The Original Mixture Problem: Designs and Models for Exploring the Entire Simplex Factor Space

Author(s):  
Minakhi Pujari ◽  
Joachim Frank

In single-particle analysis of macromolecule images with the electron microscope, variations of projections are often observed that can be attributed to the changes of the particle’s orientation on the specimen grid (“rocking”). In the multivariate statistical analysis (MSA) of such projections, a single factor is often found that expresses a large portion of these variations. Successful angle calibration of this “rocking factor” would mean that correct angles can be assigned to a large number of particles, thus facilitating three-dimensional reconstruction.In a study to explore angle calibration in factor space, we used 40S ribosomal subunits, which are known to rock around an axis approximately coincident with their long axis. We analyzed micrographs of a field of these particles, taken with 20° tilt and without tilt, using the standard methods of alignment and MSA. The specimen was prepared with the double carbon-layer method, using uranyl acetate for negative staining. In the MSA analysis, the untilted-particle projections were used as active, the tilted-particle projections as inactive objects. Upon tilting, those particles whose rocking axes are parallel to the tilt axis will change their appearance in the same way as under the influence of rocking. Therefore, each vector, in factor space, joining a tilted and untilted projection of the same particle can be regarded as a local 20-degree calibration bar.


Author(s):  
Юлия Владимировна Татаркова ◽  
Татьяна Николаевна Петрова ◽  
Олег Валериевич Судаков ◽  
Александр Юрьевич Гончаров ◽  
Ольга Николаевна Крюкова

В настоящей статье представлен обзор основных решений, доступных сегодня для формирования как краткосрочных, так и долгосрочных проекций заболеваемости болезней глаза и его придаточного аппарата в студенческой среде. С другой стороны, существует ряд проблем, связанных с многообразием факторов, влияющих на заболеваемость, статистической необоснованностью и противоречивостью имеющихся результатов анализа данных. Представлены результаты математического моделирования зависимости показателя заболеваемости от наиболее влиятельных факторов образовательной и социальной среды. Перечислены важнейшие направления разработки математических моделей распространения заболеваемости. С помощью разработанного программного комплекса проведена серия вычислительных экспериментов по оценке и прогнозированию заболеваемости обучающихся в вузах разного профиля. Показана эффективность применения методики многовариантного моделирования и прогнозирования, указаны их ограничения и возможности практического применения. По расположению обобщенной области благоприятного прогноза в факторном пространстве можно определить время воздействия неблагоприятных для зрения факторов, которое должно составлять не более 10 ... 11 часов в сутки, количество профилактических мероприятий должно составлять не менее 3 ... 4. При этом риск развития миопии составит не более 0,4, вероятность усталости глаз за компьютером составит не более 0,4, вероятность дискомфорта глаз на занятиях составит не более 0,15. Исходя из характера прогноза, определяется длительность диспансерного наблюдения, а также потребность профилактических мероприятий по устранению или ослаблению действия неблагоприятно влияющих социально-гигиенических и медико-биологических факторов конкретного больного. Использование прогностической матрицы в практическом здравоохранении позволяет существенно улучшить работу по профилактике офтальмологической заболеваемости и является одним из эффективных мероприятий диспансеризации студенческой молодежи, так как дает возможность выделить из числа обучающихся группу с высоким риском неблагоприятного исхода заболевания This article provides an overview of the main solutions available today for the formation of both short-term and long-term projections of the incidence of eye diseases and its adnexa in the student environment. On the other hand, there are a number of problems associated with a variety of factors affecting the incidence, statistical unreasonability and inconsistency of the available data analysis results. The results of mathematical modeling of the dependence of the incidence rate on the most influential factors of the educational and social environment are presented. The most important areas of developing mathematical models for the spread of morbidity are listed. With the help of the developed software package, a series of computational experiments was carried out to assess and predict the incidence of students in universities of various profiles. The effectiveness of the application of multivariate modeling and forecasting methods is shown, their limitations and practical application possibilities are indicated. By the location of the generalized region of favorable prognosis in the factor space, it is possible to determine the exposure time of factors unfavorable for vision, which should be no more than 10 ... 11 hours a day, the number of preventive measures should be at least 3 ... 4. At the same time, the risk of development myopia will be no more than 0.4, the probability of eye fatigue at the computer will be no more than 0.4, the likelihood of eye discomfort in the classroom will be no more than 0.15. Based on the nature of the forecast, the duration of the follow-up observation is determined, as well as the need for preventive measures to eliminate or weaken the action of adverse social, hygienic and biomedical factors of a particular patient. The use of the prognostic matrix in practical health care can significantly improve the work on the prevention of ophthalmic morbidity and is one of the effective medical examinations for students, since it makes it possible to distinguish among the students a group with a high risk of an unfavorable outcome of the disease


2017 ◽  
Vol 20 (2) ◽  
pp. 1387-1399 ◽  
Author(s):  
Tie-Jun Cui ◽  
Pei-Zhuang Wang ◽  
Sha-Sha Li

2002 ◽  
Vol 17 (4) ◽  
pp. 287-289 ◽  
Author(s):  
T. Balić-Žunić

The Rietveld method can be combined with the addition method to determine the absolute quantities of the phases treated by Rietveld refinement plus the quantity of phase(s) not treated by it (amorphous or unobserved). If q is the added proportion of a defined phase already present in the sample, and a1 and a2 its relative proportions as determined by Rietveld refinement prior and after the addition, the proportion of the amorphous (untreated) phase(s) in the original sample is calculated as xo=[a2−(1−q)a1−q]/(1−q)(a2−a1). The absolute quantities of the phases treated by Rietveld refinement are then determined by a correction for the content of the amorphous phase(s), or they can be calculated directly from specific equations. The advantage of the method is that no new variables are introduced in the refinement when the added standard already is a part of the original mixture.


2019 ◽  
Vol 51 (1) ◽  
pp. 39-56 ◽  
Author(s):  
Anja Terzic ◽  
Lato Pezo ◽  
Ljiljana Milicic ◽  
Nevenka Mijatovic ◽  
Zagorka Radojevic ◽  
...  

Mineral additives are extensively applied as cement replacement materials in both construction concrete and mortar. Fly ash is one of the most commonly utilized additives which improve rheological properties, as well as thermal and mechanical behavior of mortar, and as such it has been widely investigated. This industrial byproduct comprises heavy metals in its composition; therefore further research is needed to optimize its effective dosage. Moreover, certain sorptive clays, such as natural zeolite and bentonite, can prevent migration of toxic elements from fly ash by immobilizing them in their structure. Ten experimental mortars are prepared with Portland cement, river sand and addition of fly ash, zeolite and/or bentonite in accordance with chemometric experimental design rules. The aim of the study was to investigate the effect of mineral additives on thermal and mechanical performances of mortar. Thermal characteristics were monitored via dilatometric analysis and DTA method. Principal component analysis was used on the results of physico-mechanical testing (workability, bulk density, water absorption, shrinkage, compressive and flexural strength) to enable the divisions of the observed samples into groups in the factor space. The performance of Artificial Neural Network was compared with the experimental data in order to develop rapid and accurate method for prediction of mechanical parameters of mortar. The ANN model showed high overall prediction accuracy (r2 = 0.989, during training cycle). The test results indicate that incorporation of the mineral additives gave cost effective mortars with sufficiently good properties. However, tools of analytical modeling highlighted mortar with zeolite and fly ash as the optimal composition regarding its mechanical performance.


2015 ◽  
Vol 2 (1(22)) ◽  
pp. 48
Author(s):  
Олег Миколайович Сінчук ◽  
Ігор Олегович Сінчук ◽  
Альона Миколаївна Ялова ◽  
Марина Анатоліївна Віннік

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