**308**

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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 ...

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**Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric**

Kaňková, Vlasta

2023 - English
Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved on the data base. Point estimates of an optimal value and estimates of an optimal solutionset can be obtained by this approach. A consistency, a rate of convergence and normal properties, of these estimates, have been discussed (many times) not only under assumptions of independent data corresponding to the distributions with light tails, but also for weak dependent data and the distributions with heavy tails. However, it is also possible to estimate (on the data base) a confidence intervals and bounds for the optimal value and the optimal solutions. To analyze this approach we focus on a special case of static problems depending nonlineary on the probability measure. Stability results based on the Wasserstein metric and the Valander approach will be employed for the above mentioned analysis.
Keywords:
*Stochastic optimization problems; static problems; empirical measure; point estimates; interval estimates; nonlinear dependence*
Fulltext is available at external website.
Ambiguity in Stochastic Optimization Problems with Nonlinear Dependence on a Probability Measure via Wasserstein Metric

Many economic and financial applications lead to deterministic optimization problems depending on a probability measure. It happens very often (in applications) that these problems have to be solved ...

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**Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results**

Kalina, Jan

2023 - English
The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions of common statistical methods for every statistical modeling task\nand the most habitually used (“vanilla”) versions may yield rather misleading results in nonstandard situations. Linear regression is considered here as the most fundamental econometric model. First, the analysis of a world tourism dataset is presented, where the number of international arrivals is modeled for 140 countries of the world as a response of 14 pillars (indicators) of the Travel and Tourism Competitiveness Index. Heteroscedasticity is clearly recognized in the dataset. However, the Aitken estimator, which would be the standard remedy in such a situation, is revealed here to be very inappropriate. Regression quantiles represent a much more suitable solution here. The second illustration with artificial data reveals standard regression quantiles to be unsuitable for data contaminated by outlying values. Their recently proposed robust version turns out to be much more appropriate. Both\nillustrations reveal that choosing suitable methods represent an important (and often difficult) part of the analysis of economic data.
Keywords:
*linear regression; assumptions; non-standard situations; robustness; diagnostics*
Fulltext is available at external website.
Statistical Method Selection Matters: Vanilla Methods in Regression May Yield Misleading Results

The primary aim of this work is to illustrate the importance of the choice of the appropriate methods for the statistical analysis of economic data. Typically, there exist several alternative versions ...

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**COMPUTER SIMULATION STUDY OF THE STABILITY OF UNDERACTUATED BIPEDAL ROBOT MODELS (motivated by Griffin and Grizzle, 2017)**

Polach, P.; Anderle, Milan; Zezula, Pavel; Papáček, Štěpán

2023 - English
A key feature for bipedal walkers (robots and humans as well) is their stability or disturbance rejection defined as the ability to deal with unexpected disturbances. The paper by Griffin and Grizzle (2017) have significantly contributed to the shift from flat ground to slopes and steps when evaluating the walking efficiency of their robots. Similarly, in this contribution, based on the appropriate model of robot dynamics and control law, we examine the stability of walking-without-falling for different ground perturbations for a threelink compass gait walker. I.e., we perform the sensitivity analysis of the walking stability of underactuated bipedal walker with respect to certain disturbation using the alaska/MultibodyDynamics simulation tool.
Keywords:
*Mechatronics; Bipedal robot; Multibody dynamics; Acrobot; Control applications*
Fulltext is available at external website.
COMPUTER SIMULATION STUDY OF THE STABILITY OF UNDERACTUATED BIPEDAL ROBOT MODELS (motivated by Griffin and Grizzle, 2017)

A key feature for bipedal walkers (robots and humans as well) is their stability or disturbance rejection defined as the ability to deal with unexpected disturbances. The paper by Griffin and Grizzle ...

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**Texture Spectral Similarity Criteria Comparison**

Havlíček, Michal; Haindl, Michal

2023 - English
Criteria capable of texture spectral similarity evaluation are presented and compared. From the fifteen evaluated criteria, only four criteria guarantee zero or minimal spectral ranking errors. Such criteria can support texture modeling algorithms by comparing the modeled texture with corresponding synthetic simulations. Another possible application is the development of texture retrieval, classification, or texture acquisition system. These criteria thoroughly test monotonicity and mutual correlation on specifically designed extensive monotonously degrading experiments.
Keywords:
*Texture Comparison; Texture Modeling; Texture Retrieval; Texture Classification; Texture Acquisition*
Fulltext is available at external website.
Texture Spectral Similarity Criteria Comparison

Criteria capable of texture spectral similarity evaluation are presented and compared. From the fifteen evaluated criteria, only four criteria guarantee zero or minimal spectral ranking errors. Such ...

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**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. ...

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**Some Robust Approaches to Reducing the Complexity of Economic Data**

Kalina, Jan

2023 - English
The recent advent of complex (and potentially big) data in economics requires modern and effective tools for their analysis including tools for reducing the dimensionality (complexity) of the given data. This paper starts with recalling the importance of Big Data in economics and with characterizing the main categories of dimension reduction techniques. While there have already been numerous techniques for dimensionality reduction available, this work is interested in methods that are robust to the presence of outlying measurements (outliers) in the economic data. Particularly, methods based on implicit weighting assigned to individual observations are developed in this paper. As the main contribution, this paper proposes three novel robust methods of dimension reduction. One method is a dimension reduction within a robust regularized linear regression, namely a sparse version of the least weighted squares estimator. The other two methods are robust versions of feature extraction methods popular in econometrics: robust principal component analysis and robust factor analysis.
Keywords:
*dimensionality reduction; Big Data; variable selection; robustness; sparsity*
Fulltext is available at external website.
Some Robust Approaches to Reducing the Complexity of Economic Data

The recent advent of complex (and potentially big) data in economics requires modern and effective tools for their analysis including tools for reducing the dimensionality (complexity) of the given ...

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**On a stepladder model walking (with and without a decorator)**

Polach, P.; Prokýšek, R.; Papáček, Štěpán

2023 - English
This work is related to our previous studies on underactuated biped robot models and has been motivated by the need to implement the previously developed sensor and control algorithms for the real-time movement of the laboratory walking robot, designed and built at the Department of Control Theory of the Institute of Information Theory and Automation of the Czech Academy of Sciences [1, 6, 7]. Underactuated biped robots with an upper body form a subclass of legged robots, see, e.g., [4] for a review on the control of underactuated mechanical systems and [2] for a study of an asymptotically stable walking for biped robots. It is obvious that in general, the walking control of underactuated walking robots is a more challenging problem than walking control of fully actuated walking robots. As follows, we examine the well-known mechanical system of the stepladder model with and without a decorator, whose role is substituted by an external inertial force according to the D’Alembert principle. It is well known, that stepladder walking is possible due to the periodic movement (pendulating) of an operator – decorator1 The rigorous dynamical analysis of stable cyclic walking of a class of stepladder models is presented in the next section.
Keywords:
*Underactuated biped robot models; Control algorithms; Legged robots*
Fulltext is available at external website.
On a stepladder model walking (with and without a decorator)

This work is related to our previous studies on underactuated biped robot models and has been motivated by the need to implement the previously developed sensor and control algorithms for the ...

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**Average Reward Optimality in Semi-Markov Decision Processes with Costly Interventions**

Sladký, Karel

2023 - English
In this note we consider semi-Markov reward decision processes evolving on finite state spaces. We focus attention on average reward models, i.e. we establish explicit formulas for the growth rate of the total expected reward. In contrast to the standard models we assume that the decision maker can also change the running process by some (costly) intervention. Recall that the result for optimality criteria for the classical Markov decision chains in discrete and continuous time setting turn out to be a very specific case of the considered model. The aim is to formulate optimality conditions for semi-Markov models with interventions and present algorithmical procedures for finding optimal solutions.
Keywords:
*controlled semi-Markov reward processes; long-run optimality; intervention of the decision maker*
Fulltext is available at external website.
Average Reward Optimality in Semi-Markov Decision Processes with Costly Interventions

In this note we consider semi-Markov reward decision processes evolving on finite state spaces. We focus attention on average reward models, i.e. we establish explicit formulas for the growth rate of ...

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**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 ...

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