B-factor accuracy in protein crystal structures

The accuracy of B factors in protein crystal structures has been determined by comparing the same atoms in numerous, independent crystal structures of Gallus gallus lysozyme. Both B-factor absolute differences and normal probability plots indicate that the estimated B-factor errors are quite large, close to 9 Å2 in ambient-temperature structures and to 6 Å2 in low-temperature structures, and surprisingly are comparable to values estimated two decades ago. It is well known that B factors are not due to local movements only but reflect several, additional factors from crystal defects, large-scale disorder, diffraction data quality etc. It therefore remains essential to normalize B factors when comparing different crystal structures, although it has clearly been shown that they provide useful information about protein dynamics. Improved, quantitative analyses of raw B factors require novel experimental and computational tools that are able to disaggregate local movements from other features and properties that affect B factors.

Reasoning Method Based on Intervals with Symmetric Truncated Normal Density

Error parameters are inevitable in systems. In formal verification, previous reasoning methods seldom considered the probability information of errors. In this article, errors are described as symmetric truncated normal intervals consisting of the intervals and symmetric truncated normal probability density. Furthermore, we also rigorously prove lemmas and a theorem to partially simplify the calculation process of truncated normal intervals and independently verify the formulas of variance and expectation of symmetric truncated interval given by some scholars. The mathematical derivation process or verification codes are provided for most of the key formulas in this article. Hence, we propose a new reasoning method that combines the probability information of errors with the previous statistical reasoning methods. Finally, an engineering example of the reasoning verification of train acceleration is provided. After simulating the large-scale cases, it is shown that the simulation results are consistent with the theoretical reasoning results. This method needs more calculation, while it is more effective in detecting non-error’s fault factors than other error reasoning methods.

Project Portfolio Selection of Solar Energy by Photovoltaic Generation Using Gini-CAPM Multi-Criteria and Considering ROI Covariations

For some time, renewable solar energy generations using cellular photovoltaic panels have stood out among the options, especially in the segment of micro and small companies, where the return on investment is usually higher. In this context, when micro and small companies do not have the capital for the enterprises, several others, mainly small ones, have emerged to finance. However, significant difficulties occur for financiers in selecting investment portfolios, especially when considering the trade-off between return and risk and the covariations of return on investment, which are very common. In this type of selection, the Capital Asset Pricing Model criteria using the Gini risk can help significantly because this one is a more robust risk coefficient for assessments of non-normal probability distributions. However, searches for methods that meet the selection needs using the adjacent criteria are unsuccessful. Thus, this work seeks to help minimize the gap by presenting a new method for selection using the criteria. Historical and simulations data stochastic evaluations indicate that the portfolios selected by the method are attractive options for implementations. These portfolios have reasonable probabilistic expectations and satisfactory protection to avoid mistakes caused for not considering covariations in return on investment, which indicates a significant advance on the current knowledge frontier and will likely allow the increased use of the concept. The method also presents theoretical contributions in adaptations of the benchmark models, which help to minimize the adjacent literary gap of similar methods.

O meio ambiente e o uso das curvas normais de probabilidades / The environment and the use of normal probability curves

Este artigo foi feito para mostrar aos leitores como se usa as distribuições normais de probabilidades em ciência, um artigo não publicado, é o que pressupomos, de Gauss, que ficou escondido, ou melhor, despercebido, dezenas de anos sem que as pessoas percebessem, como se fosse um tesouro arqueológico matemático, usando aqui a definição e as integrações numéricas para o seu uso através de uma simples máquina de calcular Hp 50g.

Variability of Ground Motion Amplitudes Recorded in Bucharest Area during Vrancea Intermediate-Depth Earthquakes

This study focuses on the assessment of the correlation and variability of ground motion amplitudes recorded in Bucharest area during Vrancea intermediate-depth earthquakes from a database of 119 pairs of horizontal components. Empirical models for the evaluation of the peak ground velocity and displacement from spectral accelerations are proposed in this study. The distribution of the shear wave velocities from 41 boreholes at specific depths appears to follow a normal probability distribution. The analysis performed in this study has also shown that the variability of peak ground velocities and displacements does not appear to be influenced by the earthquake magnitude. In addition, it was observed that the variability in terms of shear wave velocities at specific depths is smaller than the variability of the spectral amplitudes of the recorded ground motions. The empirical site-amplification factors from the Eurocode 8 draft fail to capture the long-period spectral amplifications observed in Bucharest area during large magnitude Vrancea intermediate-depth earthquakes.

A Log-Beta Rayleigh Lomax Regression Model

For the first time, a location-scale regression model based on the logarithm of an extended Raleigh Lomax distribution which has the ability to deal and model of any survival data than classical regression model is introduced. We obtain the estimate for the model parameters using the method of maximum likelihood by considering breast cancer data. In addition, normal probability plot of the residual is used to detect the outliers and evaluate model assumptions. We use a real data set to illustrate the performance of the new model, some of its submodels and classical models consider in the study. Also, we perform the statistics AIC, BIC and CAIC to select the most appropriate model among those regression models considered in the study.

Unit Commitment for Power Generation Systems Based on Prices in Smart Grid Environment Considering Uncertainty

With the growing demand for electricity, the inability of governments to provide the necessary resources to invest in the electricity industry and the rising price of fossil fuels, the tendency is to study and pay attention to economic issues in power systems studies. In this paper a new modified version of gray wolf optimization (MGWO) is proposed to solve the unit commitment (UC) problem in a power system in case of uncertainty. Market price variation is the main source of uncertainty in the UC program. Therefore, a model based on normal probability density function (PDF) is present for reducing the market price uncertainty effect in the model. Simulations are done for a standard 10 thermal units power system, and the results of the optimization by the proposed MGWO are compared with the previous version of the GWO algorithm and particle swarm optimization (PSO) algorithm results. The simulation results confirm the superiority of the proposed MGWO algorithm over the two algorithms PSO and GWO.

The initialization of initial generating equipment maintenance schedules while a heuristic method is used

Currently, heuristic methods based on iterative changing of feasible solutions set provide a perspective tool for generation equipment maintenance scheduling in power systems. Wherein effectiveness of a heuristic method depends significantly on the initial set of possible schedules or in other words quality of the method initialization. In this case, a widely used methodology of building the initial array of solutions on the basis of pseudorandom uniform generation of control variables seems to be only palliative way to access the problem. This paper proposes alternative initialization procedure drawing on the example of generating units maintenance planning with heuristic differential evolution method. The principle of this method is to get initial set of solutions utilizing normal probability distribution to generate pseudorandom deviations from the suboptimal maintenance schedule which is to be preliminarily formed using directed search method. Following this approach allows to improve probabilistic characteristics of resultant maintenance schedule in particular to decrease median value of an objective function and its coefficient of variation, and to maximize probability to get the combination of units outage moments completely suiting operational constraints.

A Cooks Distance Approach to Control the Haz and Arc Length of Tig Mild Steel Weld

The heat affected zone and arc length parameters have a vital role to play in determining the integrity of a weld structure. The cooks distance is a statistical diagnostic employed in this study to select the best optimum combination of welding process parameters. Mild steel plate was the choice material used to produce the weld specimen, which was welded with the Tungsten inert gas method. The RSM model was used to develop an optimal solution that can explain the behavior of the welded joint with respect to the heat affected zone and arc length, different diagnostic techniques were employed which includes the normal probability plot and cooks distance plot. The model developed has sufficient merit as the results obtained shows that the cooks distance values is within the range of 0 and 1 indicating the absence of outlier in the data making the optimal solution highly acceptable.

Accounting for non-normal distribution of input variables and their correlations in robust optimization

In this work, metamodel-based robust optimization is performed using measured scatter of noise variables. Principal component analysis is used to describe the input noise using linearly uncorrelated principal components. Some of these principal components follow a normal probability distribution, others however deviate from a normal probability distribution. In that case, for more accurate description of material scatter, a multimodal distribution is used. An analytical method is implemented to propagate the noise distribution via metamodel and to calculate the statistics of the response accurately and efficiently. The robust optimization criterion as well as the constraints evaluation are adjusted to properly deal with multimodal response. Two problems are presented to show the effectiveness of the proposed approach and to validate the method. A basketball free throw in windy weather condition and forming of B-pillar component are presented. The significance of accounting for non-normal distribution of input variables using multimodal distributions is investigated. Moreover, analytical calculation of response statistics, and adjustment of the robust optimization problem are presented and discussed.