Related papers: Coarse spaces over the ages
We present a notion of precompactness, and study some of its properties, in the context of apartness spaces whose apartness structure is not necessarily induced by any uniform one. The presentation lies entirely with a Bishop-style…
For a given poset, we consider its representations by systems of subspaces of a unitary space ordered by inclusion. We classify such systems for all posets for which an explicit classification is possible.
The aim of this paper is to review the state-of-the-art of recent research concerning the numerical index of Banach spaces, by presenting some of the results found in the last years and proposing a number of related open problems.
A growing number of efforts aim to understand what people see when using a visualization. These efforts provide scientific grounding to complement design intuitions, leading to more effective visualization practice. However, published…
Spatial confounding is a persistent challenge in spatial statistics, influencing the validity of statistical inference in models that analyze spatially-structured data. The concept has been interpreted in various ways but is broadly defined…
A coarse space $X$, endowed with a linear order compatible with the coarse structure of $X$, is called linearly ordered. We prove that every linearly ordered coarse space $X$ is locally convex and the asymptotic dimension of $X$ is either…
The aim of this paper is to provide a gentle introduction to Chabauty topology, while very little background knowledge is assumed. As an example, we provide pictures for the Chabauty space of C*. Note that the description of this space is…
A general framework is developed to investigate the properties of useful choices of stationary spacelike slicings of stationary spacetimes whose congruences of timelike orthogonal trajectories are interpreted as the world lines of an…
Graphic design is an effective language for visual communication. Using complex composition of visual elements (e.g., shape, color, font) guided by design principles and aesthetics, design helps produce more visually-appealing content. The…
Qualitative data can be conveyed with strings of text. Fitting longer text into visualizations requires a) space to place the text inside the visualization; and b) appropriate text to fit the space available. For quantitative…
We review some modern theories about the structure of space and time, in particular those related to discrete space and time. Following an epistemological method we start from theories which discuss discrete space and time as a mathematical…
The purpose of this contribution is to give a coherent account of a particular narrative which links locales, geometric theories, sheaf semantics and constructive commutative algebra. We are hoping to convey a firm grasp of three ideas: (1)…
The goal is to review the notion of a complete Segal space and how certain categorical notions behave in this context. In particular, we study functoriality in complete Segal spaces via fibrations. Then we use it to define limits and…
Recommendation algorithms have been leveraged in various ways within visualization systems to assist users as they perform of a range of information tasks. One common focus for these techniques has been the recommendation of content, rather…
What does it mean for an algorithm to be fair? Different papers use different notions of algorithmic fairness, and although these appear internally consistent, they also seem mutually incompatible. We present a mathematical setting in which…
We study the concept of cone metric space in the context of ordered vector spaces by setting up a general and natural framework for it.
A number of topics involving metrics and measures are discussed, including some of the special structure associated with ultrametrics.
The notion of concept has been studied for centuries, by philosophers, linguists, cognitive scientists, and researchers in artificial intelligence (Margolis & Laurence, 1999). There is a large literature on formal, mathematical models of…
Ordinal data analysis is an interesting direction in machine learning. It mainly deals with data for which only the relationships `$<$', `$=$', `$>$' between pairs of points are known. We do an attempt of formalizing structures behind…
Our primary purpose is to isolate the abstract, mathematical properties of circuits -- both classical Boolean circuits and quantum circuits -- that are essential for their computational interpretation. A secondary purpose is to clarify the…