Related papers: A Database of Belyi Maps
A branched covering map of surfaces induces a map in the opposite direction between their arc complexes. We represent a branched covering map combinatorially using what we call a lifting picture, and use this representation to computably…
We compute the number of (weak) equivalence classes of branched covers from a surface of genus g to the sphere, with 3 branching points, degree 2k, and local degrees over the branching points of the form (2,...,2), (2h+1,1,2,...,2),…
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines,…
Four-dimensional CFTs dual to branes transverse to toric Calabi-Yau threefolds have been described by bipartite graphs on a torus (dimer models). We use the theory of dessins d'enfants to describe these in terms of triples of permutations…
Tracking of plant cells in images obtained by microscope is a challenging problem due to biological phenomena such as large number of cells, non-uniform growth of different layers of the tightly packed plant cells and cell division.…
We present an algorithm for detecting basepoints of linear series of curves in the plane. Moreover, we give an algorithm for constructing a linear series of curves in the plane for given basepoints. The underlying method of these algorithms…
In this short note, a new computation of the degree of the locus of 3-nodal plane curves in the linear system of degree d plane curves is given. The answer is expressed as a tautological class on a blow-up of the Hilbert scheme of 3 points…
In this work, we describe a method for large-scale 3D cell-tracking through a segmentation selection approach. The proposed method is effective at tracking cells across large microscopy datasets on two fronts: (i) It can solve problems…
We study a class of graphs with finitely many edges in order to understand the nature of the formal logarithm of the generating series for Severi degrees in elementary combinatorial terms. These graphs are related to floor diagrams…
Multi-way tables with specified marginals arise in a variety of applications in statistics and operations research. We provide a comprehensive complexity classification of three fundamental computational problems on tables: existence,…
This is the sequel to arXiv:math/0001089. In this paper, we complete the promised description of moduli of abelian surfaces of low degree, covering the cases of degree (1,12), (1,14), (1,16), (1,18) and (1,20). In each case, we describe…
We collect various known results (about plane curves and the moduli space of stable maps) to derive new recursive formulas enumerating low genus plane curves of any degree with various behaviors. Recursive formulas are given for the…
Three dimensional dendrites are studied with a coupled map lattice model. We study the fractal dimensions, the f(\alpha) spectrum, the size distribution of sidebranches, and the envelope formed by sidebranches.
With a bird's-eye view, we survey the landscape of Calabi-Yau threefolds, compact and non-compact, smooth and singular. Emphasis will be placed on the algorithms and databases which have been established over the years, and how they have…
This paper presents a Bayesian method for constructing Bayesian belief networks from a database of cases. Potential applications include computer-assisted hypothesis testing, automated scientific discovery, and automated construction of…
In this article we complete the work of enumerating typical abelian coverings of Cayley graphs, by reducing the problem to enumerating certain subgroups of finite abelian groups.
We develop a Belyi type theory that applies to Klein surfaces, i.e. (possibly non-orientable) surfaces with boundary which carry a dianalytic structure. In particular we extend Belyi's famous theorem from Riemann surfaces to Klein surfaces.
The paper proposes an image-guided depth completion method to estimate accurate dense depth maps with fast computation time. The proposed network has two-stage structure. The first stage predicts a first depth map. Then, the second stage…
Let $k$ be a finite field extension of the function field $\bfF_p(T)$ and $\bar{k}$ its algebraic closure. We count points in projective space $\Bbb P ^{n-1}(\bar{k})$ with given height and of fixed degree $d$ over the field $k$. If…
In this (mostly) survey article, we give a synopsis of a number of results relating to Brill--Noether theory on curves and metric graphs, together with some speculations about the behavior of one-dimensional linear series on a class of…