Shining a Light into the Dark: Cosmic Voids as Cosmological Probes of Evolving and Interacting Dark Sector Physics

The dark sector of the Universe, which comprises dark matter and dark energy, presents one of the greatest unanswered questions in all of physics. Although it dominates the current mass-energy content of the Universe, little is understood about its true nature. The extent of our understanding is reflected in the current Standard Model of Cosmology, Λ Cold Dark Matter (ΛCDM), which characterises dark matter as a non-relativistic, non-baryonic form of matter, and dark energy as a form of vacuum energy described by the cosmological constant, Λ, in the field equations of General Relativity. Although this characterisation has generally been successful, it does not provide much insight into or theoretical underpinning for the dark sector. In this thesis, I aim to address this problem by searching for the unique signatures of two alternative cosmological models featuring evolving and interacting dark sectors: an uncoupled quintessence model (φCDM) and a coupled dark energy model (CDE). These signatures will provide a way to distinguish between cosmological models featuring different dark sector physics, allowing us to observationally probe and constrain the properties of the dark sector in our Universe. I focus on the signatures of these models within cosmic voids. Using state-of-the-art adiabatic hydrodynamical simulations and a density-based void finder I developed, I study the properties of voids in the two alternative models and compare them to those in ΛCDM, focusing on their population size, volumes, ellipticities, prolateness, and average densities, over the redshift range z = 12 - 0. I discover that void densities are distinctly lower in the two alternative models than in ΛCDM, revealing that the property is sensitive to the presence of an evolving dark sector, and thus can be used as the basis of observational probes of the dark sector in our Universe

Wavelet-based Image Denoising

Käesolev töö uurib laineteisenduste kasutust piltide kvaliteedi parandamise eesmärgil, neilt müra eemaldades. See annab ülevaate erinevates müra tüüpidest ning müraeemaldusmeetoditest. Edasi keskendub töö laineteisenduspõhistele müraeemaldusskeemidele. Samuti uurib töö laineteisenduspõhise müraeemaldusmeetodi ning kokkupakkimise kombineerimise kasulikkust ja pakub välja uue lävendamise tüübi ning muudatuse eksisteerivale BayesShrink meetodile. Pakutud meetod implementeeritakse C# keeles ning selle implementatsiooni tulemusi, jõudlust ning optimaalseid parameetreid analüüsitakse eksperimentaalsete tulemuste abil.This thesis studies the use of wavelets for the purpose of improving the quality of images by removing noise from them. It presents an overview of different types of noise and denoising methods. The thesis then focuses on the wavelet transform based denoising schemes. It explores the potential of combining wavelet-based denoising and compression, and presents a new thresholding type and a modification to the existing BayesShrink method. The proposed method is implemented in the C# language and its performance and optimal parameters are analyzed through experimental results

Andmete puudumise struktuuri määramise testid

Antud töö eesmärk on anda ülevaade andmete puudumise struktuuridest ning kolmest testist, mille abil etteantud andmestike korral puudumise struktuure üksteisest eristada. Vaatluse all on järgnevad testid: Little’i test, t-testide test ja MM-test. Igat testi testiti nullhüpoteesi ja sisuka hüpoteesi tingimustes ning mõlemal juhul erineva suuruse ja ehitusega andmestike korral. Nullhüpoteesi simulatsioonides muudeti andmestiku pikkust, tunnuste arvu ja konstantset (ning võrdset) puudumise tõenäosust. Sisuka hüpoteesi simulatsioonides muudeti lisaks andmestiku mõõtmetele ka täpset puudumise struktuuri ennast. Kõik simulatsioonid sooritati R-is. MM-test osutus kasutuks. Ülejäänud kahest testist töötas Little’i test paremini väiksemate ning t-testide test suuremate andmestike korral. Kiireim ning samuti kõige töökindlam test oli t-testide test, mida võib neist kolmest kõige õnnestunumaks testiks pidada