Search results for: step-wise linear regression

Authors: Amin Saeidi

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Using a representation-theoretic approach and considering G to be a finite primitive permutation group of degree n, our aim is to determine linear codes of length n that admit G as a permutation automorphism group. We can show that in some cases, every binary linear code admitting G as a permutation automorphism group is a submodule of a permutation module defined by a primitive action of G. As an illustration of the method, we consider the sporadic simple group M₁₁ and the unitary group U(3,3). We also construct some point- and block-primitive 1-designs from the supports of some codewords of the codes in the discussion.

Keywords: linear code, permutation representation, support design, simple group

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Authors: Nolvi Francisco Baggio Filho, Roniele Belusso

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Many industrial processes require a precise linear motion. Usually, this movement is achieved with the use of rotary motors combined with electrical control systems and mechanical systems such as gears, pulleys and bearings. Other types of devices are based on linear motors, where the linear motion is obtained directly. The Linear Stepper Motor (MLP) is an excellent solution for industrial applications that require precise positioning and high speed. This study presents an MLP formed by a linear structure and static ferromagnetic material, and a mover structure in which three coils are mounted. Mechanical suspension systems allow a linear movement between static and mover parts, maintaining a constant air gap. The operating principle is based on the tendency of alignment of magnetic flux through the path of least reluctance. The force proportional to the intensity of the electric current and the speed proportional to the frequency of the excitation coils. The study of this device is still based on the use of a numerical and experimental analysis to verify the relationship among electric current applied and planar force developed. In addition, the magnetic field in the air gap region is also monitored.

Keywords: linear stepper motor, planar traction force, reluctance magnetic, industry applications

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Authors: Byung Ho Jung, Dong Hoon Lim

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Logistic regression is a statistical method for analyzing a dataset in which there are one or more independent variables that determine an outcome. Logistic regression is used extensively in numerous disciplines, including the medical and social science fields. In this paper, we address the problem of estimating parameters in the logistic regression based on MapReduce framework with RHadoop that integrates R and Hadoop environment applicable to large scale data. There exist three learning algorithms for logistic regression, namely Gradient descent method, Cost minimization method and Newton-Rhapson's method. The Newton-Rhapson's method does not require a learning rate, while gradient descent and cost minimization methods need to manually pick a learning rate. The experimental results demonstrated that our learning algorithms using RHadoop can scale well and efficiently process large data sets on commodity hardware. We also compared the performance of our Newton-Rhapson's method with gradient descent and cost minimization methods. The results showed that our newton's method appeared to be the most robust to all data tested.

Keywords: big data, logistic regression, MapReduce, RHadoop

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Authors: Sanja Podunavac-Kuzmanović, Denis Kučević, Strahinja Kovačević, Milica Karadžić, Lidija Jevrić

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The present study describes the application of chemometric methods in analysis of milk samples which were collected in a conventional dairy farm and an organic dairy farm in AP Vojvodina, Republic of Serbia. The chemometric analysis included the application of univariate regression modeling and Analysis of Variance (ANOVA) method. The ANOVA was used in order to determine the differences in fatty acids content in the milk samples from conventional and organic farm. The results of the ANOVA testing indicate that there is a highly statistically significant difference between the content of fatty acid (saturated fatty acid vs. unsaturated fatty acids) in different dairy farming. Besides, the linear univariate models have been obtained as a result of modeling the linear relationships between the milk fat content and saturated fatty acids content, and the linear relationships between the milk fat content and unsaturated fatty acids content. The models obtained on the basis of the milk samples which originate from the organic farming are statistically better than the models based on the milk samples from conventional farming.

Keywords: hemometrics, milk, organic farming, quality control

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Authors: Filippo Portera

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Usually standard algorithms employ a loss where each error is the mere absolute difference between the true value and the prediction, in case of a regression task. In the present, we present several error weighting schemes that are a generalization of the consolidated routine. We study both a binary classification model for Support Vextor Classification and a regression net for Multylayer Perceptron. Results proves that the error is never worse than the standard procedure and several times it is better.

Keywords: loss, binary-classification, MLP, weights, regression

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Authors: Farid Khosravikia, Patricia Clayton

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The main objective of this study is to evaluate the advantages and disadvantages of various machine learning techniques in forecasting ground-motion intensity measures given source characteristics, source-to-site distance, and local site condition. Intensity measures such as peak ground acceleration and velocity (PGA and PGV, respectively) as well as 5% damped elastic pseudospectral accelerations at different periods (PSA), are indicators of the strength of shaking at the ground surface. Estimating these variables for future earthquake events is a key step in seismic hazard assessment and potentially subsequent risk assessment of different types of structures. Typically, linear regression-based models, with pre-defined equations and coefficients, are used in ground motion prediction. However, due to the restrictions of the linear regression methods, such models may not capture more complex nonlinear behaviors that exist in the data. Thus, this study comparatively investigates potential benefits from employing other machine learning techniques as a statistical method in ground motion prediction such as Artificial Neural Network, Random Forest, and Support Vector Machine. The algorithms are adjusted to quantify event-to-event and site-to-site variability of the ground motions by implementing them as random effects in the proposed models to reduce the aleatory uncertainty. All the algorithms are trained using a selected database of 4,528 ground-motions, including 376 seismic events with magnitude 3 to 5.8, recorded over the hypocentral distance range of 4 to 500 km in Oklahoma, Kansas, and Texas since 2005. The main reason of the considered database stems from the recent increase in the seismicity rate of these states attributed to petroleum production and wastewater disposal activities, which necessities further investigation in the ground motion models developed for these states. Accuracy of the models in predicting intensity measures, generalization capability of the models for future data, as well as usability of the models are discussed in the evaluation process. The results indicate the algorithms satisfy some physically sound characteristics such as magnitude scaling distance dependency without requiring pre-defined equations or coefficients. Moreover, it is shown that, when sufficient data is available, all the alternative algorithms tend to provide more accurate estimates compared to the conventional linear regression-based method, and particularly, Random Forest outperforms the other algorithms. However, the conventional method is a better tool when limited data is available.

Keywords: artificial neural network, ground-motion models, machine learning, random forest, support vector machine

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Authors: Alireza Vafaei Sadr, Vida Abedi, Jiang Li, Ramin Zand

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Missing data is a common challenge in medical research and can lead to biased or incomplete results. When the data bias leaks into models, it further exacerbates health disparities; biased algorithms can lead to misclassification and reduced resource allocation and monitoring as part of prevention strategies for certain minorities and vulnerable segments of patient populations, which in turn further reduce data footprint from the same population – thus, a vicious cycle. This study compares the performance of six imputation techniques grouped into Linear and Non-Linear models on two different realworld electronic health records (EHRs) datasets, representing 17864 patient records. The mean absolute percentage error (MAPE) and root mean squared error (RMSE) are used as performance metrics, and the results show that the Linear models outperformed the Non-Linear models in terms of both metrics. These results suggest that sometimes Linear models might be an optimal choice for imputation in laboratory variables in terms of imputation efficiency and uncertainty of predicted values.

Keywords: EHR, machine learning, imputation, laboratory variables, algorithmic bias

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Authors: Alam Ali, Ashok Kumar Pathak

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Path analysis is a statistical technique used to evaluate the strength of the direct and indirect effects of variables. One or more structural regression equations are used to estimate a series of parameters in order to find the better fit of data. Sometimes, exogenous variables do not show a significant strength of their direct and indirect effect when the assumption of classical regression (ordinary least squares (OLS)) are violated by the nature of the data. The main motive of this article is to investigate the efficacy of the copula-based regression approach over the classical regression approach and calculate the direct and indirect effects of variables when data violates the OLS assumption and variables are linked through an elliptical copula. We perform this study using a well-organized numerical scheme. Finally, a real data application is also presented to demonstrate the performance of the superiority of the copula approach.

Keywords: path analysis, copula-based regression models, direct and indirect effects, k-fold cross validation technique

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Authors: K. Hema Shankari, R. Thirumalaiselvi, N. V. Balasubramanian

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The present paper addresses to the research in the area of regression testing with emphasis on automated tools as well as prioritization of test cases. The uniqueness of regression testing and its cyclic nature is pointed out. The difference in approach between industry, with business model as basis, and academia, with focus on data mining, is highlighted. Test Metrics are discussed as a prelude to our formula for prioritization; a case study is further discussed to illustrate this methodology. An industrial case study is also described in the paper, where the number of test cases is so large that they have to be grouped as Test Suites. In such situations, a genetic algorithm proposed by us can be used to reconfigure these Test Suites in each cycle of regression testing. The comparison is made between a proprietary tool and an open source tool using the above-mentioned metrics. Our approach is clarified through several tables.

Keywords: APFD metric, genetic algorithm, regression testing, RFT tool, test case prioritization, selenium tool

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Authors: Ala Rakhshandeh, Zahra Ashkar, Solmaz Dehghani Dolatabadi, Hossein Bayat

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The present study has been conducted to investigate the role of family emotional climate and emotional expression style in the academic well-being of students with military parents. Children, including 280 female students of Shahriar police officers, were selected by random sampling method, and they have been investigated through Alfred B. Hillburn's family emotional climate questionnaire (1964), King and Ammon's emotional expression questionnaire (1990), and Pitrinen, Sweeney, and Falto's academic well-being questionnaire (2014). The data were analyzed using statistical methods of correlation coefficient and stepwise multiple regression under the SPSS23 program. The results reveal that the variables of family emotional climate and emotional expression can explain 36.4% of the variance in academic well-being. This finding reveals that with an increase of standard deviation on the scores of family emotional climate and emotional expression, 0.513 and 0.155 standard deviations are added to the scores of academic well-being, respectively. The emotional climate of the family has a superior distinctive role in predicting the educational well-being of female students. Thus, the emotional climate of the family and the style of emotional expression play a meaningful role in the academic well-being of students with the military parent.

Keywords: emotional climate, family, emotional expression style, academic well-being

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Authors: Neha Bhardwaj

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In this paper, we consider positive linear operators and study the Voronovskaya type result of the operator then obtain an error estimate in terms of the higher order modulus of continuity of the function being approximated and its A-statistical convergence. Also, we compute the corresponding rate of A-statistical convergence for the linear positive operators.

Keywords: Poisson distribution, Voronovskaya, modulus of continuity, a-statistical convergence

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Authors: Yenni Anggrayni

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The lack of awareness of the significant prevalence of school absenteeism in Indonesia, which ultimately results in high rates of school dropouts, is an unresolved issue. Therefore, this study aims to investigate the root causes of chronic absenteeism qualitatively and quantitatively using the bioecological systems paradigm in secondary schools for any reason. This study used an open-ended questionnaire to collect data from 1,148 students in six West Java Province districts/cities. Univariate and stepwise multiple logistic regression analyses produced a prediction model for the components. Analysis results show that poor teacher-student relationships, bullying by peers or teachers, negative perception of education, and lack of parental involvement in learning activities are the leading causes of chronic absenteeism. Another finding is to promote home-school partnerships to improve school climate and parental involvement in learning to address chronic absenteeism.

Keywords: bullying, chronic absenteeism, dropout of school, home-school partnerships, parental involvement

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Authors: Ehsan Mehryaar, Seyed Armin Motahari Tabari

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Without a doubt, soil shear strength is the most important property of the soil. The majority of fatal and catastrophic geological accidents are related to shear strength failure of the soil. Therefore, its prediction is a matter of high importance. However, acquiring the shear strength is usually a cumbersome task that might need complicated laboratory testing. Therefore, prediction of it based on common and easy to get soil properties can simplify the projects substantially. In this paper, A hybrid model based on the classification and regression tree algorithm and logistic regression is proposed where each leaf of the tree is an independent regression model. A database of 189 points for clay soil, including Moisture content, liquid limit, plastic limit, clay content, and shear strength, is collected. The performance of the developed model compared to the existing models and equations using root mean squared error and coefficient of correlation.

Keywords: model tree, CART, logistic regression, soil shear strength

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Authors: Deepak Raj Bhat, Ryuichi Yatabe

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In this study, a residual-state creep failure model was developed based on the residual-state creep test results of clayey soils. To develop the proposed model, the regression analyses were done by using the R. The model results of the failure time (tf) and critical displacement (δc) were compared with experimental results and found in close agreements to each others. It is expected that the proposed regression model for residual-state creep failure will be more useful for the prediction of displacement of different clayey soils in the future.

Keywords: regression model, residual-state creep failure, displacement prediction, clayey soils

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Authors: Shakirat Abimbola Adesola, Shuaib Akintunde Asifat, Jelili Olalekan Amoo

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This paper presented the impact of students’ emotions on learning when receiving lectures and when taking tests. It was observed that students experience different types of emotions during the study, and this was found to have a significant effect on their academic performance. A total of one thousand six hundred and seventy-five (1675) students from the department of Computer Science in two Colleges of Education in South-West Nigeria took part in this study. The students were randomly selected for the research. Sample comprises of 968 males representing 58%, and 707 females representing 42%. A structured questionnaire, of Motivated Strategies for Learning Questionnaire (MSLQ) was distributed to the participants to obtain their opinions. Data gathered were analyzed using the IBM SPSS 20 to obtain ANOVA, descriptive analysis, stepwise regression, and reliability tests. The results revealed that emotion moderately shape students’ motivation and engagement in learning; and that self-regulation and self-determination do have significant impact on academic performance. It was further revealed that test anxiety has a significant correlation with academic performance.

Keywords: motivation, self-determination, test anxiety, academic performance, and academic engagement

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Authors: K. Khlifi, A. Haddouk, M. Hlaili, H. Mechergui

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The present paper provides a detailed analysis of prior methods and approaches for non-linear load identification in residential buildings. The main goal of this analysis is to decipher the distorted signals and to estimate the harmonics influence on power systems. We have performed an analytical study of non-linear loads behavior in the residential environment. Simulations have been performed in order to evaluate the distorted rate of the current and follow his behavior. To complete this work, an instrumental platform has been realized to carry out practical tests on single-phase non-linear loads which illustrate the current consumption of some domestic appliances supplied with single-phase sinusoidal voltage. These non-linear loads have been processed and tracked in order to limit their influence on the power grid and to reduce the Joule effect losses. As a result, the study has allowed to identify responsible circuits of harmonic pollution.

Keywords: distortion rate, harmonic analysis, harmonic pollution, non-linear load, power factor

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Authors: Ann Ukachi Madukwe, Juliana Chinwendu Njoku

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Marital conflict, conceptualized in this study as the ongoing lack of peace and satisfaction in a marital union which threatens marital stability, has become quite prevalent in modern Igbo communities. The frequent incidences of spousal battery, spousal sexual abuse, domestic violence, long term separation and in some cases outright divorce are worrisome indicators of the endemic challenge marital conflict poses in most Igbo communities. This study examined marital expectations, marital infidelity (self and spouse), and neuroticism as predictors of marital conflict. Marital expectation was described as a married person’s appraisal of how well their pre-marital desires were being met by their spouses and within the marriage relationship. It assessed different aspects of personal and interpersonal positive outcomes in a marital union. Marital infidelity referred to the likelihood that married individuals or their spouses could have indulged in intimate activities like passionate kisses and romantic dates with someone other than their spouses. Participants reported on themselves as well as their spouses. The last predictor variable neuroticism was measured as a personality trait that addresses issues of emotional instability especially as it relates to a person’s interactions. Neurotic persons were considered to have high emotional reactivity; they would have strong emotional response to issues that emotionally stable persons might overlook. Participants comprised of Igbo male and female spouses selected from Imo state using randomized cluster sampling method. The study utilized the cross sectional survey design and Stepwise linear multiple regression for data analyses. Findings showed that though marital infidelity by spouse was generally below average and spouses marital expectations were being fulfilled; marital expectations followed by marital infidelity – spouse proved to be significant predictors of marital conflict. Marital conflict reduced as marital expectations got fulfilled and increased as the level of likelihood of marital infidelity by the spouse increased. Spouses in this study also reported an increased level of neuroticism, with males being more neurotic than females. Neuroticism was found to be the least significant predictor of marital conflict compared to marital expectations and marital infidelity – spouse. Finally, the article made recommendations to spouses and marital counsellors regarding especially the need to manage the neurotic tendencies of Igbo spouses.

Keywords: Igbo spouses, marital conflict, marital expectations, Nigeria

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Authors: Huy Q. Tran, Jungwon Huh, Kiseok Kwak, Choonghyun Kang

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Infrared thermography (IRT) technique has been proven to be a good method for nondestructive evaluation of concrete material. In the building, a broad range of applications has been used such as subsurface defect inspection, energy loss, and moisture detection. The purpose of this research is to consider the qualitative and quantitative performance of reinforced concrete deteriorations using active infrared thermography technique. An experiment of three different heating regimes was conducted on a concrete slab in the laboratory. The thermal characteristics of the IRT method, i.e., absolute contrast and observation time, are investigated. A linear relationship between the observation time and the real depth was established with a well linear regression R-squared of 0.931. The results showed that the absolute contrast above defective area increases with the rise of the size of delamination and the heating time. In addition, the depth of delamination can be predicted by using the proposal relationship of this study.

Keywords: concrete building, infrared thermography, nondestructive evaluation, subsurface delamination

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Authors: Hamid Goharnejad, Amir Hossein Eghbali

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Recent investigations have demonstrated the global sea level rise due to climate change impacts. In this study climate changes study the effects of increasing water level in the strait of Hormuz. The probable changes of sea level rise should be investigated to employ the adaption strategies. The climatic output data of a GCM (General Circulation Model) named CGCM3 under climate change scenario of A1b and A2 were used. Among different variables simulated by this model, those of maximum correlation with sea level changes in the study region and least redundancy among themselves were selected for sea level rise prediction by using stepwise regression. One models of Discrete Wavelet artificial Neural Network (DWNN) was developed to explore the relationship between climatic variables and sea level changes. In these models, wavelet was used to disaggregate the time series of input and output data into different components and then ANN was used to relate the disaggregated components of predictors and predictands to each other. The results showed in the Shahid Rajae Station for scenario A1B sea level rise is among 64 to 75 cm and for the A2 Scenario sea level rise is among 90 to 105 cm. Furthermore the result showed a significant increase of sea level at the study region under climate change impacts, which should be incorporated in coastal areas management.

Keywords: climate change scenarios, sea-level rise, strait of Hormuz, forecasting

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Authors: Tarek Sayed Taha Ali

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The dependence of the axial-vector coupling constant gA on the quark masses has been investigated in the frame work of the extended linear sigma model. The field equations have been solved in the mean-field approximation. Our study shows a better fitting to the experimental data compared with the existing models.

Keywords: extended linear sigma model, nucleon properties, axial coupling constant, physic

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Authors: Saahith M. S., Sivakami R.

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In the realm of football analytics, particularly focusing on predicting football player performance, the ability to forecast player success accurately is of paramount importance for teams, managers, and fans. This study introduces an elaborate examination of predicting football player performance through the integration of data visualization methods and machine learning algorithms. The research entails the compilation of an extensive dataset comprising player attributes, conducting data preprocessing, feature selection, model selection, and model training to construct predictive models. The analysis within this study will involve delving into feature significance using methodologies like Select Best and Recursive Feature Elimination (RFE) to pinpoint pertinent attributes for predicting player performance. Various machine learning algorithms, including Random Forest, Decision Tree, Linear Regression, Support Vector Regression (SVR), and Artificial Neural Networks (ANN), will be explored to develop predictive models. The evaluation of each model's performance utilizing metrics such as Mean Squared Error (MSE) and R-squared will be executed to gauge their efficacy in predicting player performance. Furthermore, this investigation will encompass a top player analysis to recognize the top-performing players based on the anticipated overall performance scores. Nationality analysis will entail scrutinizing the player distribution based on nationality and investigating potential correlations between nationality and player performance. Positional analysis will concentrate on examining the player distribution across various positions and assessing the average performance of players in each position. Age analysis will evaluate the influence of age on player performance and identify any discernible trends or patterns associated with player age groups. The primary objective is to predict a football player's overall performance accurately based on their individual attributes, leveraging data-driven insights to enrich the comprehension of player success on the field. By amalgamating data visualization and machine learning methodologies, the aim is to furnish valuable tools for teams, managers, and fans to effectively analyze and forecast player performance. This research contributes to the progression of sports analytics by showcasing the potential of machine learning in predicting football player performance and offering actionable insights for diverse stakeholders in the football industry.

Keywords: football analytics, player performance prediction, data visualization, machine learning algorithms, random forest, decision tree, linear regression, support vector regression, artificial neural networks, model evaluation, top player analysis, nationality analysis, positional analysis

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Authors: Adriano Z. Zambom, Preethi Ravikumar

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One of the biggest challenges in nonparametric regression is the curse of dimensionality. Additive models are known to overcome this problem by estimating only the individual additive effects of each covariate. However, if the model is misspecified, the accuracy of the estimator compared to the fully nonparametric one is unknown. In this work the efficiency of completely nonparametric regression estimators such as the Loess is compared to the estimators that assume additivity in several situations, including additive and non-additive regression scenarios. The comparison is done by computing the oracle mean square error of the estimators with regards to the true nonparametric regression function. Then, a backward elimination selection procedure based on the Akaike Information Criteria is proposed, which is computed from either the additive or the nonparametric model. Simulations show that if the additive model is misspecified, the percentage of time it fails to select important variables can be higher than that of the fully nonparametric approach. A dimension reduction step is included when nonparametric estimator cannot be computed due to the curse of dimensionality. Finally, the Boston housing dataset is analyzed using the proposed backward elimination procedure and the selected variables are identified.

Keywords: additive model, nonparametric regression, variable selection, Akaike Information Criteria

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Authors: Yanisa Chaiya, Jintana Sanwong

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Let V be a vector space over a field and W a subspace of V. Let Fix(V,W) denote the set of all linear transformations on V with fix all elements in W. In this paper, we show that Fix(V,W) is a semigroup under the composition of maps and describe Green’s relations on this semigroup in terms of images, kernels and the dimensions of subspaces of the quotient space V/W where V/W = {v+W : v is an element in V} with v+W = {v+w : w is an element in W}. Let dim(U) denote the dimension of a vector space U and Vα = {vα : v is an element in V} where vα is an image of v under a linear transformation α. For any cardinal number a let a'= min{b : b > a}. We also show that the ideals of Fix(V,W) are precisely the sets. Fix(r) ={α ∊ Fix(V,W) : dim(Vα/W) < r} where 1 ≤ r ≤ a' and a = dim(V/W). Moreover, we prove that if V is a finite-dimensional vector space, then every ideal of Fix(V,W) is principle.

Keywords: Green’s relations, ideals, linear transformation semi-groups, principle ideals

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Authors: Samuel Reisman

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Background: Comparative rankings are increasingly used to evaluate health care systems. These rankings combine discrete attribute rankings into a composite overall ranking. Health care equity is a component of overall rankings, but excelling in other categories can counterbalance low inequity grades. Highly ranked inequitable health care would commend systems that disregard human rights. We simulated the ranking of a maximally inequitable health care system using a published, influential ranking methodology. Methods: We used The Commonwealth Fund’s ranking of eleven health care systems to simulate the rank of a maximally inequitable system. Eighty performance indicators were simulated, assuming maximal ineptitude in equity benchmarks. Maximal rankings in all non-equity subcategories were assumed. Subsequent stepwise simulations lowered all non-equity rank positions by one. Results: The maximally non-equitable health care system ranked first overall. Three subsequent stepwise simulations, lowering non-equity rankings by one, each resulted in an overall ranking within the top three. Discussion: Our results demonstrate that grossly inequitable health care systems can rank highly in comparative health care system rankings. These findings challenge the validity of ranking methodologies that subsume equity under broader benchmarks. We advocate limiting maximum overall rankings of health care systems to their individual equity rankings. Such limits are logical given the insignificance of health care system improvements to those lacking adequate health care.

Keywords: global health, health equity, healthcare systems, international health

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Authors: Masood Beheshtirad

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Identification of regions having potential for landslide occurrence is one of the basic measures in natural resources management. Different landslide hazard mapping models are proposed based on the environmental condition and goals. In this research landslide hazard map using multiple regression model were provided and applicability of this model is investigated in Baghdasht watershed. Dependent variable is landslide inventory map and independent variables consist of information layers as Geology, slope, aspect, distance from river, distance from road, fault and land use. For doing this, existing landslides have been identified and an inventory map made. The landslide hazard map is based on the multiple regression provided. The level of similarity potential hazard classes and figures of this model were compared with the landslide inventory map in the SPSS environments. Results of research showed that there is a significant correlation between the potential hazard classes and figures with area of the landslides. The multiple regression model is suitable for application in the Baghdasht Watershed.

Keywords: landslide, mapping, multiple model, regression

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Seyed Habib Shojaei, Reza Eivazi, Mir Sajad Shojaei, Alireza Akbari, Pooria Mazloom, Seyede Mitra Sadati, Mir Zeinalabedin Shojaei, Farnaz Farbakhsh

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To study the genetic diversity in rapeseeds and agronomic traits, an experiment was conducted using multivariate statistical methods at Agricultural Research Station of Kashmar in 2012-2013.In this experiment, ten genotypes of rapeseed in a Randomized Complete Block designs with three replications were evaluated. The following traits were studied: seed yield, number of days to the fifty percent of flowering, plant height, number of pods on main stem, length of the pod, seed yield per plant, number of seed in pod, harvest index, weight of 100 seeds, number of pods on lateral branch, number of lateral branches. In analyzing the variance, differences between cultivars were significant. The average comparative revealed that the most valuable variety was Licord regarding to the traits while the least valuable variety was Opera. In stepwise regression, harvest index, grain yield per plant and number of pods per lateral branches were entering to model. Correlation analysis showed that the grain yield with the number of pods per lateral branches and seed yield per plant have positive and significant correlation. In the factor analysis, the first five components explained more than 83% of the variance in the data. In the first factor, seed yield and the number of pods per lateral branches were of the highest importance. The traits, seed yield per plant, and pod per main stem were of a great significance in the second factor. Moreover, in the third factor, plant height and the number of lateral branches were more important. In the fourth factor, plant height and one hundred seeds weight were of the highest variance. Finally, days to fifty percent of flowering and one hundred seeds weight were more important in fifth factor.

Keywords: rapeseed, variance analysis, regression, factor analysis

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Authors: Ishapathik Das, Sumen Sen, N. Rao Chaganty, Pooja Sengupta

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Dependent multivariate count data occur in several research studies. These data can be modeled by a multivariate Poisson or Negative binomial distribution constructed using copulas. However, when some of the counts are inflated, that is, the number of observations in some cells are much larger than other cells, then the copula based multivariate Poisson (or Negative binomial) distribution may not fit well and it is not an appropriate statistical model for the data. There is a need to modify or adjust the multivariate distribution to account for the inflated frequencies. In this article, we consider the situation where the frequencies of two cells are higher compared to the other cells, and develop a doubly inflated multivariate Poisson distribution function using multivariate Gaussian copula. We also discuss procedures for regression on covariates for the doubly inflated multivariate count data. For illustrating the proposed methodologies, we present a real data containing bivariate count observations with inflations in two cells. Several models and linear predictors with log link functions are considered, and we discuss maximum likelihood estimation to estimate unknown parameters of the models.

Keywords: copula, Gaussian copula, multivariate distributions, inflated distributios

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Authors: Mamta Rajbhar, Sanjay K. Mohanty

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India's progress in achieving replacement level of fertility is largely contingent on fertility reduction in the state of Uttar Pradesh as it accounts 17% of India's population with a low level of development. Though the TFR in the state has declined from 5.1 in 1991 to 3.4 by 2011, it conceals large differences in fertility level across districts. Using data from multiple sources this paper tests the hypothesis that the improvement in human development significantly reduces the fertility levels in districts of Uttar Pradesh. The unit of analyses is district, and fertility estimates are derived using the reverse survival method(RSM) while human development indices(HDI) are are estimated using uniform methodology adopted by UNDP for three period. The correlation and linear regression models are used to examine the relationship of fertility change and human development indices across districts. Result show the large variation and significant change in fertility level among the districts of Uttar Pradesh. During 1991-2011, eight districts had experienced a decline of TFR by 10-20%, 30 districts by 20-30% and 32 districts had experienced decline of more than 30%. On human development aspect, 17 districts recorded increase of more than 0.170 in HDI, 18 districts in the range of 0.150-0.170, 29 districts between 0.125-0.150 and six districts in the range of 0.1-0.125 during 1991-2011. Study shows significant negative relationship between HDI and TFR. HDI alone explains 70% variation in TFR. Also, the regression coefficient of TFR and HDI has become stronger over time; from -0.524 in 1991, -0.7477 by 2001 and -0.7181 by 2010. The regression analyses indicate that 0.1 point increase in HDI value will lead to 0.78 point decline in TFR. The HDI alone explains 70% variation in TFR. Improving the HDI will certainly reduce the fertility level in the districts.

Keywords: Fertility, HDI, Uttar Pradesh

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Authors: Farid Khosravikia, Patricia Clayton

Abstract:

The main objective of this work is to evaluate the advantages and disadvantages of various machine learning techniques in two key steps of seismic hazard and risk assessment of different types of structures. The first step is the development of ground-motion models, which are used for forecasting ground-motion intensity measures (IM) given source characteristics, source-to-site distance, and local site condition for future events. IMs such as peak ground acceleration and velocity (PGA and PGV, respectively) as well as 5% damped elastic pseudospectral accelerations at different periods (PSA), are indicators of the strength of shaking at the ground surface. Typically, linear regression-based models, with pre-defined equations and coefficients, are used in ground motion prediction. However, due to the restrictions of the linear regression methods, such models may not capture more complex nonlinear behaviors that exist in the data. Thus, this study comparatively investigates potential benefits from employing other machine learning techniques as statistical method in ground motion prediction such as Artificial Neural Network, Random Forest, and Support Vector Machine. The results indicate the algorithms satisfy some physically sound characteristics such as magnitude scaling distance dependency without requiring pre-defined equations or coefficients. Moreover, it is shown that, when sufficient data is available, all the alternative algorithms tend to provide more accurate estimates compared to the conventional linear regression-based method, and particularly, Random Forest outperforms the other algorithms. However, the conventional method is a better tool when limited data is available. Second, it is investigated how machine learning techniques could be beneficial for developing probabilistic seismic demand models (PSDMs), which provide the relationship between the structural demand responses (e.g., component deformations, accelerations, internal forces, etc.) and the ground motion IMs. In the risk framework, such models are used to develop fragility curves estimating exceeding probability of damage for pre-defined limit states, and therefore, control the reliability of the predictions in the risk assessment. In this study, machine learning algorithms like artificial neural network, random forest, and support vector machine are adopted and trained on the demand parameters to derive PSDMs for them. It is observed that such models can provide more accurate estimates of prediction in relatively shorter about of time compared to conventional methods. Moreover, they can be used for sensitivity analysis of fragility curves with respect to many modeling parameters without necessarily requiring more intense numerical response-history analysis.

Keywords: artificial neural network, machine learning, random forest, seismic risk analysis, seismic hazard analysis, support vector machine

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