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Contrastive Language-Image Pre-Training (CLIP) is highly instrumental in machine learning applications within a large variety of domains. We investigate the geometry of this embedding, which is still not well understood. We examine the raw…
In this paper, we overlay a continuum of analytical relations which essentially serve to compute the arc-length described by a celestial body in an elliptic orbit within a stipulated time interval. The formalism is based upon a…
Cosmological probes pose an inverse problem where the measurement result is obtained through observations, and the objective is to infer values of model parameters which characterize the underlying physical system -- our Universe. Modern…
Sampling is a fundamental problem in computer science and statistics. However, for a given task and stream, it is often not possible to choose good sampling probabilities in advance. We derive a general framework for adaptively changing the…
We introduce Cayley transform ellipsoid fitting (CTEF), an algorithm that uses the Cayley transform to fit ellipsoids to noisy data in any dimension. Unlike many ellipsoid fitting methods, CTEF is ellipsoid specific, meaning it always…
From a model-building perspective, we propose a paradigm shift for fitting over-parameterized models. Philosophically, the mindset is to fit models to future observations rather than to the observed sample. Technically, given an imputation…
Attitude estimation is often a prerequisite for control of the attitude or orientation of mechanical systems. Current attitude estimation algorithms use coordinate representations for the group of rigid body orientations. All coordinate…
For shape optimization problems, governed by elliptic equations with Dirichlet boundary condition and random coefficients, we utilize a penalization technique to get the approximate problem. We consider that uncertainties exists in the…
In this note, we will consider two classical volume problems related to elliptic integrals. The first problem has a neat formula by means of elliptic integrals. We remade it with details. In the second problem, we found a messy formula. On…
Several approaches to image stitching use different constraints to estimate the motion model between image pairs. These constraints can be roughly divided into two categories: geometric constraints and photometric constraints. In this…
We develop a mathematical and numerical framework to solve state estimation problems for applications that present variations in the shape of the spatial domain. This situation arises typically in a biomedical context where inverse problems…
Ordinal embedding aims at finding a low dimensional representation of objects from a set of constraints of the form "item $j$ is closer to item $i$ than item $k$". Typically, each object is mapped onto a point vector in a low dimensional…
Simple models of gravitational arcs are crucial to simulate large samples of these objects with full control of the input parameters. These models also provide crude and automated estimates of the shape and structure of the arcs, which are…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
An algorithm is presented to fit precipitates in atom probe tomographic data sets as equivalent ellipsoids. Unlike previous techniques, which measure only the radius of gyration, these ellipsoids retain the moments of inertia and principle…
In the context of computer models, calibration is the process of estimating unknown simulator parameters from observational data. Calibration is variously referred to as model fitting, parameter estimation/inference, an inverse problem, and…
A deterministic attitude estimation problem for a rigid body in a potential field, with bounded attitude and angular velocity measurement errors is considered. An attitude estimation algorithm that globally minimizes the attitude estimation…
Functions of one or more variables are usually approximated with a basis: a complete, linearly-independent system of functions that spans a suitable function space. The topic of this paper is the numerical approximation of functions using…
We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle…
The cosmological exploitation of modern photometric galaxy surveys requires both accurate (unbiased) and precise (narrow) redshift probability distributions derived from broadband photometry. Existing methodologies do not meet those…