nonlinearity
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- MeSH
- nelineární dynamika MeSH
- plíce fyziologie MeSH
- srdce fyziologie MeSH
- zvířata MeSH
- Check Tag
- zvířata MeSH
The aim of this work is to present the efficacy of a previously introduced computational procedure, developed for evaluation of vascular responsiveness. On this reason, as an example a common study of noradrenaline (NA) effect on a rat renal artery under in vitro conditions was arbitrarily selected. The response of the arterial segment to NA doses (0.1-10 µg) was digitally recorded on a PC and employed to develop mathematical model of NA effect. Using the model, the following NA effect variables were determined: the vessel sensitivity parameter, mean effect time and rate constant, respectively, characterizing the effect intensity, duration, and regression and also classic response variables: the maximal effect and time of the maximal effect. The two-way analysis of variance followed by Bonferroni’s test revealed a significant influence of the increasing NA dose on the vessel sensitivity parameter and mean effect time. These findings indicated nonlinearity of processes underlying NA effect on the rat renal artery over the given range of NA doses. The procedure exemplified has the potential for use as an effective adjunct to routine studies of vascular responsiveness as it enables the extraction of meaningful information which cannot by obtained by common manual evaluation procedures.
- Klíčová slova
- Computational method, Digital recording, Sensitivity parameter, Mean effect time, Effect regression,
- MeSH
- arteria renalis účinky léků MeSH
- časové faktory MeSH
- financování organizované MeSH
- krysa rodu rattus MeSH
- modely kardiovaskulární MeSH
- nelineární dynamika MeSH
- noradrenalin farmakologie MeSH
- počítačová simulace MeSH
- potkani Wistar MeSH
- vazokonstrikce účinky léků MeSH
- vazokonstriktory farmakologie MeSH
- vztah mezi dávkou a účinkem léčiva MeSH
- zvířata MeSH
- Check Tag
- krysa rodu rattus MeSH
- mužské pohlaví MeSH
- zvířata 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.
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.
Interdisciplinary applied mathematics ; vol. 25
1st ed. xxvi, 434 s.
We study effects of oscillatory convective flow in extracellular space on the velocity of chemical signal propagation having a form of a front wave above a cellular layer. We found that the time-averaged propagation velocity under oscillatory flow for a particular Péclet number amplitude is slower than the velocity under steady laminar flow regime for the same value of the Péclet number, but significantly faster than under no-flow conditions. We derive asymptotic values of the propagation velocity and asymptotic characteristics of the corresponding concentration fronts in high- and low-frequency regimes and show that the reason for the observed velocity increase under the oscillatory flow stems from a nonlinear dependence of the propagation velocity on the Péclet number, particularly from the convex character of the dependence. Our findings suggest that the specific responses of cellular cultures to different flow conditions in the extracellular space (for example, expression of atherosclerosis protective genes under steady laminar flow but not under oscillatory flow) is a consequence of a nonlinear coupling between the extracellular transport and complex intracellular reaction cascades forming a positive feedback loop of the autocrine signaling. This mechanism can operate independently of, or in conjunction with, a direct stress-sensing due to mechanotransduction.
- MeSH
- autokrinní signalizace * MeSH
- biologické modely * MeSH
- hydrodynamika * MeSH
- konvekce * MeSH
- lidé MeSH
- nelineární dynamika MeSH
- zvířata MeSH
- Check Tag
- lidé MeSH
- zvířata MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Oscillatory phenomena in the brain activity and their synchronization are frequently studied using mathematical models and analytic tools derived from nonlinear dynamics. In many experimental situations, however, neural signals have a broadband character and if oscillatory activity is present, its dynamical origin is unknown. To cope with these problems, a framework for detecting nonlinear oscillatory activity in broadband time series is presented. First, a narrow-band oscillatory mode is extracted from a broadband background. Second, it is tested whether the extracted mode is significantly different from linearly filtered noise, modelled as a linear stochastic process possibly passed through a static nonlinear transformation. If a nonlinear oscillatory mode is positively detected, further analysis using nonlinear approaches such as the phase synchronization analysis can potentially bring new information. For linear processes, however, standard approaches such as the coherence analysis are more appropriate and provide sufficient description of underlying interactions with smaller computational effort. The method is illustrated in a numerical example and applied to analyze experimentally obtained human EEG time series from a sleeping subject.
- MeSH
- biologické hodiny fyziologie MeSH
- časové faktory MeSH
- elektroencefalografie metody MeSH
- lidé MeSH
- modely neurologické MeSH
- mozek fyziologie MeSH
- nelineární dynamika MeSH
- počítačové zpracování signálu MeSH
- spánek fyziologie MeSH
- spektrální analýza MeSH
- Check Tag
- lidé MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
Since typically there are many predators feeding on most herbivores in natural communities, understanding multiple predator effects is critical for both community and applied ecology. Experiments of multiple predator effects on prey populations are extremely demanding, as the number of treatments and the amount of labour associated with these experiments increases exponentially with the number of species in question. Therefore, researchers tend to vary only presence/absence of the species and use only one (supposedly realistic) combination of their numbers in experiments. However, nonlinearities in density dependence, functional responses, interactions between natural enemies etc. are typical for such systems, and nonlinear models of population dynamics generally predict qualitatively different results, if initial absolute densities of the species studied differ, even if their relative densities are maintained. Therefore, testing combinations of natural enemies without varying their densities may not be sufficient. Here we test this prediction experimentally. We show that the population dynamics of a system consisting of 2 natural enemies (aphid predator Adalia bipunctata (L.), and aphid parasitoid, Aphidius colemani Viereck) and their shared prey (peach aphid, Myzus persicae Sulzer) are strongly affected by the absolute initial densities of the species in question. Even if their relative densities are kept constant, the natural enemy species or combination thereof that most effectively suppresses the prey may depend on the absolute initial densities used in the experiment. Future empirical studies of multiple predator - one prey interactions should therefore use a two-dimensional array of initial densities of the studied species. Varying only combinations of natural enemies without varying their densities is not sufficient and can lead to misleading results.
We introduce a new nonlinear electrophoretic model for complex-forming systems with a fully charged analyte and a neutral ligand. The background electrolyte is supposed to be composed of two constituents, which do not interact with the ligand. In order to characterize the electromigration dispersion (EMD) of the analyte zone we define a new parameter, the nonlinear electromigration mobility slope, S(EMD,A). The parameter can be easily utilized for quantitative prediction of the EMD and for comparisons of the model with the simulated and experimental profiles. We implemented the model to the new version of PeakMaster 5.3 Complex that can calculate some characteristic parameters of the electrophoretic system and can plot the dependence of S(EMD,A) on the concentration of the ligand. Besides S(EMD,A), also the relative velocity slope, S(X), can be calculated. It is commonly used as a measure of EMD in electrophoretic systems. PeakMaster 5.3 Complex software can be advantageously used for optimization of the separation conditions to avoid high EMD in complexing systems. Based on the theoretical model we analyze the S(EMD,A) and reveal that this parameter is composed of six terms. We show that the major factor responsible for the electromigration dispersion in complex-forming electrophoretic systems is the complexation equilibrium and particularly its impact on the effective mobility of the analyte. To prove the appropriateness of the model we showed that there is a very good agreement between peak shapes calculated by PeakMaster 5.3 Complex (plotted using the HVLR function) and the profiles simulated by means of Simul 5 Complex. The detailed experimental verification of the new mode of PeakMaster 5.3 Complex is in the next part IV of the series.
