2019/1
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- ItemTwo network transformations(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2019) Pfaltz, John L.In this paper, we study relational networks. They may be as large as socialnetworks or as small as neural networks. We employ the concepts of closure andclosure operators to describe their structures, and introduce the idea of functionaltransformation to model their dynamic qualities.One transformation,ω, reduces a complex network to a much simpler form, yetpreserves important properties such as path connectivity and centrality measures.The other transformation,ε, expands a network by using grammar-like productions.Both are continuous (with respect to closure) and we show thatεis effectivelyω−1in thatω·ε·ω=ω.It is thought thatωmay model human memory consolidation and thatεmaymodel memory reconstruction.
- ItemAnalysis of high frame-rate movies by variational methods(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2019) Pedone, Massimiliano; Carosio, Silvia; Ruocco, Giancarlo; Del Prete, ZaccariaThe object of this study was the recognition of Regions Of Interest(ROIs)in a time series of digital images of two specific laboratory experiments. It concernsthe identification of objects in a tissue surface by high-resolution and high-speedad-hoc systems for morphological dynamic image analysis. The protocols and thealgorithms implemented are developed to retrieve biomechanical properties of twodifferentin vitrosystems; the solid filament X-MET (eX-vivo Muscle EngineeredTissue) to measure its reaction to a different frequency stimulation, and a planarsystem of co-culture of skeletal and cardiac muscle cells, where myotubes and car-diomyocytes coexist, to discriminate the interaction between different cell’s type,of its spontaneous pulse. The results of the stimulated X-MET from solid culturesystem are frequency dependent points of the macroscopic muscular strength andits contractile response. The results for the co-culture planar board measure thecorrelation of the pulsed movements of the different parts of the tissue.
- ItemArtificial grass and genuine football: The evolution of artificial turf(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2019) Haugen, Kjetil K.; Heen, Knut P.The article formulates, solves and draws inference from a game model in-tended to shed light on the evolution of artificial turf in professional Europeanfootball (soccer). The main results indicate that the quality of teams (sportsperformance-wise) defines which of the teams choose to play on artificial turf andwhich not. Furthermore, teams with low quality are predicted to be the “artificialturf pioneers”, both model-wise, as well as indicated by some empirical exampleswith data taken from the Norwegian, Swedish and Dutch leagues. The fact that ar-tificial turf may play a significant role also in the evolution of uncertainty of outcomeis interesting and commented on in the conclusion.
- ItemMeasuring uncertainty of outcome: An analytic approach(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2019) Haugen, Kjetil K.This paper proposes an alternative mathematical formulation to one (am-ong many) ways of estimating uncertainty of outcome. This alternative formulationmay make such estimation processes easier for both practitioners and researchers. Additionally, some approximative estimators1are derived, tested and discussed.Even though these estimators may not perform perfectly for football leagues, theymay have a stronger potential for use in other sports.
- ItemOn the completeness of non-symmetrical uniform convergence with some links to approach spaces(Vysoké učení technické v Brně, Fakulta strojního inženýrství, Ústav matematiky, 2019) Leseberg, Dieter; Vaziry, ZohrehThe quasitopos b-UFIL of b-uniform filter spaces [16] are an appropri-ate tool for studying convergence from a higher point of view as demonstrated inrecent papers by the above mentioned authors. In addition BORN, the category ofbornological spaces and bounded maps, can be integrated as bicoreflective subcate-gory of b-UFIL. As already shown symmetric b-uniform filter spaces have “Cauchycompletions” which generalize some important ones as for example those which wereconsidered by Wyler, Preuss, Czászár and Hausdorff, respectively. In the presentpaper we will construct a completion, called ultracompletion, for a suitable notnecessarily symmetric b-uniform filter space and compare this one with a constructpresented for quasi-uniform spaces by Carlson and Hicks in the past. Furthermore,among others, we get the result that every quasiuniform limit space in the sense ofBehling has an ultracompletion. At the end of this article, we consider some impor-tant links to generalized approach spaces, those which were introduced by Lowen.So it is shown that b-topological closure operators can be completely described byso-called approach-bornologies, which represent a common generalization of bothapproach spaces and bornological spaces, respectively. Thus, as interesting corol-lary we obtain the result that APB the category of approach-bornological spacesand contracted maps intersects b-URING, the full subcategory of b-UFIL, whoseobjects have ultracompletions.