Iterative Linear Regression Research Articles

Development of an equation for calculating vertebral shear failure tolerance without destructive mechanical testing using iterative linear regression

Equations used to determine vertebral failure tolerances without the need for destructive testing are useful for scaling applied sub-maximal forces during in vitro repetitive loading studies. However, existing equations that use vertebral bone density and morphology for calculating compressive failure tolerance are unsuitable for calculating vertebral shear failure tolerance since the primary site of failure is the pars interarticularis and not the vertebral body. Therefore, this investigation developed new equations for non-destructively determining vertebral shear failure tolerance from morphological and/or bone density measures. Shear failure was induced in 40 porcine cervical vertebral joints (20 C3-C4 and 20 C5-C6) by applying a constant posterior displacement to the caudal vertebra at 0.15mm/s. Prior to destructive testing, morphology and bone density of the posterior elements were made with digital calipers, X-rays, and peripheral quantitative computed tomography. Iterative linear regression identified mathematical relationships between shear failure tolerance, and morphological and bone density measurements. Along with vertebral level, pars interarticularis length and lamina height from the cranial vertebra, and inferior facet height from the caudal vertebra collectively explained 61.8% of shear failure tolerance variance. Accuracy for this relationship, estimated using the same group of specimens, was 211.9N or 9.8% of the measured shear failure tolerance.

Using Iterative linear regression model to time series models

In this paper we introduced a new method for fitting time series models, we called it “iterated linear regression” method. A comparison between the classical linear regression, iterated linear regression and Box-Jenkins methods using real data such as airline data and sunspot numbers is proposed.

A Fuzzy System Constructed by Rule Generation and Iterative Linear SVR for Antecedent and Consequent Parameter Optimization

This paper proposes a new fuzzy regression model, i.e., the fuzzy system constructed by rule generation and iterative linear support vector regression (FS-RGLSVR) for structural risk minimization. The FS-RGLSVR is composed of Takagi-Sugeno (TS)-type fuzzy if-then rules. These rules are automatically constructed by a self-splitting rule generation algorithm that introduces the self-splitting technique to the k-means clustering algorithm. This new algorithm regards a cluster as a fuzzy rule, where no preassignment of the cluster (rule) number is necessary. The cost function for parameter learning is defined based on structural risk instead of empirical risk minimization in order to achieve generalizability. Tuning all of the free parameters in the FS-RGLSVR using linear support vector regression (SVR) is proposed to minimize the cost function. Each of the consequent and antecedent part parameters is expressed as a linear combination coefficient in a transformed input space so that the linear SVR is applicable. This paper introduces iterative linear SVR to tune antecedent and consequent parameters. This paper demonstrates the capabilities of FS-RGLSVR by two simulated and four practical regression examples. Comparisons with fuzzy systems with different types of learning algorithms verify the performance of the FS-RGLSVR.

Evaluation of a three-band model for estimating chlorophyll-a concentration in tidal reaches of the Pearl River Estuary, China

Accurate assessment of phytoplankton chlorophyll-a (Chla) concentration in turbid waters by means of remote sensing was challenging due to the optical complexity of turbid waters. Recently, a conceptual model containing reflectance in three spectral bands in the red and near-infrared range of the spectrum was suggested for retrieving Chla concentrations in turbid productive waters. The objective of this paper was to evaluate the performance of this three-band model to estimate Chla concentration in the Pearl River Estuary (PRE), China. Reflectance spectra of surface water and water samples were collected concurrently. The samples contained variable Chla (4.80–92.60 mg/m 3) and total suspended solids (0.4–55.2 mg/L dry wt). Colored dissolved organic matter (CDOM) absorption at 400 nm was 0.40–1.41 m −1; turbidity ranged from 4 to 25 NTU (Nephelometric Turbidity Units). The three-band model was spectrally calibrated by iterative and least-square linear regression methods to select the optimal spectral bands for the most accurate Chla estimation. Strong linear relationships ( R 2 = 0.81 , RMSE=1.4 mg/m 3, N = 32 ) were established between measured Chla and the levels obtained from the calibrated three-band model [ R − 1 ( 684 ) – R − 1 ( 690 ) ] × R ( 718 ) , where R ( λ ) was the reflectance at wavelength λ . The calibrated three-band model was independently validated ( R 2 = 0.9521 , RMSE=6.44 mg/m 3, N = 16 ) and applied to retrieve Chla concentrations from the calibrated EO-1 Hyperion reflectance data in the PRE on December 21, 2006. The EO-1 Hyperion-derived Chla concentrations were further validated using synchronous in situ data collected on the same day ( R 2 = 0.64 , RMSE=2 mg/m 3, N = 9 ). The spatial tendency of Chla distribution mapping by Hyperion showed gradually increased concentrations of Chla farther from the river mouths (although decreasing from east to west), which were disturbed by the combination of river outlets and tidal current in Lingding Bay of the PRE. This observation conformed to previous observations and studies, and could reasonably be explained by geographical changes. Also, results indicated that the slope of the three-band regression line decreased as the Chla concentration increased, resulting in the first sensitive band of the three-band model to move towards short wavelengths. These findings validated the rationale behind the conceptual model and demonstrated the robustness of this algorithm for Chla retrieval from in situ data and the Hyperion satellite sensor in turbid estuarine waters of the PRE, China.

Backbone Model for Confined Masonry Walls for Performance-Based Seismic Design

In this study, a performance-based model is proposed, capable of simulating seismic behavior of typical confined masonry (CM) walls whose response is governed by shear deformations. This model is developed on the basis of both monotonic and reversed-cyclic experiments assembled in an extensive database, and derived through an iterative linear regression analysis. Owing to the limited data available and inconsistencies in observed behavior in some tests, only specimens with two tie columns, one on either edge of the wall; multiple longitudinal rebar per confining element; no bed joint reinforcement; no openings within the confined panel; and a height-to-length ratio that varies from 0.7 to 1.2, are considered for the purpose of model development. The effect of openings on strength characteristics, the capability of existing models to predict seismic behavior of CM walls, and the limitations of the proposed equations are discussed in detail. The accuracy of the model is also verified for CM walls with different characteristics. The proposed model simulates reasonably well the seismic behavior of CM walls whose properties conform to the assumptions of the model and that correspond to typical CM walls.

Backbone Model for Confined Masonry Walls for Performance-Based Seismic Design

In this study, a performance-based model is proposed, capable of simulating seismic behavior of typical confined masonry (CM) walls whose response is governed by shear deformations. This model is developed on the basis of both monotonic and reversed-cyclic experiments assembled in an extensive database, and derived through an iterative linear regression analysis. Owing to the limited data available and inconsistencies in observed behavior in some tests, only specimens with two tie columns, one on either edge of the wall; multiple longitudinal rebar per confining element; no bed joint reinforcement; no openings within the confined panel; and a height-to-length ratio that varies from 0.7 to 1.2, are considered for the purpose of model development. The effect of openings on strength characteristics, the capability of existing models to predict seismic behavior of CM walls, and the limitations of the proposed equations are discussed in detail. The accuracy of the model is also verified for CM walls with different characteristics. The proposed model simulates reasonably well the seismic behavior of CM walls whose properties conform to the assumptions of the model and that correspond to typical CM walls.

On the Determination of Ventilatory Threshold and Respiratory Compensation Point via Respiratory Frequency

This study examined the validity of a quantitative respiratory frequency (f(R)) analysis to detect the ventilatory threshold (theta(Vent)) and respiratory compensation point (RCP). Thirty-six amateur competitive cyclists completed a maximal graded exercise test on an electromagnetically-braked cycle ergometer. theta(Vent) and RCP were determined using multiple gas exchange criteria and by f(R) analysis (theta(Vent)f(R) and RCP(f(R))), employing an iterative least-squares linear regression technique. Fifteen subjects were excluded from the analyses due to a low signal-to-noise ratio and/or high risk for pseudo-threshold resulting from hyperventilation early in the exercise protocol. A Bland-Altman procedure for inter-analysis comparison completed on the remaining participants' data (n=21; age=29+/-7 years; height=177+/-9 cm; weight=76.0+/-15.8 kg; VO(2max)=4.415+/-0.971 lmin(-1); 58.7+/-10.7 ml kg(-1) min(-1)) revealed mean bias+/-95% Limits of Agreement (LOA) of 1.53+/-50.2 W for theta(Vent) and theta(Vent)f(R). The same inter-anlysis comparison (n=21) for RCP and RCP(f(R)) resulted in a mean bias+/-LOA of 12.6+/-26.9 W. The analysis techniques in the present investigation revealed substantial limits of agreement and/or bias for all estimations, and these data indicated f(R) analyses were unsatisfactory to determine theta(Vent) and RCP in trained cyclists.

Spectrophotometric analyses of chlorophyll and single carotenoids during fruit development of tomato (Solanum lycopersicum L) by means of iterative multiple linear regression analysis

When using spectrophotometric transmittance readings of fruit extracts, the analysis of single carotenoids is difficult because of coinciding absorption bands of the various carotenoids and chlorophylls present in the solution. Aimed at the separate analyses of pigments, an iteratively applied linear regression was developed based on spectral profiles of pigment standards. The iterative approach was validated by dilution series of pigments and compared with commonly applied equation systems. High coefficients of determination and low measuring uncertainties were found for chlorophyll a and b (R(2) > or = 0.99, root mean square error RMSE < or = 10%). Carotenoids were separately analyzed with R(2) = 0.99, R(2) = 0.96, and R(2) = 0.98 for lycopene, beta-carotene, and lutein, respectively. The approach based on the spectral profiles provided low measuring uncertainties even if lutein was additionally present in the solutions, which was not possible with common data analyses. Subjecting tomato tissues (Solanum lycopersicum L.) to the iterative approach, contents of in vivo measured pigments were calculated with R(2) = 0.82, R(2) = 0.84, R(2) = 0.67, and R(2) = 0.03 for chlorophyll a and b, lycopene, and beta-carotene, respectively.

Error minimization algorithm for comparative quantitative PCR analysis: Q-Anal

Current methods for comparative quantitative polymerase chain reaction (qPCR) analysis, the threshold and extrapolation methods, either make assumptions about PCR efficiency that require an arbitrary threshold selection process or extrapolate to estimate relative levels of messenger RNA (mRNA) transcripts. Here we describe an algorithm, Q-Anal, that blends elements from current methods to by-pass assumptions regarding PCR efficiency and improve the threshold selection process to minimize error in comparative qPCR analysis. This algorithm uses iterative linear regression to identify the exponential phase for both target and reference amplicons and then selects, by minimizing linear regression error, a fluorescence threshold where efficiencies for both amplicons have been defined. From this defined fluorescence threshold, cycle time (Ct) and the error for both amplicons are calculated and used to determine the expression ratio. Ratios in complementary DNA (cDNA) dilution assays from qPCR data were analyzed by the Q-Anal method and compared with the threshold method and an extrapolation method. Dilution ratios determined by the Q-Anal and threshold methods were 86 to 118% of the expected cDNA ratios, but relative errors for the Q-Anal method were 4 to 10% in comparison with 4 to 34% for the threshold method. In contrast, ratios determined by an extrapolation method were 32 to 242% of the expected cDNA ratios, with relative errors of 67 to 193%. Q-Anal will be a valuable and quick method for minimizing error in comparative qPCR analysis.

A simple method for a determination

The a term is a primary parameter that is used to indicate the deviation of the epithermal neutron distribution in the k0-standardization method of neutron activation analysis, k0-NAA. The calculation of a using a mathematical procedure is a challenge for some researchers. The calculation of a by the "bare-triple monitor" method is possible using the dedicated commercial software KAYZERO®/SOLCOI®. However, when this software is not available in the laboratory it is possible to carry out the calculation of a applying a simple iterative linear regression using any spreadsheets. This approach is described in this paper. The experimental data used in the example were obtained by the irradiation of a set of suitable monitors in the NAA #1 irradiation channel of the HANARO research reactor (KAERI, Korea). The results obtained by this iterative linear regression method agree well with the results calculated by the validated mathematical method.

Speaker adaptation of HMMs using evolutionary strategy-based linear regression

A new framework for speaker adaptation of continuous-density hidden Markov models (HMMs) is introduced. It aims to improve the robustness of speech recognizers by adapting HMM parameters to new conditions (e.g., from new speakers). It describes an optimization technique using an evolutionary strategy for linear regression-based spectral transformation. In classical iterative maximum likelihood linear regression (MLLR), a global transform matrix is estimated to make a general model better match particular target conditions. To permit adaptation on a small amount of data, a regression tree classification is performed. However, an important drawback of MLLR is that the number of regression classes is fixed. The new approach allows the degree of freedom of the global transform to be implicitly variable, as the evolutionary optimization permits the survival of only active classes. The fitness function is evaluated by the phoneme correctness through the evolution steps. The implementation requirements such as chromosome representation, selection function, genetic operators, and evaluation function have been chosen in order to lend more reliability to the global transformation matrix. Triphone experiments used the timit and arpa−rm1 databases. For new speakers, the new technique achieves 8 percent fewer word errors than the basic MLLR method.

Sperm count and chromatin structure in men exposed to inorganic lead: lowest adverse effect levels

Objectives: To obtain knowledge on male reproductive toxicity of inorganic lead at current European exposure levels and to establish lowest adverse effect levels, if any. Methods: A cross sectional survey...

Cerebral blood flow velocity declines before arterial pressure in patients with orthostatic vasovagal presyncope

ObjectivesWe studied hemodynamic changes leading to orthostatic vasovagal presyncope to determine whether changes of cerebral artery blood flow velocity precede or follow reductions of arterial pressure. BackgroundSome evidence suggests that disordered cerebral autoregulation contributes to the occurrence of orthostatic vasovagal syncope. We studied cerebral hemodynamics with transcranial Doppler recordings, and we closely examined the temporal sequence of changes of cerebral artery blood flow velocity and systemic arterial pressure in 15 patients who did or did not faint during passive 70° head-up tilt. MethodsWe recorded photoplethysmographic arterial pressure, RR intervals (electrocardiogram) and middle cerebral artery blood flow velocities (mean, total, mean/RR interval; Gosling’s pulsatility index; and cerebrovascular resistance [mean cerebral velocity/mean arterial pressure, MAP]). ResultsEight men developed presyncope, and six men and one woman did not. Presyncopal patients reported light-headedness, diaphoresis, or a sensation of fatigue 155 s (range: 25 to 414 s) before anycerebral or systemic hemodynamic change. Average cerebral blood flow velocity (CBFV) changes (defined by an iterative linear regression algorithm) began 67 s (range: 9 to 198 s) beforereductions of MAP. Cerebral and systemic hemodynamic measurements remained constant in nonsyncopal patients. ConclusionsPresyncopal symptoms and CBFV changes precede arterial pressure reductions in patients with orthostatic vasovagal syncope. Therefore, changes of cerebrovascular regulation may contribute to the occurrence of vasovagal reactions.

Determination of metallic complexing capacities of the dissolved organic material in seawater

The use of the Langmuir isotherm for the study of the complexing properties of functional groups present both in dissolved organic material and on biological surfaces in aquatic systems needs a heterogeneous model and an iterative linear regression solution. The method proposed previously by van den Berg is improved by replacing the expression used to obtain the complexing capacity and the conditional stability constant of the functional groups with stronger trace metal affinity, for the linear expression of the Langmuir isotherm proposed by Scatchard. The result is also an iterative linear regression process, which gives a convergent solution, together with better statistical weight distribution of the initial metallic titration data. It also fits better with the titration data obtained at very low dissolved metallic ion concentrations.

Effects of Partial Left Ventriculectomy on Cardiac Performance

To the Editor: We read with great interest the recent article by Gorcsan et al.1 They report heterogeneous immediate effects of partial left ventriculectomy (PLV) on the slope (Ees) of end-systolic pressure-area relations obtained with echocardiographic automated border detection in 8 patients. The average change in Ees was from 6.5±3.4 mm Hg/cm2 (before PLV) to 4.3±2.5 mm Hg/cm2 (immediately after PLV) ( P =NS). The authors, however, overlooked an error made by the iterative linear regression technique that they used to calculate Ees. In the right bottom panel of the Figure, where the decreased Ees (1.1 mm Hg/cm2) was demonstrated after PLV, the end-systolic pressure-area …

An efficient method for determining threshold voltage, series resistance and effective geometry of MOS transistors

An accurate and robust method of extracting the threshold voltage, the series resistance and the effective geometry of MOS transistors is presented. The method is based on efficient nonlinear optimization using an iterative linear regression procedure which usually converges in less than four rounds. Thereby extracted parameters are obtained from analytical expressions for the solutions to a linear system of equations whereby time consuming numerical differentiations are avoided. MOSFET parameters are explicitly identified as parameters of an underlying widely used device model that is a good approximation for operation in the linear region. The method is particularly suitable for process characterization and can be used on as few as twelve data points (three data points from each of four different size transistors). By connecting external resistors in series with the transistors, we show that the extracted values of the parameters are independent of the series resistance.

A prospective evaluation of pharmacokinetic model controlled infusion of propofol in paediatric patients

We have tested a published algorithm for pharmacokinetic model controlled infusion of propofol to supplement 67% nitrous oxide for general anaesthesia in Chinese children aged 4-10 yr. Initially we studied 10 children undergoing minor procedures with spontaneous ventilation; mean duration of surgery was 38 min and mean propofol infusion rate 497 micrograms kg-1 min-1. The precision of the model was 24.8% and bias -18.5%. The model was revised using an iterative linear least squares regression procedure and the revised model tested prospectively in another 20 children. The precision of the revised model was 21.5% (range in individuals 8.4-43.1%) and bias -0.1% (range -30 to 42%). Mean propofol infusion rate required to maintain anaesthesia was 474 micrograms kg-1 min-1 (range 125-737 micrograms kg-1 min-1). The mean blood concentration required for satisfactory anaesthesia was 6.6 micrograms ml-1 (range 3-11 micrograms ml-1) and the mean blood concentration at the time of waking, which occurred 40 min after switching off the infusion, 0.86 microgram ml-1 (range 0.40-1.45 micrograms ml-1). Our patient population required different pharmacokinetic variables from those in the previous study. Recovery was slow because of the high infusion rates required to maintain satisfactory anaesthesia and large difference between the blood concentration required for anaesthesia and that at which waking occurred.

Preliminary investigations of the clinical pharmacology of three short-acting non-depolarizing neuromuscular blocking agents, Org 9453, Org 9489 and Org 9487

Three muscle relaxants, Org 9453, Org 9489 and Org 9487, short-acting in animals, were investigated to establish their profiles in humans. Potency, time course of action, and pharmacokinetic behaviour were studied in 90 healthy patients during fentanyl/halothane/N2O anaesthesia. Neuromuscular function was monitored mechanomyographically. Plasma and urine concentrations (three patients per compound) were measured by HPLC, and these data were analyzed by iterative linear least square regression analysis. The ED90 values for Org 9453, Org 9489 and Org 9487 were 1.4, 0.45 and 1.15 mg.kg-1 respectively. The onset times of Org 9453 (1.5 mg.kg-1, 1.1 X ED90), Org 9489 (0.9 mg.kg-1, 2 X ED90) and Org 9487 (1.5 mg.kg-1, 1.3 X ED90) were 1.2, 1.6 and 1.5 min, and the durations until 25% twitch recovery were 8.6, 22.0 and 8.9 min, respectively. Clearances of these doses were 6.9, 5.8, and 11.1 ml.kg-1.min-1, and mean residence times 26, 79, and 41 min, respectively. Mean renal excretion (parent compound and metabolites) within 24 hr amounted to 5, 11.3 and 12.2% respectively. No side effects other than a moderate short-lasting decrease of blood pressure and a concomittant increase in heart rate were noted. It is concluded that Org 9453 and Org 9487 are short-acting muscle relaxants in humans.

Source types in Canadian precipitation chemistry

Precipitation data generated by Canadian Air and Precipitation Monitoring Network (CAPMoN) have been analysed by an iterative multiple linear regression method, revealing five source types or components, each with distinctive seasonal and geographic variations. Each source types has its characteristics chemical profile. The profiles suggest that two of the source types are rural (apparently derived from fertilizer and soil), two are urban/industrial (apparently derived from SO2 and NOx emissions), and one is sea salt. The NOx-derived component is highly acidic, the SO2-derived component is also very acidic, the fertilizer component is slightly alkaline, and the soil component is more alkaline. Charge balance calculations show a fairly consistent deficit in anions, a deficit which is especially important for the NOx-derived component. The anion deficit results suggest that more complete chemical analyses are required. The chemical profiles from CAPMoN data have been used to determine the component contributions to precipitation data collected in Manitoba by the provincial Ministry of the Environment. Back trajectories for the Manitoba data show distinct geographic and seasonal effects, including: (i) seasalt input to Manitoba is derived mainly from Hudson Bay and the Arctic, especially in fall and winter; (ii) the SO2 component has ubiquitous sources, including polar sources: (iii) the fertilizer component arrives mainly form the U.S. rural Midwest, especially in spring and fall; (iv) the soil component has northern sources, with perhaps transpolar and trans-Pacific origins, in spring and summer; and (v) the NOx component appears to be derived from northern sources at polar sunrise in spring.

ON THE BEST FIT CURVE THROUGH CRACK GROWTH FRACTURE RESISTANCE DATA

The ESIS recommendations for determining the fracture resistance of ductile materials make use of an offset power law to evaluate the best fit curve to crack growth fracture resistance data. Evaluation of the offset power law requires the use of non‐linear regression analysis, although an iterative linear regression analysis can be used if the data are transformed by taking logarithms. The two analyses are compared with a proposed alternative formulation for the offset power law which can be evaluated using an iterative linear regression analysis without the need to transform the data. Confidence limits are evaluated for the J‐Δa data of two steels and are shown to depend on the analysis procedures.