scholarly journals Multivariate Fink type identity and multivariate Ostrowski, comparison of means and Grüss type inequalities

2007 ◽  
Vol 46 (3-4) ◽  
pp. 351-374 ◽  
Author(s):  
George A. Anastassiou
2019 ◽  
Vol 25 (2) ◽  
pp. 189-203
Author(s):  
Sabir Hussain ◽  
Muhammad Amer Latif

Abstract Generalized Fink-type identity for multi-variables to an arbitrary time scales is obtained, giving some multi-variate Ostrowski, Iyengar and Grüss-type inequalities unifying the corresponding continuous and discrete version. Some new applications to generalized polynomials are also obtained.


2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Samaira Naz ◽  
Muhammad Nawaz Naeem ◽  
Yu-Ming Chu

AbstractIn this paper, we prove several inequalities of the Grüss type involving generalized k-fractional Hilfer–Katugampola derivative. In 1935, Grüss demonstrated a fascinating integral inequality, which gives approximation for the product of two functions. For these functions, we develop some new fractional integral inequalities. Our results with this new derivative operator are capable of evaluating several mathematical problems relevant to practical applications.


2020 ◽  
Author(s):  
Weiguang Mao ◽  
Maziyar Baran Pouyan ◽  
Dennis Kostka ◽  
Maria Chikina

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]


2008 ◽  
pp. 185-195 ◽  
Author(s):  
Mehmet Zeki Sarikaya ◽  
Nesip Aktan ◽  
Hüseyin Yildirim

2019 ◽  
Vol 43 (3) ◽  
pp. 2287-2296 ◽  
Author(s):  
Ulaş Yamancı ◽  
Remziye Tunç ◽  
Mehmet Gürdal

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