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The use of complex networks as a modern approach to understanding the world and its dynamics is well-established in literature. The adjacency matrix, which provides a one-to-one representation of a complex network, can also yield several…
The main two algorithms for computing the numerical radius are the level-set method of Mengi and Overton and the cutting-plane method of Uhlig. Via new analyses, we explain why the cutting-plane approach is sometimes much faster or much…
We describe a three precision variant of Newton's method for nonlinear equations. We evaluate the nonlinear residual in double precision, store the Jacobian matrix in single precision, and solve the equation for the Newton step with…
In this paper, we develop an iterative scheme to enable the explicit calculation of an arbitrary post-Newtonian order for a relativistic body that reduces to the Maclaurin spheroid in the appropriate limit. This scheme allows for an…
The precision frontier in collider physics is being pushed at impressive speed, from both the experimental and the theoretical side. The aim of this review is to give an overview of recent developments in precision calculations within the…
A subroutine for very-high-precision numerical solution of a class of ordinary differential equations is provided. For given evaluation point and equation parameters the memory requirement scales linearly with precision $P$, and the number…
The real roots of the cubic and quartic polynomials are studied geometrically with the help of their respective Siebeck--Marden--Northshield equilateral triangle and regular tetrahedron. The Vi\`ete trigonometric formulae for the roots of…
We initiate the study of diameter computation in geometric intersection graphs from the fine-grained complexity perspective. A geometric intersection graph is a graph whose vertices correspond to some shapes in $d$-dimensional Euclidean…
We propose a method to compute the numerical solutions of a polynomial system in complete intersection. This algorithm makes use of Bezout matrices and need only linear algebra computations. All the calculations can be done in floating…
In the present paper, we study algorithmic questions for the arc-intersection graph of directed paths on a tree. Such graphs are known to be perfect (proved by Monma and Wei in 1986). We present faster algorithms than all previously known…
Consider an arrangement of $k$ lines intersecting the unit square. There is some minimum scaling factor so that any placement of a rectangle with aspect ratio $1 \times p$ with $p\geq 1$ must non-transversely intersect some portion of the…
The computation of the topology of a real algebraic plane curve is greatly simplified if there are no more than one critical point in each vertical line: the general position condition. When this condition is not satisfied, then a finite…
We count the number of conics through two general points in complete intersections when this number is finite and give an application in terms of quasi-lines.
Spatial join processing techniques that identify intersections between complex geometries (e.g., polygons) commonly follow a two-step filter-and-refine pipeline. The filter step evaluates the query predicate on the minimum bounding…
Determining the maximum number of edges in an intersecting hypergraph on a fixed ground set under additional constraints is one of the central topics in extremal combinatorics. In contrast, there are few results on analogous problems…
Model checking is an automatic formal verification technique that is widely used in hardware verification. The state-of-the-art complete model-checking techniques, based on IC3/PDR and its general variant CAR, are based on computing…
The aim of this paper is to investigate the intersection problem between two linear sets in the projective line over a finite field. In particular, we analyze the intersection between two clubs with eventually different maximum fields of…
We present a next-to-leading order computation in QCD of one-jet and two-jet cross sections in polarized hadronic collisions. Our results are obtained in the framework of a general formalism that deals with soft and collinear singularities…
We investigate the viability of defining an intersection product on algebraic cycles on a singular algebraic variety by pushing forward intersection products formed on a resolution of singularities. For varieties with resolutions having a…
We describe a next-to-leading-order calculation of the fully exclusive parton cross section for the photoproduction of heavy quarks. We use our result to compute quantities of interest for current fixed-target experiments. We discuss…