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AbstractIn multivariate statistical inference, the Hotelling T2 statistic is used to test the equality of mean vectors for two independent groups. This statistic needs the multivariate normality and homogeneous covariance matrices assumptions. However, homogeneous covariance matrices assumption may not be provided in real applications. This case is called the multivariate Behrens-Fisher problem. There are several studies to test the equality of two mean vectors for the independent groups under the multivariate Behrens-fisher problem. But these studies do not interest in outliers at data sets. In this study, we propose solving problems caused by multivariate Behrens-Fisher and outliers in the dataset. We compare our proposed approach with other approaches regarding empirical size and power at simulated data that are both uncontaminated and contaminated. Thus we show that our proposed approach can be used to test the equality of mean vectors for two independent groups under multivariate Behrens-Fisher problem without being affected by outliers in the data. Moreover, we construct an R function in the MVTests package to use our proposed approach for real data applications. [ABSTRACT FROM AUTHOR]

The likelihood ratio test used to test complete independence cannot be used in high-dimensional data. In literature, many test statistics were proposed to cope with this problem. However, these statistics are sensitive to outliers. In this study, we suggest a test statistic that is not sensitive to outliers and can be used in high-dimensional data to test complete independence. We investigate the performance of our suggested statistic in terms of the empirical size and the empirical power by using three simulation studies and a real example dataset. And, we construct an R package to implement our proposed test statistic on real high-dimensional data in applications. [ABSTRACT FROM AUTHOR]

The current study is related to solve a nonlinear vector-borne disease with a lifelong immunity model (VDLIM) by designing a computational stochastic framework using the strength of artificial Levenberg-Marquardt backpropagation neural network (ALMBNN). The detail of the nonlinear VDLIM is provided along with its five classes. The numerical performances of the results have been presented using the ALMBNN by taking three different cases to solve the nonlinear VDLIM using the training, sample data, testing and authentication. The selection of the statics is selected as 80% for training, while the data for both testing and validations is applied 10%. The results of the nonlinear VDLIM are performed using the ALMBNN and the correctness of the scheme is observed to compare the results with the reference solutions. The calculated performance of the results to solve the nonlinear VDLIM is applied for the reduction of the mean square error. In order to check the competence, efficacy, exactness and reliability of the ALMBNN, the numerical investigations using the proportional procedures based on the MSE, correlation, regression and error histograms are presented. [ABSTRACT FROM AUTHOR]

The Hotelling T 2 statistic is used to test the hypothesis about the location parameter of multivariate Gaussian distribution, and it is significantly sensitive to outliers. Also, we cannot calculate it when the sample size is less than the number of variables because this statistic needs the inverse of the covariance matrix, and the sample covariance matrix is singular in high dimensional data. Although a new approach, based on shrinkage estimation, was proposed to solve this singularity problem, this estimator is still sensitive to outliers. On the other hand, a robust one sample Hotelling T 2 statistic was proposed by using the minimum covariance determinant (MCD) estimates instead of classical ones. Since the MCD estimates cannot be calculated when n < p , this statistic cannot be used in high-dimensional data. This study proposes to use the minimum regularized covariance determinant (MRCD) estimator instead of classical or MCD. The MRCD estimator is a robust location and scatter estimator, which can be calculated in high-dimensional data. We obtain the asymptotic distribution of the proposed test statistic using Monte Carlo simulations and examine the power and robustness properties of the test statistic with simulated datasets. As a result, we show that the approximate distribution of the test statistic is proper, and the proposed robust test statistic can be used to test the hypothesis about the location parameter of contaminated high dimensional data. Finally, we construct an R function in the MVTests package to perform our proposed test statistic. [ABSTRACT FROM AUTHOR]

In this study, we propose the robust ratio-type estimator of finite population variance considering the minimum covariance determinant (MCD) and the minimum volume ellipsoid (MVE) robust covariance matrices in simple and stratified random sampling. The mean square errors (MSE) equations are obtained for the robust ratio-type estimator. The conditions for which the proposed robust ratio-type estimator is more efficient as compared to competing estimators have been discussed. The MCD and MVE are robust against outliers. Thus, when there is an outlier in the data, simulations and empirical results show that the proposed robust ratio-type estimators under simple and stratified random sampling have a lower mean square error than the traditional estimators. In addition, we support theoretical results with contaminated real examples and simulation studies. [ABSTRACT FROM AUTHOR]

In this article, ratio estimators for the population mean have suggested using the robust covariance estimation under the simple random scheme. Zaman and Bulut have developed a class of ratio-type estimators for the mean estimation by utilizing robust regression coefficients. In this paper, we extend the estimators presented in Zaman and Bulut by using minimum covariance determinant (MCD) robust covariance estimation. The mean square error (MSE) equation for the new estimators is obtained. These theoretical results are supported with the aid of numerical example and simulation based on dataset that include outliers. [ABSTRACT FROM AUTHOR]

This matched cohort study was retrospectively performed, with cycles extracted from freeze-all-IVF treatments performed between March and November 2019, to compare the efficacy of flexible-start dydrogesterone (DYG) co-treatment ovarian stimulations (OS) with flexible-start medroxyprogesterone acetate (MPA) co-treatment OS. DYG cycles were matched 1:1 with MPA cycles using female age and antral follicle count, resulting in 236 matched cycles. OS durations and total FSH doses were similar in DYG and MPA OS cycles. The numbers of mature oocytes retrieved were similar; however, the mature oocyte retrieval rate was significantly lower (66.7 vs. 78.2%; p =.001) and the cycle cancellation rates were higher (29.2 vs. 21.2%; p =.056) in DYG co-treatments. A linear regression selected OS co-treatment protocol (0.53 DYG (0.356–0.776), p =.001) into the final model to predict a ≥ 80% mature oocyte retrieval rate. The per transfer (47.2 vs. 49.7; p =.721) and per treatment ongoing pregnancy rates (32.2 vs. 38.1%, p =.210) were similar in the two co-treatment groups. Flexible-start DYG co-treatment OS was as effective in blastocyst freeze-all-IVF cycles as MPA co-treatment, with similar ongoing pregnancy rates; however, mature oocyte retrieval was significantly decreased and cycle cancellation increased in DYG cycles. What is already known on this subject? Progestin (i.e. artificial progesterone) co-treatment has long been known to be a feasible alternative to conventional GnRH-analogue co-treatment in OS for IVF, because of the long-standing evidence that progestin formulations have in oral contraceptive therapies. The recent evolution of effective freeze-all-IVF (in which high mid-cycle progesterone levels is not of concern because of the postponement of embryo transfer) has now made it possible to investigate progestin co-treatment OS in IVF. What do the results of this study add? Ongoing pregnancy rates from blastocyst frozen embryo transfers in flexible-start dydrogesterone (DYG) co-treatment ovarian stimulation (OS) cycles were similar to rates in flexible-start medroxyprogesterone acetate (MPA) co-treatment OS cycles. The mature oocyte retrieval rate was significantly lower and the cycle cancellation rate higher in DYG than in MPA cycles. What are the implications of these findings for clinical practice and/or further research? The evidence suggests that MPA co-treatment should be preferred in OS for IVF. Further investigation is required to refine progestin co-treatment protocols, because of their potential to reduce the number of viable blastocysts. [ABSTRACT FROM AUTHOR]

In this work, the Date–Jimbo–Kashiwara–Miwa (DJKM) equation include time-dependent in (2 + 1) -dimensions that characterize the propagation of nonlinear dispersive waves in inhomogeneous media is studied. We construct rational solutions and the interaction physical phenomena between rational solution and multi-soliton wave to the time-dependent DJKM equation. The multi-soliton solutions are revealed by using the Hirota simple method, and then via the long-wave method, the M-lump solutions for two types of time-dependent are derived. Moreover, the interaction phenomena between rational solution and single-, double-soliton solutions are studied. [ABSTRACT FROM AUTHOR]

Cluster analysis is defined as a group of multivariate statistical methods that are used to classify identical, or similar units. As is the case with all other classical statistical methods, classical clustering analysis gives misleading results when there is an outlier in the multivariate data set. To solve this problem many approaches have been proposed. This study focuses on developing a new approach, aiming to make the expectation maximization (EM) clustering algorithm resistant to outliers. We proposed a new robust hybrid clustering algorithm called robust EM (ROBEM) to reach our aim. This algorithm combines the EM clustering algorithm with robust principal component analysis (ROBPCA) algorithm. Spatial EM algorithm was proposed as a robust EM algorithm in the literature, but our simulation results and sample data applications showed that the ROBEM algorithm was more successful than the spatial EM algorithm in terms of outlier detection rate and faulty classification rate. Moreover, the proposed algorithm ROBEM provides similar results to the other well known robust clustering algorithms, such as TCLUST and Trimmed k-Means. [ABSTRACT FROM AUTHOR]

Outlier detection is an extensively studied issue in robust literature. The most popular and traditional approach using to detect outliers is to calculate the Mahalanobis distance. However, conventional Mahalanobis distances may fail to detect outliers because they base on the classical sample mean vector and covariance matrix, which are sensitive to outliers. To solve this problem, the Minimum Covariance Determinant (MCD) estimators are used instead of classical estimators. However, the MCD estimators cannot be calculated in high dimensional data sets, which variable number p is higher than the sample size n. To detect outliers in high dimensional data, we propose Mahalanobis distance based on the Minimum Regularized Covariance Determinants (MRCD) estimators, which can be calculated in high dimensional data sets. We have shown that this distance is successful for outlier detection in high dimensional data sets with the simulation study and real data sets. [ABSTRACT FROM AUTHOR]

This article proposes new regression-type estimators by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods and MCD and MVE robust covariance matrices in stratified sampling. Theoretically, we obtain the mean square error (MSE) for these estimators. We compare the efficiencies based on MSE equations, between the proposed estimators and the traditional combined and separate regression estimators. As a result of these comparisons, we observed that our proposed estimators give more efficient results than traditional approaches. And, these theoretical results are supported with the aid of numerical examples and simulation based on data sets that include outliers. [ABSTRACT FROM AUTHOR]

When there is an outlier in the data set, the efficiency of traditional methods decreases. In order to solve this problem, Kadilar et al. (2007) adapted Huber-M method which is only one of robust regression methods to ratio-type estimators and decreased the effect of outlier problem. In this study, new ratio-type estimators are proposed by considering Tukey-M, Hampel M, Huber MM, LTS, LMS and LAD robust methods based on the Kadilar et al. (2007). Theoretically, we obtain the mean square error (MSE) for these estimators. We compared with MSE values of proposed estimators and MSE values of estimators based on Huber-M and OLS methods. As a result of these comparisons, we observed that our proposed estimators give more efficient results than both Huber M approach which was proposed by Kadilar et al. (2007) and OLS approach. Also, under all conditions, all of the other proposed estimators except Lad method are more efficient than robust estimators proposed by Kadilar et al. (2007). And, these theoretical results are supported with the aid of a numerical example and simulation by basing on data that includes an outlier. [ABSTRACT FROM AUTHOR]

The present study was performed to investigate whether maternal body mass index (BMI) affected the live birth (LB) outcomes of frozen embryo transfers (FET) in patients who underwent freeze-all treatment cycles. The autologous intracytoplasmic sperm injection (ICSI) cycles with blastocyst freeze-all cycles performed between February 2015 and January 2016 were retrospectively investigated. The 1188 subsequent FET performed were grouped according to maternal BMI classes for analysis; underweight (<18.5 kg/m2; 3.5%), normal-weight (18.5-24.9 kg/m2; 40.1%), overweight (25.0-29.9 kg/m2; 33.7%), or obese (classes I-III; ≥30.0 kg/m2; 22.8%). Uni- and multivariate analyses were performed, with LB as the primary outcome measure. In the categorical analyses of only the single blastocyst transfers (SBT), positive pregnancy (PP), LB and total pregnancy loss (totPL) rates were similar in the maternal BMI classes; however, the preterm delivery (PTD) rate in the obese class was significantly higher. In the multiple logistic regression models, maternal age was the most significant predictor of LB (OR = 0.9, 95%CI (0.90-0.98), p = .006) and the maternal BMI was the most significant predictor of PTD (OR = 1.1, 95% CI (1.02-1.14), p = .010). In conclusion, maternal BMI was the most significant variable in the outcome of PTD, with obese female patients at an increased risk of PTD. Impact statement What is known already? Obesity is rising worldwide to epidemic proportions and is expected to continue rising in the foreseeable future. Overweight and obesity not only increases the morbidity and mortality in the female populations but also significantly increases the risks of infertility in the women of reproductive age. Body mass index (BMI) has been the most widely used measure to describe the body weight of infertile patients. What do the results of this study add? Underweight, overweight and obesity do not significantly contribute to live birth outcomes. Maternal BMI was a significant predictor of PTD, with obesity most significantly at risk of PTD. What are the implications of these findings for clinical practice and/or further research? The evidence suggests that the weight management policy remain unchanged in IVF practice, with weight loss recommended for both young and ageing infertile patients. Performing a 'therapeutic' freeze-all IVF in the patients with weight-associated infertility may be a more suitable treatment strategy. [ABSTRACT FROM AUTHOR]

Ovarian torsion (OT) in IVF is rare, however, the consequences are significant, which include ovariotomy. In the present study, it was aimed for the first time to compare the incidence of OT between hCG triggered cycles with ICSI and fresh transfer and GnRH-agonist triggered cycles with the ICSI-freeze-all and frozen embryo transfer (FET). In total, 15,577 ICSI cycles performed between 2001 and 2016 were categorised into two groups (Group 1, n: 9978): cycles with controlled ovarian stimulation (COS) and hCG-triggered (Group 2, n: 5599) and COS, with GnRH-agonist only triggered and freeze-all. Thirteen patients (0.13%) were diagnosed with OT and corrected by laparoscopy (12) and laparotomy (1) in Group 1. One patient (0.018%) was diagnosed with OT and corrected by laparotomy in Group 2 (Group 1 vs. Group 2, p = .049). The incidence of severe ovarian hyperstimulation syndrome (OHSS) was 2.4% in Group 1 and 0.05% in Group 2 (p < .001). The use of freeze-all with GnRH agonist trigger in ART significantly reduced the incidence of OT and concomitantly OHSS, with no effect on the reproductive outcome. Impact Statement What is already known on this subject? Adnexal ovarian torsion (OT) is a well-known gynaecological event that constitutes a surgical emergency. Assisted reproduction technologies (ART) may result in ovarian conditions that predispose patients to ovarian hyperstimulation syndrome (OHSS) and torsion. What the results of this study add? The combined use of GnRH agonist trigger for final oocyte maturation after OS with freeze-all and frozen embryo transfer (FET) significantly reduces the incidence of OT, as well as OHSS. What the implications are of these findings for clinical practice and/or further research? The treatment strategy of GnRH agonist trigger with freeze-all significantly reduces the risks of adverse complications. [ABSTRACT FROM AUTHOR]

In this study, the endometrial developmental and reproductive outcomes of frozen embryo transfers (FETs) which were performed subsequent to miscarriages managed by dilation and curettage (D and C) were investigated. The intracytoplasmic sperm injection (ICSI) blastocyst freeze-all cycles performed between January 2014 and August 2016 were screened for the patients who had undergone their FET (first), miscarriages (>5 < 14 weeks), D and C, and the patients who had undergone their FET (second) (study group; n = 71); and patients who underwent FET (1st), a chemical pregnancy loss (PL) (<5 weeks) and FET (2nd) (reference group; n = 38). The live births (LB; delivery >20 weeks) of FET (2nd) were analysed in two time-interval sub-groups: ≤6 months or >6 months. In the study and reference groups, the median endometrial thickness at the second FET of the ≤6 months sub-groups was found to be significantly reduced. The relative risk for LB was significantly higher (1.65 [0.994-2.723] p = .043) in the >6 months study sub-group, with a lower risk for PL (0.62 [0.268-1.427] p = .329), whereas, there were no significant differences between the reference sub-groups. The management of miscarriage with D and C results in a significant and transient decrease in reproductive function in subsequent FET. Impact Statement What is already known on this subject? Approximately, 15-30% of positive pregnancies in assisted reproductive technology (ART) end in biochemical pregnancy losses (PLs) or miscarriages. Cervical dilation with suction or blunt curettage (D and C), has been the procedure most often used to manage the retained products of conception (RPOC) after miscarriage. Intrauterine surgery has the potential to directly affect reproduction, depending on the endometrial impact. What the results of this study add? The endometrium after D and C surgery may require 6 months to recover normal reproductive function, in terms of both live birth and PL. The extent of the damage to endometrial function is not found to be reflected in the endometrial thickness. What the implications are of these findings for clinical practice and/or further research? Patients who undergo miscarriage after their ART treatment may need to delay further treatment for 6 months to optimise their chances of LB. Alternative miscarriage management procedures need to be investigated; procedures that have lower risks for an adverse reproductive function and allow for shorter time intervals between treatments. [ABSTRACT FROM AUTHOR]

This study uses two mathematical approaches in constructing dark, bright, kink-type and singular soliton solutions to the Heisenberg ferromagnetic spin chain equation. The (2+1)-dimensional Heisenberg ferromagnetic spin chain equation describes nonlinear dynamics of magnets. The acquired results in this study may help in explaining some physical meanings of some nonlinear physical models arising in electromagnetic waves. For instance, the hyperbolic tangent arises in the calculation of magnetic moment and rapidity of special relativity, the hyperbolic cotangent arises in the Langevin function for magnetic polarization. The 2-, 3-dimensional and the contour plots of all the acquired solutions are presented. [ABSTRACT FROM AUTHOR]

In this study, classical and robust principal component analyses are used to evaluate socioeconomic development of regions of development agencies that give service on the purpose of decreasing development difference among regions in Turkey. Due to the high differences between development levels of regions outlier problem occurs, hence robust statistical methods are used. Also, classical and robust statistical methods are used to investigate if there are any outliers in data set. In classic principal component analyse, the number of observations must be larger than the number of variables. Otherwise determinant of covariance matrix is zero. In Robust method for Principal Component Analysis (ROBPCA), a robust approach to principal component analyse in high-dimensional data, even if the number of variables is larger than the number of observations, principal components are obtained. In this paper, firstly 26 development agencies are evaluated with 19 variables by using principal component analysis based on classical and robust scatter matrices and then these 26 development agencies are evaluated with 46 variables by using the ROBPCA method. [ABSTRACT FROM PUBLISHER]

In large-scale transportation problems (TPs), various methods have been developed to obtain an optimal solution. One of the methods is the transportation simplex algorithm (TSA), which obtains an optimal solution for TP. Various heuristic methods have been developed to find an initial basic feasible solution for transportation algorithms. These methods differ in terms of computational cost and finding good initial solution. In TSA, the better the basic feasible solution, the less the number of iterations the algorithm will run. At each step, it uses pivoting operation, where a loop involving the nonbasic variable with the largest cost reduction is determined. Then, it eliminates the entering basic variable. However, for large-scale problems, even the best basic feasible solution may result in high number of iterations. In this paper, we present a novel algorithm called multiloop transportation simplex algorithm which finds multiple independent loops during pivoting operation. This causes larger cost reductions in every iteration. We experimentally show that the average number of iterations and runtime to solve the TP are dramatically reduced. [ABSTRACT FROM PUBLISHER]

ABSTRACT This manuscript focuses on the new wave behaviors of the system of equations for the ion sound wave under the action of the ponderomotive force which results from a nonlinear force that a charged particle experiences in an inhomogeneous oscillating electromagnetic field due to high-frequency field. The sine-Gordon expansion method which is one of the powerful methods has been considered for finding traveling wave solutions of the system of equations for the ion sound wave under the pressure of the Langmuir wave. This algorithm yields new complex hyperbolic function solutions to the system considered in this paper. Wolfram Mathematica 9 has been successfully used throughout the paper for mathematical calculations. [ABSTRACT FROM PUBLISHER]

In this study, a new method called improved Bernoulli sub-equation function method has been proposed. This method is based on the Bernoulli sub-ODE method. After we mention the general properties of proposed method, we apply this algorithm to the (2 + 1)-dimensional Boiti–Leon–Pempinelli equation system. This gives us some new prototype solutions such as exponential and rational function solutions. Then, we have plotted two- and three-dimensional surfaces of analytical solutions. Finally, we have submitted a comprehensive conclusion. [ABSTRACT FROM AUTHOR]

In this study, we obtain some new complex analytical solutions to the Kundu–Eckhaus equation which seems in the quantum field theory, weakly nonlinear dispersive water waves and nonlinear optics using improved Bernoulli sub-equation function method. After we have mentioned the general structure of improved Bernoulli sub-equation function method, we have successfully applied this method and then obtained some new complex hyperbolic and complex trigonometric function solutions. Two- and three-dimensional surfaces of analytical solutions have been plotted via wolfram Mathematica 9 version. At the end of this article, a conclusion has been submitted by mentioning important points founded in this study. [ABSTRACT FROM AUTHOR]

In this study, we have studied to obtain some new analytical solutions to the (1 + 1)-dimensional nonlinear Dispersive Modified Benjamin–Bona–Mahony equation by using modified exp-function method. We have submitted the general structure of modified exp-function method. We have founded some new analytical solutions such as hyperbolic and rational function solutions. Afterward, we have plotted 2D and 3D surfaces of analytical solutions obtained in this study by using computer programming wolfram Mathematica 9. [ABSTRACT FROM AUTHOR]

In this work, we survey exact solutions of Sasa–Satsuma equation (SSE). We utilize extended trial equation method (ETEM) and generalized Kudryashov method to acquire exact solutions of SSE. First of all, we gain some exact solutions such as soliton solutions, rational, Jacobi elliptic, and hyperbolic function solutions of SSE by means of ETEM. Furthermore, we procure dark soliton solution of this equation by the help of generalized Kudryashov method. Lastly, for certain parameter values, we draw two- and three-dimensional graphics of imaginary and real values of some exact solutions that we achieved using these methods. [ABSTRACT FROM PUBLISHER]

In this paper, we seek exact solutions of generalized Zakharov system. We use extended trial equation method to obtain exact solutions of this system. Consequently, we obtain some exact solutions including soliton solutions, rational, Jacobi elliptic and hyperbolic function solutions of this system by using extended trial equation method. [ABSTRACT FROM PUBLISHER]

In this paper, we acquire the soliton solutions of the nonlinear Schrodinger’s equation with dual power-law nonlinearity. Primarily, we use the extended trial equation method to find exact solutions of this equation. Then, we attain some exact solutions including soliton solutions, rational and elliptic function solutions of this equation using the extended trial equation method. [ABSTRACT FROM PUBLISHER]

In this paper, using the Extended Trial Equation (ETEM), we get new traveling wave solutions of the Generalized Benjamin, the Generalized Burger-Kdv Equations (GBE, GBKE). The obtained solutions not only constitute a novel analytical viewpoint in nonlinear complex phenomena, but they also form a new stand alone basis from which physical applications in this arena can be comprehended further, and moreover investigated. Furthermore, to concretely enrich this research production, we provide illustrative, Mathematica Release 7 based, 3D graphics of the gotten solutions, with well chosen, yet structure revealing parameters. [ABSTRACT FROM AUTHOR]

In this study, the decomposition method of Adomian has been applied for the approximate solution of homogeneous differential equations with dual variable and dual coefficients. [ABSTRACT FROM AUTHOR]

In this study, the decomposition method for the approximate solutions of the linear and nonlinear deterministic or stochastic differential equations, is given by the decomposition (Adomian) and has been investigated in general. In applying the method to the nonlinear deterministic hyperbolic equations, the concept of the Adomian polynomials has been explained and one application of the method given for the general state is obtained. [ABSTRACT FROM AUTHOR]

In this paper we study an analytic solution and a reliable numerical approximation of a linear and nonlinear parabolic equations by using the Adomian's decomposition method. The solution is calculated in the form of a series with easily computable components. The numerical results show the effectiveness of the method for this type of equations. Comparing the numerical results with their exact numerical results, they show that the present approach is relatively easy and highly accurate. [ABSTRACT FROM AUTHOR]

In this manuscript, we consider the Bernoulli sub-equation function method for obtaining new exponential prototype structures to the Cahn–Allen mathematical model. We obtained new results using this technique. We plotted two- and three-dimensional surfaces of the results using Wolfram Mathematica 9. At the end of this manuscript, we submitted a conclusion in a comprehensive manner. [ABSTRACT FROM AUTHOR]

In this paper, the Alternating Group Explicit (AGE) method is developed from a judicious splitting of the implicit equations derived from the finite difference discretisation of the partial differential equations. The resulting equations can be reformulated in a (2 × 2) explicit form resulting in a new stable and efficient method. Finally, the AGE method is used to investigate the numerical solution of the Telegraph equation in various 2D forms. [ABSTRACT FROM AUTHOR]