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These lecture notes aim to provide an introduction to dark matter from the perspective of astrophysics/cosmology. We start with a rapid overview of cosmology, including the evolution of the Universe, its thermal history and structure…
Metric learning seeks to embed images of objects suchthat class-defined relations are captured by the embeddingspace. However, variability in images is not just due to different depicted object classes, but also depends on other latent…
Cosmology has come a long way from being based on a small number of observations to being a data-driven precision science. We discuss the questions "What is observable?", "What in the Universe is knowable?" and "What are the fundamental…
Doppler lensing is the apparent change in object size and magnitude due to peculiar velocities. Objects falling into an overdensity appear larger on its near side, and smaller on its far side, than typical objects at the same redshifts.…
The article introduces the concept of uniformity, which is formulated as a scheme of axioms. The connection of this concept with ordered sets is studied. The effectiveness of using axiom schemes as a convenient and short way of replacing…
We study a model of machine teaching where the teacher mapping is constructed from a size function on both concepts and examples. The main question in machine teaching is the minimum number of examples needed for any concept, the so-called…
The cosmological tensions present in the $\Lambda$ cold dark matter model that have emerged and strengthened over recent years motivate model independent approaches to analysing data. Cosmography is useful for interpreting data in cosmology…
Comparing the luminosity distance measurements to its theoretical predictions is one of the cornerstones in establishing the modern cosmology. However, as shown in Biern & Yoo, its theoretical predictions in literature are often plagued…
A promising way to introduce general relativity in the classroom is to study the physical implications of certain given metrics, such as the Schwarzschild one. This involves lower mathematical expenditure than an approach focusing on…
We explore simple but novel bouncing solutions of general relativity that avoid singularities. These solutions require curvature k=+1, and are supported by a negative cosmological term and matter with -1 < w < -1/3. In the case of moderate…
In this Essay we address several fundamental issues in cosmology: What is the nature of dark energy and dark matter? Why is the dark sector so different from ordinary matter? Why is the effective cosmological constant non-zero but so…
Contrastive learning, along with its variations, has been a highly effective self-supervised learning method across diverse domains. Contrastive learning measures the distance between representations using cosine similarity and uses…
Based on the magnitude--redshift diagram for the sample of supernovae Ia analysed by Perlmutter et al. (1999), Davis & Lineweaver rule out the special relativistic interpretation of cosmological redshifts at a confidence level of 23 sigma.…
Cosmology is built on a relativistic understanding of gravity, where the geometry of the Universe is dynamically determined by matter and energy. In the cosmological concordance model, gravity is described by General Relativity, and it is…
This paper aims to provide teachers with a tool to teach the essential features of special relativity, considering the students' difficulties highlighted by numerous studies. Our proposal presents special relativity as the solution to the…
The vast majority of physical objects we are dealing with are almost exclusively made of atoms. Due to their discrete level structure, single atoms have proved to be emitters of light which is incompatible with the classical description of…
This is a written version of a series of lectures aimed at undergraduate students in astrophysics/particle theory/particle experiment. We summarize the important progress made in recent years towards understanding high energy astrophysical…
An introduction to the physics and mathematics of the expanding universe, using no more than high-school level / undergraduate mathematics. Covered are the basics of scale factor expansion, the dynamics of the expanding universe, various…
In this paper we discuss how teaching of mathematics for middle school and high school students can be improved dramatically when motivation of concepts and ideas is done through the classical problems and the history of mathematics. This…
Our group has developed a technique that makes use of the observed non-linear relation between the ultraviolet and the X-ray luminosity in quasars to provide an independent measurement of their distances, thus turning quasars into…