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TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Papáček, Štěpán; Matonoha, Ctirad
2023 - English
Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
Keywords:
Dynamical system; Singular perturbation; Averaging; Parameter estimation; Slow-fast decomposition; Damped oscillations
Fulltext is available at external website.
TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular ...
GA 19-07635S: Outputs and Results
Rehák, Branislav
2023 - English
This manuscript aims to deliver a survey of results obtained during the solution of the project No. GA19-07635S of the Czech Science Foundation. The timespan dedicated to the work on this project was 1.3.2019 - 30.6.2022. The main area dealt with were\nnonlinear multi-agent systems and their synchronization, further, attention was paid to some auxiliary results in the area of nonlinear observers. This Report briefly introduces the Project, provides a summary of the results obtained and also sketches an outline how these results will be applied and extended in future.
Keywords:
multi-agent systems; nonlinear multi-agent systems; synchronization
Fulltext is available at external website.
GA 19-07635S: Outputs and Results
This manuscript aims to deliver a survey of results obtained during the solution of the project No. GA19-07635S of the Czech Science Foundation. The timespan dedicated to the work on this project was ...
Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties
Papáček, Štěpán; Matonoha, Ctirad; Duintjer Tebbens, Jurjen
2023 - English
This study presents an application of one special technique, further called as Bohl-Marek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. We continue in direction of papers devoted to inverse problems of parameter estimation for mathematical models describing the drug-induced enzyme production networks [3]. However, being aware of the complexity of general physiologically based pharmacokinetic (PBPK) models, here we focus on the case of enzyme-catalyzed reactions with a substrate transport chain [5]. Although our ultimate goal is to develop a reliable method for fitting the model parameters to given experimental data, here we study certain numerical issues within the framework of optimal experimental design [6]. Before starting an experiment on a real biochemical network, we formulate an optimization problem aiming to maximize the information content of the corresponding experiment. For the above-sketched optimization problem, the computational costs related to the two formulations of the same biochemical network, being (i) the classical formulation x˙(t) = Ax(t) + b(t) and (ii) the 'quasi-linear' Bohl-Marek formulation x˙M(t) = M(x(t)) xM(t), can be determined and compared.
Keywords:
Mathematical modeling; Biochemical network; Pharmacokinetic (PBPK) models
Fulltext is available at external website.
Bohl-Marek decomposition applied to a class of biochemical networks with conservation properties
This study presents an application of one special technique, further called as Bohl-Marek decomposition, related to the mathematical modeling of biochemical networks with mass conservation properties. ...
Modeling the spread of loanwords in South-East Asia using sailing navigation software and Bayesian networks
Kratochvíl, F.; Kratochvíl, Václav; Saad, G.; Vomlel, Jiří
2022 - English
A loanword is a word permanently adopted from one language and incorporated into another language without translation. In this paper, we study loanwords in the South-East Asia Archipelago, home to a large number of languages. Our paper is inspired by the works of Hoffmann et al. (2021) Bayesian methods are applied to probabilistic modeling of family trees representing the history of language families and by Haynie et al. (2014) modeling the diffusion of a special class of loanwords, so-called Wanderw ̈orter in languages of Australia, North America, and South America. We assume that in the South-East Asia Archipelago Wanderwörter spread along specific maritime trade routes whose geographical characteristics can help unravel the history of Wanderwörter diffusion in the area. For millennia trade was conducted using sailing ships which were constrained by the monsoon system and in certain areas also by strong sea currents. Therefore rather than the geographical distances, the travel times of sailing ships should be considered as a major factor determining the intensity of contact among cultures. We use sailing navigation software to estimate travel times between different ports and show that the estimated travel times correspond well to the travel times of a Chinese map of the sea trade routes from the early seventeenth century. We model the spread of loanwords using a probabilistic graphical model - a Bayesian network. We design a novel heuristic Bayesian network structure learning algorithm that learns the structure as a union of spanning trees for graphs of all loanwords in the training dataset. We compare this algorithm with BIC optimal Bayesian networks by measuring how well these models predict the true presence/absence of a loanword. Interestingly, Bayesian networks learned by our heuristic spanning tree-based algorithm provide better results than the BIC optimal Bayesian networks.
Keywords:
loanwords; Bayesian methods; probabilistic graphical model
Fulltext is available at external website.
Modeling the spread of loanwords in South-East Asia using sailing navigation software and Bayesian networks
A loanword is a word permanently adopted from one language and incorporated into another language without translation. In this paper, we study loanwords in the South-East Asia Archipelago, home to a ...
Diffusion Kalman filtering under unknown process and measurement noise covariance matrices
Vlk, T.; Dedecius, Kamil
2022 - English
The state-of-the-art algorithms for Kalman filtering in agent networks with information diffusion impose the requirement of well-defined state-space models. In particular, they assume that both the process and measurement noise covariance matrices are known and properly set. This is a relatively strong assumption in the signal processing domain. By design, the Kalman filters are rather sensitive to its violation, which may potentially lead to their divergence. In this paper, we propose a novel distributed filtering algorithm with increased robustness under unknown process and measurement noise covariance matrices. It is formulated as a Bayesian variational message passing procedure for simultaneous analytically tractable inference of states and measurement noise covariance matrices.
Keywords:
Collaborative estimation; State estimation; Variational Bayesian methods
Fulltext is available at external website.
Diffusion Kalman filtering under unknown process and measurement noise covariance matrices
The state-of-the-art algorithms for Kalman filtering in agent networks with information diffusion impose the requirement of well-defined state-space models. In particular, they assume that both the ...
Hybrid evaluation of the industrial global impact on Mexican aquifers under uncertain criteria evaluations
Flores Casamayor, H.; Carpitella, Silvia; Izquierdo, J.; Mora-Rodríguez, J.; Delgado-Galván, X.
2022 - English
The present paper proposes an integrated methodological approach to address the problem of managing five aquifers of Guanajuato state, Mexico, according to such relevant criteria as environmental, social, economic and hydrological aspects. The goal of this research consists in formalizing a structured framework to first evaluate the various degrees of importance of criteria and to secondly get a classification of aquifers by minimizing uncertainty of evaluations. To such an aim, the Analytic Hierarchy Process (AHP) is used for calculating the vector of criteria weights, while the Fuzzy Logic (FL) theory supports in deriving quantitative evaluations of aquifers under each selected criterion. The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is then proposed to formalize the final ranking of aquifers, something that will be helpful to understand which alternative matches all the differently weighted criteria in the most suitable way at a practical level. In such a way, getting a comprehensive and strategic overview about the problem of interest will be possible.
Keywords:
Analytic Hierarchy Process (AHP); Fuzzy Logic (FL) theory; Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS)
Fulltext is available at external website.
Hybrid evaluation of the industrial global impact on Mexican aquifers under uncertain criteria evaluations
The present paper proposes an integrated methodological approach to address the problem of managing five aquifers of Guanajuato state, Mexico, according to such relevant criteria as environmental, ...
Jak to v těch datech najít?
Zitová, Barbara; Šorel, Michal
2022 - Czech
Přednáška si klade za cíl seznámit odbornou veřejnost s aktivitami oddělení Zpracování obrazové informace ÚTIA AV ČR v.v.i. v oblasti analýz dat projektu Copernicus. Oddělení se dlouhodobě zabývá vývojem metod digitálního zpracování obrazu a hlubokého učení. Během posledních dvou let vzniklo několik demonstračních studentských prací ve spolupráci s MFF UK a FJFI ČVUT využívajících data z družic Sentinel, jako například rozpoznávání typů plodin z časových řad snímků ze satelitu Sentinel-2, automatická segmentace oblastí podle způsobu využití či typu povrchu pomocí metod strojového učení, přesnější detekce mraků v datech ze Sentinel-2, ve spolupráci s Ústavem pro hydrodynamiku AV ČR postupy pro odhad vlhkosti povrchové vrstvy krajiny z dat družice Sentinel-2 a zvyšování rozlišení tepelných dat Sentinel-3 pomocí metod hlubokého učení. V druhé části budou přiblíženy možnosti aplikace metod vyvinutých pro jiné oblasti (separace zdrojů \ninformace) v DPZ. The lecture aims to introduce the activities of the Image Processing Department of the Institute of Image Information of the CAS in the field of Copernicus data analysis to the professional public. The department has long been involved in the development of digital image processing and deep learning methods. During the last two years, in cooperation with the MFF UK and FJFI CTU, several student demonstration projects using data from Sentinel satellites have been finished, such as crop type recognition from Sentinel-2 time-series images, automatic segmentation of areas by land use or surface type using machine learning methods learning, more accurate cloud detection in Sentinel-2 data, in collaboration with the Institute of Hydrodynamics of the CAS Czech Republic, procedures for estimating landscape surface moisture from Sentinel-2 data and increasing the resolution of Sentinel-3 thermal data using deep learning methods. The second part will present the application of developed methods for other areas in remote sensing.
Keywords:
remote sensing; satellite imaging; machine learning
Fulltext is available at external website.
Jak to v těch datech najít?
Přednáška si klade za cíl seznámit odbornou veřejnost s aktivitami oddělení Zpracování obrazové informace ÚTIA AV ČR v.v.i. v oblasti analýz dat projektu Copernicus. Oddělení se dlouhodobě zabývá ...
Two Composition Operators for Belief Functions Revisited
Jiroušek, Radim; Kratochvíl, Václav; Shenoy, P. P.
2022 - English
In probability theory, compositional models are as powerful as Bayesian networks. However, the relation between belief-function graphical models and the corresponding compositional models is much more complicated due to several reasons. One of them is that there are two composition operators for belief functions. This paper deals with their main properties and presents sufficient conditions under which they yield the same results.
Keywords:
probability theory; Bayesian networks; belief functions
Fulltext is available at external website.
Two Composition Operators for Belief Functions Revisited
In probability theory, compositional models are as powerful as Bayesian networks. However, the relation between belief-function graphical models and the corresponding compositional models is much more ...
Modeling COVID Pandemics: Strengths and Weaknesses of Epidemic Models
Šmíd, Martin
2022 - English
We generally discuss modeling the present COVID pandemics. We argue that useful models have to be simple in the first case, yet their uncertainty has to be handled properly. In order to study circumstances of the upcoming wave of infection,\nwe construct a simple stochastic model and present predictions it gives. We conclude that the autumn wave is most likely unavoidable and suggest concentrating to mitigation.
Keywords:
COVID; Epidemic Models; stochastic model
Fulltext is available at external website.
Modeling COVID Pandemics: Strengths and Weaknesses of Epidemic Models
We generally discuss modeling the present COVID pandemics. We argue that useful models have to be simple in the first case, yet their uncertainty has to be handled properly. In order to study ...
Analysis of Impact of Covariates Entering Stochastic Optimization Problem
Volf, Petr
2022 - English
In the contribution we study consequences of imperfect information to precision of stochastic optimization solution. In particular, it is assumed that the characteristics of optimization problem are influenced by a set of covariates. This dependence is described via a regression model. Hence, the uncertainty is then caused by statistical estimation of regression parameters. The contribution will analyze several regression model cases, together with their application. Precision of results will be explored, both theoretically as well as with the aid of simulations.
Keywords:
stochastic optimization; regression model; statistical estimation
Fulltext is available at external website.
Analysis of Impact of Covariates Entering Stochastic Optimization Problem
In the contribution we study consequences of imperfect information to precision of stochastic optimization solution. In particular, it is assumed that the characteristics of optimization problem are ...
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