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Ergin, M., and Ö. Koşkan. "Assessing transformation methods for group comparisons under violated assumptions: type I error rate and test power." Arquivo Brasileiro de Medicina Veterinária e Zootecnia 75, no. 5 (2023): 883–92. http://dx.doi.org/10.1590/1678-4162-13026.
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ABSTRACT In this study, some transformation methods that are applied when the assumptions of analysis of variance are not met are evaluated in terms of type I error rate and the test power, under circumstances with different distributions, number of groups, number of observations, variance ratios, and different standard deviation differences. The data set used in the study consisted of random numbers generated from N (0,1), and χ2(3) distributions using the random function of the Numpy library in the Python programming language. The logarithmic, square root and root transformations were evaluated on ANOVA based on simulation combinations. It was observed that the transformation techniques of taking the square root after adding 0.5 and 0.375 to the data were relatively more reliable compared to other transformations in terms of type I error rate. However, in every case, type I error rate determined at the beginning of the experiment increased both before and after the transformation was applied. In particular, interestingly, the third and fourth degree root transformations gave better results of test power in the right skewed distribution. In addition, we compared the transformation techniques in question to determine the normality of the data and the homogeneity of variances by a real data.
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Ahrens, William H., Darrell J. Cox, and Girish Budhwar. "Use of the Arcsine and Square Root Transformations for Subjectively Determined Percentage Data." Weed Science 38, no. 4-5 (1990): 452–58. http://dx.doi.org/10.1017/s0043174500056824.
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The arcsine and square root transformations were tested on 82 weed control data sets and 62 winter wheat winter survival data sets to determine effects on normality of the error terms, homogeneity of variance, and additivity of the model. Transformations appeared to correct deficiencies in these three parameters in the majority of data sets, but had adverse effects in certain other data sets. Performing the recommended transformation in conjunction with omitting treatments having identical replicate observations provided a high percentage of correction of non-normality, heterogeneity of variance, and nonadditivity. The arcsine transformation, not generally recommended for data sets having values from 0 to 20% or 80 to 100%, was as effective in correcting non-normality, heterogeneity of variance, and nonadditivity in these data sets as was the recommended square root transformation. A majority of data sets showed differences between transformed and nontransformed data in mean separations determined using LSD (0.05), although most of these differences were minor and had little effect on interpretation of results.
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Nerger, Lars, Tijana Janjić, Jens Schröter, and Wolfgang Hiller. "A Unification of Ensemble Square Root Kalman Filters." Monthly Weather Review 140, no. 7 (2012): 2335–45. http://dx.doi.org/10.1175/mwr-d-11-00102.1.
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Abstract In recent years, several ensemble-based Kalman filter algorithms have been developed that have been classified as ensemble square root Kalman filters. Parallel to this development, the singular “evolutive” interpolated Kalman (SEIK) filter has been introduced and applied in several studies. Some publications note that the SEIK filter is an ensemble Kalman filter or even an ensemble square root Kalman filter. This study examines the relation of the SEIK filter to ensemble square root filters in detail. It shows that the SEIK filter is indeed an ensemble square root Kalman filter. Furthermore, a variant of the SEIK filter, the error subspace transform Kalman filter (ESTKF), is presented that results in identical ensemble transformations to those of the ensemble transform Kalman filter (ETKF), while having a slightly lower computational cost. Numerical experiments are conducted to compare the performance of three filters (SEIK, ETKF, and ESTKF) using deterministic and random ensemble transformations. The results show better performance for the ETKF and ESTKF methods over the SEIK filter as long as this filter is not applied with a symmetric square root. The findings unify the separate developments that have been performed for the SEIK filter and the other ensemble square root Kalman filters.
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Thinh, Hoang Xuan, Nguyen Truong Giang, and Vu Van Khiem. "A Comparative Analysis of Data Transformation Methods for Constructing a Surface Roughness Model in Turning Processes." International Journal of Mechanical Engineering and Robotics Research 13, no. 4 (2024): 428–34. http://dx.doi.org/10.18178/ijmerr.13.4.428-434.
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Data conversion methods are used to transform datasets into new datasets, which may exhibit a distribution pattern different from the original dataset. Enhancing model accuracy is one of the applications of data transformation. This study compared the effectiveness of three data transformation methods: square root, logarithmic, and inverse transformation. This comparison was conducted in the context of constructing a surface roughness model for a turning process. Surface roughness plays a crucial role in determining corrosion resistance, chemical corrosion resistance, fatigue strength, and joint accuracy. These parameters significantly impact the product's operational ability and durability. An experimental turning process was performed, comprising a total of eighteen experiments designed using the Box-Behnken method. Surface roughness was selected as the response for each experiment. The three aforementioned data transformation methods were applied to the surface roughness dataset. Four surface roughness regression models were constructed, including a model without data transformation, a model with square root transformation, a model with logarithmic transformation, and a model with inverse transformation. The effectiveness of the three data transformation methods was compared using four metrics: Coefficient of Determination (R2), Adjusted Coefficient of Determination (R2(adj)), Mean Absolute Error (%MAE), and Mean Squared Error (%MSE). The study revealed that the logarithmic transformation was the most effective, followed by the square root transformation. The accuracy of the surface roughness regression model improved when utilizing these two transformations. The inverse transformation exhibited the least effectiveness among the three data transformation methods.
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Hildebrandt, Anna K., Matthias Dietzen, Thomas Lengauer, Hans-Peter Lenhof, Ernst Althaus, and Andreas Hildebrandt. "Efficient computation of root mean square deviations under rigid transformations." Journal of Computational Chemistry 35, no. 10 (2013): 765–71. http://dx.doi.org/10.1002/jcc.23513.
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Thinh, Hoang Xuan, and Tran Van Dua. "Optimal Surface Grinding Regression Model Determination with the SRP Method." Engineering, Technology & Applied Science Research 14, no. 3 (2024): 14713–18. http://dx.doi.org/10.48084/etasr.7573.
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The construction of the regression models used to control machining processes is the objective of many experimental studies. Therefore, the effectiveness of the machining process control largely depends on the regression model’s accuracy. This study was conducted to determine the optimal regression model of surface grinding. Accordingly, eight different surface grinding regression models were constructed, including one model without data transformation and seven models that utilized various data transformations. The seven data transformations employed entailed square root transformation, logarithmic transformation, inverse transformation, exponential transformation, asinh transformation, Box-Cox transformation, and Johnson transformation. The process of determining the optimal model was carried out considering five parameters: R2, R2(adj), R2(pred) (predicted R2), MAE (Mean Absolute Error), and MSE (Mean Squared Error). SRP (Simple Ranking Process) was the optimization method followed to identify the best regression model. The Box-Cox transformation was recognized as the most accurate surface grinding regression model.
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Tsyganov, A. V., and Yu V. Tsyganova. "Decentralized square-root information Kalman filtering based on J-orthogonal transformations." Journal of Physics: Conference Series 1745, no. 1 (2021): 012112. http://dx.doi.org/10.1088/1742-6596/1745/1/012112.
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Kaptsov, Oleg V. "Iterations and Groups of Formal Transformations." Journal of Siberian Federal University. Mathematics & Physics 14, no. 5 (2021): 584–88. http://dx.doi.org/10.17516/1997-1397-2021-14-5-584-588.
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In this paper, we consider the problem of formal iteration. We construct an area preserving mapping which does not have any square root. This leads to a counterexample to Moser’s existence theorem for an interpolation problem. We give examples of formal transformation groups such that the iteration problem has a solution for every element of the groups
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BINNENHEI, CARSTEN. "IMPLEMENTATION OF ENDOMORPHISMS OF THE CAR ALGEBRA." Reviews in Mathematical Physics 07, no. 06 (1995): 833–69. http://dx.doi.org/10.1142/s0129055x95000323.
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The implementation of non-surjective Bogoliubov transformations in Fock states over CAR algebras is investigated. Such a transformation is implementable by a Hilbert space of isometries if and only if the well-known Shale-Stinespring condition is met. In this case, the dimension of the implementing Hilbert space equals the square root of the Watatani index of the associated inclusion of CAR algebras, and both are determined by the Fredholm index of the corresponding one-particle operator. Explicit expressions for the implementing operators are obtained, and the connected components of the semigroup of implementable transformations are described.
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Yuan, Munan, Xiru Li, and Haibao Tan. "An Elastic Fine-Tuning Dual Recurrent Framework for Non-Rigid Point Cloud Registration." Sensors 25, no. 11 (2025): 3525. https://doi.org/10.3390/s25113525.
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Non-rigid transformation is based on rigid transformation by adding distortions to form a more complex but more consistent common scene. Many advanced non-rigid alignment models are implemented using supervised learning; however, the large number of labels required for the training process makes their application difficult. Here, an elastic fine-tuning dual recurrent computation for unsupervised non-rigid registration is proposed. At first, we transform a non-rigid transformation into a series of combinations of rigid transformations using an outer recurrent computational network. Then, the inner loop layer computes elastic-controlled rigid incremental transformations by controlling the threshold to obtain a finely coherent rigid transformation. Finally, we design and implement loss functions that constrain deformations and keep transformations as rigid as possible. Extensive experiments validate that the proposed method achieves state-of-the-art performance with 0.01219 earth mover’s distances (EMDs) and 0.0153 root mean square error (RMSE) in non-rigid and rigid scenes, respectively.
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Rendevski, Vladimir, Boris Aleksovski, Milena Kolevska, et al. "Effects of data transformation on multivariate analyses in intracerebral hemorrhage." Macedonian Pharmaceutical Bulletin 62, no. 2 (2016): 37–42. http://dx.doi.org/10.33320/maced.pharm.bull.2016.62.02.004.
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Multivariate statistical approaches have been increasingly applied in hemorrhagic stroke data analysis. Nevertheless, several aspects regarding their relevance and validity in respect of the application of data transformations have not been studied in details. This paper examines the effects of different data transformations in the standard statistical methods of the multivariate analysis of the intracerebral hemorrhage (ICH) parameters in small group samples. Two different methods for data transformations (log transformation (log(Xi )), square root transformation (√Xi ))have been carried out. The initial volume of the ICH have been studied using several test for skewness, kurtosis, histogram distribution method and different quartile-quartile (Q-Q) and probability-probability (P-P) plots as criteria for normal distribution. Multivariate analyses for the prediction of the perifocal edema was performed using raw and transformed data. Our results indicate that the data transformation operations should be performed very carefully because different analytical outputs lead to different scientific conclusions.
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Fang, Liang, and Yiping Hong. "Uncertain revised regression analysis with responses of logarithmic, square root and reciprocal transformations." Soft Computing 24, no. 4 (2019): 2655–70. http://dx.doi.org/10.1007/s00500-019-03821-x.
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Thirel, Guillaume, Léonard Santos, Olivier Delaigue, and Charles Perrin. "On the use of streamflow transformations for hydrological model calibration." Hydrology and Earth System Sciences 28, no. 21 (2024): 4837–60. http://dx.doi.org/10.5194/hess-28-4837-2024.
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Abstract. The calibration of hydrological models through the use of automatic algorithms aims at identifying parameter sets that minimize the deviation of simulations from observations (often streamflows). Further, the choice of objective function (i.e. the criterion or combination of criteria for optimization) can significantly impact the parameter set values identified as optimal by the algorithm. This article discusses how mathematical transformations, which are sometimes applied to the target variable before calculating the objective function, impact model simulations. Such transformations, for example square root or logarithmic, aim at increasing the weight of errors made in specific ranges of a hydrograph. We show in a catchment set that the impact of these transformations on the obtained time series can sometimes be different from their expected behaviour. Extreme transformations, such as squared or inverse squared transformations, lead to models that are specialized for extreme streamflows but show poor performance outside the range of the targeted streamflows and are less robust. Other transformations, such as the power 0.2 and the Box–Cox and logarithmic transformations, can be categorized as more generalist and show good performance for the medium range of streamflows, along with acceptable performance for extreme streamflows.
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Nakonechny, Alexander, Grigory Kudin, Petr Zinko, and Taras Zinko. "GUARANTEED ROOT-MEAN-SQUARE ESTIMATES OF LINEAR MATRIX TRANSFORMATIONS UNDER CONDITIONS OF STATISTICAL UNCERTAINTY." Journal of Automation and Information sciences 2 (March 1, 2021): 24–37. http://dx.doi.org/10.34229/1028-0979-2021-2-3.
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Linear estimation of observations in conditions of various types of interference in order to obtain unbiased estimates is the subject of research in numerous scientific publications. The problem of linear regression analysis in conditions when the elements of vector observations are known matrices that allow small deviations from the calculated ones was studied in previous publications of the authors. Using the technology of pseudo inverse operators, as well as the perturbation method, the problem was solved under the condition that linearly independent matrices are subject to small perturbations. The parameters of the linear estimates were presented in the form of expansions in a small parameter. Over the past decades, solving linear estimation problems under uncertainty has been carried out within the framework of the well-known minimax estimation method. Formally, the problems that arise in this direction are solved in the presence of some spaces for unknown observation parameters, as well as spaces to which observation errors may belong. The coefficients of the linear estimates are determined in the process of optimizing the guaranteed mean-square error of the desired estimate. Thus, the subject of scientific research can be problems of linear estimation of unknown rectangular matrices based on observations from errors with unknown correlation matrices of errors: unknown matrices belong to some bounded set, correlation matrices of random perturbations of the observation vector are unknown, but it is possible to assume cases when they belong to one or another defined bounded set. Some formulations of problems of linear estimation of observations are investigated in the proposed publication. The problem of linear estimation for a vector of observations of a special form is considered, the components of which are known rectangular matrices that are subject to small perturbations. Variants of the problem statement are proposed, which allow obtaining an analytical solution in the first approximation of a small parameter. A test example is presented.
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Marini, Richard P., and Michele Choma Marini. "ANALYZING PERCENTAGE DATA." HortScience 28, no. 5 (1993): 563a—563. http://dx.doi.org/10.21273/hortsci.28.5.563a.
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Data generated from horticulture experiments often are expressed as percentages. Since these data may not approximate normality, we often automatically transform the data before analysis. Is this automatic transformation always correct? Non-transformed data may already approximate a normal distribution. Should these data be transformed? What does transforming a normal data set do to it? To address these questions, a real data set was used to check the assumption of normality and examine regression models before and after transformation of normal and non-normal percentage data. Transformations include both standard arcsin of the square root of the proportion and a log (log) transformation. We will show that transforming normal data can make it non-normal and alter conclusions. Testing assumptions before and after transformation will be emphasized. The SAS procedures GLM and UNIVARIATE will be used to generate output and demonstrate results of normality tests and different conclusions resulting from unnecessary transformations.
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Paiva-Peredo, Ernesto, Diego Gonzales-Rodriguez, Herrera William Trujillo, Soria Quijaite Juan Jesús, Diana Quispe-Arpasi, and Paulino Christian Ovalle. "Transformations for non-destructive evaluation of brix in mango by reflectance spectroscopy and machine learning." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 1 (2024): 532–46. https://doi.org/10.11591/ijece.v14i1.pp532-546.
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Mango is a very popular climacteric fruit in America and Europe. Among the internal properties of the mango, total soluble solids (TSS) are an adequate indicator to estimate the quality of mango, however, the measurement of this indicator requires destructive tests. Several research have addressed similar issues; they have made use of pre-processing transformations without making it clear which of them is statistically better. Here, we created a new spectral database to build machine learning (ML) models. We analyzed a total of 18 principal component regression (PCR) models and 18 partial least squared regression (PLSR) models, where 4 types of transformations, 3 different feature extractors, and 3 different pre-processing techniques are combined. The research proposes a double cross validation (CV) both to determine the optimal number of components and to obtain the final metrics. The best model had a root mean square error (RMSE) of 1.1382 °Brix and a RMSE on the transformed scale of 0.5140. The best model used 4 components, used y2 transformation, reflectance R as the independent variable and MSC as a pre- processing technique.
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Karkulovska, P. S., and M. S. Karkulovska. "Simulation of statistical mean and variance of normally distributed random values, transformed by nonlinear functions $\sqrt{|X|}$ and $\sqrt{X}$." Mathematical Modeling and Computing 9, no. 2 (2022): 318–25. http://dx.doi.org/10.23939/mmc2022.02.318.
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This paper presents theoretical studies of formation regularities for the statistical mean and variance of normally distributed random values with the unlimited argument values subjected to nonlinear transformations of functions $\sqrt{|X|}$ and $\sqrt{X}$. It is shown that for nonlinear square root transformation of a normally distributed random variable, the integrals of higher order mean $n>1$ satisfy the inequality $\overline{(y-\overline{Y})^n}\neq 0$. On the basis of the theoretical research, the correct boundaries $m,\sigma \to \infty$ of error transfer formulas are suggested.
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Hasan, Güveli, Baki Adnan, and Güveli Ebru. "The Impact of the Cognitive Conflict Approach on the Elimination of the Misconception in Square Root Numbers." Education Quarterly Reviews 5, Special Issue 2 (2022): 39–52. https://doi.org/10.31014/aior.1993.05.04.604.
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This study aims to determine the effect of the cognitive conflict approach on the elimination of misconceptions in square root numbers. For this purpose, this study was conducted with 8th-grade students of a secondary school in a region of Turkey. A three tiered diagnostic test was used to determine the impact of the 5-step cognitive conflict approach in the study. This test was used as a pre-test before applications and the same test was used as a post-test after applications in the same class. The test results of the students were divided into 4 groups called "misconception", "lack of knowledge", "lack of confidence", "scientific knowledge", and these groups were also divided into categories (A, B, ...). 5-step cognitive conflict approach made some transformations between categories. The greatest transformation was the transformation of misconceptions into scientific knowledge. However, it was seen that some misconceptions (B category) continued after the applications. In light of these findings, it is suggested that teachers pay attention to the mathematical language and mathematical representations they use during instruction. Moreover, the topic of root numbers should definitely be explained using the Pythagorean Theorem, and the guidebooks should be revised accordingly.
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Saidel and, Gerald M., and Erin H. Liu. "Model Transformations to Evaluate Transient Thermal Responses at a Tissue Surface." Journal of Biomechanical Engineering 123, no. 4 (2001): 370–72. http://dx.doi.org/10.1115/1.1385844.
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For a spatially distributed model describing the transient temperature response of a thermistor-tissue system, Wei et al., [J. Biomech. Eng., 117:74–85, 1995] obtained an approximate transformation for fast analysis of the temperature response at the tissue surface. This approximate transformation reduces the model to a single ordinary differential equation. Here, we present an exact transformation that yields a single differential-integral equation. Numerical solutions from the approximate and exact transformations were compared to evaluate the differences with several sets of parameter values. The maximum difference between the exact and approximate solutions did not exceed 15 percent and occurred for only a short time interval. The root-mean-square error of the approximate solution was no more than 5 percent and within the level of experimental noise. Under the experimental conditions used by Wei et al., the approximate transformation is justified for estimating model parameters from transient thermal responses.
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Paiva-Peredo, Ernesto, Diego Gonzales-Rodriguez, William Trujillo Herrera, Juan Jesús Soria Quijaite, Diana Quispe-Arpasi, and Christian Ovalle Paulino. "Transformations for non-destructive evaluation of brix in mango by reflectance spectroscopy and machine learning." International Journal of Electrical and Computer Engineering (IJECE) 14, no. 1 (2024): 532. http://dx.doi.org/10.11591/ijece.v14i1.pp532-546.
Full textAbstract:
Mango is a very popular climacteric fruit in America and Europe. Among the internal properties of the mango, total soluble solids (TSS) are an adequate indicator to estimate the quality of mango, however, the measurement of this indicator requires destructive tests. Several research have addressed similar issues; they have made use of pre-processing transformations without making it clear which of them is statistically better. Here, we created a new spectral database to build machine learning (ML) models. We analyzed a total of 18 principal component regression (PCR) models and 18 partial least squared regression (PLSR) models, where 4 types of transformations, 3 different feature extractors, and 3 different pre-processing techniques are combined. The research proposes a double cross validation (CV) both to determine the optimal number of components and to obtain the final metrics. The best model had a root mean square error (RMSE) of 1.1382 °Brix and a RMSE on the transformed scale of 0.5140. The best model used 4 components, used y<sup>2</sup> transformation, reflectance R as the independent variable and MSC as a pre-processing technique.
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Asghari, Mohammad, Amir M. Fathollahi-Fard, S. M. J. Mirzapour Al-e-hashem, and Maxim A. Dulebenets. "Transformation and Linearization Techniques in Optimization: A State-of-the-Art Survey." Mathematics 10, no. 2 (2022): 283. http://dx.doi.org/10.3390/math10020283.
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To formulate a real-world optimization problem, it is sometimes necessary to adopt a set of non-linear terms in the mathematical formulation to capture specific operational characteristics of that decision problem. However, the use of non-linear terms generally increases computational complexity of the optimization model and the computational time required to solve it. This motivates the scientific community to develop efficient transformation and linearization approaches for the optimization models that have non-linear terms. Such transformations and linearizations are expected to decrease the computational complexity of the original non-linear optimization models and, ultimately, facilitate decision making. This study provides a detailed state-of-the-art review focusing on the existing transformation and linearization techniques that have been used for solving optimization models with non-linear terms within the objective functions and/or constraint sets. The existing transformation approaches are analyzed for a wide range of scenarios (multiplication of binary variables, multiplication of binary and continuous variables, multiplication of continuous variables, maximum/minimum operators, absolute value function, floor and ceiling functions, square root function, and multiple breakpoint function). Furthermore, a detailed review of piecewise approximating functions and log-linearization via Taylor series approximation is presented. Along with a review of the existing methods, this study proposes a new technique for linearizing the square root terms by means of transformation. The outcomes of this research are anticipated to reveal some important insights to researchers and practitioners, who are closely working with non-linear optimization models, and assist with effective decision making.
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Tehrani, Ali Moradi, Evert Slob, and Wim Mulder. "Quasi-analytical method for frequency-to-time conversion in CSEM applications." GEOPHYSICS 77, no. 5 (2012): E357—E363. http://dx.doi.org/10.1190/geo2011-0432.1.
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Frequency-to-time transformations are of interest to controlled-source electromagnetic methods when time-domain data are inverted for a subsurface resistivity model by numerical frequency-domain modeling at a selected, small number of frequencies whereas the data misfit is determined in the time domain. We propose an efficient, Prony-type method using frequency-domain diffusive-field basis functions for which the time-domain equivalents are known. Diffusive fields are characterized by an exponential part whose argument is proportional to the square root of frequency and a part that is polynomial in integer powers of the square root of frequency. Data at a limited number of frequencies suffice for the transformation back to the time. In the exponential part, several diffusion-time values must be chosen. Once a suitable range of diffusion-time values are found, the method is quite robust in the number of values used. The highest power in the polynomial part can be determined from the source and receiver type. When the frequency-domain data are accurately approximated by the basis functions, the time-domain result is also accurate. This method is accurate over a wider time range than other methods and has the correct late-time asymptotic behavior. The method works well for data computed for layered and 3D subsurface models.
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Alber, S. A., and D. W. Schaffner. "Evaluation of data transformations used with the square root and schoolfield models for predicting bacterial growth rate." Applied and Environmental Microbiology 58, no. 10 (1992): 3337–42. http://dx.doi.org/10.1128/aem.58.10.3337-3342.1992.
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Yuan, Sihan, and Daniel J. Eisenstein. "Decorrelating the errors of the galaxy correlation function with compact transformation matrices." Monthly Notices of the Royal Astronomical Society 486, no. 1 (2019): 708–24. http://dx.doi.org/10.1093/mnras/stz899.
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Abstract Covariance matrix estimation is a persistent challenge for cosmology, often requiring a large number of synthetic mock catalogues. The off-diagonal components of the covariance matrix also make it difficult to show representative error bars on the 2-point correlation function (2PCF) since errors computed from the diagonal values of the covariance matrix greatly underestimate the uncertainties. We develop a routine for decorrelating the projected and anisotropic 2PCF with simple and scale-compact transformations on the 2PCF. These transformation matrices are modelled after the Cholesky decomposition and the symmetric square root of the Fisher matrix. Using mock catalogues, we show that the transformed projected and anisotropic 2PCF recover the same structure as the original 2PCF while producing largely decorrelated error bars. Specifically, we propose simple Cholesky-based transformation matrices that suppress the off-diagonal covariances on the projected 2PCF by ${\sim } 95{{\ \rm per\ cent}}$ and that on the anisotropic 2PCF by ${\sim } 87{{\ \rm per\ cent}}$. These transformations also serve as highly regularized models of the Fisher matrix, compressing the degrees of freedom so that one can fit for the Fisher matrix with a much smaller number of mocks.
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Ivan Gorbenko and Serhii Kandii. "The analysis of Hermite factor of BKZ algorithm on small lattices." Computer Science and Cybersecurity, no. 1 (September 12, 2024): 22–34. http://dx.doi.org/10.26565/2519-2310-2024-1-02.
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Lattice cryptography is one of the promising directions in modern cryptography research. Digital signatures and key encapsulation mechanisms on lattices have already been used in practice. In the future, such quantum-resistant transformations on lattices replace all standards that are not resistant to attacks on quantum computers. This makes the analysis of their security extremely relevant. Analysis of the security of cryptographic transformations on lattices is often reduced to the estimation of the minimum block size in the lattice reduction algorithm. For the expansion of small vectors, a reduction algorithm can be obtained for a given block size, the GSA model is often used, which uses the so-called Hermitian factor to predict the size of the vectors that the lattice reduction algorithm can obtain given the parameters. Asymptotic formulas have been developed to evaluate it in practice, but the question of their accuracy on cryptographic lattices has not been fully investigated. The work obtained estimates of the accuracy of the existing asymptotic estimates of the Hermite factor for lattices of sizes 120, 145, 170 for the classical BKZ algorithm. Research was conducted using the fpylll library. It was shown that the existing estimators are equivalent from a practical point of view and have a sufficiently small root mean square deviation from the true values. A formula was obtained that binds the root-mean-square error of approximation of the Hermit factor to the cryptographic parameters of lattices. The obtained results are useful for refining the security assessments of existing cryptographic transformations.
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Nascimento, Jhennifer dos Santos, Luciano Gonçalves Batista, Wagner Faria Barbosa, et al. "Data transformations for ANOVA assumption violations in agrarian sciences subfields: a systematic review, simulation study, and practical guidelines." REVISTA DELOS 17, no. 61 (2024): e2782. http://dx.doi.org/10.55905/rdelosv17.n61-138.
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The use of data transformations for validating variance analysis has been a technique adopted by the scientific community since the 20th century. In this study, we conducted a systematic review covering four subareas of agricultural sciences (entomology, plant science, forestry, and soil science) to investigate how this technique has been applied in these fields. In addition to the systematic review, we conducted a simulation study to evaluate the effectiveness of logarithmic, square root, arcsine, and Box-Cox transformations in correcting violations of the assumptions of normality and homogeneity of variances, as these were the most frequently used transformations in the systematic review. Although some transformations effectively homogenize variances, few correct both non-normality and heterogeneity simultaneously. To facilitate the screening phase in the systematic review, we developed a web application as an alternative for users who are not familiar with or uncomfortable using Python's interface. Finally, we offer practical guidelines for applying ANOVA with transformations, providing the audience with a helpful tool to minimize the errors and misconceptions identified in the systematic review.
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Nashed, Gamal G. L. "Exact Axially Symmetric Solution inf(T)Gravity Theory." Advances in High Energy Physics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/857936.
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A general tetrad field with sixteen unknown functions is applied to the field equations off(T)gravity theory. An analytic vacuum solution is derived with two constants of integration and an angleΦthat depends on the angle coordinateϕand radial coordinater. The tetrad field of this solution is axially symmetric and the scalar torsion vanishes. We calculate the associated metric of the derived solution and show that it represents Kerr spacetime. Finally, we show that the derived solution can be described by two local Lorentz transformations in addition to a tetrad field that is the square root of the Kerr metric. One of these local Lorentz transformations is a special case of Euler’s angles and the other represents a boost when the rotation parameter vanishes.
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Tang, Siyu, Chong Du, and Tangzhe Nie. "Inversion Estimation of Soil Organic Matter in Songnen Plain Based on Multispectral Analysis." Land 11, no. 5 (2022): 608. http://dx.doi.org/10.3390/land11050608.
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Sentinel-2A multi-spectral remote sensing image data underwent high-efficiency differential processing to extract spectral information, which was then matched to soil organic matter (SOM) laboratory test values from field samples. From this, multiple-linear stepwise regression (MLSR) and partial least square (PLSR) models were established based on a differential algorithm for surface SOM modeling. The original spectra were subjected to basic transformations with first- and second-derivative processing. MLSR and PLSR models were established based on these methods and the measured values, respectively. The results show that Sentinel-2A remote sensing imagery and SOM content correlated in some bands. The correlation between the spectral value and SOM content was significantly improved after mathematical transformation, especially square-root transformation. After differential processing, the multi-band model had better predictive ability (based on fitting accuracy) than single-band and unprocessed multi-band models. The MLSR and PLSR models of SOM had good prediction functionality. The reciprocal logarithm first-order differential MLSR regression model had the best prediction and inversion results (i.e., most consistent with the real-world data). The MLSR model is more stable and reliable for monitoring SOM content, and provides a feasible method and reference for SOM content-mapping of the study area.
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Zarychta, Roksana, Adrian Zarychta, and Katarzyna Bzdęga. "Ecogeomorphological Transformations of Aeolian Form—The Case of a Parabolic Dune, Poland." Remote Sensing 13, no. 19 (2021): 3937. http://dx.doi.org/10.3390/rs13193937.
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The range of natural environmental degradation caused by anthropogenic activity may include geomorphological forms such as dunes resulting from the build-up activity of the wind. In effect, such environmental transformation affects changes connected not only with their relief, but also with the presence and health of diverse plant and animal inhabitants. The subject of the survey was a parabolic dune with asymmetric shape, the sand of which was subjected to exploitation over many years. Terrain data acquired by means of GNSS (Global Navigation Satellite Systems) served to elaborate the present relief of the surveyed dune and to reconstruct its primary relief. These were mainly places where the impacts of human activities were recorded. For this purpose, ordinary kriging (OK) estimation was performed. Simultaneously, satellite data and UAV (Unmanned Aerial Vehicle) imaging were acquired, and subjected to image fusion in order to acquire near infrared bands (NIR), red, green, blue in high spatial resolution. These in turn were applied so as to estimate the condition of the vegetation overplanting the dune and surrounding terrain. The correctness of the modelling was verified by cross-validation (CV), which disclosed low error values. Such values in present and primary relief were, respectively, mean error (ME) at −0.009 and −0.014, root mean square error (RMSE) at 0.564 and 0.304 and root mean square standardised error (RMSSE) at 0.999 and 1.077. Image fusion, with use of pansharpening allowed a colour-infrared composition (CIR) and a Modified Chlorophyll Absorption in Reflectance Index 1 (MCARI1) to be obtained. Their analysis disclosed that vegetation on the dune is characterised by worse health condition as compared with the surrounding area thereof. The proposed approach enabled the environmental condition of the surveyed dune to be analysed, and thereby it allows for a determination of the consequences of further uncontrolled sand recovery without taking into account the historical cartographic materials customarily considered to be the main source of information.
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Leipnik, R. B. "Reduction of second order linear dynamical systems, with large dissipation, by state variable transformations." Journal of the Australian Mathematical Society. Series B. Applied Mathematics 32, no. 2 (1990): 207–22. http://dx.doi.org/10.1017/s0334270000008432.
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AbstractLinear dynamical systems of the Rayleigh form are transformed by linear state variable transformations , where A and B are chosen to simplify analysis and reduce computing time. In particular, A is essentially a square root of M, and B is a Lyapunov quotient of C by A. Neither K nor C is required to be symmetric, nor is C small. The resulting state-space systems are analysed by factorisation of the evolution matrices into reducible factors. Eigenvectors and eigenvalues are determined by these factors. Conditions for further simplification are derived in terms of Kronecker determinants. These results are compared with classical reductions of Rayleigh, Duncan, and Caughey, which are reviewed at the outset.
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Hill, James M., and Alex McNabb. "On Dankwerts' transformation for two variable coupled systems." Bulletin of the Australian Mathematical Society 41, no. 3 (1990): 355–69. http://dx.doi.org/10.1017/s0004972700018220.
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The problem of obtaining explicit solutions to coupled linear reaction-diffusion partial differential equations is generally recognised as technically very difficult. Frequently it is possible to deduce seemingly simple expressions for Laplace or Fourier transforms of the solution but such transforms tend not to be amenable to simple inversion and usually involve, for example, square roots within a square root. Fortunately however, a general uncoupling procedure has previously been established which provides explicit integral expressions in terms of classical heat functions. Such expressions are especially useful for problems with zero boundary data but non-zero initial data. The purpose of this paper is to provide the formal details necessary to deduce corresponding uncoupling transformations for two dependent variables, which preserve zero initial data and constant boundary data. For the case of one dependent variable such a transformation is known as Dankwerts' transformation. For coupled systems the existence of a Dankwerts' transformation means that together with the existing uncoupling transformation, solutions of boundary value problems involving constant boundary data, can be decomposed, just as for the single heat equation, into a contribution from the initial condition and zero boundary data and a contribution from non-zero boundary data and zero initial condition. The problem considered is highly non-trivial and the final expressions obtained are correspondingly complicated. Nevertheless the end results are explicit and together with standard integration routines constitute a powerful solution procedure.
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Fernández, Claudio Ignacio, Ata Haddadi, Brigitte Leblon, Jinfei Wang, and Keri Wang. "Comparison between Three Registration Methods in the Case of Non-Georeferenced Close Range of Multispectral Images." Remote Sensing 13, no. 3 (2021): 396. http://dx.doi.org/10.3390/rs13030396.
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Cucumber powdery mildew, which is caused by Podosphaera xanthii, is a major disease that has a significant economic impact in cucumber greenhouse production. It is necessary to develop a non-invasive fast detection system for that disease. Such a system will use multispectral imagery acquired at a close range with a camera attached to a mobile cart’s mechanic extension. This study evaluated three image registration methods applied to non-georeferenced multispectral images acquired at close range over greenhouse cucumber plants with a MicaSense® RedEdge camera. The detection of matching points was performed using Speeded-Up Robust Features (SURF), and outliers matching points were removed using the M-estimator Sample Consensus (MSAC) algorithm. Three geometric transformations (affine, similarity, and projective) were considered in the registration process. For each transformation, we mapped the matching points of the blue, green, red, and NIR band images into the red-edge band space and computed the root mean square error (RMSE in pixel) to estimate the accuracy of each image registration. Our results achieved an RMSE of less than 1 pixel with the similarity and affine transformations and of less than 2 pixels with the projective transformation, whatever the band image. We determined that the best image registration method corresponded to the affine transformation because the RMSE is less than 1 pixel and the RMSEs have a Gaussian distribution for all of the bands, but the blue band.
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Ilic, Sinisa. "Comparison of compression ratios for ECG signals by using three time-frequency transformations." Facta universitatis - series: Electronics and Energetics 20, no. 2 (2007): 223–32. http://dx.doi.org/10.2298/fuee0702223i.
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In this paper are presented compression results of ECG signal by using three time-frequency transformations: Discrete Wavelet Transform, Wavelet Packets and Modified Cosine Transform. By using transforms mentioned, samples of signals are transformed to appropriate groups of transformation coefficients. Almost all coefficients below the determined threshold are rounded to zero values and by inverse transform the similar signal to original one is created. By using run-length coder, consecutive zero value coefficients can be replaced by single value that shows how many consecutive coefficients with zero value exists. In this way small number of coefficients is stored, and compression is obtained. Depending on transform used, different number of coefficients is rounded to zero in different positions, hence the reconstructed signal is more or less similar to the original one. In general there exists measures that show how much reconstructed signal is similar to the original one, and the most used is Percentage Root mean square Difference (PRD). Comparison of compression is performed in obtaining the larger compression ratio for the smaller PRD.
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Krill, C. E., J. Li, C. M. Garland, et al. "Precursors of amorphization in supersaturated Nb-Pd solid solutions." Journal of Materials Research 10, no. 2 (1995): 280–91. http://dx.doi.org/10.1557/jmr.1995.0280.
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The possibility that crystal-to-amorphous phase transformations can be induced by one or more underlying instabilities of the crystalline phase has been investigated in highly supersaturated solid solutions of Nb-Pd. Several unusual properties were discovered that may be identified as precursor effects of the collapse of the bcc α-Nb terminal solution to the amorphous phase. Elastic neutron diffraction measurements of α-Nb solutions found, with increasing Pd concentration, an anomalously large increase of the average atomic root-mean-square displacement to about half of the value at which the Lindemann criterion predicts the lattice should melt. Low-temperature heat capacity measurements yielded a concomitant decrease in the Debye temperature, suggesting that supersaturation causes an elastic modulus to soften. Single crystals of α-Nb solutions at high supersaturations have a highly anisotropic structure that is visible in transmission electron microscopy images; it is consistent with the development of a soft phonon mode leading to a bcc-to-ω phase transformation. Considered together with the results of other recent experiments, these findings suggest that shear instability of the crystalline phase plays an important role in the crystal-to-amorphous transformation and that the average static mean-square displacement of atoms in the lattice acts as a useful parameter for the stability of the crystal with respect to amorphization.
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Pinheiro, Ana Caroline, and Paulo Canas Rodrigues. "Hierarchical Time Series Forecasting of Fire Spots in Brazil: A Comprehensive Approach." Stats 7, no. 3 (2024): 647–70. http://dx.doi.org/10.3390/stats7030039.
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This study compares reconciliation techniques and base forecast methods to forecast a hierarchical time series of the number of fire spots in Brazil between 2011 and 2022. A three-level hierarchical time series was considered, comprising fire spots in Brazil, disaggregated by biome, and further disaggregated by the municipality. The autoregressive integrated moving average (ARIMA), the exponential smoothing (ETS), and the Prophet models were tested for baseline forecasts, and nine reconciliation approaches, including top-down, bottom-up, middle-out, and optimal combination methods, were considered to ensure coherence in the forecasts. Due to the need for transformation to ensure positive forecasts, two data transformations were considered: the logarithm of the number of fire spots plus one and the square root of the number of fire spots plus 0.5. To assess forecast accuracy, the data were split into training data for estimating model parameters and test data for evaluating forecast accuracy. The results show that the ARIMA model with the logarithmic transformation provides overall better forecast accuracy. The BU, MinT(s), and WLS(v) yielded the best results among the reconciliation techniques.
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Hemant Jasuja, S K Shakya, and KG Singh. "Modeling Nitrogen Movement in Rice Irrigated Using Sewage Water." Journal of Agricultural Engineering (India) 43, no. 3 (2006): 10–16. http://dx.doi.org/10.52151/jae2006433.1183.
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A numerical model is described to simulate water and nitrogen transport and transformations under transient soil water flow conditions. The nitrogen transformation processes considered were nitrification, denitrification, immobilization, mineralization, and ionic exchange of ammonium. The model was evaluated using experimental data from a lysimetric study. Two sets of lysimeters were irrigated with sewage water, whereas, one set was irrigated with tubewell water. Each set had four lysimeters having depths of 1.2, 1.5, 1.8, and 2.0m. Soil and leachate samples were collected and analyzed at regular intervals for NH; -N and N03-N. Model predictions of NH4+-N and N03-N were in close agreement with the observed values except for 37th day observations for NH4+-N and II Oth day observations in case ofN03-N. To evaluate the model performance a paired t test and root mean square error (RMSE) methods were applied. The RMSE values ranged from 0.1 to 3.9 and 0.05 to 2.55 for the ammonium and nitrate distributions, respectively.
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Yilmaz, Nazan. "Coordinate Transformation Using the Least Squares Method: A Case Study on Trabzon, Türkiye." Geodetski glasnik, no. 55 (December 31, 2024): 32–47. https://doi.org/10.58817/2233-1786.2024.58.55.32.
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The ED50 datum uses the Hayford ellipsoid and the Greenwich meridian as the prime meridian. In Turkey, the ED50 datum with the Hayford ellipsoid was used until 2001, after which the ITRF datum with the GRS80 ellipsoid became the standard. To utilize coordinate systems across different datums, these systems must be associated and transformed accordingly. This study determines 2D transformation parameters for converting the ED50 datum to the ITRF-96 datum. For this transformation, common points in both the ED50 and ITRF systems were selected in the Maçka and Ortahisar districts of Trabzon province. The two-dimensional similarity (Helmert) and Affine transformation methods were applied to these common points to establish the relationship between the two systems within the study area. Statistical data was gathered to evaluate the performance of the transformation parameters and process. Additionally, test points within the study areas were selected, and their ED50 datum coordinates were transformed to ITRF-96 coordinates using these parameters. The differences between the transformed coordinates and the current coordinates of these test points were analyzed, with root mean square error (RMSE), minimum and maximum errors, and mean absolute error (MAE) values calculated. In this study, a total of 197 points were used in Değirmendere, and 106 points were used in Maçka. It was observed that the sensitivity parameters of the transformation in the Maçka region are better than those in Değirmendere, potentially due to the number of common points. When comparing the Affine and Similarity transformations, the similarity transformation yielded significantly better results. All calculations were conducted using MATLAB R2022b software.
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Stoyan, Vladimir, and Sergey Voloshchuk. "ON THREE-DIMENSIONAL INITIAL-BOUNDARY PROBLEMS OF THICK ELASTIC PLATES’ DYNAMICS." Journal of Automation and Information sciences 3 (May 1, 2021): 34–49. http://dx.doi.org/10.34229/1028-0979-2021-3-3.
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Complex problems of three-dimensional elasticity theory for thick elastic plates with arbitrary geometry of their lateral surface are solved. Analytical dependencies of the components of the elastic dynamic displacements’ field of the plate’s inner points from the boundary-surface external-dynamic disturbing factors, defined by continuous functions or their values’ vectors, are constructed. It is assumed, that these disturbances have a classically defined powerful character, or are specified by a certain number of differential transformations of the field’s components of the plate’s dynamic displacement points. The absence of quantitative and qualitative restrictions on the determined transformations of the initial-boundary problems of the considered plates’ dynamics makes it incorrect and unsolvable by methods of classical and computational mathematics. The methodology of root-mean square mathematical modeling of discretely and continuously specified observations for the initial-boundary plate’s condition by the system of modeling functions and their values’ vectors is proposed in the paper. Constructed in this way field’s components of spatial-dynamic displacements of the plate’s points, precisely satisfying classical Lyame equation, with the available information on its initial-boundary condition, are agreed according to the root-mean square criterion. The problem of the obtained solutions’ ambiguity is investigated, their accuracy evaluation in accordance with the information on the external- dynamic condition of the investigated plate is conducted. The plate’s dynamics in the particular mode, for cases of information lack on external- dynamic influences on it and under the conditions of its geometric background according to spatial coordinates. The computer realization of the obtained mathematical results is engineeringly simple and can be easily implemented with the help of well-known methods of computational mathematics.
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Buszewski, Bogusław, and Radosław Zbytniewski. "Test of Some Aspects of Modelling the Sorption of Hydrophobic Compounds in Soils." Adsorption Science & Technology 20, no. 3 (2002): 231–42. http://dx.doi.org/10.1260/026361702760254423.
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A study was carried out on the sorption of the herbicide linuron in podzolic soil (one of the typical soils of Poland), the sorption isotherms being obtained using batch equilibrium studies. Modelling sorption phenomena involving the interactions of chemicals and particularly herbicides is very difficult because of the strong heterogeneity of the soil matrix. The present work presents the results of applying the most common models, i.e. Freundlich and Linear, as well as the newer concept of the Dual Reactive Domain model. The data obtained were validated using various statistical and chemometric methods. The results suggest that applying the non-linear least-squares method to obtain isotherm parameters gave a much better description of the sorption phenomena than often obtained using linear transformations of the adsorption equations. The study also showed that appropriate weighting schemes should be included in any model calculations. To test the goodness-of-fit of the model to the experimental data both the correlation coefficient and the Residual Root Mean Square Error were obtained. The models were also compared using the Extra Sum of Squares Principle statistical test.
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Yoshida, H. A., K. L. Robb, J. K. Virzi, and M. P. Parrella. "Efficacy of Selected Microbial and Related Insecticides Against Fifth Instar Beet Armyworm Larvae, Summer, California, 1985." Insecticide and Acaricide Tests 11, no. 1 (1986): 381. http://dx.doi.org/10.1093/iat/11.1.381a.
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Abstract The materials were applied to individual 4-wk-old chrysanthemum plants, cv. Hurricane, with a 1-gaI B&G sprayer at 60 psi 15 Aug. Five fifth-stage larvae were immediately placed on each plant and confined with an inverted, ventilated 1 qt plastic container. Mortality was assessed after 48 h and each surviving larva was placed individually on untreated commercial beet armyworm diet. Mortality was assessed every 48 h thereafter until all surviving larvae had pupated. To correct for differences in escaping larvae between treatments, the data were expressed as percent mortality for each replicate. Arcsin square root transformations were performed on the data prior to ANOVA.
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Yoshida, H. A., R. L. Robb, J. K. Virzi, and M. P. Parrella. "Control of Fifth Instar Beet Armyworm Larvae on Chrysanthemum, Summer, California, 1985." Insecticide and Acaricide Tests 11, no. 1 (1986): 380–81. http://dx.doi.org/10.1093/iat/11.1.380b.
Full textAbstract:
Abstract Materials were applied to individual 4-wk-old chrysanthemum plants, cvs. Hurricane, with a 1-gal B&G sprayer at 60 psi 27 Aug. Five fifth-stage larvae were immediately placed on each plant and confined with an inverted, ventilated 1-qt plastic container. Mortality was assessed after 48 h and each surviving larva was placed individually on untreated commercial beet armyworm diet. Mortality was assessed every 48 h thereafter until all surviving larvae had pupated. To correct for differences in escaping larvae between treatments, the data were expressed as percent mortality for each ceplicate. Arcsin square root transformations were performed on the data prior to ANOVA.
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MAK, M. K., and T. HARKO. "CAUSAL BULK VISCOUS COSMOLOGIES IN CONFORMALLY FLAT SPACETIME." International Journal of Modern Physics D 09, no. 04 (2000): 475–93. http://dx.doi.org/10.1142/s0218271800000463.
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The evolution of a causal bulk viscous cosmological fluid filled open conformally flat spacetime is considered. By means of appropriate transformations the equation describing the dynamics and evolution of the very early Universe can be reduced to a first order Abel type differential equation. In the case of a bulk viscosity coefficient proportional to the square root of the density, ξ~ρ1/2, an exact and two particular approximate solutions are obtained. The resulting cosmologies start from a singular state and generally have a noninflationary behavior, the deceleration parameter tending, in the large time limit, to zero. The thermodynamic consistency of the results is also checked.
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Abramochkin, Eugeny G., Svetlana N. Khonina, and Roman V. Skidanov. "Three-Airy Beams, Their Propagation in the Fresnel Zone, the Autofocusing Plane Location, as Well as Generalizing Beams." Photonics 11, no. 4 (2024): 312. http://dx.doi.org/10.3390/photonics11040312.
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A family of 2D light fields consisting of the product of three Airy functions with linear arguments has been studied theoretically and experimentally. These fields, called three-Airy beams, feature a parameter shift and have a cubic phase and a super-Gaussian circular intensity in the far zone. Transformations of three-Airy beams in the Fresnel zone have been studied using theoretical, numerical, and experimental means. It has been shown that the autofocusing plane of a three-Airy beam is similar to the square root of the shift parameter. We also introduce generalized three-Airy beams containing nine free parameters, and obtain their Fourier transform in a closed form.
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Huisman, A. E., D. J. Brown, and N. M. Fogarty. "Ability of sire breeding values to predict progeny bodyweight, fat and muscle using various transformations across environments in terminal sire sheep breeds." Animal Production Science 56, no. 1 (2016): 95. http://dx.doi.org/10.1071/an14666.
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Data used for the genetic evaluation of the terminal sire sheep breeds in Australia originate from a large range of genotypes and environments. This means there are large differences in the level of production and therefore contemporary group means and variances within the data. This study examined four transformations to account for the heterogeneity of variance in the observed data and their effect on the ability of estimated breeding values of sires (sire EBV) to predict progeny performance. This predictive ability was described by regressing offspring performance on sire EBV. The expected value of this regression is 0.5, which indicates that half of the sire EBV differences can be expected in the progeny. The transformations of observed data were investigated in low, medium and high production environments for weight and ultrasound scan traits (fat and muscle) in terminal sire sheep breeds. There were records from over 300 000 sheep in the LAMBPLAN terminal sire dataset, predominately from Poll Dorset, Texel, Suffolk and White Suffolk breeds. The transformation methods applied to the observed data were: traits expressed as a percentage of the contemporary group mean; traits re-scaled to a common contemporary group mean in units of measurement; a logarithmic transformation; and a square root transformation. The heritabilities and other variance ratios estimated from the transformed traits were not significantly different from those using the observed data. Phenotypes transformed to a proportion of the contemporary group mean, either as a percentage or in units of measurement, resulted in the most consistent EBV across all production environments for weight and fat traits, with little effect of transformations for muscle traits. The transformation of data to the contemporary mean in units of measurement for weight and fat traits has been implemented in the Sheep Genetics evaluation system. The consistency of the progeny–sire EBV regressions around 0.5 in the data from these purebred industry flocks is heartening for terminal sire evaluation.
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Zhao, Yibo, Shaogang Lei, Xiaotong Han, et al. "Research on the Inversion Method of Dust Content on Mining Area Plant Canopies Based on UAV-Borne VNIR Hyperspectral Data." Drones 9, no. 4 (2025): 256. https://doi.org/10.3390/drones9040256.
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Monitoring dust on plant canopies around open-pit coal mines is crucial to assessing environmental pollution and developing effective dust suppression strategies. This research focuses on the Ha’erwusu open-pit coal mine in Inner Mongolia, China, using measured dust content on plant canopies and UAV-borne VNIR hyperspectral data as the data sources. The study employed five spectral transformation forms—first derivative (FD), second derivative (SD), logarithm transformation (LT), reciprocal transformation (RT), and square root (SR)—alongside the competitive adaptive reweighted sampling (CARS) method to extract characteristic bands associated with canopy dust. Various regression models, including extreme learning machine (ELM), random forest (RF), partial least squares regression (PLSR), and support vector machine (SVM), were utilized to establish dust inversion models. The spatial distribution of canopy dust was then analyzed. The results demonstrate that the geometric and radiometric correction of the UAV-borne VNIR hyperspectral images successfully restored the true spatial information and spectral features. The spectral transformations significantly enhance the feature information for canopy dust. The CARS algorithm extracted characteristic bands representing 20 to 30% of the total spectral bands, evenly spread across the entire range, thereby reducing the estimation model’s computational complexity. Both feature extraction and model selection influence the inversion accuracy, with the LT-CARS and RF combination offering the best predictive performance. Canopy dust content decreases with increasing distance from the dust source. These findings offer valuable insights for canopy dust retention monitoring and offer a solid foundation for dust pollution management and the development of suppression strategies.
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Yoshida, H. A., K. L. Robb, J. K. Virzi, and M. P. Parrella. "Efficacy of Selected Microbial and Related Insecticides Against Second Instar Beet Armyworm Larvae, Pall, California, 1985." Insecticide and Acaricide Tests 11, no. 1 (1986): 381. http://dx.doi.org/10.1093/iat/11.1.381.
Full textAbstract:
Abstract The materials were applied to individual 4-wk-old chrysanthemum plants with a 1-gaI B&G sprayer at 60 psi 11 Oct. five second-stage larvae were immediately confined to each plant for 48 h by an inverted, ventilated 1 qt plastic container. Mortality was assessed after 48 h and each surviving larva was placed individually on untreated commercial beet armyworm diet. Mortality was assessed every 48 thereafter until all surviviing larvae had pupated. The pupae were held for adult emergence. To correct for differences in escaping larvae between treatments, the data were expressed as percent mortality for each replicate. Arcsin square root transformations were performed on the data prior to analysis by ANOVA.
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Trübenbacher, E. "A Lorentz Invariant Schrödinger Equation for Spin 0." Zeitschrift für Naturforschung A 44, no. 9 (1989): 801–10. http://dx.doi.org/10.1515/zna-1989-0905.
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Abstract Using the concept of distributions, the square root of the operator - Δ + m2 is taken in a mathematically well defined way for one component wave functions. A new representation of proper Lorentz transformations for one component wave functions makes it possible to construct a relativistic quantum mechanics for spin 0, comprising a Lorentz invariant wave equation, a scalar product, and a positive definite density satisfying, together with a current, a continuity equation, and coupling of scalar and vector potentials. Some interesting consequences of the theory concerning the concept of particle trajectory and velocity of propagation of the probability amplitude are discussed in detail. As an example of practical application a perturbation theory for discrete states is set up.
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Spera, Mauro, and Tilmann Wurzbacher. "Determinants, Pfaffians and Quasi-Free Representations of the CAR Algebra." Reviews in Mathematical Physics 10, no. 05 (1998): 705–21. http://dx.doi.org/10.1142/s0129055x98000227.
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In this paper we apply the theory of quasi-free states of CAR algebras and Bogolubov automorphisms to give an alternative C*-algebraic construction of the Determinant and Pfaffian line bundles discussed by Pressley and Segal and by Borthwick. The basic property of the Pfaffian of being the holomorphic square root of the Determinant line bundle (after restriction from the Hilbert space Grassmannian to the Siegel manifold, or isotropic Grassmannian, consisting of all complex structures on an associated Hilbert space) is derived from a Fock–anti-Fock correspondence and an application of the Powers–Størmer purification procedure. A Borel–Weil type description of the infinite dimensional Spin c- representation is obtained, via a Shale–Stinespring implementation of Bogolubov transformations.
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Morin, Antoine. "Variability of Density Estimates and the Optimization of Sampling Programs for Stream Benthos." Canadian Journal of Fisheries and Aquatic Sciences 42, no. 9 (1985): 1530–34. http://dx.doi.org/10.1139/f85-191.
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Several sets of published data were reanalyzed to examine the effect of mean density size and type of sampler, and functional group of the collected organisms on the variance in estimates of stream benthos density. The logarithm of variance (log s2) is a quadratic function of the logarithm of mean density ([Formula: see text], individuals∙m−9). Because of the curvilinear relationship between the logarithm of variance and the logarithm of mean density, I suggest that none of the commonly used transformations (square root, fourth root or logarithmic) will stabilize the variance at all the densities encountered. Information about sampler size (Q, square metres) further improves the prediction of the logarithm of sampling variance, which increases with an increase in mean density and decreases with an increase in the size of the sampler On average density estimates obtained with artificial substrates were as variable as those from natural substrates, although some artificial substrates (baskets of rocks) yielded less variable density estimates than average. The number of replicates necessary to obtain a given precision decreases with increasing mean density and sampler size, whereas the total area to be sampled increases with sampler size. Although I suggest that the use of small samplers reduces the cost of estimates of density, the sampler size that minimizes the sum of the sampling and processing effort can depend on the mean density.
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Posta, J., S. Mihók, S. Márkus, and I. Komlósi. "Analysis of Hungarian sport horse show jumping results using different transformations and models." Archives Animal Breeding 52, no. 5 (2009): 451–58. http://dx.doi.org/10.5194/aab-52-451-2009.
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Abstract. The aim of this paper is to estimate heritabilities and to compare data transformation methods and models for Hungarian Sporthorse show jumping results. The analysis is based on data collected between 1996 and 2005. The linear animal model included fixed effects of gender, breeder, rider, age, and start (coded as year of competition, type of competition and height of obstacle). Square root, cubic and fourth roots, Blom score and cotangent transformed ranks were used as measurements of performance. Difference the height of the obstacle and fault points, height of the obstacle and height of the obstacle and fault point were also used as performance traits. Variance and covariance components were estimated with VCE-5 software package. Model fit was evaluated by log-likelihood values and Akaike’s information criterion (AIC). Heritability was low for each performance trait and each model. The poorest goodnessof- fit model was the difference between height of the obstacle and fault points, whereas the best fitting genetic model based on AIC was from using the cotangent transformation.