Search results for: linear correlation

Authors: Okolie Chukwulozie Paul, Iwenofu Chinwe Onyedika, Sinebe Jude Ebieladoh, M. C. Nwosu

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The research work is based on the statistical analysis of the processing data. The essence is to analyze the data statistically and to generate a design model for the production mix of soap manufacturing products in Bejoy manufacturing company Nkpologwu, Aguata Local Government Area, Anambra state, Nigeria. The statistical analysis shows the statistical analysis and the correlation of the data. T test, Partial correlation and bi-variate correlation were used to understand what the data portrays. The design model developed was used to model the data production yield and the correlation of the variables show that the R2 is 98.7%. However, the results confirm that the data is fit for further analysis and modeling. This was proved by the correlation and the R-squared.

Keywords: General Linear Model, correlation, variables, pearson, significance, T-test, soap, production mix and statistic

Procedia PDF Downloads 443

Authors: S. Zenia, A. Menasseria, A. E. Kheidous, F. Lariouna, A. Smai, H. Saadi, F. Haddadj, A. Milla, F. Marniche

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The objective of this study was to estimate the correlation ship between different pheasant external egg quality traits. A total of 938 eggs were collected. Egg weight (g), egg length (mm), egg width (mm), volume (cm3), shape index egg, surface area and water loss were measured. The overall mean values obtained for the different variables are respectively 29.2 ± 2,24, 43.01 ± 1,84, 34.05 ± 1,44, 25.63 ± 2.88 cm3, 79.00 ± 3%, 68% and 13%. Concerning studied regressions, it was considered only the most important regressions. Those that show significant links between the different parameters studied. The ANOVA procedure was applied to estimate correlations for the examined traits. The weights of the eggs being observed before incubation and before hatching are linearly correlated with a positive correlation coefficient of order 0.75. Egg length and the weight before incubation had a good and positive correlation with a coefficient r = 0.6. However, density had high and negative correlations with egg height r = -0.78. Shape index had a good linear and negative r= - 0.71 correlation with water loss.

Keywords: correlation, egg, morphometry of eggs, analysis of variance

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Authors: John Eric C. Bargas, Maria Cecilia M. Marcos

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One of the most common ground improvement techniques is Deep Soil Mixing (DSM). As the technique progresses, there is still lack in the development when it comes to depth control. This was the issue experienced during the installation of DSM in one of the National projects in the Philippines. This study assesses the feasibility of using equipment drilling parameters such as hydraulic pressure, drilling speed and rotational speed in determining the Standard Penetration Test N-value of a specific soil. Hydraulic pressure and drilling speed with a constant rotational speed of 30 rpm have a positive correlation with SPT N-value for cohesive soil and sand. A linear trend was observed for cohesive soil. The correlation of SPT N-value and hydraulic pressure yielded a R²=0.5377 while the correlation of SPT N-value and drilling speed has a R²=0.6355. While the best fitted model for sand is polynomial trend. The correlation of SPT N-value and hydraulic pressure yielded a R²=0.7088 while the correlation of SPT N-value and drilling speed has a R²=0.4354. The low correlation may be attributed to the behavior of sand when the auger penetrates. Sand tends to follow the rotation of the auger rather than resisting which was observed for very loose to medium dense sand. Specific Energy and the product of hydraulic pressure and drilling speed yielded same R² with a positive correlation. Linear trend was observed for cohesive soil while polynomial trend for sand. Cohesive soil yielded a R²=0.7320 which has a strong relationship. Sand also yielded a strong relationship having a coefficient of determination, R²=0.7203. It is feasible to use hydraulic pressure and drilling speed to estimate the SPT N-value of the soil. Also, the product of hydraulic pressure and drilling speed can be a substitute to specific energy when estimating the SPT N-value of a soil. However, additional considerations are necessary to account for other influencing factors like ground water and physical and mechanical properties of soil.

Keywords: ground improvement, equipment drilling parameters, standard penetration test, deep soil mixing

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Authors: Roger L. Goodwin

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This paper presents a rank correlation curve. The traditional correlation coefficient is valid for both continuous variables and for integer variables using rank statistics. Since the correlation coefficient has already been established in rank statistics by Spearman, such a calculation can be extended to the correlation curve. This paper presents two survey questions. The survey collected non-continuous variables. We will show weak to moderate correlation. Obviously, one question has a negative effect on the other. A review of the qualitative literature can answer which question and why. The rank correlation curve shows which collection of responses has a positive slope and which collection of responses has a negative slope. Such information is unavailable from the flat, "first-glance" correlation statistics.

Keywords: Bayesian estimation, regression model, rank statistics, correlation, correlation curve

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: Khodzhaberdi Allaberdiev

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Substituted phenols are widely used for the synthesis of advanced polycondensation polymers. In terms of the structure regularity and practical value of obtained polymers are of special interest the p-substituted phenols. The lanthanide induced shifts (LIS) of the aromatic ring and the OH protons by addition Eu(fod)3 to various p-substituted phenols in CDCL3 solvent were measured Nuclear Magnetic Resonance spectroscopy. A linear relationship has been observed between the LIS of protons (∆=δcomplex –δsubstrate) and Eu(fod)3/substrate molar ratios. The LIS protons of the investigated phenols decreases in the following order: ОН > ortho > meta. The LIS of these protons also depends on both steric and electronic effects of p-substituents. The effect on the LIS of protons steric hindrance of substituents by way of example p-substituted alkyl phenols was studied. Alkyl phenols exhibit pronounced europium- induced shifts, their sensitivity increasing in the order: CH3 > C2H5 > sym-C5H11 > tert-C5H11 > tert-C4H9, i.e. in parallel with decreasing steric hindrance. The influence steric hindrance p-substituents of phenols on the LIS of protons in sequence following decreases: OH> meta >ortho. Contrary to the expectations, it is found that the LIS of the ortho protons an excellent linear correlation with meta-substituent constants, σm for 14 p-substituted phenols: ∆H2, 6=8.165-9.896 σm (r2=0,999). Moreover, a linear correlation between the LIS of the ortho protons and ionization constants, РКa of p-substituted phenols has been revealed. Similarly, the linear relationships for the LIS of the meta and the OH protons were obtained. Use the LIS of the phenolic hydroxyl groups for linear relationships is necessary with care, because of the signal broadening of the OH protons. New constants may be determinate with unusual case by this approach.

Keywords: novel correlations, NMR spectroscopy, phenols, shift reagent

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Authors: Wael M Albadri, Hassnen M Jafer, Ehab H Sfoog

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Relationship between undrained shear strength (Su) and over consolidation ratio (OCR) of clay soil (marine clay) is very important in the field of geotechnical engineering to estimate the settlement behaviour of clay and to prepare a small scale physical modelling test. In this study, a relationship between shear strength and OCR parameters was determined using the laboratory vane shear apparatus and the fully automatic consolidated apparatus. The main objective was to establish non-linear correlation formula between shear strength and OCR and comparing it with previous studies. Therefore, in order to achieve this objective, three points were chosen to obtain 18 undisturbed samples which were collected with an increasing depth of 1.0 m to 3.5 m each 0.5 m. Clay samples were prepared under undrained condition for both tests. It was found that the OCR and shear strength are inversely proportional at similar depth and at same undrained conditions. However, a good correlation was obtained from the relationships where the R2 values were very close to 1.0 using polynomial equations. The comparison between the experimental result and previous equation from other researchers produced a non-linear correlation which has a similar pattern with this study.

Keywords: shear strength, over-consolidation ratio, vane shear test, clayey soil

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Authors: Skezeer John B. Paz, Ederlina G. Nocon

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Finding an optimal binary linear code is a central problem in coding theory. A binary linear code C = [n, k, d] is called optimal if there is no linear code with higher minimum distance d given the length n and the dimension k. There are bounds giving limits for the minimum distance d of a linear code of fixed length n and dimension k. The lower bound which can be taken by construction process tells that there is a known linear code having this minimum distance. The upper bound is given by theoretic results such as Griesmer bound. One way to find an optimal binary linear code is to make the lower bound of d equal to its higher bound. That is, to construct a binary linear code which achieves the highest possible value of its minimum distance d, given n and k. Some optimal binary linear codes were presented by Andries Brouwer in his published table on bounds of the minimum distance d of binary linear codes for 1 ≤ n ≤ 256 and k ≤ n. This was further improved by Markus Grassl by giving a detailed construction process for each code exhibiting the lower bound. In this paper, we construct new optimal binary linear codes by using some construction processes on existing binary linear codes. Particularly, we developed an algorithm applied to the codes already constructed to extend the list of optimal binary linear codes up to 257 ≤ n ≤ 300 for k ≤ 7.

Keywords: bounds of linear codes, Griesmer bound, construction of linear codes, optimal binary linear codes

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Authors: Mehrnaz Alibeikloo, Hadi Khabbaz, Behzad Fatahi

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Probabilistic analysis has become one of the most popular methods to quantify and manage geotechnical risks due to the spatial variability of soil input parameters. The correlation length is one of the key factors of quantifying spatial variability of soil parameters which is defined as a distance within which the random variables are correlated strongly. This paper aims to assess the impact of correlation length on the long-term settlement of soft soils improved with preloading. The concept of 'worst-case' spatial correlation length was evaluated by determining the probability of failure of a real case study of Vasby test fill. For this purpose, a finite difference code was developed based on axisymmetric consolidation equations incorporating the non-linear elastic visco-plastic model and the Karhunen-Loeve expansion method. The results show that correlation length has a significant impact on the post-construction settlement of soft soils in a way that by increasing correlation length, probability of failure increases and the approach to asymptote.

Keywords: Karhunen-Loeve expansion, probability of failure, soft soil settlement, 'worst case' spatial correlation length

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Authors: S. Zhang, L. Zhang, X. Chen

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Due to the large uncertainty on the mechanical properties of FRP (fibre reinforced plastic), the reliability evaluation of FRP structures are currently receiving much attention in industry. However, possible statistical correlation between ply mechanical properties has been so far overlooked, and they are mostly assumed to be independent random variables. In this study, the statistical correlation between ply mechanical properties of uni-directional and plain weave composite is firstly analyzed by a combination of Monte-Carlo simulation and finite element modeling of the FRP unit cell. Large linear correlation coefficients between the in-plane mechanical properties are observed, and the correlation coefficients are heavily dependent on the uncertainty of the fibre volume ratio. It is also observed that the correlation coefficients related to Poisson’s ratio are negative while others are positive. To experimentally achieve the statistical correlation coefficients between in-plane mechanical properties of FRP, all concerned in-plane mechanical properties of the same specimen needs to be known. In-plane shear modulus of FRP is experimentally derived by the approach suggested in the ASTM standard D5379M. Tensile tests are conducted using the same specimens used for the shear test, and due to non-uniform tensile deformation a modification factor is derived by a finite element modeling. Digital image correlation is adopted to characterize the specimen non-uniform deformation. The preliminary experimental results show a good agreement with the numerical analysis on the statistical correlation. Then, failure probability of laminate plates is calculated in cases considering and not considering the statistical correlation, using the Monte-Carlo and Markov Chain Monte-Carlo methods, respectively. The results highlight the importance of accounting for the statistical correlation between ply mechanical properties to achieve accurate failure probability of laminate plates. Furthermore, it is found that for the multi-layer laminate plate, the statistical correlation between the ply elastic properties significantly affects the laminate reliability while the effect of statistical correlation between the ply strength is minimal.

Keywords: failure probability, FRP, reliability, statistical correlation

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Authors: Nureni O. Adeboye, Dawud A. Agunbiade

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This research attempts to investigate the effects of heteroscedasticity and periodicity in a Panel Data Regression Model (PDRM) by extending previous works on balanced panel data estimation within the context of fitting PDRM for Banks audit fee. The estimation of such model was achieved through the derivation of Joint Lagrange Multiplier (LM) test for homoscedasticity and zero-serial correlation, a conditional LM test for zero serial correlation given heteroscedasticity of varying degrees as well as conditional LM test for homoscedasticity given first order positive serial correlation via a two-way error component model. Monte Carlo simulations were carried out for 81 different variations, of which its design assumed a uniform distribution under a linear heteroscedasticity function. Each of the variation was iterated 1000 times and the assessment of the three estimators considered are based on Variance, Absolute bias (ABIAS), Mean square error (MSE) and the Root Mean Square (RMSE) of parameters estimates. Eighteen different models at different specified conditions were fitted, and the best-fitted model is that of within estimator when heteroscedasticity is severe at either zero or positive serial correlation value. LM test results showed that the tests have good size and power as all the three tests are significant at 5% for the specified linear form of heteroscedasticity function which established the facts that Banks operations are severely heteroscedastic in nature with little or no periodicity effects.

Keywords: audit fee lagrange multiplier test, heteroscedasticity, lagrange multiplier test, Monte-Carlo scheme, periodicity

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Authors: Manal Azzidani

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This research consideres the extension of special functions called Positive Linear Operators. the bounded linear operator which defined from normed space to Banach space will extend to the closure of the its domain, And extend identified linear functional on a vector subspace by Hana-Banach theorem which could be generalized to the positive linear operators.

Keywords: extension, positive operator, Riesz space, sublinear function

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Authors: Dhanashree Aole, V. Hariharan, Swati Surushe

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Corrosion can cause serious and expensive damage to the automobile components. Various proven techniques for controlling and preventing corrosion depend on the specific material to be protected. Electrochemical Impedance Spectroscopy (EIS) and salt spray tests are commonly used to assess the corrosion degradation mechanism of coatings on metallic surfaces. While, the only test which monitors the corrosion rate in real time is known as Linear Polarisation Resistance (LPR). In this study, electrochemical tests (EIS & LPR) and spray test are reviewed to assess the corrosion resistance and durability of different coatings. The main objective of this study is to correlate the test results obtained using linear polarization resistance (LPR) and Electrochemical Impedance Spectroscopy (EIS) with the results obtained using standard salt spray test. Another objective of this work is to evaluate the performance of various coating systems- CED, Epoxy, Powder coating, Autophoretic, and Zn-trivalent coating for vehicle underbody application. The corrosion resistance coating are assessed. From this study, a promising correlation between different corrosion testing techniques is noted. The most profound observation is that electrochemical tests gives quick estimation of corrosion resistance and can detect the degradation of coatings well before visible signs of damage appear. Furthermore, the corrosion resistances and salt spray life of the coatings investigated were found to be according to the order as follows- CED> powder coating > Autophoretic > epoxy coating > Zn- Trivalent plating.

Keywords: Linear Polarization Resistance (LPR), Electrochemical Impedance Spectroscopy (EIS), salt spray test, sacrificial and barrier coatings

Procedia PDF Downloads 525

Authors: Pawasuth Saengdee, Chamras Promptmas, Ting Zeng, Silke Leimkühler, Ulla Wollenberger

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Sulfite has been used as a versatile preservative to limit the microbial growth and to control the taste in some food and beverage. However, it has been reported to cause a wide spectrum of severe adverse reactions. Therefore, it is important to determine the amount of sulfite in food and beverage to ensure consumer safety. An efficient electrocatalytic biosensor for sulfite detection was developed by immobilizing of human sulfite oxidase (hSO) on 3-aminoproplytriethoxysilane (APTES) modified indium tin oxide (ITO) electrode. Cyclic voltammetry was employed to investigate the electrochemical characteristics of the hSO modified ITO electrode for various pretreatment and binding conditions. Amperometry was also utilized to demonstrate the current responses of the sulfite sensor toward sodium sulfite in an aqueous solution at a potential of 0 V (vs. Ag/AgCl 1 M KCl). The proposed sulfite sensor has a linear range between 0.5 to 2 mM with a correlation coefficient 0.972. Then, the additional polymer layer of PVA was introduced to extend the linear range of sulfite sensor and protect the enzyme. The linear range of sulfite sensor with 5% coverage increases from 2.8 to 20 mM at a correlation coefficient of 0.983. In addition, the stability of sulfite sensor with 5% PVA coverage increases until 14 days when kept in 0.5 mM Tris-buffer, pH 7.0 at 4 8C. Therefore, this sensor could be applied for the detection of sulfite in the real sample, especially in food and beverage.

Keywords: sulfite oxidase, bioelectrocatalytsis, indium tin oxide, direct electrochemistry, sulfite sensor

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Authors: Wei Yang, Xiaohui Cui, Weiping Zhu, Liqun Liu

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The rapid development of the Confucius Institute is attracting more and more attention from mainstream media around the world. Mainstream media plays a large role in public information dissemination and public opinion. This study presents efforts to analyze the correlation and functional relationship between domestic and foreign mainstream media by analyzing the amount of reports on the Confucius Institute. Three kinds of correlation calculation methods, the Pearson correlation coefficient (PCC), the Spearman correlation coefficient (SCC), and the Kendall rank correlation coefficient (KCC), were applied to analyze the correlations among mainstream media from three regions: mainland of China; Hong Kong and Macao (the two special administration regions of China denoted as SARs); and overseas countries excluding China, such as the United States, England, and Canada. Further, the paper measures the functional relationships among the regions using a regression model. The experimental analyses found high correlations among mainstream media from the different regions. Additionally, we found that there is a linear relationship between the mainstream media of overseas countries and those of the SARs by analyzing the amount of reports on the Confucius Institute based on a data set obtained by crawling the websites of 106 mainstream media during the years 2004 to 2014.

Keywords: mainstream media, Confucius institute, correlation analysis, regression model

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Authors: Myung Hwan Na, Ho- Chun Song, EunHee Hong

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We widely use normal linear mixed-effects model to analysis data in repeated measurement. In case of detecting heteroscedasticity and the non-normality of the population distribution at the same time, normal linear mixed-effects model can give improper result of analysis. To achieve more robust estimation, we use heavy tailed linear mixed-effects model which gives more exact and reliable analysis conclusion than standard normal linear mixed-effects model.

Keywords: reliability, tires, field data, linear mixed-effects model

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Authors: Fatma Susilawati Mohamad, Azizah Abdul Manaf, Fadhillah Ahmad, Zarina Mohamad, Wan Suryani Wan Awang

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A simple and robust multi-class linear classifier is proposed and implemented. For a pair of classes of the linear boundary, a collection of segments of hyper planes created as perpendicular bisectors of line segments linking centroids of the classes or part of classes. Nearest Neighbor and Linear Discriminant Analysis are compared in the experiments to see the performances of each classifier in discriminating ripeness of oil palm. This paper proposes a multi-class linear classifier using Linear Discriminant Analysis (LDA) for image identification. Result proves that LDA is well capable in separating multi-class features for ripeness identification.

Keywords: multi-class, linear classifier, nearest neighbor, linear discriminant analysis

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Authors: S. H. Nasseri, A. Ebrahimnejad

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Fuzzy set theory has been applied to many fields, such as operations research, control theory, and management sciences. In this paper, we consider two classes of fuzzy linear programming (FLP) problems: Fuzzy number linear programming and linear programming with trapezoidal fuzzy variables problems. We state our recently established results and develop fuzzy primal simplex algorithms for solving these problems. Finally, we give illustrative examples.

Keywords: fuzzy linear programming, fuzzy numbers, duality, sensitivity analysis

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Authors: Hyon I. Paek, Sang Rim Kim, Hyon A. Ryu

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In functional linear regression, one typical problem is to reduce dimension. Compared with multivariate linear regression, functional linear regression is regarded as an infinite-dimensional case, and the main task is to reduce dimensions of functional response and functional predictors. One common approach is to adapt functional principal component analysis (FPCA) on functional predictors and then use a few leading functional principal components (FPC) to predict the functional model. The leading FPCs estimated by the typical FPCA explain a major variation of the functional predictor, but these leading FPCs may not be mostly correlated with the functional response, so they may not be significant in the prediction for response. In this paper, we propose a supervised functional principal component analysis method for a functional response model with FPCs obtained by considering the correlation of the functional response. Our method would have a better prediction accuracy than the typical FPCA method.

Keywords: supervised, functional principal component analysis, functional response, functional linear regression

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Authors: Afsaneh Mohammadnejad, Marianne Nygaard, Jan Baumbach, Shuxia Li, Weilong Li, Jesper Lund, Jacob v. B. Hjelmborg, Lene Christensen, Qihua Tan

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Cognitive impairment in the elderly is a key issue affecting the quality of life. Despite a strong genetic background in cognition, only a limited number of single nucleotide polymorphisms (SNPs) have been found. These explain a small proportion of the genetic component of cognitive function, thus leaving a large proportion unaccounted for. We hypothesize that one reason for this missing heritability is the misspecified modeling in data analysis concerning phenotype distribution as well as the relationship between SNP dosage and the phenotype of interest. In an attempt to overcome these issues, we introduced a model-free method based on the generalized correlation coefficient (GCC) in a genome-wide association study (GWAS) of cognitive function in twin samples and compared its performance with two popular linear regression models. The GCC-based GWAS identified two genome-wide significant (P-value < 5e-8) SNPs; rs2904650 near ZDHHC2 on chromosome 8 and rs111256489 near CD6 on chromosome 11. The kinship model also detected two genome-wide significant SNPs, rs112169253 on chromosome 4 and rs17417920 on chromosome 7, whereas no genome-wide significant SNPs were found by the linear mixed model (LME). Compared to the linear models, more meaningful biological pathways like GABA receptor activation, ion channel transport, neuroactive ligand-receptor interaction, and the renin-angiotensin system were found to be enriched by SNPs from GCC. The GCC model outperformed the linear regression models by identifying more genome-wide significant genetic variants and more meaningful biological pathways related to cognitive function. Moreover, GCC-based GWAS was robust in handling genetically related twin samples, which is an important feature in handling genetic confounding in association studies.

Keywords: cognition, generalized correlation coefficient, GWAS, twins

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Authors: S. Deswal, M. Pal

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The paper aims to compare the performance of vertical and inclined multiple plunging jets and to model and predict their mass transfer capacity by multi-linear regression based approach. The multiple vertical plunging jets have jet impact angle of θ = 90O; whereas, multiple inclined plunging jets have jet impact angle of θ = 600. The results of the study suggests that mass transfer is higher for multiple jets, and inclined multiple plunging jets have up to 1.6 times higher mass transfer than vertical multiple plunging jets under similar conditions. The derived relationship, based on multi-linear regression approach, has successfully predicted the volumetric mass transfer coefficient (KLa) from operational parameters of multiple plunging jets with a correlation coefficient of 0.973, root mean square error of 0.002 and coefficient of determination of 0.946. The results suggests that predicted overall mass transfer coefficient is in good agreement with actual experimental values; thereby suggesting the utility of derived relationship based on multi-linear regression based approach and can be successfully employed in modelling mass transfer by multiple plunging jets.

Keywords: mass transfer, multiple plunging jets, multi-linear regression, earth sciences

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Authors: Arun Kumar Singh, Rupesh M. Das, Shailendra Saini

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The effect of solar cycle and seasons on the total electron content has been investigated over high latitude region during 24th solar cycle (2010-2014). The total electron content data has been observed with the help of Global Ionospheric Scintillation and TEC monitoring (GISTM) system installed at Indian permanent scientific 'Maitri station' [70˚46’00”S 11˚43’56” E]. The dependence of TEC over a solar cycle has been examined by the performing linear regression analysis between the vertical total electron content (VTEC) and daily total sunspot numbers (SSN). It has been found that the season and level of geomagnetic activity has a considerable effect on the VTEC. It is observed that the VTEC and SSN follow better agreement during summer seasons as compared to winter and equinox seasons and extraordinary agreement during minimum phase (during the year 2010) of the solar cycle. There is a significant correlation between VTEC and SSN during quiet days of the years as compared to overall days of the years (2010-2014). Further, saturation effect has been observed during maximum phase (during the year 2014) of the 24th solar cycle. It is also found that Ap index and SSN has a linear correlation (R=0.37) and the most of the geomagnetic activity occurs during the declining phase of the solar cycle.

Keywords: high latitude ionosphere, sunspot number, correlation, vertical total electron content

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Authors: Jan Henrik Wosnitza

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The logistic regression has developed into a standard approach for estimating conditional probabilities in a wide range of applications including credit risk prediction. The article at hand contributes to the current literature on logistic regression fourfold: First, it is demonstrated that the binary logistic regression automatically meets its model assumptions under very general conditions. This result explains, at least in part, the logistic regression's popularity. Second, the requirement of homoscedasticity in the context of binary logistic regression is theoretically substantiated. The variances among the groups of defaulted and non-defaulted obligors have to be the same across the level of the aggregated default indicators in order to achieve linear logits. Third, this article sheds some light on the question why nonlinear logits might be superior to linear logits in case of a small amount of data. Fourth, an innovative methodology for estimating correlations between obligor-specific log-odds is proposed. In order to crystallize the key ideas, this paper focuses on the example of credit risk prediction. However, the results presented in this paper can easily be transferred to any other field of application.

Keywords: correlation, credit risk estimation, default correlation, homoscedasticity, logistic regression, nonlinear logistic regression

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Authors: Nor Zila Abd Hamid, Mohd Salmi M. Noorani

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This study is focused on the development of prediction models of the Ozone concentration time series. Prediction model is built based on chaotic approach. Firstly, the chaotic nature of the time series is detected by means of phase space plot and the Cao method. Then, the prediction model is built and the local linear approximation method is used for the forecasting purposes. Traditional prediction of autoregressive linear model is also built. Moreover, an improvement in local linear approximation method is also performed. Prediction models are applied to the hourly ozone time series observed at the benchmark station in Malaysia. Comparison of all models through the calculation of mean absolute error, root mean squared error and correlation coefficient shows that the one with improved prediction method is the best. Thus, chaotic approach is a good approach to be used to develop a prediction model for the Ozone concentration time series.

Keywords: chaotic approach, phase space, Cao method, local linear approximation method

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Authors: Sadegh Marzban, Mohamad Sobhan Sheikh Andalibi, Farnaz Ghassemi, Farzad Towhidkhah

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Parkinson's disease (PD), which is characterized by the tremor at rest, rigidity, akinesia or bradykinesia and postural instability, affects the quality of life of involved individuals. The concept of a fractal is most often associated with irregular geometric objects that display self-similarity. Fractal dimension (FD) can be used to quantify the complexity and the self-similarity of an object such as tremor. In this work, we are aimed to propose a new method for evaluating hyperkinetic movements such as tremor, by using the FD and other correlated parameters in patients who are suffered from PD. In this study, we used 'the tremor data of Physionet'. The database consists of fourteen participants, diagnosed with PD including six patients with high amplitude tremor and eight patients with low amplitude. We tried to extract features from data, which can distinguish between patients before and after medication. We have selected fractal dimensions, including correlation dimension, box dimension, and information dimension. Lilliefors test has been used for normality test. Paired t-test or Wilcoxon signed rank test were also done to find differences between patients before and after medication, depending on whether the normality is detected or not. In addition, two-way ANOVA was used to investigate the possible association between the therapeutic effects and features extracted from the tremor. Just one of the extracted features showed significant differences between patients before and after medication. According to the results, correlation dimension was significantly different before and after the patient's medication (p=0.009). Also, two-way ANOVA demonstrates significant differences just in medication effect (p=0.033), and no significant differences were found between subject's differences (p=0.34) and interaction (p=0.97). The most striking result emerged from the data is that correlation dimension could quantify medication treatment based on tremor. This study has provided a technique to evaluate a non-linear measure for quantifying medication, nominally the correlation dimension. Furthermore, this study supports the idea that fractal dimension analysis yields additional information compared with conventional spectral measures in the detection of poor prognosis patients.

Keywords: correlation dimension, non-linear measure, Parkinson’s disease, tremor

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Authors: Justice Dadzie, Stacy H. Surman, Ruth K. Annan-Brew, Ifesinachi J. Ezugwu, Evans Addison

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This study aimed to explore the correlation between students' performance in educational statistics and research methods in education, as well as investigate potential differences in performance based on their undergraduate programs. A cross-sectional design was employed, and data was collected from 170 students enrolled in master of philosophy programs in the department of education and psychology. The correlation analysis revealed a strong positive correlation between students' performance in intermediate statistics in education and research methods in education. This indicates a close relationship between the two domains. The MANOVA analysis showed no significant differences in the linear combination of intermediate statistics in education and research methods in education scores across the different undergraduate programs. The tests of between-subjects effects further confirmed that the student's performance in intermediate statistics in education and research methods in education did not differ significantly across the different undergraduate programs. These findings contribute to the existing literature by providing insights into the correlation between educational statistics and research methods, and the influence of undergraduate program backgrounds on students' performance in these domains. The strong positive correlation between intermediate statistics and research methods highlights the importance of a solid foundation in statistics for understanding and applying research methods. Moreover, the consistent relationship across different academic backgrounds emphasizes the need for targeted interventions and support systems to enhance graduate students' competencies in these critical areas.

Keywords: educational statistics, research methods, undergraduate programs, students performance

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Authors: Kaycee Bills

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This study will determine if students with disabilities have higher student loan debt payments than other student populations. The hypothesis was that students with disabilities would have significantly higher student loan debt payments than other students due to the length of time they spend in school. Using the Bachelorette and Beyond Study Wave 2015/017 dataset, quantitative methods were employed. These data analysis methods included linear regression and a correlation matrix. Due to the exploratory nature of the study, the significance levels for the overall model and each variable were set at .05. The correlation matrix demonstrated that students with certain types of disabilities are more likely to fall under higher student loan payment brackets than students without disabilities. These results also varied among the different types of disabilities. The result of the overall linear regression model was statistically significant (p = .04). Despite the overall model being statistically significant, the majority of the significance values for the different types of disabilities were null. However, several other variables had statistically significant results, such as veterans, people of minority races, and people who attended private schools. Implications for how this impacts the economy, capitalism, and financial wellbeing of various students are discussed.

Keywords: disability, student loan debt, higher education, social work

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Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: spectral decomposition, linear RHS, homogeneous linear systems, eigenvalues of the Jacobian

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Authors: Joel Mintz, Kyle Huntley, Waseem Wahood, Samuel Raine, Farzanna Haffizulla

Abstract:

The effect of different state government interventions on COVID-19 health outcomes is currently unknown. Stay at home (SAH) orders, all non-essential business closures and school closures in the Northeastern US were examined. A linear correlation between the peak number of new daily COVID-19 positive tests, hospitalizations and deaths per capita and the elapsed time between government issued guidance and a fixed number of COVID-19 deaths in each state was performed. Earlier government interventions were correlated with lower peak healthcare burden. Statewide closures of schools and non-essential businesses showed significantly greater (p<.001) correlation to peak COVID-19 disease burden as compared to a statewide SAH. The implications of these findings require further study to determine the effectiveness of these interventions.

Keywords: Coronavirus, epidemiology, government intervention, public health, social distancing

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Authors: Khodzhaberdi Allaberdiev

Abstract:

Aromaticity, one of the most important concepts in organic chemistry, has attracted considerable interest from both experimentalists and theoreticians. The geometry optimization of p-substituted o-(N-dialkyl)aminomethylphenols, o-DEAMPH XC₆ H₅CH ₂Y (X=p-OCH₃, CH₃, H, F, Cl, Br, COCH₃, COOCH₃, CHO, CN and NO₂, Y=o-N (C₂H₅)₂, o-DEAMPHs have been performed in the gas phase using the B3LYP/6-311+G(d,p) level. Aromaticities of the considered molecules were investigated using different indices included geometrical (HOMA and Bird), electronic (FLU, PDI and SA) magnetic (NICS(0), NICS(1) and NICS(1)zz indices. The linear dependencies were obtained between some aromaticity indices. The best correlation is observed between the Bird and PDI indices (R² =0.9240). However, not all types of indices or even different indices within the same type correlate well among each other. Surprisingly, for studied molecules in which geometrical and electronic cannot correctly give the aromaticity of ring, the magnetism based index successfully predicts the aromaticity of systems. 1H NMR spectra of compounds were obtained at B3LYP/6–311+G(d,p) level using the GIAO method. Excellent linear correlation (R²= 0.9996) between values the chemical shift of hydrogen atom obtained experimentally of 1H NMR and calculated using B3LYP/6–311+G(d,p) demonstrates a good assignment of the experimental values chemical shift to the calculated structures of o-DEAMPH. It is found that the best linear correlation with the Hammett substituent constants is observed for the NICS(1)zz index in comparison with the other indices: NICS(1)zz =-21.5552+1,1070 σp- (R²=0.9394). The presence intramolecular hydrogen bond in the studied molecules also revealed changes the aromatic character of substituted o-DEAMPHs. The HOMA index predicted for R=NO2 the reduction in the π-electron delocalization of 3.4% was about double that observed for p-nitrophenol. The influence intramolecular H-bonding on aromaticity of benzene ring in the ground state (S0) are described by equations between NICS(1)zz and H-bond energies: experimental, Eₑₓₚ, predicted IR spectroscopical, Eν and topological, EQTAIM with correlation coefficients R² =0.9666, R² =0.9028 and R² =0.8864, respectively. The NICS(1)zz index also correlates with usual descriptors of the hydrogen bond, while the other indices do not give any meaningful results. The influence of the intramolecular H-bonding formation on the aromaticity of some substituted o-DEAMPHs is criteria to consider the multidimensional character of aromaticity. The linear relationships as well as revealed between NICS(1)zz and both pyramidality nitrogen atom, ΣN(C₂H₅)₂ and dihedral angle, φ CAr – CAr -CCH₂ –N, to characterizing out-of-plane properties.These results demonstrated the nonplanar structure of o-DEAMPHs. Finally, when considering dependencies of NICS(1)zz, were excluded data for R=H, because the NICS(1) and NICS(1)zz values are the most negative for unsubstituted DEAMPH, indicating its highest aromaticity; that was not the case for NICS(0) index.

Keywords: aminomethylphenols, DFT, aromaticity, correlations

Procedia PDF Downloads 180