Linear Correlation Model Research Articles

Estimation of Locomotion States of a Rat by Neural Signals from the Motor Cortices Based on a Linear Correlation Model

We are developing a brain-machine interface (BMI) called “RatCar," a small vehicle controlled by the neural signals of a rat's brain. An unconfined adult rat with a set of bundled neural electrodes in the brain rides on the vehicle. Each bundle consists of four tungsten wires isolated with parylene polymer. These bundles were implanted in the primary motor and premotor cortices in both hemispheres of the brain. In this paper, methods and results for estimating locomotion speed and directional changes are described. Neural signals were recorded as the rat moved in a straight line and as it changed direction in a curve. Spike-like waveforms were then detected and classified into several clusters to calculate a firing rate for each neuron. The actual locomotion velocity and directional changes of the rat were recorded concurrently. Finally, the locomotion states were correlated with the neural firing rates using a simple linear model. As a result, the abstract estimation of the locomotion velocity and directional changes were achieved.

Changes in sand fractions of Binggou section and the expansion and contraction of the Tengger desert during 50–30 ka

AbstractSigns of the evolutionary process are well preserved in the aeolian deposits of desert margins and enable reconstruction of desert expansion and contraction. The sand content (percentage >63 µm) of loess in the loess–desert transitional zone was used as a proxy indicator for determining the proximity of the desert margin. According to the dominant wind direction, generally NW–SE in the northwest Chinese Loess Plateau, a transect was projected to observe spatial changes in sedimentological characteristics of aeolian deposits during the Last Glacial Period. The transect consists of 12 loess sections, starting at Shapotou in the transitional region between the Loess Plateau and the Tengger Desert and ending at Tianshui, which is located at the north foot of the Western Qinling Mountains in the southernmost part of the Loess Plateau. It shows the properties of temporal and spatial distribution of the Malan loess, with reduced sand content from northwest to southeast. A linear correlation model of sand content and distance was obtained, which was similar to the east of the Chinese Loess Plateau. According to this model, and on the basis of optically stimulated luminescence (OSL) dating from Binggou section, a detailed and quantificational expansion and contraction for the Tengger Desert was established. Copyright © 2006 John Wiley & Sons, Ltd.

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.

SURROGATE ANALYSIS OF MULTICHANNEL DATA WITH FREQUENCY DEPENDANT TIME LAG

Recently a new technique for generating linear surrogates of multichannel data was introduced. This technique, referred to as the coherent digitally filtered surrogate method, preserves both the individual power spectra, and the coherence function, of the original data. This method is somewhat limited in that it can only be applied to multichannel data in which the cross-spectrum is real. We present here an alteration to this algorithm that can be used to test any linear-correlation model, with arbitrary complex cross-spectra. This is of particular interest for experiments in which two channels are coupled with some time lag, and it is necessary to determine if the coupling is linear. We also demonstrate that this algorithm can be used along with the synchronization to provide a much better estimate for the degree of phase-locking between two signals than the coherence analysis techniques traditionally used in neuroscience.

Development and validation of an in vitro–in vivo correlation for buspirone hydrochloride extended release tablets

The aim of this study was to develop an in-vitro–in-vivo correlation (IVIVC) for two buspirone hydrochloride extended release formulations and to compare their plasma concentrations over time with the commercially available immediate release (IR) tablets. In vitro release rate data were obtained for each formulation using the USP Apparatus 2, paddle stirrer at 50 and 100 rpm in 0.1 M HCl and pH 6.8 phosphate buffer. A three-way crossover study in 18 healthy subjects studied a 30 mg “Fast” (12 h) and 30 mg “Slow” (24 h) formulation of buspirone hydrochloride given once a day, and 2×15 mg immediate release tablets dosed at a 12 h interval. The similarity factor ( f 2) was used to analyze the dissolution data. A linear correlation model was developed using percent absorbed data and percent dissolved data from the two formulations. Predicted buspirone hydrochloride concentrations were obtained by use of a curve fitting equation for the immediate release data to determine the volume of distribution and fraction absorbed constants. Prediction errors were estimated for C max and area under the curve (AUC) to determine the validity of the correlation. pH 6.8 at 50 rpm was found to be the most discriminating dissolution method. Linear regression analyses of the mean percentage of dose absorbed versus the mean in vitro release resulted in a significant correlation ( r 2>0.95) for the two formulations. An average percent prediction error for C max was −0.16%, but was 16.1%, for the AUCs of the two formulations.

Radial Basis Function Neural Networks Based QSPR for the Prediction of log P

AbstractQuantitative structure‐property relationship (QSPR) method is used to study the correlation models between the structures of a set of diverse organic compounds and their log P. Molecular descriptors calculated from structure alone are used to describe the molecular structures. A subset of the calculated descriptors, selected using forward stepwise regression, is used in the QSPR models development. Multiple linear regression (MLR) and radial basis function neural networks (RBFNNs) are utilized to construct the linear and non‐linear correlation model, respectively. The optimal QSPR model developed is based on a 7‐17‐1 RBFNNs architecture using seven calculated molecular descriptors. The root mean square errors in predictions for the training, predicting and overall data sets are 0.284, 0.327 and 0.291 log P units, respectively.

Prediction of trace metal partitioning between minerals and aqueous solutions: a linear free energy correlation approach

Trace metal partitioning between authigenic minerals and aqueous solutions is of great interest to both geochemical and environmental communities. In this paper, we have developed a linear free energy correlation model that correlates metal partition coefficients with metal cation properties: −2.303 RT log K d + ΔG f,M Z+ 0 = a ∗ M H X Δ G n,M Z+ 0 + β ∗ M H X r M Z+ + b ∗ M H X where a ∗ M H X , β ∗ M H X , and b ∗ M H X are constants, which can be determined by a regression analysis. For isovalent metal partitioning, because of the constraint of K d = 1 for the host metal, this correlation can be also expressed as: −2.303 RT log K d = a ∗ M H X (Δ G n,M H Z+ 0 − Δ G n,M 0 ) + β ∗ M H X ( r M Z+ − r n,M H Z+ ) − (Δ G f,M Z+ 0 − Δ G 0 f,M H Z+ ). Host minerals from an isostructural family have the same linear free energy relationship, as long as the relationship is expressed as a function of the differences in cation properties between substituent and host metals. We have applied our model to both isovalent and non-isovalent metal partitioning in carbonate minerals. The model closely fits experimental data, demonstrating the robustness of the proposed linear free energy relationship. Using the model, we have predicted the partition coefficients of divalent and trivalent metals between various carbonate minerals and aqueous solutions. The differences between the predicted and experimental values are generally less than 1 logarithmic unit for divalent cations and less than 0.4 logarithmic unit for trivalent cations. Magnesite is predicted to have the largest partition coefficients among the carbonate minerals with a calcite structure and therefore, can be a good scavenger for toxic metals. The kinetic effect on metal partitioning can be described graphically by a “seesaw” line anchored at a host cation. To explain the rate dependence of partition coefficients, we have proposed a conceptual model that relates metal partitioning to surface adsorption. The conceptual model suggests that as the rate of host mineral precipitation increases, the ratio of substituent to host cation in a solid approaches what is in the adsorbed layer. The linear free energy correlation model developed in this paper provides a useful tool for systematizing the existing experimental data and for predicting unknown partition coefficients.

Estimación del volumen espiratorio forzado en un segundo a partir del tiempo de apnea voluntaria en sujetos sanos

Cross sectional study to evaluate a linear correlation model to calculate forced expiratory volume in one second (FEV1) on the basis of breath-holding time (BHT) in healthy subjects aged 16 years or older. BHT was defined as the maximum time in seconds that a person can voluntarily hold his or her breath measured between the end of a deep breath until he or she begins to exhale in the third of three consecutive maneuvers. To calculate FEV1 on the basis of BHT (FEV1-BHT) the general straight-line equation (y = a + bx) was applied, with x being Logn of BHT and y being FEV1. The a and b values had been previously estimated by gender using multiple linear regression in which FEV1 measured spirometrically was the dependent variable and the age and Logn of BHT were the independent variables. One hundred ninety-seven subjects [97 women (49.2%) and 100 men (50.8%)] were enrolled. Mean FEV1 measured by spirometry (FEV1-Sp) and FEV1-BHT were similar. The correlation (R2) between FEV1 and BHT for women and men was 0.585 (95% CI 0.213-0.753) and 0.702 (95% CI 0.630-1.496), respectively. The ratio FEV1-BHT:FEV1-Sp was higher than 80% for 96 women (98.96%) and 98 men (98.0%). FEV1 can be reliably estimated using BHT.

Enantioselective liquid-solid extraction for screening of structurally related chiral stationary phases

An enantioselective liquid-solid batch extraction method is described for the screening of novel chiral stationary phases (CSPs) during optimization studies of chiral selectors derived form a common lead structure. Extraction enantioselectivity (α) values can be calculated from the enantiomeric excess ee-values of the selectand, which are measured in the liquid phase by enantioselective HPLC. Extraction α-values have been correlated with chromatographic α-values. The influence was studied of several experimental parameters of the assay (pHa, buffer concentration, temperature, selector/selectand and phase ratio) on the enantiomeric excess (ee) values of the selectands and the enantioselectivity of the CSPs, respectively. The derived statistically significant model has then been implemented to predict chromatographic α-values of novel CSPs. For example, an ee of 89.3% for DNB-Leu as selectand could be achieved in batch extraction for a novel synthesized but mechanistically similarly-acting CSP derived form quinine. This corresponds to a calculated extraction α-value of 17.7. Based on this αextraction a chromatographic α-value of 28.8 was predicted by the linear correlation model; the experimental HPLC α-value of 31.7 was in good agreement and demonstrated the validity of the proposed screening method. The method is particularly helpful in SO optimization studies.

Quantitative component analysis of mixtures for risk assessment: application to eye irritation.

A methodology called quantitative component analysis of mixtures (QCAM) was used to analyze an existing set of product formulation data to determine if the irritating ingredients in the mixtures could be identified. Eye irritation scores, based on a rat model, for 18 mixtures having a composite total of 37 components, were analyzed by QCAM. QCAM relates a net toxicity measure of a mixture to the toxicities of the individual components of the mixture through linear, quadratic, and pairwise cross-component concentration-dependent interactions. A correlation model is established using a particular genetic algorithm employing either multidimensional linear regression or partial least-squares regression fitting. Cornea eye irritation and average eye irritation are well-explained in terms of a linear model of, at most, three components over the set of mixtures. Moreover, extensive cornea and average eye irritations are due to only one of these three components of the mixtures. Also, one of the three significant components was predicted to decrease the extent of eye irritation, and subsequently identified as an "anti-irritant" in contact lens solutions. A reasonable linear correlation model could also be developed for conjunctiva irritation, but no significant iris irritation model could be constructed. The addition of quadratic and/or cross-component concentration terms to a linear correlation model did not statistically improve the overall resultant model. The QCAM models permit estimation of the intrinsic (self) toxicity of each of the components of a mixture, and may aid in the reduction, and ultimate elimination, of the need for animal eye irritation studies.

Molecular modeling parameters predict antioxidant efficacy of 3-indolyl compounds.

Many dietary constituents, such as indole-3-carbinol, are chemoprotective in toxicity and carcinogenicity bioassays. Indole-3-carbinol and related congeners appear to protect partly via radical and electrophile scavenging. To develop better chemoprotective indoles with lower intrinsic toxicity, we performed molecular graphic and quantum-mechanical analyses of model indolyl compounds to ascertain the determinant molecular features for antioxidant activity. We examined eight structurally related 3-indolyl compounds for relationships between antioxidation potential (using in vitro lipid peroxidation assays) and electronic, polar, and steric parameters, including bond dissociation energies, bond lengths, dipole moments, electronic charge densities, and molecular size parameters. Electronic features of the 3-methylene carbon and 1-nitrogen were not predictive of antioxidative potency due to extensive charge delocalization of the cation radical following electron abstraction from the nitrogen. Antioxidant efficacy of 3-indolyl compounds was most strongly predicted by molecular size parameters and by the energy of electron abstraction as calculated from the difference in heat of formation between the parent compound and its cation radical. A highly predictive multiple linear regression correlation model (r2 = 0.97) was obtained using the parameters of heat of formation, molecular weight, log P, and diplole moment.

Correlation between environmental parameters and leaf injury in Nicotiana tabacum L. cv. ?Bel-W 3?

Tobacco plants (Nicotiana tabacum L. cv. 'Bel-W3') were exposed to ambient air for 25 weeks during the 1987 growing season next to an air pollution monitoring station in Brera (Milan, Italy). The research objective was to study the influence of selected environmental parameters on leaf damage in this plant, which is widely used as an ozone indicator. A multiple linear correlation model was estimated between leaf damage and available meteorological and air pollution data. Leaf injury was positively correlated with ozone integrated exposure and temperature, but negatively with vapour pressure deficit. A linear correlation model was used to estimate ozone integrated exposure from the leaf injury index.

A Linear Spatial Correlation Model, With Applications to Positron Emission Tomography

A Linear Spatial Correlation Model, With Applications to Positron Emission Tomography

A Linear Spatial Correlation Model, with Applications to Positron Emission Tomography

Abstract A simple spatial-correlation model is presented for repeated measures data. Correlation between observations on the same subject is assumed to decay as a linear function of the squared distance separating the regions in three-dimensional space where the observations are made. This quadratic decay (QD) model has many attractive theoretical properties. The covariance structure of the “normalized” data, formed by subtracting the subject average, is the same as that generated by random linear trends plus centered white noise, which leads to a simple method for simulating the original data. It also implies that the first three principal components of the normalized observations are the spatial coordinates of the regions. Thus principal components analysis can be used as an exploratory tool to verify the QD model, provided the white noise component is small. Certain simple predictions can be made, such as the fact that the variances of the normalized observations increase linearly with the squared dist...

Bootstrap of the linear correlation model

In the linear correlation model one observes an i.i.d. sequence (Xi, F$), i^l, of {p + l)-variate random vectors satisfying Yi=Xif}+ei. In this paper, we show the validity of the bootstrap for the LSE of p under minimal moment assumptions, answering a question posed by D. FREEDMAK

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.

Neighborhood Context and College Plans: An Ordinal Path Analysis

This article develops a procedure for path analysis of ordinal variables using only ordinal statistics and presents an ordinal path analysis of data previously analyzed by Sewell and Armer (1966a). Substantively, it shows that when ordinal statistics and path analysis are used, neighborhood context has very important direct and indirect effects on college plans. This is true when neighborhood socioeconomic status is trichotomous or dichotomous. Methodologically, it demonstrates that path analysis techniques can be successfully applied to ordinal data using ordinal statistics rather than assuming equalinterval scales and applying interval statistics, or using dummy variables. Possibly, small effect of neighborhood context reported by Sewell and Armer is a consequence of their ignoring a curvilinear relationship between neighborhood context and college plans, their assuming interval data, and their use of a linear multiple correlation model when in fact their data did not conform to underlying assumptions. This article develops a procedure for path analysis of ordinal variables using only ordinal statistics and presents an ordinal path analysis of data previously analyzed by Sewell and Armer (1966a) in their article, Neighborhood Context and College Plans.' In it, they tested hypothesis that: the socioeconomic status of high school district-since it presumably reflects shared norms and aspirations of its members would have an important effect on educational aspirations of its youth over and above that of family socioeconomic status or individual ability (1966a: 162). Sewell and Armer first treated their variables as attributes. They showed that neighborhood socioeconomic status has a positive zero-order effect on college plans of high school seniors. (Their data-set described universe of seniors attending Milwaukee high schools during 1957-58 academic year.) Then they presented cross-tabulations between each test factor (sex, intelligence, and socioeconomic status) and independent and dependent variables. In order to determine whether original relationship between neighborhood and college plans still held, they tested it by controlling for test factors singly and in combination. Finally, they assumed interval measurement and carried out a multiple correlation analysis. They entered test factors first and then independent variable neighborhood context-to determine magnitude of variance in college plans it independently explains. The researchers did not carry out a causal analysis of interrelations between neighborhood context and 3 test factors. They felt their research hypothesis did not require it (1966b:708), and that precise causal order of variables was unobtainable ( 1966b:709). Given their analytic procedures and symmetric measures of correlation, they found that: . . neighborhood status results in an absolute increase in explained variance of college plans of 1.8 percent beyond effects of sex, socioeconomic status, and intelligence [ 199 ] * Revised version of a paper presented at annual meeting of Eastern Sociological Society, New York, April 1971. The author is indebted to Paul F. Lazarsfeld for suggesting that he study this problem, and to Robert Somers, Neil Henry, Robert HaLuser, and numerous colleagues for their helpful comments on earlier drafts. Preparation of this article was facilitated by general research grants from Academic Senate of University of California, Santa Barbara, and by grants of computer time from National Institute of Mental Health. 1 For earlier methodological and substantive comments on Sewell and Armer's analysis see Boyle (1966), Michael (1966), Sewell and Armer (1966b), Turner (1966). This content downloaded from 207.46.13.183 on Thu, 21 Apr 2016 06:29:34 UTC All use subject to http://about.jstor.org/terms 200 / SOCIAL FORCES / vol. 51, dec. 1972 ( 1 966a: 167). Contrariwise, results reported below based on a reanalysis of very same data, but using ordinal statistics and path analysis, indicate that neighborhood context has very important direct and indirect effects on college plans.