A Basis Construction for the Shi Arrangement of the TypeBℓorCℓ

2014 ◽  
Vol 43 (4) ◽  
pp. 1435-1448 ◽  
Author(s):  
Daisuke Suyama
Keyword(s):  
Basis Construction ◽  
Shi Arrangement

Fast algorithm of Hoteling basis construction

1998 ◽  
Author(s):  
Vitalij N. Kurashov ◽  
Olexandr M. Soloveyko ◽  
Yurij S. Musatenko
Keyword(s):  
Fast Algorithm ◽  
Basis Construction

scholarly journals The freeness of Ish arrangements

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Takuro Abe ◽  
Daisuke Suyama ◽  
Shuhei Tsujie
Keyword(s):  
Catalan Numbers ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Free Arrangement ◽  
International Audience ◽  
New Interpretation ◽  
Necessary And Sufficient ◽  
Shi Arrangement

International audience The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement and posed some problems. One of them is whether the Ish arrangement is a free arrangement or not. In this paper, we verify that the Ish arrangement is supersolvable and hence free. Moreover, we give a necessary and sufficient condition for the deleted Ish arrangement to be free L’arrangement Ish a été introduit par Armstrong pour donner une nouvelle interprétation des nombres $q; t$-Catalan de Garsia et Haiman. Armstrong et Rhoades ont montré qu’il y avait des ressemblances frappantes entre l’arrangement Shi et l’arrangement Ish et ont posé des conjectures. L’une d’elles est de savoir si l’arrangement Ish est un arrangement libre ou pas. Dans cet article, nous vérifions que l’arrangement Ish est supersoluble et donc libre. De plus, on donne une condition nécessaire et suffisante pour que l’arrangement Ish réduit soit libre.

scholarly journals Accelerating many-nucleon basis generation for high performance computing enabled ab initio nuclear structure studies

2019 ◽  
Vol 33 (3) ◽  
pp. 522-533 ◽  
Author(s):  
Daniel Langr ◽  
Tomáš Dytrych ◽  
Kristina D Launey ◽  
Jerry P Draayer
Keyword(s):  
Ab Initio ◽  
Nuclear Structure ◽  
High Performance ◽  
Model Framework ◽  
Significant Acceleration ◽  
Model Spaces ◽  
Basis Construction ◽  
Nuclear Structure Calculations ◽  
Performance Computing ◽  
Structure Calculations

We present the problem of generating a many-nucleon basis in [Formula: see text]-scheme for ab initio nuclear structure calculations in a symmetry-adapted no-core shell model framework. We first discuss and analyze the basis construction algorithm whose baseline implementation quickly becomes a significant bottleneck for large model spaces and heavier nuclei. The outcomes of this analysis are utilized to propose a new scalable version of the algorithm. Its performance is consequently studied empirically using the Blue Waters supercomputer. The measurements show significant acceleration achieved with over two orders of magnitude speedups realized for larger model spaces.

scholarly journals Adaptive POD–DEIM basis construction and its application to a nonlinear population balance system

AIChE Journal ◽  
2017 ◽  
Vol 63 (9) ◽  
pp. 3832-3844 ◽  
Author(s):  
Lihong Feng ◽  
Michael Mangold ◽  
Peter Benner
Keyword(s):  
Population Balance ◽  
Balance System ◽  
Basis Construction
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