Minimal representation of semiorders with intervals of same length

2005 ◽  
pp. 162-175 ◽  
Author(s):  
Jutta Mitas
Keyword(s):  
Minimal Representation

scholarly journals Race and ethnicity representation in clinical trials: findings from a literature review of Phase I oncology trials

2021 ◽  
Author(s):  
D Ross Camidge ◽  
Haeseong Park ◽  
Karen E Smoyer ◽  
Ira Jacobs ◽  
Lauren J Lee ◽  
...  
Keyword(s):  
Clinical Trials ◽  
Phase I ◽  
Predominantly White ◽  
Race And Ethnicity ◽  
Phase I Trials ◽  
Minimal Representation ◽  
Phase I Clinical Trials ◽  
Demographic Representation ◽  
The Usa ◽  
Race Ethnicity

Aim: To provide an assessment of published literature on the demographic representation in Phase I trials of biopharmaceutical oncology agents. Materials & methods: We conducted a rapid evidence assessment to identify demographic representation reported in Phase I clinical trials for biopharmaceutical oncology agents published in 2019. Results: Globally, the population was predominantly White/Caucasian (62.2%). In the USA, the distribution was heavily skewed toward White/Caucasian (84.2%), with minimal representation of Blacks/African–Americans (7.3%), Asians (3.4%), Hispanics/Latinos (2.8%) or other race/ethnicity groups. Conclusion: Our data highlight that Phase I oncology trials do not reflect the population at large, which may perpetuate health disparities. Further research is needed to understand and address barriers to participation, particularly among under-represented groups

MULTIPLICITY-FREE DECOMPOSITIONS OF THE MINIMAL REPRESENTATION OF THE INDEFINITE ORTHOGONAL GROUP

2008 ◽  
Vol 19 (10) ◽  
pp. 1187-1201 ◽  
Author(s):  
MASAYASU MORIWAKI
Keyword(s):  
Unitary Representation ◽  
Orthogonal Group ◽  
Irreducible Unitary Representation ◽  
Unitary Representations ◽  
Minimal Representation ◽  
Infinite Dimensional ◽  
Irreducible Unitary Representations ◽  
Direct Product Group ◽  
Multiplicity Free ◽  
Kirillov Dimension

Kazhdan, Kostant, Binegar–Zierau and Kobayashi–Ørsted constructed a distinguished infinite-dimensional irreducible unitary representation π of the indefinite orthogonal group G = O(2p, 2q) for p, q ≥ 1 with p + q > 2, which has the smallest Gelfand–Kirillov dimension 2p + 2q - 3 among all infinite-dimensional irreducible unitary representations of G and hence is called the minimal representation. We consider, for which subgroup G′ of G, the restriction π|G′ is multiplicity-free. We prove that the restriction of π to any subgroup containing the direct product group U(p1) × U(p2) × U(q) for p1, p2 ≥ 1 with p1 + p2 = p is multiplicity-free, whereas the restriction to U(p1) × U(p2) × U(q1) × U(q2) for q1, q2 ≥ 1 with q1 + q2 = q has infinite multiplicities.

Learning the Minimal Representation of a Dynamic System from Transition Data

2021 ◽  
Author(s):  
Mohammed Amine Bennouna ◽  
Dessislava Pachamanova ◽  
Georgia Perakis ◽  
Omar Skali Lami
Keyword(s):  
Dynamic System ◽  
Minimal Representation

MINIMAL 3-BRAID REPRESENTATIONS

1994 ◽  
Vol 03 (02) ◽  
pp. 163-177 ◽  
Author(s):  
R. D. KEEVER
Keyword(s):  
Conjugacy Class ◽  
Canonical Form ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Minimal Representation ◽  
Class A ◽  
Minimal Representations ◽  
Necessary And Sufficient

This paper provides necessary and sufficient conditions for a representation of any 3-braid to be minimal (with regard to the number of crossings) and includes an algorithm to obtain such a representation, the number of distinct minimal representations of a given 3-braid, as well as a unique canonical form for each braid in B3. Also presented are necessary and sufficient conditions for any 3-string braid word to be a minimal representation of its conjugacy class. A canonical form for each conjugacy class in B3 is given.

An Automorphic Theta Module for Quaternionic Exceptional Groups

2000 ◽  
Vol 52 (4) ◽  
pp. 737-756 ◽  
Author(s):  
Wee Teck Gan
Keyword(s):  
Eisenstein Series ◽  
Minimal Representation ◽  
Exceptional Groups ◽  
Theta Correspondences

AbstractWe construct an automorphic realization of the global minimal representation of quaternionic exceptional groups, using the theory of Eisenstein series, and use this for the study of theta correspondences.

Tensor Square of the Minimal Representation of O(p, q)

2007 ◽  
Vol 50 (1) ◽  
pp. 48-55 ◽  
Author(s):  
Alexander Dvorsky
Keyword(s):  
Tensor Product ◽  
Hyperbolic Space ◽  
Irreducible Representations ◽  
Plancherel Measure ◽  
Minimal Representation ◽  
Direct Integral ◽  
Tensor Square ◽  
Real Hyperbolic Space

AbstractIn this paper, we study the tensor product π = σmin ⊗ σmin of the minimal representation σmin of O(p, q) with itself, and decompose π into a direct integral of irreducible representations. The decomposition is given in terms of the Plancherel measure on a certain real hyperbolic space.

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