20230806 00:02 
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20230723 00:01 
On the structure and values of betweenness centrality in dense betweennessuniform graphs
Ghanbari, B. ; Hartman, David ; Jelínek, V. ; Pokorná, Aneta ; Šámal, R. ; Valtr, P.
Betweenness centrality is a network centrality measure based on the amount ofshortest paths passing through a given vertex. A graph is betweennessuniform (BUG)if all vertices have an equal value of betweenness centrality. In this contribution, wefocus on betweennessuniform 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 betweenness centrality values below 6/7 are attained for at least one BUG. Furthermore,among graphs with diameter at least three, there are no betweennessuniform 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 complement.
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20230723 00:01 
Rooting algebraic vertices of convergent sequences
Hartman, David ; Hons, T. ; Nešetřil, J.
Structural convergence is a framework for convergence of graphs by Nešetřil andOssona de Mendez that unifies the dense (left) graph convergence and BenjaminiSchramm 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.
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20230507 00:00 
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.
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 PragueDejvice 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 windtunnel is discussed in the study The PALM dynamical core contains a solver for the NavierStokes 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 airflow 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
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20230328 00:39 
Interaktivní nástroj pro podporu vyhodnocování dat ze standardizovaných testů
Martinková, Patrícia ; Potužníková, E. ; Netík, Jan
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. 2931. ISBN 9788028000905. [ČAPV 2022: Proměny výchovy a vzdělávání a jejich reflexe v pedagogickém výzkumu /30./. Babice / virtual (CZ), 29.08.202231.08.2022]. 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.
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20230129 22:31 
Some modiﬁcations of the limitedmemory variable metric optimization methods
Vlček, Jan ; Lukšan, Ladislav
Several modiﬁcations of the limitedmemory variable metric (or quasiNewton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rankone (SR1) update formula is derived in a similar way as for the block BFGS update in Vlˇcek and Lukˇsan (Numerical Algorithms 2019). The block SR1 formula is then modiﬁed to obtain an update which can reduce the required number of arithmetic operations per iteration. Since it usually violates the corresponding secant conditions, this update is combined with the shifting investigated in Vlˇcek and Lukˇsan (J. Comput. Appl. Math. 2006). Moreover, a new eﬃcient way how to realize the limitedmemory shifted BFGS method is proposed. For a class of methods based on the generalized shifted economy BFGS update, global convergence is established. A numerical comparison with the standard LBFGS and BNS methods is given.
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20230108 22:31 
Introduction to statistical inference based on scalarvalued scores
Fabián, Zdeněk
In the report we maintain consistently the following point of view: Given a continuous model, there are not the observed values, which are to be used in probabilistic and statistical considerations, but their ”treated forms”,the values of the scalarvalued score function corresponding to the model. Based on this modiﬁed concept of the score function, we develop theory of score random variables, study their geometry and deﬁne their new characteristics, ﬁnite even in cases of heavytailed models. A generalization for parametric families provides a new approach to parametric point estimation.
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20230108 22:31 
A New Look to Information and Uncertainty of Continuous Distributions
Fabián, Zdeněk
We deﬁne information and uncertainty function of a family of continuous distributions. Their values are relative information and uncertainty of an observation from the given parametric family, their mean values are the generalized Fisher information and a new measure of variability, the score variance. In a series of examples we show why to use new concepts instead of the diﬀerential entropy.
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20230108 22:31 
Score correlation for skewed distributions
Fabián, Zdeněk
Based on the new concept of the scalarvalued score function of continuous distributions we introduce the score correlation coeﬃcient ”tailored” to the assumed probabilistic model and study its properties by means of simulation experiments. It appeared that the new correlation method is useful for enormously skewed distributions.
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20230108 22:31 
ScalarValued Score Functions and their use in Parametric Estimation
Fabián, Zdeněk
In the paper we describe and explain a new direction in probabilistic and statistical reasoning, the approach based on scalarvalued score functions of continuous random variables. We show basic properties of score functions of standard distributions, generalize the approach for parametric families and show how to use them for solutions of problems of parametric statistics.
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