Linear programming
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This article deals with continuous-time Linear Time-Invariant (LTI) Single-Input Single-Output (SISO) systems affected by unstructured multiplicative uncertainty. More specifically, its aim is to present an approach to the construction of uncertain models based on the appropriate selection of a nominal system and a weight function and to apply the fundamentals of robust stability investigation for considered sort of systems. The initial theoretical parts are followed by three extensive illustrative examples in which the first order time-delay, second order and third order plants with parametric uncertainty are modeled as systems with unstructured multiplicative uncertainty and subsequently, the robust stability of selected feedback loops containing constructed models and chosen controllers is analyzed and obtained results are discussed.
- MeSH
- nejistota * MeSH
- programování lineární * MeSH
- Publikační typ
- časopisecké články MeSH
... whiskers 40\n\n3.5.10 Curves 41\n\nV\n4 Statistical modelling\n\n4.1 Regression model 43\n\n4.2 General linear ... ... model 45\n\n4.3 Generalized linear model 47\n\n4.4 Searching for the “correct” model 51\n\n4.5 Model ...
First edition x, 245 stran : ilustrace ; 24 cm
- Konspekt
- Biologické vědy
- NLK Obory
- biologie
- statistika, zdravotnická statistika
- knihovnictví, informační věda a muzeologie
- NLK Publikační typ
- kolektivní monografie
The linear theory of electromigration, including the first-order nonlinear approximation, is generalized to systems with any equilibria fast enough to be considered instantaneous in comparison with the timescale of peak movement. For example, this theory is practically applied in the electrokinetic chromatography (EKC) mode of the CZE. The model enables the calculation of positions and shapes of analyte and system peaks without restricting the number of selectors, the complexation stoichiometry, or simultaneous acid-base equilibria. The latest version of our PeakMaster software, PeakMaster 6-Next Generation, implements the theory in a user-friendly way. It is a free and open-source software that performs all calculations and shows the properties of the background electrolyte and the expected electropherogram within a few seconds. In this paper, we mathematically derive the model, discuss its applicability to EKC systems, and introduce the PeakMaster 6 software.
We discuss several possible phenomena in electrophoretic systems with complexing agents present in the background electrolyte. In our previous work, we extended the linear theory of electromigration with the first-order nonlinear term, which originally applied to acid-base equilibria only, by generalizing it to any fast chemical equilibria. This extension provides us with a fresh insight into the well-established technique of elecktrokinetic chromatography (EKC). We combine mathematical analysis of the generalized model with its solution by means of the new version of our software PeakMaster 6, and experimental data. We re-examine the fundamental equations by Wren and Rowe and Tiselius in the frame of the generalized linear theory of electromigration. Besides, we show that selector concentration can increase inside the interacting-analyte zone due to its complexation with the analyte, which contradicts the generally accepted idea of a consumption of a portion of the selector inside the zone. Next, we focus our discussion on interacting buffers (i.e., buffer constituents that form a complex with the selector). We demonstrate how such side-interaction of the selector with another buffer constituent can influence measuring analyte-selector interactions. Finally, we describe occurrence and mobilities of system peaks in these EKC systems. We investigate systems with fully charged analytes and neutral cyclodextrins as selectors. Although the theory is not limited in terms of the charge and/or the degree of (de)protonation of any constituent, this setup allows us to find analytical solutions to generalized model under approximate, yet realistic, conditions and to demonstrate all important phenomena that may occur in EKC systems. An occurrence of system peaks in a system with fully charged selector is also investigated.
Functional connectivity (FC) analysis is a prominent approach to analyzing fMRI data, especially acquired under the resting state condition. The commonly used linear correlation FC measure bears an implicit assumption of Gaussianity of the dependence structure. If only the marginals, but not all the bivariate distributions are Gaussian, linear correlation consistently underestimates the strength of the dependence. To assess the suitability of linear correlation and the general potential of nonlinear FC measures, we present a framework for testing and estimating the deviation from Gaussianity by means of comparing mutual information in the data and its Gaussianized counterpart. We apply this method to 24 sessions of human resting state fMRI. For each session, matrix of connectivities between 90 anatomical parcel time series is computed using mutual information and compared to results from its multivariate Gaussian surrogate that conserves the correlations but cancels any nonlinearity. While the group-level tests confirmed non-Gaussianity in the FC, the quantitative assessment revealed that the portion of mutual information neglected by linear correlation is relatively minor-on average only about 5% of the mutual information already captured by the linear correlation. The marginality of the non-Gaussianity was confirmed in comparisons using clustering of the parcels-the disagreement between clustering obtained from mutual information and linear correlation was attributable to random error. We conclude that for this type of data, practical relevance of nonlinear methods trying to improve over linear correlation might be limited by the fact that the data are indeed almost Gaussian.
- MeSH
- algoritmy MeSH
- dospělí MeSH
- Fourierova analýza MeSH
- kyslík krev MeSH
- lidé MeSH
- lineární modely MeSH
- magnetická rezonanční tomografie MeSH
- mladý dospělý MeSH
- nervové dráhy fyziologie MeSH
- normální rozdělení MeSH
- odpočinek fyziologie MeSH
- shluková analýza MeSH
- software MeSH
- Check Tag
- dospělí MeSH
- lidé MeSH
- mladý dospělý MeSH
- mužské pohlaví MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- práce podpořená grantem MeSH
INTRODUCTION: Given the physiological role of placental growth hormone (PGH) during intrauterine development and growth, genetic variation in the coding Growth hormone 2 (GH2) gene may modulate developmental programming of adult stature. Two major GH2 variants were described worldwide, determined by single polymorphism (rs2006123; c.171 + 50C > A). We sought to study whether GH2 variants may contribute to adult anthropometric measurements. METHODS: Genotyping of GH2 SNP rs2006123 by RFLP, testing its genetic association with adult height and Body Mass Index (BMI) by linear regression analysis, and combining the results of three individual study samples in meta-analysis. STUDY SAMPLES: HYPEST (Estonia), n = 1464 (506 men/958 women), CADCZ (Czech), n = 871 (518/353); UFA (Bashkortostan), n = 954 (655/299); meta-analysis, n = 3289 (1679/1610). RESULTS: Meta-analysis across HYPEST, CADCZ and UFA samples (n = 3289) resulted in significant association of GH2 rs2006123 with height (recessive model: AA-homozygote effect: beta (SE) = 1.26 (0.46), P = 5.90 × 10⁻³; additive model: A-allele effect: beta (SE) = 0.45 (0.18), P = 1.40 × 10⁻²). Among men (n = 1679), the association of the A-allele with taller stature remained significant after multiple-testing correction (additive effect: beta = 0.86 (0.28), P = 1.83 × 10⁻³). No association was detected with BMI. Notably, rs2006123 was in strong LD (r² ≥ 0.87) with SNPs significantly associated with height (rs2665838, rs7209435, rs11658329) and mapped near GH2 in three independent meta-analyses of GWA studies. CONCLUSIONS: This is the first study demonstrating a link between a placental gene variant and programming of growth potential in adulthood. The detected association between PGH encoding GH2 and adult height promotes further research on the role of placental genes in prenatal programming of human metabolism.
- MeSH
- dospělí MeSH
- frekvence genu MeSH
- genetické asociační studie MeSH
- index tělesné hmotnosti MeSH
- jednonukleotidový polymorfismus * MeSH
- lidé středního věku MeSH
- lidé MeSH
- multigenová rodina MeSH
- placentární hormony genetika metabolismus MeSH
- růstový hormon genetika metabolismus MeSH
- senioři MeSH
- těhotenství MeSH
- tělesná výška MeSH
- vazebná nerovnováha MeSH
- vývoj kostí * MeSH
- vývoj plodu * MeSH
- Check Tag
- dospělí MeSH
- lidé středního věku MeSH
- lidé MeSH
- mužské pohlaví MeSH
- senioři MeSH
- těhotenství MeSH
- ženské pohlaví MeSH
- Publikační typ
- časopisecké články MeSH
- metaanalýza MeSH
- práce podpořená grantem MeSH
- Geografické názvy
- Baškortostán MeSH
- Česká republika MeSH
- Estonsko MeSH
