Related papers: Elliptical Insights: Understanding Statistical Met…
Elliptic functions are largely studied and standardized mathematical objects. The two usual approaches are due to Jacobi and Weierstrass. From a contour integral which allowed us to unify many summation formulae (Euler-MacLaurin, Poisson,…
This paper attempts to situate statistics in relation to qualitative research methods and other means of "finding out". It compares and contrasts aspects of qualitative research methods and statistical inquiry and attempts to answer the…
We begin by studying the surface area of an ellipsoid in n-dimensional Euclidean space as the function of the lengths of the semi-axes. We write down an explicit formula as an integral over the unit sphere in n-dimensions and use this…
Isogenies, the mappings of elliptic curves, have become a useful tool in cryptology. These mathematical objects have been proposed for use in computing pairings, constructing hash functions and random number generators, and analyzing the…
Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…
This paper introduces epistemic graphs as a generalization of the epistemic approach to probabilistic argumentation. In these graphs, an argument can be believed or disbelieved up to a given degree, thus providing a more fine--grained…
This is an attempt to present axioms for Euclidean geometry, aiming at the following goals: to work with geometric notions (thus not merely identify points with pairs of numbers, giving a special status to a particular coordinate system);…
Fitting concentric geometric objects to digitized data is an important problem in many areas such as iris detection, autonomous navigation, and industrial robotics operations. There are two common approaches to fitting geometric shapes to…
The ability to read, write, and speak mathematics is critical to students becoming comfortable with statistical models and skills. Faster development of those skills may act as encouragement to further engage with the discipline. Vocabulary…
This is the first paper in a series of eight where in the first three we develop a systematic approach to the geometric algebras of multivectors and extensors, followed by five papers where those algebraic concepts are used in a novel…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
In this paper, we demonstrate the intimate relationships among some geometric figures and the families of elliptic curves with positive ranks. These geometric figures include \textit{\textbf{Heron triangles}}, \textit{\textbf{Brahmagupta…
When dealing with a parametric statistical model, a Riemannian manifold can naturally appear by endowing the parameter space with the Fisher information metric. The geometry induced on the parameters by this metric is then referred to as…
When inclusions in a composite are separated by a very small gap, high contrast between the inclusion and matrix properties can induce strong amplification of the underlying field inside the narrow region. Quantifying this field…
This paper provides an overview of modern digital geometry and topology through mathematical principles, algorithms, and measurements. It also covers recent developments in the applications of digital geometry and topology including image…
In this paper we discuss various connections between geometric discrepancy measures, such as discrepancy with respect to convex sets (and convex sets with smooth boundary in particular), and applications to numerical analysis and…
High-dimensional representations for words, text, images, knowledge graphs and other structured data are commonly used in different paradigms of machine learning and data mining. These representations have different degrees of…
In this paper we consider aspects of geometric observability for hypergraphs, extending our earlier work from the uniform to the nonuniform case. Hypergraphs, a generalization of graphs, allow hyperedges to connect multiple nodes and…
Metric embedding is a powerful tool used extensively in mathematics and computer science. We devise a new method of using metric embeddings recursively, which turns out to be particularly effective in $\ell_p$ spaces, $p>2$, yielding…
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable harmonic analysis. We give a brief description of these…