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These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…

I compare and discuss critically several measures of statistical significance in common use in astrophysics and in high energy physics. I also exhibit some relationships among them.

We use the Halo Model to explore the implications of assuming that galaxy luminosities in groups are randomly drawn from an underlying luminosity function. We show that even the simplest of such order statistics models -- one in which this…

We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…

Cosmological correlators are very important objects in cosmology as they offer us a huge amount of information of the early universe. They reside on the future boundary of a de Sitter space and can be calculated by two methods. First method…

Coordination geometries describe how the neighbours of a central particle are arranged around it. Such geometries can be thought to lie in an abstract topological space; a model of this space could provide a mathematical basis for…

This study introduces a novel approach to terrain feature classification by incorporating spatial point pattern statistics into deep learning models. Inspired by the concept of location encoding, which aims to capture location…

We present the microscopic formulation of inclusion statistics, a counterpoint to exclusion statistics in which particles tend to coalesce more than ordinary bosons. We derive the microscopic occupation multiplicities of 1-body quantum…

I give a compact, pedagogical review of our present understanding of the universe as based on general relativity. This includes the uniform models, with special reference to the cosmological 'constant'; and the equations for…

The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations…

In this paper, we focus on stochastic comparisons of extreme order statistics stemming from multiple-outlier scale models with dependence. Archimedean copula is used to model dependence structure among nonnegative random variables.…

An array of large observational programs using ground-based and space-borne telescopes is planned in the next decade. The forthcoming wide-field sky surveys are expected to deliver a sheer volume of data exceeding an exabyte. Processing the…

Large scale numerical experiments are commonplace today in theoretical physics. The high performance algorithms described herein are the most compact, efficient methods known for representing and analyzing systems modeled well by sets or…

In these notes we present a selection of topics, each section approximately amounting to one lecture. We begin with a brief recapitulation of General Relativity, and the Standard Model of Cosmology. This is followed by lectures on important…

The ordinal patterns of a fixed number of consecutive values in a time series is the spatial ordering of these values. Counting how often a specific ordinal pattern occurs in a time series provides important insights into the properties of…

We developed a modification to the calculation of the two-point correlation function commonly used in the analysis of large scale structure in cosmology. An estimator of the two-point correlation function is constructed by contrasting the…

This paper reviews developments in statistics for spatial point processes obtained within roughly the last decade. These developments include new classes of spatial point process models such as determinantal point processes, models…

Homotopy coherence has a considerable history, albeit also by other names. For this volume highlighting symmetries, the appropriate use is: Homotopy coherence of representations, at one time known as strong homotopy representations. We…

In these lectures I review the present status of the so-called Standard Cosmological Model, based on the hot Big Bang Theory and the Inflationary Paradigm. I will make special emphasis on the recent developments in observational cosmology,…

A broader perspective is suggested for the study of higher dimensional cosmological models. [1986: Considerations involving the Einstein constraints and the Ricci form of the evolution equations for spatially homogeneous spacetimes in 4 or…