“…In addition, prognosis-related genes were identified using survival analysis and further used to build a network of competitive endogenous RNAs (ceRNAs; DEcircRNA–miRNA–mRNA). Finally, the functional analysis and drug–gene interaction analysis of mRNAs in the ceRNA network was performed. …”
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“…Proteins with the highest variances (top 500 proteins) were annotated for the pathway enrichment analysis. Functional analysis of differentially expressed proteins in NAG and AG was performed. …”
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“…Tumor tissues were analyzed by IHC, qRT-PCR, and Affymetrix Mouse Gene 2.0 ST Array followed by functional analysis using IPA®. Heart, lung, liver, kidney, and colon tissues were analyzed by qRT-PCR and Western blot. …”
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“…We also clustered two risk groups in each cohort according to the signature and performed survival analysis, functional analysis, tumor immune microenvironment analysis and drug sensitivity analysis. …”
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“…id=NaviCenta) was used to focus functional analysis results to the placenta specific context. …”
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“…The performance of the proposed signature was evaluated via Kaplan–Meier survival analysis, receiver operating characteristic curves, and principal component analysis. Functional analysis was implemented to uncover the potential prognostic mechanisms. …”
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“…The OA-depleted viruses spanned Siphoviridae (95 vOTUs), Myoviridae (70 vOTUs), and Microviridae (5 vOTUs), while 30 Siphoviridae vOTUs were enriched in OA patients. Functional analysis of the gut bacteriome and virome also uncovered their functional signatures in relation to OA. …”
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“…The main features of this book are the uses of strong methods of functional analysis and applications to the analysis of asymptotic behavior of solutions to partial differential equations, Abelian and Tauberian type theorems for integral transforms as well as for the summability of Fourier series and integrals. …”
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“…To achieve these objectives Stochastic Systems presents: ·         A clear and brief review of essential concepts on probability theory, random functions, stochastic calculus, Monte Carlo simulation, and functional analysis   ·          Probabilistic models for random variables and functions needed to formulate stochastic equations describing realistic problems in engineering and applied sciences   ·          Practical methods for quantifying the uncertain parameters in the definition of stochastic equations, solving approximately these equations, and assessing the accuracy of approximate solutions   Stochastic Systems provides key information for researchers, graduate students, and engineers who are interested in the formulation and solution of stochastic problems encountered in a broad range of disciplines. …”
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“…The selected examples impressively demonstrate how the combination of functional analysis, crystallography, investigation of dynamics and computational studies has made it possible to create a conclusive picture, or, more precisely, “a molecular movie”. …”
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“…Later on, applications were found in many other areas of mathematics: harmonic analysis, approximation theory, theoretical numerical analysis, geometry of Banach spaces, nonlinear functional analysis, etc. Besides this the theory has a considerable internal beauty and must by now be regarded as an independent branch of analysis, with its own problems and methods. …”
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“…For professionals in operator algebras and functional analysis, it provides a readable tour of the current state of the field.…”
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“…This section can also serves as a text for first courses in topology.Part II, chapter 4 through 7, details the basics of measure and integration and stands independently for use in a separate measure theory course.Part III addresses more advanced topics, including elaborated and abstract versions of measure and integration along with their applications to functional analysis, probability theory, and conventional analysis on the real line. …”
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“…Part I is intended to be a somewhat self-contained introduction to op­ erator theory and functional analysis, especially those elements necessary for application to problems in electromagnetics. …”
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“…A general background in functional analysis is required, but much of the theory is explained from scratch, anad the physical background of the mathematical theory is kept clearly in mind. …”
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“…The research contracts of the Department of Mathematics of INCREST with the National Council for Sciences and Technoloa,y of Romania provided the means for developping the research activi­ ty in Functional Analysis; these contracts constitute the gene­ rous framework for these meetings.…”
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“…The author combines techniques from the theory of partial differential equations and functional analysis with probabilistic ideas, paving the way to new mathematical theorems which may be fruitfully used in the treatment of the problem at hand. …”
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“…For this quarter century, these topics have been playing a central role in both pure and applied mathematics and having a great influence to the developm ent of the functional analysis, harmonic analysis and numerical analysis whose tools make a a substantial contribution to the investigation of nonlinear partial differential equations, particularly the Navier-Stokes and the Euler equations.      …”
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“…The main material is preceded by an introductory section in which all prerequisites from functional analysis are presented.…”
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“…The second half deals with general measures and functional analysis, including Hilbert spaces, Fourier series, and the Riesz representation theorem for positive linear functionals on continuous functions with compact support. …”
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