scholarly journals On a Rogers-Ramanujan type identity from crystal base theory

2017 ◽  
Vol 146 (1) ◽  
pp. 55-67 ◽  
Author(s):  
Jehanne Dousse ◽  
Jeremy Lovejoy
Keyword(s):  
Crystal Base ◽  
Type Identity ◽  
Base Theory

Acid-base properties of metals and glasses of Na2O.P2O5-xB2O3 system

1984 ◽  
Vol 49 (10) ◽  
pp. 2355-2362 ◽  
Author(s):  
Juraj Leško ◽  
Marie Dorušková ◽  
Jan Tržil
Keyword(s):  
Boron Oxide ◽  
A Priori ◽  
Optical Basicity ◽  
Galvanic Cell ◽  
Acid Base ◽  
Tetrahedral Configuration ◽  
Relative Basicity ◽  
Base Theory ◽  
Base Properties

Boron oxide in the Na2O.P2O5-x B2O3 system behaves as a Lux base. Its addition to Na2O.P2O5 brings about transformation of a Co(II) indicator from octahedral to tetrahedral configuration, increase in the optical basicity ΛPb(II), increase in the relative basicity of the melt as determined by means of a galvanic cell, and depolymerization reactions releasing PO43- ions. In the Na2O-B2O3 system free of P2O5, boron oxide behaves as a Lux acid. The amphoretic nature of B2O3 is explained in terms of Lux's acid-base theory extended in analogy with the protolysis theory. The theoretical optical basicity values do not indicate the amphoretic behaviour of B2O3 because in this approach boron oxide is a priori regarded as more acidic than Na2O.P2O5.

scholarly journals NOTES ON BOUNDED INDUCTION FOR THE COMPOSITIONAL TRUTH PREDICATE

2017 ◽  
Vol 10 (3) ◽  
pp. 455-480 ◽  
Author(s):  
BARTOSZ WCISŁO ◽  
MATEUSZ ŁEŁYK
Keyword(s):  
Reflection Principle ◽  
Peano Arithmetic ◽  
Truth Predicate ◽  
Base Theory ◽  
Modified Theory ◽  
Induction Scheme

AbstractWe prove that the theory of the extensional compositional truth predicate for the language of arithmetic with Δ0-induction scheme for the truth predicate and the full arithmetical induction scheme is not conservative over Peano Arithmetic. In addition, we show that a slightly modified theory of truth actually proves the global reflection principle over the base theory.

scholarly journals Weaker cousins of Ramsey's theorem over a weak base theory

2021 ◽  
pp. 103028
Author(s):  
Marta Fiori-Carones ◽  
Leszek Aleksander Kołodziejczyk ◽  
Katarzyna W. Kowalik
Keyword(s):  
Weak Base ◽  
Ramsey's Theorem ◽  
Base Theory ◽  
Ramsey’S Theorem

scholarly journals Gröbner–Shirshov bases method for Gelfand–Dorfman–Novikov algebras

2017 ◽  
Vol 16 (01) ◽  
pp. 1750001 ◽  
Author(s):  
L. A. Bokut ◽  
Yuqun Chen ◽  
Zerui Zhang
Keyword(s):  
Word Problem ◽  
Type Theorem ◽  
Novikov Algebra ◽  
Base Theory ◽  
Novikov Algebras

We establish Gröbner–Shirshov base theory for Gelfand–Dorfman–Novikov algebras over a field of characteristic [Formula: see text]. As applications, a PBW type theorem in Shirshov form is given and we provide an algorithm for solving the word problem of Gelfand–Dorfman–Novikov algebras with finite homogeneous relations. We also construct a subalgebra of one generated free Gelfand–Dorfman–Novikov algebra which is not free.

An Axiomatic Data Base Theory

1978 ◽  
pp. 259-289 ◽  
Author(s):  
Sten-Åke Tärnlund
Keyword(s):  
Data Base ◽  
Base Theory

scholarly journals Non-negative Independent Factor Analysis for single cell RNA-seq

2020 ◽  
Author(s):  
Weiguang Mao ◽  
Maziyar Baran Pouyan ◽  
Dennis Kostka ◽  
Maria Chikina
Keyword(s):  
Factor Analysis ◽  
Single Cell ◽  
Matrix Factorization ◽  
Component Analysis ◽  
Computational Techniques ◽  
Cell Type ◽  
Analysis Model ◽  
Factor Analysis Model ◽  
Type Identity ◽  
Wide Range

AbstractMotivationSingle cell RNA sequencing (scRNA-seq) enables transcriptional profiling at the level of individual cells. With the emergence of high-throughput platforms datasets comprising tens of thousands or more cells have become routine, and the technology is having an impact across a wide range of biomedical subject areas. However, scRNA-seq data are high-dimensional and affected by noise, so that scalable and robust computational techniques are needed for meaningful analysis, visualization and interpretation. Specifically, a range of matrix factorization techniques have been employed to aid scRNA-seq data analysis. In this context we note that sources contributing to biological variability between cells can be discrete (or multi-modal, for instance cell-types), or continuous (e.g. pathway activity). However, no current matrix factorization approach is set up to jointly infer such mixed sources of variability.ResultsTo address this shortcoming, we present a new probabilistic single-cell factor analysis model, Non-negative Independent Factor Analysis (NIFA), that combines features of complementary approaches like Independent Component Analysis (ICA), Principal Component Analysis (PCA), and Non-negative Matrix Factorization (NMF). NIFA simultaneously models uni- and multi-modal latent factors and can so isolate discrete cell-type identity and continuous pathway-level variations into separate components. Similar to NMF, NIFA constrains factor loadings to be non-negative in order to increase biological interpretability. We apply our approach to a range of data sets where cell-type identity is known, and we show that NIFA-derived factors outperform results from ICA, PCA and NMF in terms of cell-type identification and biological interpretability. Studying an immunotherapy dataset in detail, we show that NIFA identifies biomedically meaningful sources of variation, derive an improved expression signature for regulatory T-cells, and identify a novel myeloid cell subtype associated with treatment response. Overall, NIFA is a general approach advancing scRNA-seq analysis capabilities and it allows researchers to better take advantage of their data. NIFA is available at https://github.com/wgmao/[email protected]

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