**778**

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**On the structure and values of betweenness centrality in dense betweenness-uniform graphs**

Ghanbari, B.; Hartman, David; Jelínek, V.; Pokorná, Aneta; Šámal, R.; Valtr, P.

2023 - English
Betweenness centrality is a network centrality measure based on the amount ofshortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of betweenness centrality. In this contribution, wefocus on betweenness-uniform graphs with betweenness centrality below one. Wedisprove a conjecture about the existence of a BUG with betweenness valueαforany rational numberαfrom the interval (3/4,∞) by showing that only very few be-tweenness centrality values below 6/7 are attained for at least one BUG. Furthermore,among graphs with diameter at least three, there are no betweenness-uniform graphswith a betweenness centrality smaller than one. In graphs of smaller diameter, thesame can be shown under a uniformity condition on the components of the comple-ment.
Available in digital repository of the ASCR
On the structure and values of betweenness centrality in dense betweenness-uniform graphs

Betweenness centrality is a network centrality measure based on the amount ofshortest paths passing through a given vertex. A graph is betweenness-uniform (BUG)if all vertices have an equal value of ...

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**Different Boundary Conditions For LES Solver PALM 6.0 Used for ABL in Tunnel Experiment**

Řezníček, Hynek; Geletič, Jan; Bureš, Martin; Krč, Pavel; Resler, Jaroslav; Vrbová, Kateřina; Trush, Arsenii; Michálek, Petr; Beneš, L.; Sühring, M.

2023 - English
We tried to reproduce results measured in the wind tunnel experiment with a CFD simulation provided by numerical model PALM. A realistic buildings layout from the Prague-Dejvice quarter has been chosen as a testing domain because solid validation campaign for PALM simulation of Atmospheric Boundary Layer (ABL) over this quarter was documented in the past. The question of input data needed for such simulation and capability of the model to capture correctly the inlet profile and its turbulence structure provided by the wind-tunnel is discussed in the study The PALM dynamical core contains a solver for the Navier-Stokes equations. By default, the model uses the Large Eddy Simulation (LES) approach in which the bulk of the turbulent motions is explicitly resolved. It is well validated tool for simulations of the complex air-flow within the real urban canopy and also within its reduced scale provided by wind tunnel experiments. However the computed flow field between the testing buildings did not correspond well to the measured wind velocity in some points. Different setting of the inlet boundary condition was tested but none of them gave completely developed turbulent flow generated by vortex generators and castellated barrier wall place at the entrance of the aerodynamic section of the wind tunnel.\n
Keywords:
*large eddy simulation; wind tunnel; atmospheric boundary layer; PALM model; turbulence*
Fulltext is available at external website.
Different Boundary Conditions For LES Solver PALM 6.0 Used for ABL in Tunnel Experiment

We tried to reproduce results measured in the wind tunnel experiment with a CFD simulation provided by numerical model PALM. A realistic buildings layout from the Prague-Dejvice quarter has been ...

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**Rooting algebraic vertices of convergent sequences**

Hartman, David; Hons, T.; Nešetřil, J.

2023 - English
Structural convergence is a framework for convergence of graphs by Nešetřil andOssona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem asking whether for a given sequenceof graphs (Gn) converging to a limit L and a vertexrofLit is possible to find asequence of vertices (rn) such thatLrooted atris the limit of the graphsGnrootedatrn. A counterexample was found by Christofides and Král’, but they showed thatthe statement holds for almost all vertices r of L. We offer another perspective to theoriginal problem by considering the size of definable sets to which the rootrbelongs.We prove that if r is an algebraic vertex (i.e. belongs to a finite definable set), thesequence of roots (rn) always exists.
Available in digital repository of the ASCR
Rooting algebraic vertices of convergent sequences

Structural convergence is a framework for convergence of graphs by Nešetřil andOssona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem ...

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**A Bootstrap Comparison of Robust Regression Estimators**

Kalina, Jan; Janáček, Patrik

2022 - English
The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more preferable alternatives. It has been repeatedly recommended to use the least squares together with a robust estimator, where the latter is understood as a diagnostic tool for the former. In other words, only if the robust estimator yields a very different result, the user should investigate the dataset closer and search for explanations. For this purpose, a hypothesis test of equality of the means of two alternative linear regression estimators is proposed here based on nonparametric bootstrap. The performance of the test is presented on three real economic datasets with small samples. Robust estimates turn out not to be significantly different from non-robust estimates in the selected datasets. Still, robust estimation is beneficial in these datasets and the experiments illustrate one of possible ways of exploiting the bootstrap methodology in regression modeling. The bootstrap test could be easily extended to nonlinear regression models.
Keywords:
*linear regression; robust estimation; nonparametric bootstrap; bootstrap hypothesis testing*
Fulltext is available at external website.
A Bootstrap Comparison of Robust Regression Estimators

The ordinary least squares estimator in linear regression is well known to be highly vulnerable to the presence of outliers in the data and available robust statistical estimators represent more ...

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**Interaktivní nástroj pro podporu vyhodnocování dat ze standardizovaných testů**

Martinková, Patrícia; Potužníková, E.; Netík, Jan

2022 - Czech
ZÁKLADNÍ ÚDAJE: Proměny výchovy a vzdělávání a jejich reflexe v pedagogickém výzkumu: Sborník příspěvků XXX. výroční konference České asociace pedagogického výzkumu. Brno: Masarykova univerzita, 2022 - (Švaříček, R., Voňková, H.), s. 29-31. ISBN 978-80-280-0090-5. [ČAPV 2022: Proměny výchovy a vzdělávání a jejich reflexe v pedagogickém výzkumu /30./. Babice / virtual (CZ), 29.08.2022-31.08.2022]. ABSTRAKT: V příspěvku představujeme možnosti využití modulu interaktivního nástroje pro vyhodnocování dat ze znalostních testů na příkladu dat z maturitní zkoušky z matematiky. Představujeme metody pro detekci odlišného fungování položek pro různé typy škol nebo pro porovnání vybrané školy s ostatními. Ukazujeme, že nástroj má potenciál přispět k informovanému využívání dat z testování a rozhodování na úrovni škol i vzdělávací politiky. In this work, we present features of an interactive tool module for supporting analyses of data from achievement tests by presenting an example of data from the Matura (graduation) exam in mathematics. We present methods for detection of different functioning of items for different types of school, or for comparison of a selected school with other schools. We show that the tool has a potential to help with informed use of achievement test data and to support decision making on both the school and the system levels.
Keywords:
*achievement tests; group differences; interactive tool*
Available at various institutes of the ASCR
Interaktivní nástroj pro podporu vyhodnocování dat ze standardizovaných testů

ZÁKLADNÍ ÚDAJE: Proměny výchovy a vzdělávání a jejich reflexe v pedagogickém výzkumu: Sborník příspěvků XXX. výroční konference České asociace pedagogického výzkumu. Brno: Masarykova univerzita, 2022 ...

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**Recent Trends in Machine Learning with a Focus on Applications in Finance**

Kalina, Jan; Neoral, Aleš

2022 - English
Machine learning methods penetrate to applications in the analysis of financial data, particularly to supervised learning tasks including regression or classification. Other approaches, such as reinforcement learning or automated machine learning, are not so well known in the context of finance yet. In this paper, we discuss the advantages of an automated data analysis, which is beneficial especially if a larger number of datasets should be analyzed under a time pressure. Important types of learning include reinforcement learning, automated machine learning, or metalearning. This paper overviews their principles and recalls some of their inspiring applications. We include a discussion of the importance of the concept of information and of the search for the most relevant information in the field of mathematical finance. We come to the conclusion that a statistical interpretation of the results of theautomatic machine learning remains crucial for a proper understanding of the knowledge acquired by the analysis of the given (financial) data.
Keywords:
*statistical learning; automated machine learning; metalearning; financial data analysis; stock market investing*
Fulltext is available at external website.
Recent Trends in Machine Learning with a Focus on Applications in Finance

Machine learning methods penetrate to applications in the analysis of financial data, particularly to supervised learning tasks including regression or classification. Other approaches, such as ...

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**The 2020 Election In The United States: Beta Regression Versus Regression Quantiles**

Kalina, Jan

2021 - English
The results of the presidential election in the United States in 2020 desire a detailed statistical analysis by advanced statistical tools, as they were much different from the majority of available prognoses as well as from the presented opinion polls. We perform regression modeling for explaining the election results by means of three demographic predictors for individual 50 states: weekly attendance at religious services, percentage of Afroamerican population, and population density. We compare the performance of beta regression with linear regression, while beta regression performs only slightly better in terms of predicting the response. Because the United States population is very heterogeneous and the regression models are heteroscedastic, we focus on regression quantiles in the linear regression model. Particularly, we develop an original quintile regression map, such graphical visualization allows to perform an interesting interpretation of the effect of the demographic predictors on the election outcome on the level of individual states.
Keywords:
*elections results; electoral demography; quantile regression; heteroscedasticity; outliers*
Fulltext is available at external website.
The 2020 Election In The United States: Beta Regression Versus Regression Quantiles

The results of the presidential election in the United States in 2020 desire a detailed statistical analysis by advanced statistical tools, as they were much different from the majority of available ...

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**Multifractal approaches in econometrics and fractal-inspired robust regression**

Kalina, Jan

2021 - English
While the mainstream economic theory is based on the concept of general economic equilibrium, the economies throughout the world have recently been facing serious transformations and challenges. Thus, instead of a convergence to equilibrium, the economies can be regarded as unstable, turbulent or chaotic with properties characteristic for fractal or multifractal processes. This paper starts with a discussion of recent data analysis tools inspired by fractal or multifractal concepts. We pay special attention to available data analysis tools based on reciprocal weights assigned to individual observations - these are inspired by an assumed fractal structure of multivariate data. As an extension, we consider here a novel version of the least weighted squares estimator of parameters for the linear regression model, which exploits reciprocal weights. Finally, we perform a statistical analysis of 31 datasets with economic motivation and compare the performance of the least weighted squares estimator with various weights. It turns out that the reciprocal weights, inspired by the fractal theory, are not superior to other choices of weights. In fact, the best prediction results are obtained with trimmed linear weights.
Keywords:
*chaos in economics; fractal market hypothesis; reciprocal weights; robust regression; prediction*
Available in digital repository of the ASCR
Multifractal approaches in econometrics and fractal-inspired robust regression

While the mainstream economic theory is based on the concept of general economic equilibrium, the economies throughout the world have recently been facing serious transformations and challenges. Thus, ...

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**Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election**

Kalina, Jan; Vidnerová, Petra

2021 - English
Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however vulnerable to leverage points in the regression model, an alternative approach denoted as implicitly weighted regression quantiles have been proposed. The aim of current work is to apply them to the results of the second round of the 2018 presidential election in the Czech Republic. The election results are modeled as a response of 4 demographic or economic predictors over the 77 Czech counties. The analysis represents the first application of the implicitly weighted regression quantiles to data with more than one regressor. The results reveal the implicitly weighted regression quantiles to be indeed more robust with respect to leverage points compared to standard regression quantiles. If however the model does not contain leverage points, both versions of the regression quantiles yield very similar results. Thus, the election dataset serves here as an illustration of the usefulness of the implicitly weighted regression quantiles.
Keywords:
*linear regression; quantile regression; robustness; outliers; elections results*
Fulltext is available at external website.
Application Of Implicitly Weighted Regression Quantiles: Analysis Of The 2018 Czech Presidential Election

Regression quantiles can be characterized as popular tools for a complex modeling of a continuous response variable conditioning on one or more given independent variables. Because they are however ...

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**On kernel-based nonlinear regression estimation**

Kalina, Jan; Vidnerová, Petra

2021 - English
This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric applications, and regularization networks, which represent machine learning tools very rarely used in econometric modeling. This paper recalls both approaches and describes their common features as well as differences. For the Nadaraya-Watson estimator, we explain its connection to the conditional expectation of the response variable. Our main contribution is numerical analysis of suitable data with an economic motivation and a comparison of the two nonlinear regression tools. Our computations reveal some tools for the Nadaraya-Watson in R software to be unreliable, others not prepared for a routine usage. On the other hand, the regression modeling by means of regularization networks is much simpler and also turns out to be more reliable in our examples. These also bring unique evidence revealing the need for a careful choice of the parameters of regularization networks
Keywords:
*nonlinear regression; machine learning; kernel smoothing; regularization; regularization networks*
Available in digital repository of the ASCR
On kernel-based nonlinear regression estimation

This paper is devoted to two important kernel-based tools of nonlinear regression: the Nadaraya-Watson estimator, which can be characterized as a successful statistical method in various econometric ...

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