Related papers: Projective Plane Subdivision Method For Initial Or…
A simple procedure is developed to determine orbital elements of an object orbiting in a central force field which contribute more than three independent celestial positions. By manipulation of formal three point Gauss method of orbit…
Orientation is a key attribute of objects, crucial for understanding their spatial pose and arrangement in images. However, practical solutions for accurate orientation estimation from a single image remain underexplored. In this work, we…
Planes are familiar mathematical objects which lie at the subtle boundary between continuous geometry and discrete combinatorics. A plane is geometrical, certainly, but the ways that two planes can interact break cleanly into discrete sets:…
The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Less well known is Erd\H{o}s' distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear points in the…
In this paper we address the problem of computing a preliminary orbit of a celestial body from one topocentric position vector and a very short arc (VSA) of optical observations. Using the conservation laws of the two-body dynamics, we…
This study proposes a new automated strategy for designing and optimizing three-dimensional interplanetary low-thrust (LT) trajectories. The method formulates the design as a hybrid optimal control problem and solves it using a two-step…
Projection methods are popular algorithms for iteratively solving feasibility problems in Euclidean or even Hilbert spaces. They employ (selections of) nearest point mappings to generate sequences that are designed to approximate a point in…
We present a novel algorithm for deciding whether a given planar curve is an image of a given spatial curve, obtained by a central or a parallel projection with unknown parameters. The motivation comes from the problem of establishing a…
In this paper we present in detail Newton's method and its modification, based on the Continuous analog of Newton's method for computing periodic orbits of the planar three-body problem. The linear system at each step of the method is…
We present a novel 3D object detection framework, named IPOD, based on raw point cloud. It seeds object proposal for each point, which is the basic element. This paradigm provides us with high recall and high fidelity of information,…
These notes are intended as an easy-to-read supplement to part of the background material presented in my talks on enumerative geometry. In particular, the numbers $n_3$ and $n_4$ of plane rational cubics through eight points and of plane…
The Erd\H{o}s distinct distance problem is a ubiquitous problem in discrete geometry. Somewhat less well known is Erd\H{o}s' distinct angle problem, the problem of finding the minimum number of distinct angles between $n$ non-collinear…
Differential Equations are among the most important Mathematical tools used in creating models in the science, engineering, economics, mathematics, physics, aeronautics, astronomy, dynamics, biology, chemistry, medicine, environmental…
Periodic orbits are important objects of discrete dynamical systems, but finding them is not always easy. We present a self-contained introductory account, aimed at non-experts, to prove their existence and study their stability using the…
This paper presents the first purely numerical (i.e., non-algebraic) subdivision algorithm for the isotopic approximation of a simple arrangement of curves. The arrangement is "simple" in the sense that any three curves have no common…
In this paper we present algorithms for an efficient implementation of the Localized Orthogonal Decomposition method (LOD). The LOD is a multiscale method for the numerical simulation of partial differential equations with a continuum of…
We propose and compare goal-oriented projection based model order reduction methods for the estimation of vector-valued functionals of the solution of parameter-dependent equations. The first projection method is a generalization of the…
We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…
This paper presents an efficient way of detecting directed objects by predicting their center coordinates and direction angle. Since the objects are of uniform size, the proposed model works without predicting the object's width and height.…
Electrical impedance tomography (EIT) is an imaging modality in which the conductivity distribution inside a target is reconstructed based on voltage measurements from the surface of the target. Reconstructing the conductivity distribution…