Linear Correlation Models Research Articles

A two-year investigation towards an effective quality control of incoming potatoes as an acrylamide mitigation strategy in french fries

The current entrance quality control used in the french fries industry is done based on colour evaluation with a United States Department of Agriculture/Munsell colour chart (after a short frying test, typically 180°C for 3 min). On the basis of a study carried out during two consecutive potato storage seasons, the possibility of a more effective entrance control of the raw potato tubers in order to identify batches of potatoes prone to acrylamide formation was evaluated. The current entrance control was compared to two other colour evaluation methods (CIE L*a*b* colour parameters and a process-specific Agtron analyser) and to reducing sugar content determination. Seasonal variability did not affect the slopes of the linear correlation models, for most of the parameters studied. The determination of colour formation measured by the Agtron methodology and reducing sugar content allowed a better identification of batches of potatoes prone to acrylamide formation compared with the current entrance control. Different scenarios represented by decision trees for quality control measures for incoming potatoes were evaluated while considering the investigation value of 600 µg kg–1 for french fries recently prescribed by the European Commission. Samples were categorised based on predictions of threshold values and acrylamide levels in the final product.

Increasing treatment accuracy for cervical cancer patients using correlations between bladder-filling change and cervix–uterus displacements: Proof of principle

PurposeTo investigate application of pre-treatment established correlations between bladder-filling changes and cervix–uterus displacements in adaptive therapy. Materials and methodsThirteen cervical cancer patients participated in this prospective study. Pre-treatment, and after delivery of 40Gy, a full bladder CT-scan was acquired, followed by voiding the bladder and acquisition of 4 other 3D scans in a 1h period with a naturally filling bladder (variable bladder filling CT-scans, VBF-scans). For the pre-treatment VBF-scans, linear correlations between bladder volume change and displacements of the tip of the uterus (ToU) and the center of mass (CoM) of markers implanted in the fornices of the vagina relative to the full bladder planning scan were established. Prediction accuracy of these correlation models was assessed by comparison with actual displacements in CT-scans, both pre-treatment and after 40Gy. Inter-fraction ToU and marker-CoM displacements were derived from the established correlations and twice-weekly performed in-room bladder volume measurements, using a 3D ultrasound scanner. ResultsTarget displacement in VBF-scans ranged from up to 65mm in a single direction to almost 0mm, depending on the patient. For pre-treatment VBF-scans, the linear correlation models predicted the mean 3D position change for the ToU of 26.1mm±10.8 with a residual of only 2.2mm±1.7. For the marker-CoM, the 8.4mm±5.3 mean positioning error was predicted with a residual of 0.9mm±0.7. After 40Gy, the mean ToU displacement was 26.8mm±15.8, while prediction based on the pre-treatment correlation models yielded a mean residual error of 9.0mm±3.7. Target positioning errors in the fractioned treatments were very large, especially for the ToU (−18.5mm±11.2 for systematic errors in SI-direction). ConclusionsPre-treatment acquired VBF-scans may be used to substantially enhance treatment precision of cervical cancer patients. Application in adaptive therapy is promising and warrants further investigation. For highly conformal (IMRT) treatments, the use of a full bladder drinking protocol results in unacceptably large systematic set-up errors.

Cortical Activation during Clock Reading as a Quadratic Function of Dementia State

In patients with Alzheimer's disease (AD), neuroimaging studies have demonstrated decreased brain activation, while increased activation was detected in patients with mild cognitive impairment (MCI). It can be hypothesized that increased cerebral activity seen in patients with MCI reflects neural compensation at the beginning of neurodegenerative processes. Later, as patients develop AD, neural integrity is increasingly impaired. This is accompanied by decreased neural activation. In this study we examined cognitive performance and functional magnetic resonance imaging activation on a Clock Reading task (CRT) and a Spatial Control task (SCT) in healthy controls, patients with MCI, and patients with early AD. Correlations between neural-functional activation and cognitive state, measured by the Mini Mental Status Examination, were determined using rank, linear and quadratic correlation models. It could be shown that CRT, in comparison to SCT, specifically activates brain regions in the ventral visual stream and precuneus known to be involved in conceptual processing and spatial imagery. The correlation between brain activity and cognitive state followed a quadratic rather than a linear pattern in several brain regions, including the lingual gyrus, cuneus, and precuneus. The strongest brain activity was found in patients with MCI and less severely impaired early AD subjects. These findings support the hypothesis that patients in early stages of dementia compensate for neuronal loss by the recruitment of additional neural resources reflected by increased neural activation, as measured by the blood oxygen level-dependent signal.

Improvement of charge-transfer indices for multifunctional amino acids: Application to lysozyme†

Valence topological Charge-Transfer (CT) indices are applied to the calculation of pH at the isoelectric point (pI). The model is generalized for molecules with heteroatoms. The ability of the indices for the description of molecular charge distribution is established by comparing them with the pI of 21 amino acids. Linear correlation models are obtained. The CT indices improve multivariable regression equations for pI. The variance decreases by 95%. No superimposition of the corresponding Gk –Jk and pairs is observed in most fits, which diminishes the risk of collinearity. The inclusion of heteroatoms in π-electron system is beneficial for the description of pI, the because of either the role of the additional p orbitals provided by heteroatom or the role of steric factors in π-electron conjugation. The use of CT/valence CT indices {Gk , Jk , } gives limited results for modelling amino acid pI. The inclusion of the number of acidic/basic groups improves the models. The effect is specially noticeable for amino acids with more than two functional groups. The fitting line for 21 amino acids is used to estimate lysozyme pI replacing (1 + Δn/n T) with (M + Δn)/n T. The results for lysozyme fragments can estimate the pI of the whole protein with 1–13% error. †Presented at the 13th International Workshop on QSARs in the Environmental Sciences (QSAR 2008), 8–12 June 2008, Syracuse, USA.

Bird species richness patterns of northern Taiwan: primary productivity, human population density, and habitat heterogeneity

ABSTRACTEnergy, climate, habitat heterogeneity, and human activity are important correlates of spatial variation in species richness. We examined the correlation between species richness and these variables using the birds that breed in northern Taiwan. We conducted general linear models (GLMs) and spatial correlation models to examine the relationship between bird species richness (BSR) and environmental variables. We found that normalized difference vegetation index (NDVI) was the most important predictor of BSR. We suggest productivity is the primary process of BSR. Additionally, we hypothesized that scale dependency might exist in the relationship between BSR and NDVI in Taiwan. Human population density, the second most important factor, was inversely correlated with BSR. The factor and BSR did not have similar response to NDVI, which contradicted observations in most of the previous studies on human population vs. species richness. We proposed that the human population density had an effect on NDVI, which in turn had an effect on BSR. Moreover, we hypothesized that the contradiction between our study and the previous studies might arise from a higher level of human disturbance in Taiwan than in other areas. The necessity of conserving native species in intensively developed lowlands of Taiwan cannot be overemphasized. Number of land cover type was another significant predictor of BSR. Habitat heterogeneity may have an effect on BSR in Taiwan.

Optimization of CD34+ collection for autologous transplantation using the evolution of peripheral blood cell counts after mobilization with chemotherapy and G-CSF

Background: Peripheral blood progenitor cells (PBPC) collection after high dose chemotherapy can be influenced by several factors. We searched for parameters that may predict the best day to start harvesting of PBPC in order to collect most CD34+ cells with the least number of aphereses. Methods: We studied patients who underwent mobilization chemotherapy for autologous transplantation. The influence of age, sex, diagnosis, number of previous chemotherapy cycles, peripheral blood (PB) counts at day of mobilization (D0), day of neutrophils <1.0 × 10 9 l −1 and day of nadir and interval between both (delta) on harvesting was investigated. Multivariate linear correlation models were built to predict the best harvesting with principles of parsimony. In patients where sequential CD34+ cell count was performed, the theoretical day of peak was calculated by interpolation in polynomial regression. Results: One hundred and thirty four patients entered the analysis: 36 Hodgkin’s lymphoma (HL), 65 B-large cell lymphoma (NHL) and 33 multiple myeloma (MM). Day of harvesting correlated with nr CHT, hemoglobin on D0, day of granulocytes <1.0 × 10 9 l −1, delta and dosis of mobilization therapy. The day of CD34+ peak could be calculated by the formula = (−0.41) × Hemoglobin D0 + (day peripheral CD34+ cells = 10 × 10 6 μl −1) × 0.99 + 7.8. This model could explain 81% of the variance of the peak day and was stable by bootstrap resampling. Day of peripheral CD34+ cells = 10 × 10 6 μl −1 preceded the calculated peak by 3–9 days. Conclusions: Although the day of best collection can be predicted using only sequential PB counts after mobilization chemotherapy, a model of prediction using peripheral CD34+ cell count is important especially for optimizing collection in poor mobilizing patients.

Monitoring Level of Service Near Urban Highway Segments by Noise Level Evaluation

When possible, existing highway levels of service should be monitored by field measurements. As is the case with all fieldwork, traffic measurements are relatively expensive; they take time, personnel and equipment This research look after the feasibility of developing an acoustic sensing model to monitor the traffic flow at the highway sections instead of continuous counting of volume or other method of traffic monitor and surveillance devices. Vehicle tires radiate the major source of road noise. These phenomena can be used by cross-correlating the acoustic responses from roadside microphones with highway measure of effectiveness. The results demonstrated the feasibility of detecting LOS in the acoustic manner. The statistical regression technique gives power correlation model between the noise level as Noise Equivalent level or Noise Pollution Level and the density on the road sections. Other linear correlation models can be seen between these noise levels and the Level of Service of the highway but with less significant. This noise measurement receiver continually measures noise levels and can give around-the-clock picture of LOS variations at highway section This model allows the designer/planner to obtain quickly the first approximation of the expected LOS.

Calculating Reversible Potentials for Pt−H and Pt−OH Bond Formation in Basic Solutions

Two redox reactions on platinum electrodes in base, the formation of underpotential deposited hydrogen, forming a Pt-H bond, and the electro-oxidation of water, forming a Pt-OH bond, were studied by two methods. The first applies a linear relationship between reaction energy in solution and standard reversible potential, an approach recently used in this lab to predict the formation potential of the surface-bonded species. This method depends on the availability of accurate surface adsorption bond strengths from measurement or theory and can be applied in two formats, the empirical model and the linear correlation model. The second method treats the reaction within the so-called double-layer model where reactants and products on the surface are well defined and are experiencing the influence of the electrolyte. When this approach is used, two coordination shells of hydrogen bonded water molecules are found necessary to sufficiently stabilize the hydroxide ion in this model, unlike acid for which past work showed only one shell around the hydronium ion is needed. The calculated reversible potentials for both reactions by the empirical and linear correlation models are in good agreement with the experimental onset potentials observed in cyclic voltammetry measurements for Pt(111) surface electrodes when empirical or accurately calculated H, OH, and H(2)O adsorption energies are used. The double layer models for these reactions also yield satisfactory results, and it is concluded that the models should be useful for studying electron-transfer reactions in base, as has already been done for forming Pt-H and Pt-OH in acid solution.

Valence Topological Charge-Transfer Indices for Dipole Moments: Percutaneous Enhancers

Valence topological charge-transfer (CT) indices are applied to the calculation of dipole moments. The algebraic and vector semisum CT indices are defined. The combination of CT indices allows the estimation of the dipole moments. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moments of homologous series of percutaneous enhancers (phenyl alcohols and 4-alkylanilines). Linear and quadratic correlation models are obtained. CT indices improve the multivariable quadratic regression equations for the dipole moment. The variance decreases 97% (4-alkylanilines). No superposition of the corresponding G(k)-J(k)and G(k)(V)-J(k)(V) pairs is observed in the fits, which diminishes the risk of co-linearity. The inclusion of the heteroatom in the pi-electron system is beneficial for the description of the dipole moment, owing to either the role of the additional p orbitals provided by the heteroatom or the role of steric factors in the pi-electron conjugation. Inclusion of a conjugated double bond in the alkyl chain lends to more rigid structures with dipole moment variations lower than 1%.

Applicability and limitation of OSARs for the toxicity of electrophilic chemicals.

The appropriate selection and application of quantitative structure-activity relationships (QSARs) for the prediction of toxicity is based on the prior assignment of a chemical to its mode of toxic action. This classification is often derived from structural characteristics with the underlying assumption that chemically similar compounds have similar mechanisms of action, which is often but not necessarily the case. Instead of using structural characteristics for classification toward a mode of toxic action, we used Escherichia coli based bioanalytical assays to classify electrophilic chemicals. Analyzing a series of reactive organochlorines, epoxides, and compounds with an activated double bond, three subclasses of reactive toxicity were distinguished: "glutathione depletion-related toxicity", "DNA damage", and "unspecific reactivity". For both subsets of specifically reacting compounds a direct correlation between effects and chemical reactivity was found. Reaction rate constants with either glutathione or 2'-deoxyguanosine, which was used as a model for complex DNA, served well to set up preliminary QSARs for either glutathione depletion-related toxicity or toxicity based on DNA damage in the model organism E. coli. The applicability of QSARs for electrophilic chemicals based on mechanistically relevant reaction rate constants is a priori limited to a small subset of compounds with strictly identical mechanism of toxic action and similar metabolic rates. In contrast, the proposed bioanalytical assays not only allowed the experimental identification of molecular mechanisms underlying the observable toxicity but also their toxicity values are applicable to quantitatively predict toxic effects in higher organisms by linear correlation models, independent of the assigned mode of toxic action.

Valence Topological Charge-Transfer Indices for Dipole Moments

New valence topological charge-transfer indices are applied to the calculation of dipole moments. The algebraic and vector semisum charge-transfer indices are defined. The combination of the charge-transfer indices allows the estimation of the dipole moments. The model is generalized for molecules with heteroatoms. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moments of a homologous series of phenyl alcohols. Linear and non-linear correlation models are obtained. The new charge-transfer indices improve the multivariable non-linear regression equations for the dipole moment. When comparing with previous results, the variance decreases 92%. No superposition of the corresponding Gk–Jk and – pairs is observed. This diminishes the risk of co-linearity. Inclusion of the oxygen atom in the π-electron system is beneficial for the description of the dipole moment, owing to either the role of the additional p orbitals provided by the heteroatom or the role of steric factors in the π-electron conjugation. Linear and non-linear correlations between the fractal dimension and various descriptors point not only to a homogeneous molecular structure but also to the ability to predict and tailor drug properties.

Left ventricular dysfunction is associated with prolonged average ventricular fibrillation cycle length in patients with implantable cardioverter defibrillators.

In cellular studies, ventricular refractoriness (ERP) is prolonged in heart failure (CHF), but clinical evidence is lacking. The average ventricular fibrillation cycle length (VFCL) has been shown to correlate with local ERP. We hypothesized that the VFCL increases with left ventricular (LV) dysfunction. Therefore, we evaluated intracardiac VFCL recorded by implantable defibrillators (ICD) in patients with and without LV dysfunction. We analyzed intracardiac VFCL recorded by sensing leads of Ventak MINI (Guidant) ICD in 49 patients (35 men; age 54 +/- 13 years; 25 (51%) with coronary artery disease; mean LV ejection fraction (EF) 41 +/- 17%, range 76-10) from the European Ventak MINI Investigator Group. No patients were receiving antiarrhythmic drugs, including beta-blockers. Mean and median VFCL were obtained at predischarge testing during first charge time (4.5 +/- 2.7 s, range 1.4-11). Mean median VFCL was 186 +/- 21ms (range 150-230 ms). Patients with LVEF >/= 50% (n = 14) had shorter median VFCL than patients with LVEF < 50% (n = 35), (171 +/- 14 vs. 191 +/- 20 ms; p = 0.002). Median VFCL correlated with LVEF (r = -0.41; p = 0.003) and age (r = 0.28, p = 0.04), but was not significantly associated with charge time and defibrillation threshold at implant. Similar results occurred with mean VFCL. In multiple linear regression and correlation models, only LVEF% was a significant predictor (p < 0.05 for all models) of median VFCL. LV dysfunction prolongs averaged VFCL in patients at risk for malignant ventricular arrhythmias who have implantable cardioverter defibrillators. This phenomenon might be related to alterations in the ventricular refractory period.

Development and validation of a non-linear IVIVC model for a diltiazem extended release formulation FDA-UMAB contract—223943401.

To develop and validate internally an in vitro–in vivo correlation (IVIVC) for a diltiazem multi-particulate bead extended release formulation. In vitro dissolution of diltiazem capsules was examined using the following methods: USP Apparatus II (paddle) at 100 rpm and USP Apparatus III at 30 dpm. Seven healthy subjects received three diltiazem formulations (90 mg): slow (S), moderate (M), fast (F) releasing and an oral solution (90 mg). Serial blood samples were collected over 48 h and analyzed by a validated HPLC assay using ultraviolet detection. The f2 metric (similarity factor) was used to analyze the dissolution data. Linear and non-linear (quadratic, cubic, and sigmoid functions) correlation models were developed using pooled fraction dissolved (FRD) and fraction absorbed (FRA) data from various combinations of the formulations. Predicted diltiazem concentrations were obtained by convolution of the in vivo dissolution rates. Prediction errors were estimated for Cmax and AUC to determine the validity of the correlation. Apparatus II using purified water was found to be the most discriminating dissolution method. Significant intersubject (CV%>50) was observed for Cmax and AUC. The quadratic M/F IVIVC model provided a significant relationship between FRD and FRA when using either two or three of the formulations. An average percent prediction error for Cmax and AUC for all formulations was 12.4% and 9.2%, respectively. The prediction errors observed for Cmax and AUC suggest that the predictability of the quadratic IVIVC model is inconclusive, as such, external validation studies are required. Copyright © 2002 John Wiley & Sons, Ltd.

A new topological index to elucidate apolar hydrocarbons.

A new topological charge-transfer index is applied to elucidate the polar character of hydrocarbons. The dipole moments calculated by algebraic and vector semisums of charge-transfer indices are defined in this work. The combination of the charge-transfer indices allows the estimation of the molecular dipole moments. The ability of the indices for the description of the molecular charge distribution is established by comparing them with the dipole moment of a heterogeneous set of 57 polar and 53 apolar hydrocarbons. Linear and nonlinear correlation models are obtained. The new charge-transfer index, mu(vec), elucidates whether hydrocarbons are apolar, and improves the multivariable nonlinear regression equation for the dipole moment. When comparing with previous results, smaller superpositions of the corresponding pairs Gk, Jk are observed in our fits. This diminishes the risk of colinearity.

Consistency of least squares estimates in a system of linear correlation models

We consider a system of linear response models with random explanatory variables in which the global matrix parameter is subject to arbitrary constraints. A generalized least squares estimate (GLSE) of the global parameter is defined by its property of mi

Correlation of Penicillin Structure with Rate Constants for Basic Hydrolysis

The rates of degradation of 16 different penicillins have been determined at 35°C in borate buffer, pH9.2, by use of stability-indicating HPLC assay procedures. The best-fit was sought between pseudo first-order hydrolytic rate constants and different types of structural descriptor. Constitutional, topological, geometric and electrostatic descriptors were calculated using WHIM-3D/QSAR and CODESSA software. Advanced semi-empirical and ab-initio calculations were performed using AMPAC software. CODESSA was used to develop (multi)linear correlation models, perform cluster analysis of the experimental data and molecular descriptors, and interpret the developed models. The best correlations with the rates of hydrolysis of the drugs were found for topological, electrostatic and quantum-chemical descriptors.

A Study of the Relationship Between Freshwater Runoff and Benthos Abundance: a Scale-oriented Approach

In some coastal environments, freshwater runoff is one of the main potential sources of auxiliary energy. Little is known, however, about the mechanisms by which this energy input influences biological production, particularly at intermediate and high trophic levels. Moreover, the evidence available does not allow to link runoff variability one unambiguously to the dynamics of marine fauna. Here, an empirical approach based on exploratory data analysis is used to test for a link between these components of the ecosystem. Linear regression and correlation models were used to examine the relationship between runoff and abundance, biomass and mean weight per individual of juvenile populations (<1 year old) of five dominant epibenthic species sampled on suspended collectors (i.e.Obelia longissima, Hiatella arctica, Mytilus edulis, Semibalanus balanoidesandBalanus crenatus), over a 10-year period. The study was carried out in a large coastal ecosystem, the Estuary and north-western Gulf of St. Lawrence, for both regulated and non-regulated runoff situations. Notwithstanding the regression or correlation model, the spatial scale, the runoff signal, the runoff index, the species or the biological descriptor used, no significant relationships were observed. Results are discussed in light of current hypotheses proposed to account for the effects of runoff on marine fauna.

Correlation analysis in liquid chromatography of metal chelates : II. One-dimensional retention-mobile phase composition (physicochemical property) models in reversed-phase liquid chromatography

The applicability of linear correlation models for describing the effect of mobile phase composition and properties on the retention of metal chelates in reversed-phase liquid chromatography is demonstrated. The macroscopic (dielectric constant, surface tension, viscosity, concentration of organic modifier, distribution constant in an n-octanol-water system, etc.) and microscopic (characteristics of donor and acceptor ability) parameters of binary water-organic mixtures are used as variables. Although each of the studied parameters alone is somewhat limited in application, together they allow retention values to be estimated and the chromatographic behaviour of metal chelates to be predicted. The dominant influence of mobile phase composition and proton-donating ability on chelate retention in reversed-phase liquid chromatography is confirmed.

A linear model of crystal field correlation effects in Mn2+

Previous work on correlation effects in 3dn systems has been dominated by the nonlinear Koide and Pryce model which is based on a simplified picture of covalent bonding. Because of the deficiencies of this model, it is of interest to test linear correlation models which are not based on specific mechanisms. In this light, we assess the spin-correlated crystal field model, which has recently shown some success in explaining correlation effects in lanthanide crystal field splittings.

Statistical Explanation in Cross-cultural Research: a Comparison of the Utility of Linear and Curvilinear Correlation

Data from 483 societies included in the Ethnographic Atlas were used to compare the relative utility of linear (r) and curvilinear (Eta) correlation models in cross-cultural research. The societies included in the sample were selected in accordance with the procedures recommended by Murdock. The variables included in the study were selected so as to represent four important areas of evolutionary theory: energy supply (agricultural levels), differentiation (class stratification and the division of labor used in metal working, weaving, and pottery making), societal scale (mean size of local communities and settlement pattern), and integrative mode (central states). In addition to supporting the hypothesis that energy supply, differentiation, societal scale, and integrative mode are interrelated, the results indicate that the linear correlation model, r, frequently results in underestimations of the true strength of relationship between variables. It is suggested that comparativists should regularly test for curvilinear relationships in order to avoid possible errors in estimation.