34,484 research outputs found
Ball: An R package for detecting distribution difference and association in metric spaces
The rapid development of modern technology facilitates the appearance of
numerous unprecedented complex data which do not satisfy the axioms of
Euclidean geometry, while most of the statistical hypothesis tests are
available in Euclidean or Hilbert spaces. To properly analyze the data of more
complicated structures, efforts have been made to solve the fundamental test
problems in more general spaces. In this paper, a publicly available R package
Ball is provided to implement Ball statistical test procedures for K-sample
distribution comparison and test of mutual independence in metric spaces, which
extend the test procedures for two sample distribution comparison and test of
independence. The tailormade algorithms as well as engineering techniques are
employed on the Ball package to speed up computation to the best of our
ability. Two real data analyses and several numerical studies have been
performed and the results certify the powerfulness of Ball package in analyzing
complex data, e.g., spherical data and symmetric positive matrix data
Signed Young Modules and Simple Specht Modules
By a result of Hemmer, every simple Specht module of a finite symmetric group
over a field of odd characteristic is a signed Young module. While Specht
modules are parametrized by partitions, indecomposable signed Young modules are
parametrized by certain pairs of partitions. The main result of this article
establishes the signed Young module labels of simple Specht modules. Along the
way we prove a number of results concerning indecomposable signed Young modules
that are of independent interest. In particular, we determine the label of the
indecomposable signed Young module obtained by tensoring a given indecomposable
signed Young module with the sign representation. As consequences, we obtain
the Green vertices, Green correspondents, cohomological varieties, and
complexities of all simple Specht modules and a class of simple modules of
symmetric groups, and extend the results of Gill on periodic Young modules to
periodic indecomposable signed Young modules.Comment: To appear in Adv. Math. 307 (2017) 369--416. Proposition 4.3 (F4),
(F5) corrected, Lemma 4.9 adjusted accordingl
- …