363 research outputs found
Vacuum ultraviolet photoabsorption spectra of nitrile ices for their identification on Pluto
Icy bodies, such as Pluto, are known to harbor simple and complex molecules. The recent New Horizons flyby of Pluto has revealed a complex surface composed of bright and dark ice surfaces, indicating a rich chemistry based on nitrogen (N2), methane (CH4), and carbon monoxide (CO). Nitrile (CN) containing molecules such as acetonitrile (CH3CN), propionitrile (CH3CH2CN), butyronitrile (CH3CH2CH2CN), and isobutyronitrile ((CH3)2CHCN) are some of the nitrile molecules that are known to be synthesized by radiative processing of such simple ices. Through the provision of a spectral atlas for such compounds we propose that such nitriles may be identified from the ALICE payload on board New Horizons</i
Noncentral bimatrix variate generalised beta distributions
In this paper, we determine the density functions of nonsymmetrised doubly
noncentral matrix variate beta type I and II distributions. The nonsymetrised
density functions of doubly noncentral and noncentral bimatrix variate
generalised beta type I and II distributions are also obtained.Comment: 14 page
A real quaternion spherical ensemble of random matrices
One can identify a tripartite classification of random matrix ensembles into
geometrical universality classes corresponding to the plane, the sphere and the
anti-sphere. The plane is identified with Ginibre-type (iid) matrices and the
anti-sphere with truncations of unitary matrices. This paper focusses on an
ensemble corresponding to the sphere: matrices of the form \bY= \bA^{-1} \bB,
where \bA and \bB are independent matrices with iid standard
Gaussian real quaternion entries. By applying techniques similar to those used
for the analogous complex and real spherical ensembles, the eigenvalue jpdf and
correlation functions are calculated. This completes the exploration of
spherical matrices using the traditional Dyson indices .
We find that the eigenvalue density (after stereographic projection onto the
sphere) has a depletion of eigenvalues along a ring corresponding to the real
axis, with reflective symmetry about this ring. However, in the limit of large
matrix dimension, this eigenvalue density approaches that of the corresponding
complex ensemble, a density which is uniform on the sphere. This result is in
keeping with the spherical law (analogous to the circular law for iid
matrices), which states that for matrices having the spherical structure \bY=
\bA^{-1} \bB, where \bA and \bB are independent, iid matrices the
(stereographically projected) eigenvalue density tends to uniformity on the
sphere.Comment: 25 pages, 3 figures. Added another citation in version
Measuring Cognitive Reflection without Maths: Development and Validation fo the Verbal Cognitive Reflection Test
The Cognitive Reflection Test (CRT) became popular for its impressive power to predict how well people reason and make decisions. Despite the popularity of the CRT, a major issue complicates its interpretation: the numerical nature of the CRT confounds reflection ability with mathematical ability. We have addressed this issue by developing the Verbal CRT (CRT-V), a novel 10-item measure of cognitive reflection (https://osf.io/xehbv/), using non-mathematical problems with good statistical and psychometric properties and with low familiarity. First, we selected suitable items with relatively low familiarity and optimal difficulty as identified in two different populations (Studies 1 and 2) and with high content validity as judged by an expert panel (Study 3). Second, we demonstrated good criterion and construct validity for the test in different populations with a wide range of variables (Studies 4-6, 8) and a good internal consistency and test-retest reliability (Study 7). The Verbal CRT was less associated with math anxiety, objective and subjective numeracy than the original CRT and it was test equivalent across gender, age groups and administration setting. In contrast with the original CRT (Hedge’s g = 0.29, 95% CI[0.17, 0.40]), the Verbal CRT showed no gender differences (Hedge’s g = -0.06, 95% CI[-0.18, 0.06]). The Verbal CRT can complement existing, numerical, tests of cognitive reflection
Randomized trials, generalizability, and meta-analysis: Graphical insights for binary outcomes
BACKGROUND: Randomized trials stochastically answer the question. "What would be the effect of treatment on outcome if one turned back the clock and switched treatments in the given population?" Generalizations to other subjects are reliable only if the particular trial is performed on a random sample of the target population. By considering an unobserved binary variable, we graphically investigate how randomized trials can also stochastically answer the question, "What would be the effect of treatment on outcome in a population with a possibly different distribution of an unobserved binary baseline variable that does not interact with treatment in its effect on outcome?" METHOD: For three different outcome measures, absolute difference (DIF), relative risk (RR), and odds ratio (OR), we constructed a modified BK-Plot under the assumption that treatment has the same effect on outcome if either all or no subjects had a given level of the unobserved binary variable. (A BK-Plot shows the effect of an unobserved binary covariate on a binary outcome in two treatment groups; it was originally developed to explain Simpsons's paradox.) RESULTS: For DIF and RR, but not OR, the BK-Plot shows that the estimated treatment effect is invariant to the fraction of subjects with an unobserved binary variable at a given level. CONCLUSION: The BK-Plot provides a simple method to understand generalizability in randomized trials. Meta-analyses of randomized trials with a binary outcome that are based on DIF or RR, but not OR, will avoid bias from an unobserved covariate that does not interact with treatment in its effect on outcome
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