Related papers: Projecting onto the Unit Dual Quaternion Set

We apply a recently developed technique to extract for the first time the neutron F_2^n structure function from inclusive proton and deuteron data in the nucleon resonance region, and test the validity of quark-hadron duality in the…

Iterative phase retrieval algorithms typically employ projections onto constraint subspaces to recover the unknown phases in the Fourier transform of an image, or, in the case of x-ray crystallography, the electron density of a molecule.…

Regularization is often used in high-dimensional regression settings to generate a sparse model, which can save tremendous computing resources and identify predictors that are most strongly associated with the response. When the predictors…

3D scatterplots are a well-established plotting technique that can be used to represent data with three or more dimensions. On paper and computer monitors they are essentially two-dimensional projections of the three-dimensional Cartesian…

By double ideal quotient, we mean $(I:(I:J))$ where ideals $I$ and $J$. In our previous work [11], double ideal quotient and its variants are shown to be very useful for checking prime divisor and generating primary component. Combining…

Two algorithms are introduced for the computation of discrete integral transforms with a multiscale approach operating in discrete three-dimensional (3D) volumes while considering its real-time implementation. The first algorithm, referred…

Object functionality is often expressed through part articulation -- as when the two rigid parts of a scissor pivot against each other to perform the cutting function. Such articulations are often similar across objects within the same…

Dimensional metrology and positioning operations are used in many fields of particle accelerator projects. This lecture gives the basic tools to designers in the field of measure by analysing the spatial layout of measurement systems since…

Rotation representations are foundational in fields such as computer graphics, robotics, and machine learning, where precise and efficient modeling of 3D orientations is critical. This paper comprehensively investigates diverse…

This paper proposes a methodology to calculate both the first and second derivatives of a vector function of one variable in a single computation step. The method is based on the nested application of the dual number approach for first…

Vector calculus in three-dimensional space is ubiquitous in applications of mathematics in physics and engineering. Its two-dimensional version is, however, quite rare. Here we try to provide a pedagogical account of the subject. It is…

Object detection is a critical part of visual scene understanding. The representation of the object in the detection task has important implications on the efficiency and feasibility of annotation, robustness to occlusion, pose, lighting,…

We consider linear regression problems with a varying number of random projections, where we provably exhibit a double descent curve for a fixed prediction problem, with a high-dimensional analysis based on random matrix theory. We first…

This paper revisits the topic of rotation estimation through the lens of special unitary matrices. We begin by reformulating Wahba's problem using $SU(2)$ to derive multiple solutions that yield linear constraints on corresponding…

Let a polyhedral convex set be given by a finite number of linear inequalities and consider the problem to project this set onto a subspace. This problem, called polyhedral projection problem, is shown to be equivalent to multiple objective…

Uniform random rotations are a useful primitive in applications such as fast Johnson-Lindenstrauss embeddings, kernel approximation, communication-efficient learning, and recent AI compression pipelines, but they are computationally…

Double machine learning is a statistical method for leveraging complex black-box models to construct approximately unbiased treatment effect estimates given observational data with high-dimensional covariates, under the assumption of a…

Thinning is the removal of contour pixels/points of connected components in an image to produce their skeleton with retained connectivity and structural properties. The output requirements of a thinning procedure often vary with…

It is known that quaternions represent rotations in 3D Euclidean and Minkowski spaces. However, product by a quaternion gives rotation in two independent planes at once and to obtain single-plane rotations one has to apply by half-angle…

So far, the use of different variants of dimensional regularization has been investigated extensively for two-loop virtual corrections. We extend these studies to real corrections that are also required for a complete computation of…