A Stochastic Linearization Technique Based on Minimum Mean Square Deviation of Potential Energies

1991 ◽  
pp. 327-338 ◽  
Author(s):  
Xiangting Zhang ◽  
Isaac Elishakoff ◽  
Ruichong Zhang
Author(s):  
Nguyen Cao Thang ◽  
Luu Xuan Hung

The paper presents a performance analysis of global-local mean square error criterion of stochastic linearization for some nonlinear oscillators. This criterion of stochastic linearization for nonlinear oscillators bases on dual conception to the local mean square error criterion (LOMSEC). The algorithm is generally built to multi degree of freedom (MDOF) nonlinear oscillators. Then, the performance analysis is carried out for two applications which comprise a rolling ship oscillation and two degree of freedom one. The improvement on accuracy of the proposed criterion has been shown in comparison with the conventional Gaussian equivalent linearization (GEL).


2021 ◽  
Vol 13 (1) ◽  
Author(s):  
Andrew T. McNutt ◽  
Paul Francoeur ◽  
Rishal Aggarwal ◽  
Tomohide Masuda ◽  
Rocco Meli ◽  
...  

AbstractMolecular docking computationally predicts the conformation of a small molecule when binding to a receptor. Scoring functions are a vital piece of any molecular docking pipeline as they determine the fitness of sampled poses. Here we describe and evaluate the 1.0 release of the Gnina docking software, which utilizes an ensemble of convolutional neural networks (CNNs) as a scoring function. We also explore an array of parameter values for Gnina 1.0 to optimize docking performance and computational cost. Docking performance, as evaluated by the percentage of targets where the top pose is better than 2Å root mean square deviation (Top1), is compared to AutoDock Vina scoring when utilizing explicitly defined binding pockets or whole protein docking. Gnina, utilizing a CNN scoring function to rescore the output poses, outperforms AutoDock Vina scoring on redocking and cross-docking tasks when the binding pocket is defined (Top1 increases from 58% to 73% and from 27% to 37%, respectively) and when the whole protein defines the binding pocket (Top1 increases from 31% to 38% and from 12% to 16%, respectively). The derived ensemble of CNNs generalizes to unseen proteins and ligands and produces scores that correlate well with the root mean square deviation to the known binding pose. We provide the 1.0 version of Gnina under an open source license for use as a molecular docking tool at https://github.com/gnina/gnina.


2019 ◽  
Vol 15 (1) ◽  
pp. 258-264 ◽  
Author(s):  
Hamid Reza Ghaieni ◽  
Saeed Tavangar ◽  
Mohammad Moein Ebrahimzadeh Qhomi

Purpose The purpose of this paper is to present simple correlation for calculating nitrated hydroxyl-terminated polybutadiene (NHTPB) enthalpy of formation. Design/methodology/approach It uses multiple linear regression methods. Findings The proposed correlation has determination coefficient 0.96. The correlation has root mean square deviation and the average absolute deviations values 53.4 and 46.1 respectively. Originality/value The predictive power of correlation is checked by cross-validation method (R2=0.96, Q L O O 2 = 0.96 ).


1993 ◽  
Vol 15 (4) ◽  
pp. 1-6
Author(s):  
Di Paola Mario ◽  
Nguyen Dong Anh

Stochastic linearization method is one of the most useful tools for analysis of nonlinear systems under random excitation. The fundamental idea of the classical stochastic linearization consists in replacing the original nonlinear equation by a linear one in such a way that the difference between two equations is minimized in the mean square value. In this paper a new version of the stochastic linearization is proposed. It is shown that for two nonlinear systems considered the new version gives good results for both the weak and strong nonlinearities.


2018 ◽  
Vol 56 ◽  
pp. 130-135
Author(s):  
M. V. Tserenyuk ◽  
O. M. Tserenyuk

In addition to assessing the absolute performance of animals, the impact of certain technological approaches, breeding influence and other external organized factors on the consolidation of pigs groups on certain grounds should be evaluated. Breeding consolidation is a desirable breeding process that is realized through more motivated consolidation of intra-breeding structural units for maintaining a significant level of intergroup differentiation and variability. If the issue relates to the rearing young animals that are introduced into the herd, this is the most urgent issue that needs to be monitored. The purpose of the research is to determine the consociality of the main signs of reproductive ability of the gilts, which are checked at different rates of artificial insemination of sows of the main herd. The research was carried out at the Shubs`ke farm in the Bogoduhivsky District of Kharkiv Oblast at the pig farm for the pure breeding of the Welsh breed pigs (breeding reproductive status from 2014). In order to evaluate the optimal multiplicity (from single to triple), a gilts with a total of 30 heads was selected. The main indicators of reproductive ability of gilts (multiplicity, weight of nest at birth and excommunication and keeping piglets before weaning on day 28) were evaluated. Recalculation on the weight of the litter at weaning at the weight of the nest at extermination in 60 days was carried out in accordance with the current instruction on the boning of pigs. The results of researches were worked out according to traditional methods by the method of variation statistics. Consolidation of individual indicators of reproductive capacity of gilts was calculated to the total number of evaluated animals. In the previous stage of the research, it was found that the use of multiple insemination of gilts compared to single insemination is positively reflected at the level of their reproductive ability. A decrease in the percentage of non-productive inseminants in animal groups has been established. Triple insemination of gilts allows for 1.14 piglets to be obtained more compared to single insemination of the same pigs (p < 0.01). Also, for three times insemination of gilts, in comparison with single insemination, larger nest for weaning were obtained (by 14.24 kg, converted to 60th day p < 0.01). At the same time, the reduction in the keeping of piglets to weaning for increase frequency of insemination of gilts. According to the multiplicity of gilts, the most consolidated level of symptoms per group was obtained for single insemination. Increasing the multiplicity of insemination negatively affected the consolidation of the multiplicity of the piglets (as for determining the coefficients of phenotypic consolidation due to the mean square deviation, so, and for determining the coefficient of variability). The least consolidated in terms of multiplicity were uterus for double insemination. It should also be noted that there is little difference, in general, on the indicators of the theonotypical consolidation of the multiplicity of piglets between different groups of animals. So this difference between the most contrasting groups was 0.447 points for determining the coefficients due to the mean square deviation and 0.397 points for the determination due to the coefficient of variability, respectively. By weight of the same litters at birth, the most consolidated group was gilts, which was inseminated twice. The least consolidated are trimmed three times, respectively. The difference as a whole, according to the indicators of the theonotype consolidation of the mass of the litter’s piglets at birth, between different groups of pigs was even smaller. The difference between the most contrasting groups was 0.270 points for determining the coefficients due to the mean square deviation and 0.260 points for the determination due to the coefficient of variability, respectively. On the basis of the mass of the litter at weaning, the most consolidated level of symptoms was obtained in the group of gilts for triple insemination. The least consolidated group, respectively, was gilts for single insemination. At the same time, on the basis of the weight of the litter at weaning, the slightest differences were obtained after the consolidation of the signs between different groups of pigs. The difference between the most contrasting groups was 0.173 points for determining the coefficients due to the mean square deviation and 0.248 points for the determination due to the coefficient of variation, respectively. At different rates of insemination of gilts, there are no significant differences between the groups between the groups in terms of the consolidation of signs of reproductive ability. Also, there was no clear effect on increasing the multiplicity of insemination of gilts to the consolidation of their signs of reproductive qualities.


2017 ◽  
Vol 26 (12) ◽  
pp. 1743004 ◽  
Author(s):  
John Estes ◽  
Michael Kavic ◽  
Matthew Lippert ◽  
John H. Simonetti

Pulsars (PSRs) are some of the most accurate clocks found in nature, while black holes (BHs) offer a unique arena for the study of quantum gravity. As such, PSR–BH binaries provide ideal astrophysical systems for detecting effects of quantum gravity. With the success of aLIGO and the advent of instruments like the Square Kilometer Array (SKA) and Evolved Laser Interferometer Space Antenna (eLISA), the prospects for discovery of such PSR–BH binaries are very promising. We argue that PSR–BH binaries can serve as ready-made testing grounds for proposed resolutions to the BH information paradox. We propose using timing signals from a PSR beam passing through the region near a BH event horizon as a probe of quantum gravitational effects. In particular, we demonstrate that fluctuations of the geometry outside a BH lead to an increase in the measured root-mean-square deviation of arrival times of PSR pulsar traveling near the horizon.


2021 ◽  
Vol 74 (7) ◽  
pp. 1628-1633
Author(s):  
Alla P. Podavalenko ◽  
Tatjana D. Nessonova ◽  
Victorija I. Zadorozhna ◽  
Larisa М. Hrytsenko

The aim: To improve epidemiological monitoring of pertussis by analyzing the disease morbidity during 1995-2017 in Ukraine, to make a prognosis. Materials and methods: Analysis of the pertussis morbidity during 1995-2017 using the data of the Ministry of Health of Ukraine. The cyclicity was determined by Fourier spectral analysis. The models of prognosis were constructed using polyharmonic regression and an exponential smoothing algorithm. Cartographic analysis and integrated indicators (multiyear index of the prevalence rate, mean square deviation, mean the multiyear pace of the gain in the prevalence rate) were used to determine the areas of risk. Summarized data were used to calculate the generalized coefficient. Results: The pertussis morbidity cycle has 5 years intervals in Ukraine. The prognosis is for increasing the pertussis morbidity from 4.91-5.54 to 5.48-7.06 per 100.000 people. The generalized coefficient was significantly higher in western part (83.3%) than in central (50.0%) and eastern (16.6%) parts. The study showed that population reproduction rates, natural population increase, and the proportion of people against vaccination were higher in the western part than in other parts of the country. Conclusions: The pertussis cyclicity depends on the internal mechanisms of interaction in the ecological system. There is a prognosis of worsening the epidemic situation of pertussis spreading. The risk area is the western part of Ukraine, which is characterized by active demographic processes and a greater number of people who are negative about vaccination.


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