Performance assessment of six bias correction methods using observed and RCM data at upper Awash basin, Oromia, Ethiopia

Selecting a suitable bias correction method is important to provide reliable inputs for evaluation of climate change impact. Their influence was studied by comparing three discharge outputs from the SWAT model. The result after calibration with original RCM indicate that the raw RCM are heavily biased, and lead to streamflow simulation with large biases (NSE = 0.1, R2 = 0.53, MAE = 5.91 mm/°C, and PBIAS = 0.51). Power transformation and linear scaling methods performed best in correcting the frequency-based indices, while the LS method performed best in terms of the time series-based indices (NSE = 0.87, R2 = 0.78, MAE = 3.14 mm/°C, PBIAS = 0.24) during calibration. Meanwhile, daily translation was underestimating simulated streamflow compared with observed and considered as the least performing method. Precipitation correction method has higher visual influence than temperature, and its performance in streamflow simulations was consistent and significantly considerable. Power transformation and variance scaling showed highly qualified performance compared to others with indicated time series value (NSE = 0.92, R2 = 0.88, MAE = 1.58 mm/°C and PBIAS = 0.12) during calibration and validation of streamflow. Hence, PT and VARI methods were the dominant methods which remove biasness from RCM models at Akaki River basin.

Continued Roots, Power Transform and Critical Properties

We consider the problem of calculation of the critical amplitudes at infinity by means of the self-similar continued root approximants. Region of applicability of the continued root approximants is extended from the determinate (convergent) problem with well-defined conditions studied before by Gluzman and Yukalov (Phys. Lett. A 377 2012, 124), to the indeterminate (divergent) problem my means of power transformation. Most challenging indeterminate for the continued roots problems of calculating critical amplitudes, can be successfully attacked by performing proper power transformation to be found from the optimization imposed on the parameters of power transform. The self-similar continued roots were derived by systematically applying the algebraic self-similar renormalization to each and every level of interactions with their strength increasing, while the algebraic renormalization follows from the fundamental symmetry principle of functional self-similarity, realized constructively in the space of approximations. Our approach to the solution of the indeterminate problem is to replace it with the determinate problem, but with some unknown control parameter b in place of the known critical index β. From optimization conditions b is found in the way making the problem determinate and convergent. The index β is hidden under the carpet and replaced by b. The idea is applied to various, mostly quantum-mechanical problems. In particular, the method allows us to solve the problem of Bose-Einstein condensation temperature with good accuracy.

Nomogram of age-specific anti-Müllerian hormone levels in healthy Egyptian females

Background Anti-Müllerian hormone (AMH) is an important determinant of ovarian reserve in fertility workups in many clinical settings. Thus, we investigated the age dependent decline in AMH specific to the Egyptian population and sought to establish an age dependent reference interval parametrically. Methods Serum samples were collected from 841 apparently healthy women. AMH was measured using an electro-chemiluminescent technique. Box-Cox power transformation was used to make the AMH distribution Gaussian for parametric derivation of reference intervals. Results Power of 0.4 was found optimal for Gaussian transformation of AMH reference values. We demonstrate the strong negative relation between circulating AMH and female age with Spearman’s correlation coefficient of rS = −0.528. Age-specific reference interval was determined for every 5 years of age from 16 to 49, and nomogram was constructed by smoothing the lines connecting adjacent lower and upper reference limits. Conclusion The age-specific reference intervals and the age-AMH nomogram could be valuable in the clinical practice of in reproductive medicine. To our knowledge, this is the first study to confirm AMH levels in Egyptian females. We were able to explore age-related AMH levels specific to Egyptian females in the fertile age group and to treat skewed AMH data in a multi-step scheme using power transformation. Thus, a more accurate nomogram was constructed accommodating a profile delineated for a wide age range and a rescaled AMH axis improving its usability.

Critical Indices and Self-Similar Power Transform

“Odd” factor approximants of the special form suggested by Gluzman and Yukalov (J. Math. Chem. 2006, 39, 47) are amenable to optimization by power transformation and can be successfully applied to critical phenomena. The approach is based on the idea that the critical index by itself should be optimized through the parameters of power transform to be calculated from the minimal sensitivity (derivative) optimization condition. The critical index is a product of the algebraic self-similar renormalization which contributes to the expressions the set of control parameters typical to the algebraic self-similar renormalization, and of the power transform which corrects them even further. The parameter of power transformation is, in a nutshell, the multiplier connecting the critical exponent and the correction-to-scaling exponent. We mostly study the minimal model of critical phenomena based on expansions with only two coefficients and critical points. The optimization appears to bring quite accurate, uniquely defined results given by simple formulas. Many important cases of critical phenomena are covered by the simple formula. For the longer series, the optimization condition possesses multiple solutions, and additional constraints should be applied. In particular, we constrain the sought solution by requiring it to be the best in prediction of the coefficients not employed in its construction. In principle, the error/measure of such prediction can be optimized by itself, with respect to the parameter of power transform. Methods of calculation based on optimized power-transformed factors are applied and results presented for critical indices of several key models of conductivity and viscosity of random media, swelling of polymers, permeability in two-dimensional channels. Several quantum mechanical problems are discussed as well.

GARCH Models under Power Transformed Returns: Empirical Evidence from International Stock Indices

This study evaluates the empirical performance of four power transformation families: extended Tukey, Modulus, Exponential, and Yeo--Johnson, in modeling the return in the context of GARCH(1,1) models with two error distributions: Gaussian (normal) and Student-t. We employ an Adaptive Random Walk Metropolis method in Markov Chain Monte Carlo scheme to draw parameters. Using 19 international stock indices from the Oxford-Man Institute and basing on the log likelihood, Akaike Information Criterion, Bayesian Information Criterion, and Deviance Information Criterion, the use of power transformation families to the return series clearly improves the fit of the normal GARCH(1,1) model. In particular, the Modulus transformation family provides the best fit. Under Student's t-error distribution assumption, the GARCH(1,1) models under power transformed returns perform better in few cases.

Reactive power transformation using а passive electronic transducer

Transformation of reactive power into active power, which can be used to perform work for various purposes, is of practical use. Goal. The aim of the work is analysis of the processes of resonant conversion of reactive power into active power in the proposed converter circuit. Methodology. A practical solution to this problem can be real-ized using a converter circuit consisting of two in-ductively coupled parallel and series resonant circuits. The use of a parallel circuit with resonance currents minimizes the impact on the processes in the reactive power source. The use of a series circuit with a voltage resonance allows maximizing the original active power in the converter load. Results. The simplest scheme of a passive electronic converter of reactive power into active power is proposed. The conditions are determined, whose fulfillment minimizes the influence of the proposed scheme on the processes in the reactive power source at the maxi-mum current in the converter load. Originality. Efficiency of the device under test means maximum cur-rent and power in the load with minimum impact on the inductance of the reactive power source. Practical value. The parameters of a real circuit have been calculated, which allows for practically lossless conversion of reactive power into active power with a minimum effect on the current in the source.