Related papers: A Database of Belyi Maps

The aim of this paper is to establish necessary and sufficient algorithmic conditions to guarantee that an algebra is actually a 3-dimensional skew polynomial algebra in the sense of Bell and Smith.

Degree distributions of graph representations for compact urban patterns are scale-dependent. Therefore, the degree statistics alone does not give us the enough information to reach a qualified conclusion on the structure of urban spatial…

The Hilbert scheme of projective 3-folds of codimension 3 or more that are linear scrolls over the projective plane or over a smooth quadric surface or that are quadric or cubic fibrations over the projective line is studied. All known such…

This manuscript presents a general recursive formula to estimate the size of fibers associated with algebraic maps from graphs to summary statistics of importance for social network analysis, such as number of edges (graph density), degree…

We introduce a numerical method for reconstructing a multidimensional surface using the gradient of the surface measured at some values of the coordinates. The method consists of defining a multidimensional spline function and minimizing…

This survey gives a brief overview of theoretically and practically relevant algorithms to compute geodesic paths and distances on three-dimensional surfaces. The survey focuses on polyhedral three-dimensional surfaces.

More precise estimation of the greedy algorithm complexity for a special case of the set cover problem is given in this paper.

We study several natural instances of the geometric hitting set problem for input consisting of sets of line segments (and rays, lines) having a small number of distinct slopes. These problems model path monitoring (e.g., on road networks)…

The problem of categorical data analysis in high dimensions is considered. A discussion of the fundamental difficulties of probability modeling is provided, and a solution to the derivation of high dimensional probability distributions…

We give an algorithm for a surgery description of a $p$-fold cyclic branched cover of $B^3$ branched along a tangle. We generalize constructions of Montesinos and Akbulut-Kirby.

In this paper I present several novel, efficient, algorithmic techniques for solving some multidimensional geometric data management and analysis problems. The techniques are based on several data structures from computational geometry…

Although Bayesian density estimation using discrete mixtures has good performance in modest dimensions, there is a lack of statistical and computational scalability to high-dimensional multivariate cases. To combat the curse of…

We present all Belyi maps P^1(C) -> P^1(C) having almost simple primitive monodromy groups (not isomorphic to A_n or S_n) containing rigid and rational generating triples of degree between 50 and 250. This also leads to new polynomials…

We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in $X$ and $Y$ are low with respect to their genera. The finite base fields $\FF_q$ are arbitrary, but their sizes…

We present an approach to a large class of enumerative problems concerning rational curves in projective spaces. This approach uses analysis to obtain topological information about moduli spaces of stable maps. We demonstrate it by…

In the field of algebraic systems biology, the number of minimal polynomial models constructed using discretized data from an underlying system is related to the number of distinct reduced Gr\"obner bases for the ideal of the data points.…

Extracting planes from a 3D scene is useful for downstream tasks in robotics and augmented reality. In this paper we tackle the problem of estimating the planar surfaces in a scene from posed images. Our first finding is that a surprisingly…

We characterize the number of points for which there exist non-empty Terracini sets of points in $\mathbb{P}^n$. Then we study minimally Terracini finite sets of points in $\mathbb{P}^n$ and we obtain a complete description in the case of…

The problem of covering random points in a plane with sets of a given shape has several practical applications in communications and operations research. One especially prominent application is the coverage of randomly-located points of…

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to…