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Elliptic curves have a well-known and explicit theory for the construction and application of endomorphisms, which can be applied to improve performance in scalar multiplication. Recent work has extended these techniques to hyperelliptic…
Eclipse mapping uses the shape of the eclipse of an exoplanet to measure its two-dimensional structure. Light curves are mostly composed of longitudinal information, with the latitudinal information only contained in the brief ingress and…
We introduce a new iterative method for computing solutions of elliptic equations with random rapidly oscillating coefficients. Similarly to a multigrid method, each step of the iteration involves different computations meant to address…
Complex networks are at the core of an intense research activity. However, in most cases, intricate and costly measurement procedures are needed to explore their structure. In some cases, these measurements rely on link queries: given two…
In [arXiv:2207.03377] the first closed formula of a faithful entanglement measure applicable to realistic electron systems has been derived. In the present work, we build on this key achievement with the ultimate goal of guiding the…
In this note we show that one open four dimensional ellipsoid embeds symplectically into another if and only the ECH capacities of the first are no larger than those of the second. This proves a conjecture due to Hofer. The argument uses…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
In this paper we obtain the closed forms of some hypergeometric functions. As an application, we obtain the explicit forms of the Bergman kernel functions for intersection of two complex ellipsoids $\{z \in \mathbb{C}^3 \colon |z_1|^p +…
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
In this paper we study the inversion in an ellipse and some properties, which generalizes the classical inversion with respect to a circle. We also study the inversion in an ellipse of lines, ellipses and other curves. Finally, we…
To separate the overlapped cells, a bottleneck detection approach is proposed in this paper. The cell image is segmented by slope difference distribution (SDD) threshold selection. For each segmented binary clump, its one-dimensional…
We consider the moduli spaces $\mathcal{M}_d(\ell)$ of a closed linkage with n links and prescribed lengths in d-dimensional Euclidean space. For d>3 these spaces are no longer manifolds generically, but they have the structure of a…
The Electron Localization Function (ELF) by Becke and Edgecombe [J. Chem. Phys. {\bf 92}, 5397 (1990)] is routinely adopted as a descriptor of atomic shells and covalent bonds. Since the ELF and its related quantities find useful…
Multilayer networks provide a powerful framework for modeling complex systems that capture different types of interactions between the same set of entities across multiple layers. Core-periphery detection involves partitioning the nodes of…
Merge trees are fundamental structures in topological data analysis. Interleaving distance is a widely accepted metric for comparing merge trees, with applications in visualization and scientific computing. While a greedy algorithm exists…
In general it requires at least 7 point correspondences to compute the fundamental matrix between views. We use the cross ratio invariance between corresponding epipolar lines, stemming from epipolar line homography, to derive a simple…
In this paper, we address the problem of how many randomly labeled patterns can be correctly classified by a single-layer perceptron when the patterns are correlated with each other. In order to solve this problem, two analytical schemes…
The global many-electron wave function overlap matrix accounts for all effects beyond the Born-Oppenheimer approximation in the discrete variable local diabatic representation, a numerically exact framework for modeling nonadiabatic conical…
We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane…
Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an elipsoid using…