Search results for "fraktaalit"
showing 4 items of 14 documents
Bayesian semiparametric long memory models for discretized event data
2020
We introduce a new class of semiparametric latent variable models for long memory discretized event data. The proposed methodology is motivated by a study of bird vocalizations in the Amazon rain forest; the timings of vocalizations exhibit self-similarity and long range dependence. This rules out Poisson process based models where the rate function itself is not long range dependent. The proposed class of FRActional Probit (FRAP) models is based on thresholding, a latent process. This latent process is modeled by a smooth Gaussian process and a fractional Brownian motion by assuming an additive structure. We develop a Bayesian approach to inference using Markov chain Monte Carlo and show g…
Dimension of projection : Marstrand's theorem
2022
Tässä tutkielmassa todistetaan Marstrandin projektiolause käyttäen apuna potentiaaliteoriaa. Projektiolauseen mukaan 2-ulotteisen Borel joukon ortogonaaliprojektion Hausdorffin dimensio on luvun 1 ja kyseisen Borel joukon dimension minimi melkein kaikkiin eri suuntiin. Intuitiivisesti lause kertoo, että joukon varjon dimensio on suurin mahdollinen. Marstrandin projektiolauseen todistamiseksi tutkielmassa rakennetaan teoria alkaen yleisen mittateorian perustuloksista. Mittateorian pohjalta määritellään Hausdorffin mitta, jonka avulla määritellään joukon Hausdorffin dimensio. Intuitiivisesti Hausdorffin dimensio kuvaa joukon geometrista kokoa ja se on yksikäsitteinen jokaiselle joukolle. Haus…
Mathematical and Coding Lessons Based on Creative Origami Activities
2019
AbstractThis paper considers how creativity and creative activities can be encouraged in regular mathematical classes by combining different teaching approaches and academic disciplines. We combined origami and paper folding with fractals and their mathematical properties as well as with coding in Scratch in order to facilitate learning mathematics and computer science. We conducted a case study experiment in a Serbian school with 15 high school students and applied different strategies for learning profound mathematical and coding concepts such as fractals dimension and recursion. The goal of the study was to employ creative activities and examine students’ activities during this process i…
Regularity and modulus of continuity of space-filling curves
2019
We study critical regularity assumptions on space-filling curves that possess certain modulus of continuity. The bounds we obtain are essentially sharp, as demonstrated by an example. peerReviewed