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The Equation |x| - |Ax| = b
Rohn, Jiří
We formulate conditions on A and b under which the double absolute value equation |x| - |Ax| = b possesses in each orthant a unique solution which, moreover, belongs to the interior of that orthant.
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Globální implicitní funkce
Rohn, Jiří
Tento text pochází z roku 1973 a nebyl dosud zveřejněn. Jeho hlavním výsledkem je věta o existenci a jednoznačnosti globální implicitní funkce v Rn. Tomuto výsledku předchází řada pomocných tvrzení.
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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.
Betweenness centrality is a network centrality measure based on the amount of shortest 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, we focus on betweenness-uniform graphs with betweenness centrality below one. We disprove a conjecture about the existence of a BUG with betweenness value α for any 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 betweenness-uniform graphs with a betweenness centrality smaller than one. In graphs of smaller diameter, the same can be shown under a uniformity condition on the components of the complement.
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Rooting algebraic vertices of convergent sequences
Hartman, David ; Hons, T. ; Nešetřil, J.
Structural convergence is a framework for convergence of graphs by Nešetřil and Ossona de Mendez that unifies the dense (left) graph convergence and Benjamini-Schramm convergence. They posed a problem asking whether for a given sequence of graphs (Gn) converging to a limit L and a vertex r of L it is possible to find a sequence of vertices (rn) such that L rooted at r is the limit of the graphs Gn rooted at rn. A counterexample was found by Christofides and Král’, but they showed that the statement holds for almost all vertices r of L. We offer another perspective to the original problem by considering the size of definable sets to which the root r belongs. We prove that if r is an algebraic vertex (i.e. belongs to a finite definable set), the sequence of roots (rn) always exists.
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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.
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.
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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. 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.
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Some modifications of the limited-memory variable metric optimization methods
Vlček, Jan ; Lukšan, Ladislav
Several modifications of the limited-memory variable metric (or quasi-Newton) line search methods for large scale unconstrained optimization are investigated. First the block version of the symmetric rank-one (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 limited-memory 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 L-BFGS and BNS methods is given.
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Introduction to statistical inference based on scalar-valued 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 scalar-valued 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 heavy-tailed models. A generalization for parametric families provides a new approach to parametric point estimation.
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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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