Sum Of Squared Values Research Articles

Development of weather-based prediction models for leaf rust in wheat in the Indo-Gangetic plains of India

Weather based prediction models for leaf rust were developed using disease severity and weather data recorded at four locations viz. Ludhiana, Kanpur, Faizabad and Sabour of the All India Wheat and Barley Improvement Project. Weeks 7–9 of the crop growing season at Ludhiana, Faizabad and Sabour and weeks 10–12 at Kanpur were identified as critical periods for relating weather variables to disease. Highly significant correlation coefficients were found between disease severity and a greater number of weather variables in these critical 3-week periods than at other times. The correlation coefficients were greatest for the Humid Thermal Ratio (HTR), Maximum Temperature (MXT) and Special Humid Thermal Ratio (SHTR), and these three weather variables were selected as predictor variables. Linear regressions with these predictor variables (individually) during the critical periods, and a multiple regression with MXT and relative humidity (RH), serve as four disease prediction models, with sufficient lead-time to take control measures. Validation of these prediction models with independent disease severity data showed that the regression equation with MXT (Model-1) was the best among the prediction models, with four out of six simulations matching observed disease severity classes and also having lowest residual sum of squares (SSE) value of 2727. Models 4 (multiple regression), 2 (HTR) and 3 (SHTR) with SSE values of 2881, 3092 and 3732, respectively are in order of decreasing accuracy of prediction. The model using MXT can be used to predict the disease severity in the Indo-Gangetic Plains and provide the basis for efficient disease control.

Black sesame (Sesamum indicum L.) seeds extracts by CO2 supercritical fluid extraction: Isotherms of global yield, kinetics data, total fatty acids, phytosterols and neuroprotective effects

In Brazilian folk medicine, black sesame (Sesamum indicum L.) seeds are one of the most important ingredients present in the tea used to treat stroke victims. Nevertheless, extracts by supercritical extraction of black sesame seeds have not been applied in neuroprotection studies. The objective of this work was to investigate some process variables of supercritical fluid extraction in black sesame to generate extracts applicable in stroke research. Two isothermal (40 and 60°C) were explored, combined with pressures that ranged from 200 to 400bar, at a constant mass flow rate of 5.9×10−5kg/s. The global yields ranged from 37 to 53% in dry basis. The highest mass yield was obtained at 60°C and 400bar. The fatty acid composition comprised a high unsaturated/saturated ratio. Chromatographic analysis of phytosterol content in the high global yield extract revealed higher amounts of β-sitosterol+sitostanol, cholesterol, campesterol+campestanol+24-methylene cholesterol, Δ-5 avenasterol and stigmasterol, while lower levels of Δ-5,24 stigmastadienol, brassicasterol, clerosterol+Δ-5-23 stigmastadienol, Δ-7 avenasterol, eritrodiol and Δ-7 stigmasterol were present in the black sesame extract. Overall extraction curves from the supercritical fluid extraction (SFE) in lower and higher global yields (200 and 400bar at 60°C) fitted the Tan and Liou, Goto et al. and Sovová models. These models presented the best residual sum of squares values. Pilot experiments suggest that black sesame extract is neuroprotective following endothelin-1-induced focal ischemia into the motor cortex of adult male rat, observing a decrease in leukocyte infiltration in the group treated with SFE of black sesame seeds when compared with control group.

Practical demonstration of the CIEDE2000 corrections to CIELAB using a small set of sample pairs

A set of 10 color pairs was proposed and produced in 2002 to show the advantages of the CIEDE2000 color‐difference formula with respect to CIELAB. These 10 color pairs illustrated each of the five corrections to CIELAB proposed by CIEDE2000. The 10 color pairs were visually assessed, under reference conditions close to those proposed by CIEDE2000, by two groups of 31 and 21 inexperienced observers, using two different gray scales. Average visual results in these experiments fitted CIEDE2000 predictions much better than CIELAB, as shown by a decrease of Standardized Residual Sum of Squares values of about 20 units. Current visual results showed only the improvement of CIEDE2000 upon CIELAB in predictions of perceived color differences, but they are not recommended for testing new advanced color‐difference formulas. © 2012 Wiley Periodicals, Inc. Col Res Appl, 38, 429–436, 2013.

An Efficient Unified K-Means Clustering Technique for Microarray Gene Expression Data

Problem statement: Using microarray techniques one could monitor the expressions levels of thousands of genes simultaneously. One challenge was how to derive meaningful insights into expressed data. This might be carried out by clustering techniques such as hierarchical and k-means, but most of the clustering techniques were largely heuristic in nature and are associated with some unresolved issues like how to fix the precise number of clusters and how to visualize the results in a pictorial form. Approach: Determine accurate number of clusters from gene expression data and validate the results using correctness ratio and sum of squares criteria. A new approach suggested to addresses the primary issue of k-means clustering algorithm that predefining number of clusters. This approach provides accurate number of clusters by minimizing the squared error function and maximizing the correctness ratio value. Results: The experimental results have shown the efficiency of our method by calculating and comparing the sum of squares with different k values. It was concluded that the number of clusters were accurate with minimum sum of squares value and maximum value of correctness ratio. Conclusion: The results showed that the quality of clusters and performance of this new approach is improved.

DRYING OF EGGPLANT SLICES IN THIN LAYERS AT DIFFERENT AIR TEMPERATURES

ABSTRACT The effect of water-blanching treatment and air temperature on drying kinetics of eggplant slices were investigated at air temperatures (50, 60, 70 and 80C). Both the blanching and air temperature influenced the drying time of eggplant slices. Moisture ratios were fitted to 11 different mathematical models using nonlinear regression analysis. The regression results showed that the logarithmic, Wang and Singh, and Midilli et al. models satisfactorily described the drying behavior of eggplant slices with highest R2 value and lowest χ2, root mean square error and residual sum of squares values. The effective moisture diffusivity increases as temperature increases and range between 5.575 and 9.745 × 10-10 m2/s for unblanched samples, and between 5.851 and 11.077 × 10-10 m2/s for blanched samples. The activation energy values of unblanched and blanched samples were estimated to be 18.27 and 20.76 kJ/mol, respectively. PRACTICAL APPLICATIONS In this study, a laboratory convective hot-air dryer was used for the thin-layer drying of blanched/unblanched eggplant slices and experimental moisture ratio was compared with 11 thin-layer drying models. The blanching treatment followed by hot-air drying may provide a practical method for the preservation of eggplant and the production of dried eggplant slices. The dried product is a valuable ingredient in the preparation of soups, premixed foods, etc.

The chemical rank estimation for excitation-emission matrix fluorescence data by region-based moving window subspace projection technique and Monte Carlo simulation

A novel method, region-based on moving window subspace projection technique (RMWSPT) coupled with Monte Carlo simulation, was developed for the chemical rank estimation of excitation-emission matrix (EEM) fluorescence data arrays. RMWSPT determines the chemical rank by performing singular value decomposition (SVD) on the unfolded matrices of original data array and the subarrays yielded by a moving window, and through employing the subspace projection technique on the difference between the corresponding sub-bands of the significant eigenvectors and those of subarrays. Compared with the traditional methods, it utilizes the information from eigenvectors combined with the projection residual sum of squares values to estimate the rank of the EEM data arrays instead of using the eigenvalues. Two simulated and two real EEM data arrays were analyzed to demonstrate the excellent performance of the RMWSPT. Moreover, its performance was compared with that of other three factor-determining methods, i.e., factor indicator function (IND), the core consistency diagnostic (CORCONDIA) test and two-mode subspace comparison (TMSC) approaches. The results showed that the newly proposed method can accurately and quickly determine the chemical rank to fit the trilinear model, and it can deal with more complex situations in the presence of severe collinearity and trace concentration. The RMWSPT method thus lights a new avenue to determine the chemical rank of EEM data arrays and may hold great potential to be extended as a promising alternative for the chemical rank estimation.

Modeling of biomass production by Spirulinaplatensis as function of phosphate concentrations and pH regimes

Batch cultivations were performed to evaluate the influence of phosphate concentrations (0.25, 0.5, 0.75, and 1.0 g L −1) for pH regimes (9.5, 10.0, and 10.5) on the biomass production by Spirulina platensis. The best condition for cell growth (3.099 g L −1) was found at 0.5 g L −1 phosphate and pH value of 10.0. Cultivation time, phosphate, and pH caused to increase significantly ( p < 0.01) in biomass production by S. platensis. Lag time was observed up to 4 h. After then, biomass production increased sharply ( p < 0.01) from 0.020 g L −1 to 2.063, 2.213, 1.532, and 0.797 g L −1 at 0.25, 0.5, 0.75, and 1.0 g L −1 phosphate values, respectively. Modified Gompertz model could be regarded as sufficient to describe the biomass production by S. platensis with high determination coefficients and low sum of square value indicated that. Biological parameters for biomass production were successfully predicted by modified Gompertz model.

Application of Quartz Crystal Nanobalance for Simultaneous Determination of Vanillylmandelic and Homovanillic Acids by a Net Analyte Signal-Based Method

Homovanillic acid (HVA) and vanillylmandelic acid (VMA) were selectively determined by quartz crystal nanobalance sensor in conjunction with net analyte signal (NAS)-based method called HLA/GO. An orthogonal design was applied for the formation of calibration and prediction sets including HVA, VMA, and some common and structurally similar urine compounds. The selection of the optimal time range involved the calculation of the NAS regression plot in any considered time window for each test sample. The searching of a region with maximum linearity of NAS regression plot (minimum error indicator) and minimum of predicted error sum of squares value was carried out by applying a moving window strategy. Based on the obtained results, the differences on the adsorption profiles in the time range between 1 and 300 s were used to determine mixtures of compounds by HLA/GO method. Several figures of merit like selectivity, sensitivity, analytical sensitivity, and limit of detection were calculated for both compounds. The results showed that the method was successfully applied for the determination of VMA and HVA.

Experimental and QSAR of Acetophenones as Antibacterial Agents

Antibacterial activity of 20 acetophenone derivatives was evaluated against two Gram-positive and three Gram-negative organisms, namely, Bacillus subtilis NCIM 2718, Staphylococcus aureus NCIM5021, Salmonella typhi NCIM2501, Enterobacter aerogenes NCIM5139, and Proteus vulgaris NCIM2813 by two-fold dilution method. The most active amongst this group of compounds were 4-methyl, 2-hydroxy, 3-bromo, 4-ethoxy, 3-nitro and 4-nitro acetophenones. Quantitative structure-activity relationships were developed by dividing the data into training and validation sets, the former was used to develop and the latter was used to test the models. Spatial, electronic and topological descriptors were predominantly found to influence the activity. The statistical measures such as r( 2) (0.76-0.91), cross-validated r( 2) (0.56-0.85), F-ratio and predicted residual sum of square values were found to be in the acceptable range. The developed models were able to predict the activity of the validation data set within the 99% confidence limit (except for two data points). 4-Nitroacetophenone was found to be the most slimicidal in nature. Bacterial Adhesion to Hydrocarbons (BATH) assay indicated that Staphylococcus aureus NCIM5021 had the most hydrophobic cell surface of these five organisms. Cell surface hydrophobicity of organisms also had an impact on the antibacterial activity of the acetophenones.

A GENERAL METHOD FOR ESTIMATION OF BOUNDARY CONDITIONS OVER THE SURFACE OF SHIELDS SURROUNDED BY RADIATING ENCLOSURES

An optimization analysis is employed to estimate the unknown boundary conditions over the surface of enclosures and shields in radiation equilibrium from the knowledge of the boundary condition over the surface of an enclosure surrounding them. The discrete transfer method is employed to solve the radiative transfer equation. The conjugate gradient method is used for minimization of a convenient objective function, which is represented by the sum of square values of net heat flux through the shields. The performance of the present technique is evaluated by several numerical experiments on two- and three-dimensional enclosure shield systems.

Evaluating dissolution profiles of an anti-HIV agent using ANOVA and non-linear regression models in JMP software

A powerful statistical method was designed using JMP software to detect factors contributing to differences in the dissolution process of an antiviral drug delivered in an oral dosage form. Due to the large number of dissolution media available for solid dosage forms, a statistical method to choose the appropriate medium is critical for testing solid dosage forms. We have developed an analysis of variance model to analyze the overall dissolution profile obtained from the various media. In vitro tests were performed using a standard USP basket apparatus (Vankel Inc., Cary, NC), and the analysis used the restricted/residual maximum likelihood method (JMP software) to partition the variance due to media (pH 1.2 and 6.8, +SDS, water alone and at pH 1.2 with pepsin), time (repeated measure) and capsule (random effect). This allowed correct standard error estimates to be used to compare dissolution in different media using planned linear contrasts. The model provided us with statistically powerful criteria to identify significant differences in capsule dissolution across time and to quantify capsule-to-capsule population variance estimate. The time specific linear contrasts showed the largest sum of square values (SS) occurred at 180 min (SS=0.268) for the simulated SIF (pH 6.8) versus SGF (pH 1.2) comparison (DF=166, MSE=3.92×10 −3). The dissolution processes were further characterized using a non-linear regression fit of a power law function to the data for each capsule. This resulted in a method to statistically differentiate between the dissolution processes of the capsules in different media.

Perceptual cue weighting of voiceless stop consonants as represented by mismatch negativity and P300

Changes in high-frequency content form the basis of differentiating between the perception of voiceless stop consonants, /p/ and /t/. Behavioral studies show that two cues, the formant transition onset frequency and the relative amplitude of the burst component of the stop consonant, contribute to the perception of these consonants, and that the weight of these cues differs for normal-hearing versus hearing-impaired individuals. Our goal in the current study was to obtain a measure of cue weighting electrophysiologically in twelve normal-hearing adults and compare the results with those previously reported in behavioral studies. Two physiological indices of perceptual discrimination of acoustical changes, the attention-independent mismatch negativity (MMN) and the attention-dependent P300, were measured by varying each cue independently and in combination. This resulted in three MMN and three P300 responses per subject in response to (a) changing the formant transition cue with a constant, neutral relative amplitude, (b) changing the relative amplitude cue with a constant, neutral formant transition cue, and (c) changing both cues. Measures from individual and group mean waveforms will be used to determine cue weighting based on sum of square values derived from multivariate analysis of variance. Results will be discussed relative to behavioral perception and attention.

NON-LINEAR LEAST SQUARE CURVE FITTING OF COPOLYMERIZATION MODELS TO THE ALTERNATING TRIAD FRACTION OF COPOLYMERS OF STYRENE AND CITRACONIC ANHYDRIDE, AND COPOLYMERS OF STYRENE AND MALEIC ANHYDRIDE PREPARED IN N,N-DIMETHYLFORMAMIDE

Copolymers of styrene (ST) and citraconic anhydride (α-methylmaleic anhydride) (CA) were prepared in a very polar solvent, N,N-dimethylformamide (DMF), at 50.0°C with AIBN. The monomer unit triad fractions were determined by 13C NMR in acetone-d 6 solution. Non linear least square (NLLS) curve fitting was performed for the copolymerization models of the terminal model, the penultimate unit effect model, the complex participation model, the complex dissociation model, and the so-called comppen model. The theoretical equations for the ST-centered alternating triad mole fraction were fitted by NLLS minimization routine to the triad fraction data of the ST-CA copolymers and that of the ST-maleic anhydride (MA) copolymers prepared in identical polymerization conditions. It was found that for rigidly alternating copolymers of ST-MA, the difference among the copolymerization models disappeared and all models merged together. The difference among the copolymerization models were somewhat more apparent for less alternating copolymers of ST-CA copolymers. The sum of squares values indicated that the copolymerization models, which involved some complex participation, fit the data better with the comppen model. This was a combination of a complex participation and penultimate unit effects, which performed best.

The effect of the number of meaningful experimental data on the fitness of the theoretical copolymerisation models

Fifteen copolymers of maleic anhydride (MA or 0) and styrene (ST or 1) were prepared in a wide range of MA mole fraction in feed of f0=0.01–0.90. ST (1) centred triad mole fractions (F010, F(011+110), F111) were determined from quaternary 13C NMR spectra of aromatic “next to chain” carbon of ST units. Non-linear least squares (NLLS) curve fitting was used to fit the theoretical equations of the (1) terminal-, (2) penultimate unit effect-, (3) complex participation-, (4) complex dissociation- and (5) comppen-model to the experimental data of the triad mole fractions and the copolymer composition (Scheme. 1 )>. The sum of squares (SS) and the reactivity ratios were calculated from these fitting processes. The smallest SS value of F010 data, the test functions a and b and the “order grade matrix” consistently show that the (3) complex participation model is the most applicable model; while the (2) penultimate model is closely indicated for this copolymerisation. The (5) comppen model, unexpectedly, is the third best fit model. It can be explained by the small number of the meaningful experimental data (which is 10 for copolymer samples of f0=0.01–0.40) compared to the number of variable parameters (p) of the comppen model (which is seven). It is suggested when the number of the meaningful experimental data (i.e. the triad fractions vary widely from 0 to 1) is much greater than the number of variable parameters (p) of the comppen model, the comppen model will be proved by the SS value to be the best fitted model in describing this MA–ST copolymerisation.

Theoretical study of the copolymerization of styrene and maleic anhydride prepared in carbon tetrachloride and inN,N-dimethylformamide

Styrene (ST or 1) and maleic anhydride (MA or 0) were copolymerized in carbon tetrachloride (CCl4) and in N,N-dimethylformamide (DMF) with a wide range of MA mole fraction in the feed (f0 = 0.01 to 0.90) at 50°C. The DEPT 13C NMR subspectra of methylene carbon of ST(1) units were used to determine the ST(1) centered triad mole fractions (F010, F(011 + 110), F111). Non-linear least squares (NLLS) curve fitting was used to fit the theoretical equations of the five copolymerization models, namely, the (1) terminal, (2) penultimate unit effect, (3) complex participation, (4) complex dissociation and (5) comppen models, to these experimental data in order to calculate the sum of squares (SS) and the reactivity ratios. The complex participation model is indicated as the model providing the best fit by the smallest SS values calculated from F010 data and by the variation pattern of the test functions α and β for both copolymerization systems. The F test for SS of F010 data can only show an improvement of fit of the complex participation model over the penultimate unit effect model with less than 90% probability confidence for the MA + ST/CCl4 system and with 97.5% probability confidence for the MA+ ST/DMF system. This is consistent with the result obtained from the “order grade matrix” method reported previously.

Theoretical study of the copolymerization of styrene and maleic anhydride prepared in carbon tetrachloride and in N,N-dimethylformamide

Styrene (ST or 1) and maleic anhydride (MA or 0) were copolymerized in carbon tetrachloride (CCl4) and in N,N-dimethylformamide (DMF) with a wide range of MA mole fraction in the feed (f0 = 0.01 to 0.90) at 50°C. The DEPT 13C NMR subspectra of methylene carbon of ST(1) units were used to determine the ST(1) centered triad mole fractions (F010, F(011 + 110), F111). Non-linear least squares (NLLS) curve fitting was used to fit the theoretical equations of the five copolymerization models, namely, the (1) terminal, (2) penultimate unit effect, (3) complex participation, (4) complex dissociation and (5) comppen models, to these experimental data in order to calculate the sum of squares (SS) and the reactivity ratios. The complex participation model is indicated as the model providing the best fit by the smallest SS values calculated from F010 data and by the variation pattern of the test functions α and β for both copolymerization systems. The F test for SS of F010 data can only show an improvement of fit of the complex participation model over the penultimate unit effect model with less than 90% probability confidence for the MA + ST/CCl4 system and with 97.5% probability confidence for the MA+ ST/DMF system. This is consistent with the result obtained from the “order grade matrix” method reported previously.

Experimental design for the identification of macrokinetic models and model discrimination

An experimental design method for the identification of macrokinetic models was developed applying an extended D-optimal design criterion. The D-optimal design criterion was modified to consider variable measurement variances as well as multivariate macrokinetic models. The macrokinetics of formate dehydrogenase (FDH) production with Candida boidinii were thus identified within 10 steady state experiments in a labscale continuous stirred tank reactor (10 model parameters). Closed loop control (nutristat) was applied to set-up the operating states suggested by this experimental design method. After each set of steady state experiments the quality of macrokinetic parameters was characterized statistically. For model discrimination a parameter discrimination algorithm based on entropy formulations was adapted. Again a multivariate criterion considering variable measurement variances was developed. This discrimination algorithm was applied to discriminate the macrokinetic model of FDH production with Candida boidinii out of 10 different macrokinetic approaches. An unequivocal discrimination result could be obtained calculating model specific probabilities. These were compared with commonly used sum of squares values. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 564-576, 1997.

Classification of human gait with acceleration waveforms

We have attempted to classify the acceleration signal in walking both level and up and downstairs using wavelet analysis. The acceleration signal close to the body's center of gravity was measured while the subjects walked in a corridor and up and down a stairway in their own shoes. The data for four steps were analyzed and Daubecies 3 wavelet transform was applied to sequential data. The discriminate variables were the waveformsre lated to leve1-4and-5. The sum of square values at each step was compared at level-4 and -5. Downward walking could be discriminated from other types of walking showing the largest value for the level -5 calculation. Then level walking was compared with upstairs walking for level -4 calculation. It was possible to discriminate the continuous dynamic responses of walking by wavelet transform.

ミニコンによる非線形最小二乗あてはめ計算の一改良案

Non-linear least square method has become an indispensable procedure for the analysis of pharmacokinetic data. This method, however, occasionally gives much bigger sum of square value to make the computation chaotic. To overcome this difficulty, various procedures have been devised. In this connection, after deliberation of characteristic features of normal equation and its coefficient matrix, "temporal discard" procedure was designed. When failed to give smaller sum of square value, the row and the column of the coefficient matrix which includes the biggest or the smallest element on the principal diagonal are discarded. The search for the least square parameters is continued with smaller normal matrix thus obtained. Preliminary test calculation gave satisfactory results.

Analysis of deoxyribonucleic acid histograms from flow cytofluorometry. Estimation of the distribution of cells within S phase.

Further investigation of a previously described method for the mathematical analysis of deoxyribonucleic acid histograms was undertaken in an attempt to determine whether the large fluctuations in the computed percentages of cells in adjacent S phase compartments, which we have frequently observed, were real or artifactual. Using both real and simulated data, it was found that the observed fluctuation is due primarily to the program’s attempt to fit even small random error in the data points. Using “perfect” simulated data, fluctuation between adjacent compartment sizes is negligible. The introduction of even a small amount of error (<1%), however, results in large fluctuations when the program is allowed to achieve a minimal sum of squares value. If the computation is terminated earlier, fluctuation is considerably reduced, although the total estimated percentage of cells in S phase is usually unchanged. The fluctuation can also be greatly reduced by specifying fewer S phase compartments, corresponding to fewer unknown parameters to be evaluated. On the other hand, if the number of S phase compartments is too few, an adequate fit to the data cannot be achieved. The optimal number of S phase compartments was found to be related to the observed coefficient of variation of fluorescence intensity. In general, the smaller the coefficient of variation, the greater the number of S phase compartments that must be specified in order to achieve an acceptable fit to the deoxyribonucleic acid histograms while avoiding anomalous fluctuation in the function representing the distribution of cells within S. The method is illustrated with an example of a synchronous cell population lacking distinct G, and G2+M peaks.