Numerical optimization of parameters in systems of differential equations

summary:We present results on the estimation of unknown parameters in systems of ordinary differential equations in order to fit the output of models to real data. The numerical method is based on the nonlinear least squares problem along with the solution of sensitivity equations corresponding to the differential equations. We will present the performance of the method on the problem of fitting the output of basic compartmental epidemic models to data from the Covid-19 epidemic. This allows us to draw several conclusions on the natural limitations of these models and their validity

Mixed Precision in Uncertainty Quantification Methods

This work is concerned with analysing and exploiting mixed precision arithmetic in un- certainty quantification methods with emphasis on the multilevel Monte Carlo (MLMC) method. Although mixed precision can improve performance, it should be used carefully to avoid unwanted effects on the solution accuracy. We provide a rigorous analysis of uncertainty quantification methods in finite precision arithmetic. Based on this analysis, we exploit mixed precision arithmetic in uncertainty quantification methods to improve runtime while preserving the overall error. We begin by stating the model problem, an elliptic PDE with random coefficients and a random right-hand side. Such a problem arises, for example, in uncertainty quantification for groundwater flow. Our focus is on approximating a quantity of interest given as the expected value of a functional of the solution of the PDE problem. To this end, we use the conforming finite element method for approximation in the spatial variable and the MLMC method for approximation of the expected value. We provide a novel rigorous analysis of the MLMC method in finite precision arithmetic and based on this we formulate an adaptive algorithm which determines the optimal precision value on each level of discretisation. To our knowledge, this is a new approach. Our...Tato práce se zabývá analýzou a využitím tzv. aritmetiky se smíšenou přesností (mixed precision arithmetic) v metodách pro kvantifikaci nejistoty (uncertainty quan- tification methods) s důrazem na víceúrovňovou metodu Monte Carlo (multilevel Monte Carlo, MLMC). Aritmetika se smíšenou přesností může být využita ke zvýšení výpočet- ního výkonu, ale měla by být využívána obezřetně, abychom se vyvarovali nežádoucích efektů na přesnost výsledku. Tato práce přináší exaktní analýzu metod pro kvantifikaci nejistoty v aritmetice se smíšenou přesností. Na základě této analýzy využijeme ar- itmetiku se smíšenou přesností ke zrychlení běhu algoritmů pro kvantifikaci nejistoty, přičemž celková chyba zůstane zachována. Začneme tím, že uvedeme modelový problém, eliptickou parciální diferenciální rovnici s náhodnými koeficienty a náhodnou pravou stranou. Problém tohoto typu dostáváme například při modelování proudění podzemní vody. Zaměřujeme se na aproximaci veličiny, která je dána jako střední hodnota nějakého funkcionálu řešení dané parciální diferenciální rovnice. K tomuto účelu používáme konformní metodu konečných prvků pro aproximaci v prostorové proměnné a metodu MLMC pro aproximaci střední hodnoty. Tato práce přináší novou exaktní analýzu metody MLMC v aritmetice s konečnou přesností. Na základě této analýzy...Katedra numerické matematikyDepartment of Numerical MathematicsFaculty of Mathematics and PhysicsMatematicko-fyzikální fakult

Characterization of ultra-thin tungsten layers

Atomic force microscopy and surface resistivity measurement were used for characterization of ultra-thin tungsten layers deposited on purified silicon with 200 nm thermic silicon dioxide substrate. Radio-frequency magnetron sputtering was used for tungsten deposition. © Research India Publications

Design of scanning system for mechanoscopic analysis

The work deals with hardware and software proposal of a system suitable for control and visualization of scanning process based on resistivity measurement. Three axis positioning system with conductive contact probe is utilized. The user application was created in MATLAB programming environment. Important part of the design represents the definition of requirements, choice of the appropriate tools, functions and structures needed for reliable realization. Proposed user application allows setting key parameters of the measurement, appropriate method of data acquisition as well as performing online 3D visualization of measured data. The functionality of the application is verified via measurement of a several selected samples. Results of these measurements are also presented

Historical Map Toponym Extraction for Efficient Information Retrieval

ERDF ”Research and Development of Intelligent Components of Advanced Technologies for the Pilsen Metropolitan Area (InteCom)” (no.:CZ.02.1.01/0.0/0.0/17 048/0007267), Grant No. SGS-2022-016 ”Advanced methods of data processing and analysis

Oxidation of the carcinogenic non-aminoazo dye 1-phenylazo-2-hydroxy- naphthalene (Sudan I) by cytochromes P450 and peroxidases: a comparative study

ABSTRACT Sudan I [1-(phenylazo)-2-hydroxynaphthalene, C.I. Solvent Yellow 14, CAS No: 842-07-9] is used as the compound employed in chemical industry and to color materials such as hydrocarbon solvents, oils, fats, waxes, plastics, printing inks, shoe and floor polishes and gasoline. Such a wide used could result in a considerable human exposure. Sudan I is known to cause developments of tumors in the liver or urinary bladder in rats, mice, and rabbits, and is considered a possible weak human carcinogen and mutagen. This carcinogen is also a potent contact allergen and sensitizer. Here, we compare the data concerning the Sudan I oxidative metabolism catalyzed by cytochrome P450 (CYP) and peroxidase enzymes, which has been investigated in our laboratory during the last two decades. These two types of enzymes are responsible both for Sudan I detoxication and activation. Among the Sudan I metabolites, C-hydroxylated derivatives and a dimer of Sudan I are suggested to be the detoxication metabolites formed by CYPs and peroxidases, respectively. Metabolic activation of Sudan I by both types of enzymes leads to formation of reactive species (the benzenediazonium ion by CYP and Sudan I radicals by peroxidase) that bind to DNA and RNA, generating covalent adducts in vitro and in vivo. Whereas the structure of the major adduct formed by the benzenediazonium ion in DNA has already been identified to be the 8-(phenylazo)guanine adduct, the structures of adducts formed by peroxidase, have not been characterized as yet. Biological significance of the DNA adducts of Sudan I activated with CYP and peroxidase enzymes and further aims of investigations in this field are discussed in this study

Oxidation of the carcinogenic non-aminoazo dye 1-phenylazo-2-hydroxy-naphthalene (Sudan I) by cytochromes P450 and peroxidases: a comparative study

Sudan I [1-(phenylazo)-2-hydroxynaphthalene, C.I. Solvent Yellow 14, CAS No: 842-07-9] is used as the compound employed in chemical industry and to color materials such as hydrocarbon solvents, oils, fats, waxes, plastics, printing inks, shoe and floor polishes and gasoline. Such a wide used could result in a considerable human exposure. Sudan I is known to cause developments of tumors in the liver or urinary bladder in rats, mice, and rabbits, and is considered a possible weak human carcinogen and mutagen. This carcinogen is also a potent contact allergen and sensitizer. Here, we compare the data concerning the Sudan I oxidative metabolism catalyzed by cytochrome P450 (CYP) and peroxidase enzymes, which has been investigated in our laboratory during the last two decades. These two types of enzymes are responsible both for Sudan I detoxication and activation. Among the Sudan I metabolites, C-hydroxylated derivatives and a dimer of Sudan I are suggested to be the detoxication metabolites formed by CYPs and peroxidases, respectively. Metabolic activation of Sudan I by both types of enzymes leads to formation of reactive species (the benzenediazonium ion by CYP and Sudan I radicals by peroxidase) that bind to DNA and RNA, generating covalent adducts in vitro and in vivo. Whereas the structure of the major adduct formed by the benzenediazonium ion in DNA has already been identified to be the 8-(phenylazo)guanine adduct, the structures of adducts formed by peroxidase, have not been characterized as yet. Biological significance of the DNA adducts of Sudan I activated with CYP and peroxidase enzymes and further aims of investigations in this field are discussed in this study

Quality of sensorimotor control on lower limbs in relation to lateral preference in young athletes (soccer players).

Objectives: Our thesis is focused on correlation of lateral (side) preferencies of lower limbs and quality of sensorimotor control. Our aim is to figure out whether there is difference in laterality of sensorimotor control of lower limbs and if so, whether there is correlation with side preferency. Methods: Study is made on 18 volunteers. We tested somatosenzoric system, specifically two-point discrimination, graphesthesia, pallesthesia, statesthesia, kinesthesia. We used a questionnare to determine side preferency of lower limbs. We used paired sample t- tests, with level of importance p=0,05. Results: According to t-tests, there are no differencies in sensorimotor control in lower limbs. According to those results, it is not possible to determine the difference in sensorimotor control due to lower limb preferency. Summary: There is no difference in sides in sensorimotor control of lower limbs

The reflective effect of manipulative therapy on blood pressure.

The topic of the thesis is The reflective effect of manipulative therapy on blood pressure. The aim of the thesis is to summarize current knowledge, which talk about the relationship between the ma-nipulative therapy and the changes of blood pressure. One of the purpose of the thesis is to clarify the using of manipulative therapy in the treatment of arterial hypertension. In the thesis another methods of manipulative therapy are discussed to give broad overwiev and to have a posibble to comparison. Powered by TCPDF (www.tcpdf.org