Nonlinear
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Předmětem článkuje nelineární robustní 3D filtrace MR obrazu, která umožňuje realizaci vysokého prostorového rozlišení při zachování únosné míry šumu. Důraz je kladen na rozdílné vlastnosti 2D a 3D filtrů a na rozdíl mezi lineárními a nelineániími robustními technikami filtrace. Základní pojmy jsou vysvětleny v matematicky odlehčené podobě a postupy nelineární filtrace jsou dokumentovány na číselných příkladech. Rozdíly mezi jednotlivými metodami jsou zobrazeny v grafické formě. Software pro nelineární filtraci 3D MR obrazů je realizován v prostředí Matlab a zahrnuje čtení souborů podle normy Interfile, vlastní numerické výpočty, grafickou prezentaci a archivaci výsledků.
Nonlinear robust 3D filtering of MR image is a subject of the paper. It enables to realize high space resolution with guaranteed acceptable level of noise. Different properties of 2D and 3D filters plus the difference between linear and nonlinear robust techniques are pointed. Basic terms are explained in simple and „light" mathematical form and the procedures of nonlinear filtering are explained on numerical examples. The method differences are depicted using graphical form. The software for nonlinear filtering of 3D MR images is realized in Matlab environment including Interfile reading, numeric calculations, graphical presentation and result archivation.
elektronický časopis
- Konspekt
- Psychologie
- NLK Obory
- psychologie, klinická psychologie
- biologie
- NLK Publikační typ
- elektronické časopisy
379 s.
Interdisciplinary applied mathematics ; vol. 25
1st ed. xxvi, 434 s.
549 s. : obr., tab., grafy ; 24 cm
elektronický časopis
- MeSH
- optika a fotonika MeSH
- Konspekt
- Fyzika
- NLK Obory
- fyzika, biofyzika
- NLK Publikační typ
- elektronické časopisy
Recent evidence suggests that energy metabolism contributes to molecular mechanisms controlling stem cell identity. For example, human embryonic stem cells (hESCs) receive their metabolic energy mostly via glycolysis rather than mitochondrial oxidative phosphorylation. This suggests a connection of metabolic homeostasis to stemness. Nicotinamide adenine dinucleotide (NAD) is an important cellular redox carrier and a cofactor for various metabolic pathways, including glycolysis. Therefore, accurate determination of NAD cellular levels and dynamics is of growing importance for understanding the physiology of stem cells. Conventional analytic methods for the determination of metabolite levels rely on linear calibration curves. However, in actual practice many two-enzyme cycling assays, such as the assay systems used in this work, display prominently nonlinear behavior. Here we present a diaphorase/lactate dehydrogenase NAD cycling assay optimized for hESCs, together with a mechanism-based, nonlinear regression models for the determination of NAD(+), NADH, and total NAD. We also present experimental data on metabolic homeostasis of hESC under various physiological conditions. We show that NAD(+)/NADH ratio varies considerably with time in culture after routine change of medium, while the total NAD content undergoes relatively minor changes. In addition, we show that the NAD(+)/NADH ratio, as well as the total NAD levels, vary between stem cells and their differentiated counterparts. Importantly, the NAD(+)/NADH ratio was found to be substantially higher in hESC-derived fibroblasts versus hESCs. Overall, our nonlinear mathematical model is applicable to other enzymatic amplification systems.
- MeSH
- buněčné extrakty MeSH
- elektroforéza kapilární MeSH
- embryonální kmenové buňky metabolismus MeSH
- kalibrace MeSH
- lidé MeSH
- NAD metabolismus MeSH
- nelineární dynamika * MeSH
- oxaziny metabolismus MeSH
- regresní analýza MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
We extended the linearized model of electromigration, which is used by PeakMaster, by calculation of nonlinear dispersion and diffusion of zones. The model results in the continuity equation for the shape function ϕ(x,t) of the zone: ϕ(t) = -(v(0) + v(EMD) ϕ)ϕ(x) + δϕ(xx) that contains linear (v(0)) and nonlinear migration (v(EMD)), diffusion (δ), and subscripts x and t stand for partial derivatives. It is valid for both analyte and system zones, and we present equations how to calculate characteristic zone parameters. We solved the continuity equation by Hopf-Cole transformation and applied it for two different initial conditions-the Dirac function resulting in the Haarhoff-van der Linde (HVL) function and the rectangular pulse function, which resulted in a function that we denote as the HVLR function. The nonlinear model was implemented in PeakMaster 5.3, which uses the HVLR function to predict the electropherogram for a given background electrolyte and a composition of the sample. HVLR function also enables to draw electropherograms with significantly wide injection zones, which was not possible before. The nonlinear model was tested by a comparison with a simulation by Simul 5, which solves the complete nonlinear model of electromigration numerically.
