79 research outputs found
Complexes of Dirac Operators in Clifford Algebras
No full textIn this paper we study complexes of Dirac operators
(or variations of Dirac
operators) in the real or complex Clifford algebras \cc_m i.e. complexes in
which the first map is induced by the matrix [\pp_{\ux_1},\ldots ,\pp_{\ux_k}]
where \pp_{\ux_i} is the Dirac operator with respect to the variable
x_i\in\cc_m.
In particular we prove that,
if , the complex in the case of operators
can be described in terms of relations coming
from the so called {\em radial algebra}. Moreover we show that if the dimension is less than , then
the Fischer decomposition does not hold
There is cumulative status bias and status entrenchment in NBA Awards: A rejoinder to McMahan & Shor
No full textPeter McMahan and Eran Shor (MS) published an article in Sociological Science critiquing our study on cumulative status bias in NBA All-Star elections (Biegert, Kühhirt, and Van Lancker 2023). In this article, we affirm the presence of cumulative status bias in NBA Awards. Crucially, MS focus only on the accumulated component of cumulative status bias, ignoring the impact of immediately preceding status signals, which decouple quality and status. Furthermore, we identify theoretical and empirical issues with their model extensions of All-Star elections and their reapplication to All-NBA selections. (1) We deem MS’ argument for legitimate deviations between status and quality deeply problematic. (2) We argue that their inclusion of additional variables is not theoretically plausible in several instances, nor does it improve the models, which still support our findings. (3) We argue that All-NBA selections are a different application, not a better one, with no direct implications for the role of cumulative status bias in NBA All-Star elections. (4) We highlight flaws in MS’ models, such as irrelevant covariates, an indiscriminate approach to confounding and mediation, mismeasurement, and problematic post-treatment and post-outcome controls. (5) Our re-analysis confirms that, even in the All-NBA setting, previous status distinctions cumulatively bias outcomes
There is cumulative status bias and status entrenchment in NBA Awards: a rejoinder to McMahan and Shor
No full textPeter McMahan and Eran Shor (MS) published a paper in Sociological Science critiquing our study on cumulative status bias in NBA All-Star elections (Biegert, Kühhirt, and Van Lancker 2023, BKVL). In this article, we affirm the presence of cumulative status bias in NBA Awards. Crucially, MS focuses only on the accumulated component of cumulative status bias, ignoring the impact of immediately preceding status signals, which decouple quality and status. Further, we identify theoretical and empirical issues with their model extensions of All-Star elections and their reapplication to All-NBA selections. 1) We deem MS’ argument for legitimate deviations between status and quality deeply problematic. 2) We argue that their inclusion of additional variables is not theoretically plausible in several instances, nor does it improve the models, which still support our findings. 3) We argue that All-NBA selections are a different application, not a better one, with no direct implications for the role of cumulative status bias in NBA All-Star elections. 4) We highlight flaws in MS’ models, such as irrelevant covariates, an indiscriminate approach to confounding and mediation, mismeasurement, and problematic post-treatment and post-outcome controls. 5) Our re-analysis confirms that even in the All-NBA setting previous status distinctions cumulatively bias outcomes
Modelling sediment pick-up and depostion in a dune model
No full textOften river bed form modelling is done with an equilibrium bed load transport formula like that of Meyer-Peter & Müller (1948). However, a physically more correct way would be to model it with separate models for the sediment pick-up and deposition processes as described by Nakagawa & Tsujimoto (1980). Besides the physics of the sediment transport itself, using such a method allows for the modelling of higher-order processes as well like spatial lag in bed load transport.As shown by Shimizu et al. (2009) applying the aforementioned pick-up and deposition model in a dune evolution model, makes is possible to model dunes well. Specifically it made it possible to determine a transition to upper stage plane beds, as well as capturing hysteresis well.In this paper we will explore the effect of using different kinds of bed load models in a relatively simple dune evolution model. The Nakagawa & Tsujimoto (1980) bed load model, will be implemented in the dune evolution model of Paarlberg et al. (2009). Results of this model version will be compared with the original version (using the Meyer-Peter & Müller formula) and a later version that directly models spatial lag with a relaxation equation
Habitat suitability models for the analysis and prediction of macrobenthos in the North Sea
No full text
Spherical monogenics: an algebraic approach
No full textThe space of spherical monogenics M(k) in R(m) can be regarded as a model for the irreducible representation of Spin(m) with weight (k + 1/2, 1/2, ..., 1/2). In this paper we construct an orthonormal basis for M(k). To describe the symmetry behind this procedure, we define certain Spin(m - 2)invariant representations of the Lie algebra sl(2) on M(k)
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