2 research outputs found
Constraint-basierte Lösungsmethoden für das Phasenproblem in der Kristallographie
The phase problem is the major problem in the field of X-ray crystallography.
In the context of direct methods, that use mathematical techniques to compute
an electron density map from the diffraction data without any further
experiments, binary integer programming models for solving the phase problem
have been de- veloped. Based on descriptions of topological properties of
2-dimensional binary pictures known from the field of discrete tomography,
these models have been extended for the 3-dimensional case. As the
formulations are in general not sufficient to describe the more complex
properties of the shape of proteins, binary integer pro- grams have been
derived for describing different additional topological properties. In
general, the binary integer program for solving the phase problem, leads to a
set of different optimal solutions. The additional constraints increase the
quality of the solution set. The main property considered is one restricting
the number of components in the resulting solution. Using graph theoretical
methods and a separation algorithm, a model to describe this property has been
found and implemented. Computational results have been presented and
evaluated. It has been shown, that the added topological constraints increase
significantly the quality of the solution set. In the last chapter, a method
to find the solutions all at once based on singu- lar value decomposition and
methods to find integer points in ellipsoids has been developed. In further
work, the efficiency of this method for the phase problem should be evaluated
and the method could be implemented and tested. In order to further increase
the solutions’ quality, more additional constraints could be formulated and
added. If the running time of the solving algorithm could be decreased, a
refinement of the model would be possible. Bigger grids could be considered
showing more de- tails of the reconstructed protein. More phase values than
just four ones could be introduced. A restriction of the electron density
distribution to a finite number of states instead of regarding just the two
binary ones would be a possible extension. So, based on the promising results
presented here, lots of further work extending and refining the developed
approaches is possible.Röntgenkristallographie ist derzeit die Standardmethode zur Ermittlung der
drei- dimensionalen Struktur biologischer MakromolekĂĽle, wie z. B. von
Proteinen, und liefert damit eine wichtige Basis der Strukturbiologie sowie
der modernen Biotechnologie. Aus Röntgenexperimenten erhält man
Beugungsmuster, aus welchen dann die Struktur des zu untersuchenden Kristalls
berechnet werden soll. Diese wird durch die zugehörige
Elektronendichteverteilung beschrieben. Allerdings liefert das Beugungsmuster
nur die Beträge der komplexen Fourierkoeffizienten der Elektronendichte, nicht
die zugehörigen Phasenwerte. Das Problem, diese Phasenwerte zu ermitteln, ist
das Phasenproblem in der Röntgenkristallographie. Die Informationen, welche
aus dem Röntgenexperiment gewonnen werden können, sind nicht ausreichend um
dieses Phasenproblem zu lösen. Daher erhält man nicht nur eine, sondern eine
Menge zulässiger Lösungen. Zusätzliche Informationen über die
Elektronendichteverteilung können dann hinzugezogen werden um die Qualität
dieser Lösungen zu verbessern. In dieser Arbeit wird ein ganzzahliger linearer
Optimierungsansatz zur Lösung des Phasenproblems entwickelt, in dem
verschiedene topologische Eigenschaften von Proteinen modelliert und als
zusätzliche Informationen verwendet werden. Die wichtigste Eigenschaft, die so
modelliert und für die Problemlösung hinzugezogen wird, ist die
Zusammenhangseigenschaft von Proteinen. Diese sichert, dass die berechnete
Struktur nicht aus mehr als einer gegebenen Anzahl zusammenhängender
Komponenten besteht. Bei der Modellierung dieser Zusammenhangseigenschaft
werden graphentheoretische Methoden sowie ein Separationsalgorithmus genutzt.
Der Modellierungsansatz wurde implementiert und mit Daten von echten Proteinen
getestet. Die Testergebnisse zeigen, dass die Qualität der Lösungen des
Phasenproblems durch die Hinzunahme der topologischen Eigenschaften deutlich
verbessert wird
The relationship between differences in students’ computer and information literacy and response times: an analysis of IEA-ICILS data
Heldt M, Massek C, Drossel K, Eickelmann B. The relationship between differences in students’ computer and information literacy and response times: an analysis of IEA-ICILS data. Large-scale Assessments in Education. 2020;8(1): 12.#### Background
Due to the increasing use of information and communication technology, computer-related skills are important for all students in order to participate in the digital age (Fraillon, J., Ainley, J., Schulz, W., Friedman, T. & Duckworth, D. (2019). Preparing for life in a digital world: IEA International Computer and Information Literacy Study 2018 International Report. Amsterdam: International Association for the Evaluation of Educational Achievement (IEA). Retrieved from https://www.iea.nl/sites/default/files/2019-11/ICILS%202019%20Digital%20final%2004112019.pdf). Educational systems play a key role in the mediation of these skills (Eickelmann. Second Handbook of Information Technology in Primary and Secondary Education. Cham: Springer, 2018). However, previous studies have shown differences in students’ computer and information literacy (CIL). Although various approaches have been used to explain these differences, process data, such as response times, have never been taken into consideration. Based on data from the IEA-study ICILS 2013 of the Czech Republic, Denmark and Germany, this secondary analysis examines to what extent response times can be used as an explanatory approach for differences in CIL also within different groups of students according to student background characteristics (gender, socioeconomic background and immigrant background).
#### Methods
First, two processing profiles using a latent profile analysis (Oberski 2016) based on response times are determined—a fast and a slow processing profile. To detect how these profiles are related to students’ CIL, also in conjunction with students’ background characteristics (socioeconomic and immigrant background), descriptive statistics are used.
#### Results
The results show that in the Czech Republic and Germany, students belonging to the fast processing profile have on average significantly higher CIL than students allocated to the slow processing profile. In Denmark, there are no significant differences. Concerning the student background characteristics in the Czech Republic, there are significant negative time-on-task effects for all groups except for students with an immigrant background and students with a high parental occupational status. There are no significant differences in Denmark. For Germany, a significant negative time-on-task effect can be found among girls. However, the other examined indicators for Germany are ambiguous.
#### Conclusions
The results show that process data can be used to explain differences in students’ CIL: In the Czech Republic and Germany, there is a correlation between response times and CIL (significant negative time-on-task effect). Further analysis should also consider other aspects of CIL (e.g. reading literacy). What becomes clear, however, is that when interpreting and explaining differences in competence, data should also be included that relates to the completion process during testing