Related papers: An Efficient Method to Verify the Inclusion of Ell…
This work introduces a method that applies images of the extended bodies in the solar system to spacecraft camera calibration. The extended bodies consist of planets and moons that are well-modeled by triaxial ellipsoids. When imaged, the…
We give a deterministic algorithm that very quickly proves the primality or compositeness of the integers N in a certain sequence, using an elliptic curve E/Q with complex multiplication by the ring of integers of Q(sqrt(-7)). The algorithm…
Identifying independence between two random variables or correlated given their samples has been a fundamental problem in Statistics. However, how to do so in a space-efficient way if the number of states is large is not quite well-studied.…
We propose a new $(1+O(\varepsilon))$-approximation algorithm with $O(n+ 1/\varepsilon^{\frac{(d-1)}{2}})$ running time for computing the diameter of a set of $n$ points in the $d$-dimensional Euclidean space for a fixed dimension $d$,…
A classical theorem of Spencer shows that any set system with n sets and n elements admits a coloring of discrepancy O(n^1/2). Recent exciting work of Bansal, Lovett and Meka shows that such colorings can be found in polynomial time. In…
As part of our development of a computer code to perform 3D `constrained evolution' of Einstein's equations in 3+1 form, we discuss issues regarding the efficient solution of elliptic equations on domains containing holes (i.e., excised…
Many man-made objects are characterised by a shape that is symmetric along one or more planar directions. Estimating the location and orientation of such symmetry planes can aid many tasks such as estimating the overall orientation of an…
In this paper we present the successive centralization of the circumcenter reflection scheme with several control sequences for solving the convex feasibility problem in Euclidean space. Assuming that a standard error bound holds, we prove…
A new algorithms for computing discrete logarithms on elliptic curves defined over finite fields is suggested. It is based on a new method to find zeroes of summation polynomials. In binary elliptic curves one is to solve a cubic system of…
We introduce a fixed point iteration process built on optimization of a linear function over a compact domain. We prove the process always converges to a fixed point and explore the set of fixed points in various convex sets. In particular,…
We study the local geometry of testing a mean vector within a high-dimensional ellipse against a compound alternative. Given samples of a Gaussian random vector, the goal is to distinguish whether the mean is equal to a known vector within…
We study the exact counting problem for all lattice rectangles contained in the square $[0,n)\times[0,n)$, including non-axis-parallel ones. Starting from the standard parametrization by a primitive direction $(u,v)$ and two side lengths,…
Manifold reconstruction has been extensively studied for the last decade or so, especially in two and three dimensions. Recently, significant improvements were made in higher dimensions, leading to new methods to reconstruct large classes…
Weighted variants of triangle detection are an important object of study because of their prominence in fine-grained complexity. We revisit the Node-Weighted Triangle problem, where the goal is to decide if a vertex-weighted graph contains…
The recent years have seen a beautiful breakthrough culminating in a comprehensive understanding of certain scale-invariant properties of $n-1$ dimensional sets across analysis, geometric measure theory, and PDEs. The present paper surveys…
In this article, we devise a concise algorithm for computing BOCP. Our method is simple, easy-to-implement but without loss of efficiency. Given two circular-arc polygons with $m$ and $n$ edges respectively, our method runs in…
An inclusion is said to be neutral to uniform fields if upon insertion into a homogenous medium with a uniform field it does not perturb the uniform field at all. It is said to be weakly neutral if it perturbs the uniform field mildly. Such…
Binary embedding is a nonlinear dimension reduction methodology where high dimensional data are embedded into the Hamming cube while preserving the structure of the original space. Specifically, for an arbitrary $N$ distinct points in…
The Method of Ellipcenters (ME), introduced in~\cite{ME2025} for strongly convex quadratic minimization, uses two gradient evaluations per iteration: one at the current iterate and one at a companion point on the same level set. We extend…
We present a new interior-point potential-reduction algorithm for solving monotone linear complementarity problems (LCPs) that have a particular special structure: their matrix $M\in{\mathbb R}^{n\times n}$ can be decomposed as $M=\Phi U +…