out on a number of RCCBs and these, when compared with the results from the model showed good correlation. In addition, the model also enables us to explain the RCCBs characteristics for pure sinusoidal current. In the model developed, various parameters are evaluated but special attention is paid to the instantaneous value of the current and the tripping mechanism movement. A similar assessment method is then used to assess the effect of harmonics on two types of protection relay, the electromechanical instantaneous relay and time overcurrent relay. A model is built for each of them which is then simulated on the computer. Tests results compare well with the simulation results, and thus the model developed can be used to explain the relays behaviour in a harmonics environment. The author's models, analysis and tests show that RCCBs and protection relays are affected by harmonics in a way determined by the waveform and the relay constants. The method developed provides a useful tool and the basic methodology to analyse the behaviour of RCCBs and protection relays in a harmonics environment. These results have many implications, especially the way RCCBs and relays should be tested if harmonics are taken into account.

Effect of phosphatidylcholine chlorohydrins on human erythrocytes

Hypochlorite generated in vivo under pathological conditions is a known oxidant and chlorinating agent, able to react with proteins and lipids, which affects the stability of biological membranes. Reaction with unsaturated fatty acyl chains in glycerophospholipids such as phosphatidylcholine results in the formation of chlorohydrins. The aim of this study was to determine the effects of chlorohydrins formed by the reaction of hypochlorite with 1-stearoyl-2-oleoyl-, 1-stearoyl-2-linoleoyl-, and 1-stearoyl-2-arachidonylphosphatidylcholine on biophysical properties of bilayers and their effects on human erythrocytes. Using electrospray mass spectrometry we observed complete conversion of the lipids into chlorohydrins, which resulted in a decrease in the rotational correlation time and an increase in the order parameter of liposomes. Unilamellar chlorohydrin liposomes had a lower permeation coefficient for calcein than liposomes made of parent lipids. Flow cytometry demonstrated fast incorporation of uni and multilamellar chlorohydrin liposomes labeled with NBD-phosphatidylethanolamine into erythrocytes. This effect was accompanied by changes in erythrocyte shape (echinocyte formation) and aggregation. Similar but less pronounced effects were noticed for parent lipids only after longer incubation. Chlorohydrins showed also a stronger hemolytic action, proportional to the lipid:erythrocyte ratio. These results are important for understanding the effects of HOCl on mammalian cells, such as might occur in inflammatory pathology.

Effect of the Hofmeister anions upon the swelling of a self-assembled pH-responsive hydrogel

We report the effect of a range of monovalent sodium salts on the molecular equilibrium swelling of a simple synthetic microphase separated poly(methyl methacrylate)-block-poly(2-(diethylamino)ethyl methacrylate)-block-poly(methyl methacrylate) (PMMA88-b-PDEA223-b-PMMA88) pH-responsive hydrogel. Sodium acetate, sodium chloride, sodium bromide, sodium iodide, sodium nitrate and sodium thiocyanate were selected for study at controlled ionic strength and pH; all salts are taken from the Hofmeister series (HS). The influence of the anions on the expansion of the hydrogel was found to follow the reverse order of the classical HS. The expansion ratio of the gel measured in solutions containing the simple sodium halide salts (NaCl, NaBr, and NaI) was found to be strongly related to parameters which describe the interaction of the ion with water; surface charge density, viscosity coefficient, and entropy of hydration. A global study which also included nonspherical ions (NaAce, NaNO3 and NaSCN) showed the strongest correlation with the viscosity coefficient. Our results are interpreted in terms of the Collins model,(1) where larger ions have more mobile water in the first hydration cage immediately surrounding the gel, therefore making them more adhesive to the surface of the stationary phase of the gel and ultimately reducing the level of expansion.

The effect of blending on selected physical properties of crude oils and their products

A study was made of the effect of blending practice upon selected physical properties of crude oils, and of various base oils and petroleum products, using a range of binary mixtures. The crudes comprised light, medium and heavy Kuwait crude oils. The properties included kinematic viscosity, pour point, boiling point and Reid vapour pressure. The literature related to the prediction of these properties, and the changes reported to occur on blending, was critically reviewed as a preliminary to the study. The kinematic viscosity of petroleum oils in general exhibited non-ideal behaviour upon blending. A mechanism was proposed for this behaviour which took into account the effect of asphaltenes content. A correlation was developed, as a modification of Grunberg's equation, to predict the viscosities of binary mixtures of petroleum oils. A correlation was also developed to predict the viscosities of ternary mixtures. This correlation showed better agreement with experimental data (< 6% deviation for crude oils and 2.0% for base oils) than currently-used methods, i.e. ASTM and Refutas methods. An investigation was made of the effect of temperature on the viscosities of crude oils and petroleum products at atmospheric pressure. The effect of pressure on the viscosity of crude oil was also studied. A correlation was developed to predict the viscosity at high pressures (up to 8000 psi), which gave significantly better agreement with the experimental data than the current method due to Kouzel (5.2% and 6.0% deviation for the binary and ternary mixtures respectively). Eyring's theory of viscous flow was critically investigated, and a modification was proposed which extends its application to petroleum oils. The effect of blending on the pour points of selected petroleum oils was studied together with the effect of wax formation and asphaltenes content. Depression of the pour point was always obtained with crude oil binary mixtures. A mechanism was proposed to explain the pour point behaviour of the different binary mixtures. The effects of blending on the boiling point ranges and Reid vapour pressures of binary mixtures of petroleum oils were investigated. The boiling point range exhibited ideal behaviour but the R.V.P. showed negative deviations from it in all cases. Molecular weights of these mixtures were ideal, but the densities and molar volumes were not. The stability of the various crude oil binary mixtures, in terms of viscosity, was studied over a temperature range of 1oC - 30oC for up to 12 weeks. Good stability was found in most cases.

The effect of flow regimes in the distillation of systems containing two liquid phases

Single phase solutions containing three components have been observed to exhibit foaminess near a single to two liquid phase boundary. It was seen, in a sintered plate column under mass transfer conditions, that distillation systems where the liquid appeared as one phase in one part of a column and two phases in another part, exhibited foaminess when the liquid concentration was near the one phase to two phase boundary. Various ternary systems have been studied in a 50 plate. 30mm i.d. Oldershaw column and it was observed that severe foaming occurred in the middle section of the column near the one liquid phase to two liquid phase boundary and no foaming occurred at the end of the column where liquid was either one phase or two phase. This is known as Ross type foam. Mass transfer experiments with Ross type ternary systems have been carried out in a perspex simulator with small and large hole diameter trays. It was observed that by removal of the more volatile component, Ross type foam did not build up on the tray. Severe entrainment of liquid was observed in all cases leading to a 'dry' tray, even with a low free area small diameter hole tray which was expected to produce a bubbly mixture. Entrainment was more severe for high gas superficial velocities and large hole diameters. This behaviour is quite different from the build up of foam observed when one liquid phase/two liquid phase Ross systems were contacted with air above a small sintered disc or with vapour in an Oldershaw distillation column. This observation explains why distillation columns processing mixtures which change from one liquid phase to two liquid phases (or vice versa) must be severely derated to avoid flooding. Single liquid phase holdups at the spray to bubbly transition were measured using a perspex simulator similar to that of Porter & Wong (17). i.e. with no liquid cross flow. A light transmission technique was used to measure the transition from spray regime to bubbly regime. The effect of tray thickness and the ratio of hole diameter to tray thickness on the transition was evaluated using trays of the same hole diameter and free area but having thickness of 2.38 mm, 4 mm, and 6.35 mm. The liquid holdup at the transition was less with the thin metal trays. This result may be interpreted by the theory of Lockett (101), which predicts the transition liquid holdup in terms of the angle of the gas iet leaving the holes in the sieve plate. All the existing correlations have been compared and none were found to be satisfactory and these correlations have been modified in view of the experimental results obtained. A new correlation has been proposed which takes into account the effect of the hole diameter to tray thickness ratio on the transition and good agreement was obtained between the experimental results and the correlated values of the liquid holdup at the transition. Results have been obtained for two immiscible liquids [kerosene and water] on trays to determine whether foaming can be eliminated by operating in the spray regime. Kerosene was added to a fixed volume of water or water was added to a fixed volume of kerosene. In both cases, there was a transition from spray to bubbly. In the water fixed system. the liquid holdup at the transition was slightly less than the pure kerosene system. Whilst for the kerosene fixed system, the transition occurred at much lower liquid holdups. Trends In the results were similar to those for single liquid phase. New correlations have been proposed for the two cases. It has been found that Ross type foams, observed in a sintered plate column and in the Oldershaw column can be eliminated by either carrying out the separation in a packed column or by the addition of defoaming additives.

The effect of beta-adrenergic receptor antagonists on the temporal accommodative response

In this thesis a modified Canon IR optometer was used to record static and continuous responses of accommodation during sustained visual tasks. The instrument was assessed with regard to the ocular exit pupil used, its frequency response and noise levels. Experimental work concerned essentially the temporal characteristics and neurological basis of the accommodative mechanism. In the absence of visual stimuli, the accommodative system assumes a resting or tonic accommodative (TA) position, which may be modified by periods of sustained fixation. The rate of regression from a near task to TA in darkness has exhibited differences between regression rates for enunetropes (EMMs) compared with late-onset myopes (WMs). The rate of accommodative regression from a task set at 3D above TA was examined for a group of 10 EMMs and 10 LOMs for 3 conditions: saline, timolol and betaxolol. Timolol retarded the regression to TA for a sub-group of EMMs. The patterns of regression for the remaining emmetropes mirrored that for the LOMs, the drugs showing no difference in rate of regression compared with the saline condition. This provides support for the conjecture that LOMs and certain EMMs appear to be deficient in a sympathetic inhibitory component to the ciliary muscle which may attenuate adaptational changes in tonus and which leave them susceptible to the development of LOM. It is well established that the steady-state accommodative response is characterised by temporal changes in lens power having 2 dominant frequency components: a low frequency component (LFC: < 0.6Hz) and a high frequency component (HFC: 1.0-2.2Hz). This thesis investigates various aspects of these microfluctuations of accommodation.The HFC of accommodative fluctuations was shown to be present in central and peripheral lens zones, although the magnitude of the rms of accommodative microfluctuations was found to be reduced in the lens periphery. These findings concur with the proposal that the lens capsule acts as a force distributor, transmitting the tension from the zonules evenly over the whole of the lens surface.An investigation into the correlation between arterial pulse and the HFC of accommodative fluctuations showed that the peak frequency of the HFC was governed by the arterial pulse frequency. It was proposed that the microflucutations comprised a combination of neurological control (LFC) and physiological variations (HFC).The effect of timolol maleate on the steady-state accommodative response for a group of 10 emmetropes showed that timolol reduced significantly the rms of accommodative microfluctuations in treated but not untreated eyes. Consequently, the effect was considered to be locally, rather than systemically induced.The influence of the sympathetic system on within-task measurements of accommodation was examined by recording the accommodative response of 3 subjects to a sinusoidally moving target at 6 temporal frequencies from 0.05Hz to 0.5Hz for 3 drug conditions: saline, timolol and betaxolol. Timolol caused a reduced gain for frequencies below 0.3 whereas betaxolol reduced accommodative gain for all frequencies. It was proposed that the results for timolol were consistent with temporal response characteristics of sympathetic innervation of the ciliary muscle whereas the betaxolol results were thought to be a manifestation of fatigue resulting from the CNS depressant effect of the drug.

Retinal and systemic vascular function in health and disease: the effect of smoking and coronary artery disease

The purpose of the following studies was to explore the effect of systemic vascular and endothelial dysfunction upon the ocular circulation and functionality of the retina. There are 6 principal sections to the present work. Retinal vessel activity in smokers and non-smokers: the principal findings of this work were: chronic smoking affects retinal vessel motion at baseline and during stimulation with flickering light; chronic smoking leads to a vaso-constrictory shift in retinal arteriolar reactivity to flicker; retinal arteriolar elasticity is decreased in chronic smokers. The effect of acute smoking on retinal vessel dynamics in smokers and non-smokers: the principal finding of this work was that retinal reactivity in chronic smokers is blunted when exposed to clicker light provocation immediately after smoking one cigarette. Ocular blood flow in coronary artery disease: The principal findings of this work were: retrobulbar and retinal blood flow is preserved in CAD patients, despite a change pulse wave transmission; arterial retinal response to flickering light provocation is significantly delayed in CAD patients; retinal venular diameters are significantly dilated in CAD patients. Autonomic nervous system function and peripheral circulation in CAD: The principal findings in this work were: CAD patients demonstrate a sympathetic overdrive during a 24 period; a delay in peripheral vascular reactivity (nail-fold capillaries) as observed in patients suffering from CAD could be caused by either arteriosclerotic changes of the vascular walls or due to systemic haemodynamic changes. Visual function in CAD: The principal findings in this work were: overall visual function in CAD patients is preserved, despite a decrease in contrast sensitivity; applying a filtering technique selecting those with greater coefficient of variance which in turn represents a decrease in reliability, some patients appear to have an impaired visual function as assessed using FDT visual field evaluation. Multiple functional, structural and biochemical vascular endothelial dysfunctions in patients suffering from CAD: relationships and possible implications: The principal findings of this work were: BMI significantly correlated with vWF (a marker of endothelial function) in CAD patients. Retinal vascular reactivity showed a significant correlation with peripheral reactivity parameters in controls which lacked in the CAD group and could reflect a loss in vascular endothelial integrity; visual field parameters as assessed by frequency doubling technology were strongly related with systemic vascular elasticity (ambulatory arterial stiffness index) in controls but not CAD patients.

The effect of zinc and titanium on the structure of calcium-sodium phosphate based glass

An array of different structural probes has been used to define the effect of adding Zn and Ti to a sodium-calcium phosphate glass. X-ray absorption spectroscopy at the Zn K-edge suggests that the Zn atoms occupy mixed (4- and 6-fold) sites within the glass matrix. X-ray diffraction reveals a feature at 2.03 angstrom that develops with the addition of Zn and Ti and is consistent with Zn-O and Ti-O near-neighbour distances. Neutron diffraction is used to resolve two distinct P-O distances and highlights the decrease in P center dot center dot center dot P coordination number from 2.0 to 1.7 as the Ti metal concentration rises, which is attributed to the O/P fraction moving away from the metaphosphate value of 3.0 to 3.1 with the addition of Ti. Other correlations, such as those associated with CaO(x) and NaO(x) polyhedra, remain largely unaffected. These results suggest that the network forming P center dot center dot center dot P correlation is most disrupted, with the disorder parameter rising from 0.07 to 0.10 angstrom with the additional modifiers. Zn appears to be introduced into the network as a direct replacement for Ca and causes no structural variation over the composition range studied.

Statnote 32 : the partial correlation coefficient

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. The most important statistic used to measure the degree of correlation between two variables is Pearson’s ‘product moment correlation coefficient’ (‘r’). The correlation between two variables may be due to their common relation to other variables. Hence, investigators using correlation studies need to be alert to the possibilities of spurious correlation and the methods of ‘partial correlation’ are one method of taking this into account. This statnote applies the methods of partial correlation to three scenarios. First, to a fairly obvious example of a spurious correlation resulting from the ‘size effect’ involving the relationship between the number of general practitioners (GP) and the number of deaths of patients in a town. Second, to the relationship between the abundance of the nitrogen-fixing bacterium Azotobacter in soil and three soil variables, and finally, to a more complex scenario, first introduced in Statnote 24involving the relationship between the growth of lichens in the field and climate.