scholarly journals The exocenter and type decomposition of a generalized pseudoeffect algebra

2013 ◽  
Vol 33 (1) ◽  
pp. 13 ◽  
Author(s):  
David Foulis ◽  
Silvia Pulmannova ◽  
Elena Vincekova
Keyword(s):  
Pseudoeffect Algebra ◽  
Type Decomposition

scholarly journals TYPE DECOMPOSITION OF A PSEUDOEFFECT ALGEBRA

2010 ◽  
Vol 89 (3) ◽  
pp. 335-358 ◽  
Author(s):  
DAVID J. FOULIS ◽  
SYLVIA PULMANNOVÁ ◽  
ELENA VINCEKOVÁ
Keyword(s):  
Effect Algebra ◽  
Von Neumann Algebra ◽  
Von Neumann ◽  
Pseudoeffect Algebras ◽  
Noncommutative Version ◽  
Pseudoeffect Algebra ◽  
Determining Set ◽  
Direct Decompositions ◽  
Type Decomposition ◽  
Unsharp Observables

AbstractEffect algebras, which generalize the lattice of projections in a von Neumann algebra, serve as a basis for the study of unsharp observables in quantum mechanics. The direct decomposition of a von Neumann algebra into types I, II, and III is reflected by a corresponding decomposition of its lattice of projections, and vice versa. More generally, in a centrally orthocomplete effect algebra, the so-called type-determining sets induce direct decompositions into various types. In this paper, we extend the theory of type decomposition to a (possibly) noncommutative version of an effect algebra called a pseudoeffect algebra. It has been argued that pseudoeffect algebras constitute a natural structure for the study of noncommuting unsharp or fuzzy observables. We develop the basic theory of centrally orthocomplete pseudoeffect algebras, generalize the notion of a type-determining set to pseudoeffect algebras, and show how type-determining sets induce direct decompositions of centrally orthocomplete pseudoeffect algebras.

scholarly journals EMeth: An EM algorithm for cell type decomposition based on DNA methylation data

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Hanyu Zhang ◽  
Ruoyi Cai ◽  
James Dai ◽  
Wei Sun
Keyword(s):  
Dna Methylation ◽  
Tumor Cells ◽  
T Regulatory Cells ◽  
Simulated Data ◽  
Cell Types ◽  
Computational Method ◽  
Methylation Data ◽  
Cell Type ◽  
A Cell ◽  
Type Decomposition

AbstractWe introduce a new computational method named EMeth to estimate cell type proportions using DNA methylation data. EMeth is a reference-based method that requires cell type-specific DNA methylation data from relevant cell types. EMeth improves on the existing reference-based methods by detecting the CpGs whose DNA methylation are inconsistent with the deconvolution model and reducing their contributions to cell type decomposition. Another novel feature of EMeth is that it allows a cell type with known proportions but unknown reference and estimates its methylation. This is motivated by the case of studying methylation in tumor cells while bulk tumor samples include tumor cells as well as other cell types such as infiltrating immune cells, and tumor cell proportion can be estimated by copy number data. We demonstrate that EMeth delivers more accurate estimates of cell type proportions than several other methods using simulated data and in silico mixtures. Applications in cancer studies show that the proportions of T regulatory cells estimated by DNA methylation have expected associations with mutation load and survival time, while the estimates from gene expression miss such associations.

Iwasawa-type Decomposition in Compact Groups

1996 ◽  
Vol 788 (1 General Topol) ◽  
pp. 138-146
Author(s):  
GERALD ITZKOWITZ ◽  
TA SUN WU
Keyword(s):  
Compact Groups ◽  
Type Decomposition

scholarly journals LEBESGUE DECOMPOSITION FOR REPRESENTABLE FUNCTIONALS ON *-ALGEBRAS

2015 ◽  
Vol 58 (2) ◽  
pp. 491-501 ◽  
Author(s):  
ZSIGMOND TARCSAY
Keyword(s):  
Decomposition Theorem ◽  
Lebesgue Decomposition ◽  
Absolutely Continuous ◽  
Hermitian Forms ◽  
Lebesgue Type Decomposition ◽  
Representable Functional ◽  
Type Decomposition

AbstractWe offer a Lebesgue-type decomposition of a representable functional on a *-algebra into absolutely continuous and singular parts with respect to another. Such a result was proved by Zs. Szűcs due to a general Lebesgue decomposition theorem of S. Hassi, H.S.V. de Snoo, and Z. Sebestyén concerning non-negative Hermitian forms. In this paper, we provide a self-contained proof of Szűcs' result and in addition we prove that the corresponding absolutely continuous parts are absolutely continuous with respect to each other.

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