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Equivalence of superspace groups.

ABSTRACT: An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic structure unit cell) and a transformation of the internal-space lattice vectors (new modulation wavevectors are linear combinations of old modulation wavevectors plus a three-dimensional reciprocal-lattice vector). The need for non-standard settings in some cases and the desirability of employing standard settings of superspace groups in other cases are illustrated by an analysis of the symmetries of a series of compounds, comparing published and standard settings and the transformations between them. A compilation is provided of standard settings of compounds with two- and three-dimensional modulations. The problem of settings of superspace groups is discussed for incommensurate composite crystals and for chiral superspace groups.

SUBMITTER: van Smaalen S

PROVIDER: S-EPMC3553647 | biostudies-literature | 2013 Jan

REPOSITORIES: biostudies-literature

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Equivalence of superspace groups.

van Smaalen Sander S Campbell Branton J BJ Stokes Harold T HT

Acta crystallographica. Section A, Foundations of crystallography 20121114 Pt 1

An algorithm is presented which determines the equivalence of two settings of a (3 + d)-dimensional superspace group (d = 1, 2, 3). The algorithm has been implemented as a web tool findssg on SSG(3+d)D, providing the transformation of any user-given superspace group to the standard setting of this superspace group in SSG(3+d)D. It is shown how the standard setting of a superspace group can be directly obtained by an appropriate transformation of the external-space lattice vectors (the basic stru ...[more]

PMID: 23250064

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Project description:This is the first study of the measurement equivalence of the Patient Reported Outcomes Measurement Information System® (PROMIS®) Anxiety short forms in a large ethnically diverse sample. The psychometric properties and differential item functioning (DIF) were examined across different racial/ethnic, educational, age, gender and language groups. METHODS:These data are from individuals selected from cancer registries in the United States. For the analyses of race/ethnicity the reference group was non-Hispanic Whites (n = 2,263), the studied groups were non-Hispanic Blacks (n = 1,117), Hispanics (n = 1,043) and Asians/Pacific Islanders (n = 907). Within the Hispanic subsample, there were 335 interviews conducted in Spanish and 703 in English. The 11 anxiety items were from the PROMIS emotional disturbance item bank. DIF hypotheses were generated by content experts who rated whether or not they expected DIF to be present, and the direction of the DIF with respect to several comparison groups. The primary method used for DIF detection was the Wald test for examination of group differences in item response theory (IRT) item parameters accompanied by magnitude measures. Expected item scores were examined as measures of magnitude. The method used for quantification of the difference in the average expected item scores was the non-compensatory DIF (NCDIF) index. DIF impact was examined using expected scale score functions. Additionally, precision and reliabilities were examined using several methods. RESULTS:Although not hypothesized to show DIF for Asians/Pacific Islanders, every item evidenced DIF by at least one method. Two items showed DIF of higher magnitude for Asians/Pacific Islanders vs. Whites: "Many situations made me worry" and "I felt anxious". However, the magnitude of DIF was small and the NCDIF statistics were not above threshold. The impact of DIF was negligible. For education, six items were identified with consistent DIF across methods: fearful, anxious, worried, hard to focus, uneasy and tense. However, the NCDIF was not above threshold and the impact of DIF on the scale was trivial. No items showed high magnitude DIF for gender. Two items showed slightly higher magnitude for age (although not above the cutoff): worried and fearful. The scale level impact was trivial. Only one item showed DIF with the Wald test after the Bonferroni correction for the language comparisons: "I felt fearful". Two additional items were flagged in sensitivity analyses after Bonferroni correction, anxious and many situations made me worry. The latter item also showed DIF of higher magnitude, with an NCDIF value (0.144) above threshold. Individual impact was relatively small. CONCLUSIONS:Although many items from the PROMIS short form anxiety measures were flagged with DIF, item level magnitude was low and scale level DIF impact was minimal; however, three items: anxious, worried and many situations made me worry might be singled out for further study. It is concluded that the PROMIS Anxiety short form evidenced good psychometric properties, was relatively invariant across the groups studied, and performed well among ethnically diverse subgroups of Blacks, Hispanic, White non-Hispanic and Asians/Pacific Islanders. In general more research with the Asians/Pacific Islanders group is needed. Further study of subgroups within these broad categories is recommended.

Project description:AIMS:The goals of these analyses were to examine the psychometric properties and measurement equivalence of a self-reported cognition measure, the Patient Reported Outcome Measurement Information System® (PROMIS®) Applied Cognition - General Concerns short form. These items are also found in the PROMIS Cognitive Function (version 2) item bank. This scale consists of eight items related to subjective cognitive concerns. Differential item functioning (DIF) analyses of gender, education, race, age, and (Spanish) language were performed using an ethnically diverse sample (n = 5,477) of individuals with cancer. This is the first analysis examining DIF in this item set across ethnic and racial groups. METHODS:DIF hypotheses were derived by asking content experts to indicate whether they posited DIF for each item and to specify the direction. The principal DIF analytic model was item response theory (IRT) using the graded response model for polytomous data, with accompanying Wald tests and measures of magnitude. Sensitivity analyses were conducted using ordinal logistic regression (OLR) with a latent conditioning variable. IRT-based reliability, precision and information indices were estimated. RESULTS:DIF was identified consistently only for the item, brain not working as well as usual. After correction for multiple comparisons, this item showed significant DIF for both the primary and sensitivity analyses. Black respondents and Hispanics in comparison to White non-Hispanic respondents evidenced a lower conditional probability of endorsing the item, brain not working as well as usual. The same pattern was observed for the education grouping variable: as compared to those with a graduate degree, conditioning on overall level of subjective cognitive concerns, those with less than high school education also had a lower probability of endorsing this item. DIF was also observed for age for two items after correction for multiple comparisons for both the IRT and OLR-based models: "I have had to work really hard to pay attention or I would make a mistake" and "I have had trouble shifting back and forth between different activities that require thinking". For both items, conditional on cognitive complaints, older respondents had a higher likelihood than younger respondents of endorsing the item in the cognitive complaints direction. The magnitude and impact of DIF was minimal. The scale showed high precision along much of the subjective cognitive concerns continuum; the overall IRT-based reliability estimate for the total sample was 0.88 and the estimates for subgroups ranged from 0.87 to 0.92. CONCLUSION:Little DIF of high magnitude or impact was observed in the PROMIS Applied Cognition - General Concerns short form item set. One item, "It has seemed like my brain was not working as well as usual" might be singled out for further study. However, in general the short form item set was highly reliable, informative, and invariant across differing race/ethnic, educational, age, gender, and language groups.

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Equivalence of superspace groups.

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Equivalence of superspace groups.

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