Related papers: How to Reconstruct a Planar Map From its Branching…

This work proposes an algorithm for explicitly constructing a pair of neural networks that linearize and reconstruct an embedded submanifold, from finite samples of this manifold. Our such-generated neural networks, called Flattening…

We present and discuss different algorithms for converting rectangular imagery into elliptical regions. We mainly focus on methods that use mathematical mappings with explicit and invertible equations. The key idea is to start with…

In this work, we study the perception problem for sampled surfaces (possibly with boundary) using tools from computational topology, specifically, how to identify their underlying topology starting from point-cloud samples in space, such as…

We consider a modified notion of planarity, in which two nations of a map are considered adjacent when they share any point of their boundaries (not necessarily an edge, as planarity requires). Such adjacencies define a map graph. We give…

In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…

We present algorithms for reconstructing, up to unavoidable projective automorphisms, surfaces with ordinary singularities in three dimensional space starting from their silhouette, or "apparent contour" - namely the branching locus of a…

In this paper we construct developable surface patches which are bounded by two rational or NURBS curves, though the resulting patch is not a rational or NURBS surface in general. This is accomplished by reparameterizing one of the boundary…

Landmarks have long played a pivotal role in automated planning, serving as crucial elements for improving the planning algorithms. The main limitation of classical landmark extraction methods is their sensitivity to specific planning…

A two-dimensional tomographic problem is studied. The target is assumed to be a homogeneous object bounded by a smooth curve. A Non Uniform Rational Basis Splines (NURBS) curve is used as computational representation of the boundary. This…

Planar polynomial automorphisms are polynomial maps of the plane whose inverse is also a polynomial map. A map is reversible if it is conjugate to its inverse. Here we obtain a normal form for automorphisms that are reversible by an…

Any graph which is not vertex transitive has a proper induced subgraph which is unique due to its structure or the way of its connection to the rest of the graph. We have called such subgraph as an anchor. Using an anchor which, in fact, is…

In this article we describe a program -- called planar_draw -- to draw maps on oriented surfaces in the plane. The drawings are coded as tikz files that can easily be manipulated and used in latex documents. Next to plane maps -- a case for…

We introduce a learning framework for automated floorplan generation which combines generative modeling using deep neural networks and user-in-the-loop designs to enable human users to provide sparse design constraints. Such constraints are…

The pathway is a biological term that refers to a series of interactions between molecules in a cell that causes a certain product or a change in the cell. Pathway analysis is a powerful method for gene expression analysis. Through pathway…

In this paper, we present an algorithm for reparametrizing algebraic plane curves from a numerical point of view. That is, we deal with mathematical objects that are assumed to be given approximately. More precisely, given a tolerance…

In the context of complex algebraic varieties, the decomposition theorem for semi-small maps provides a decomposition of the direct image of the constant sheaf. In this work, we develop a decomposition theorem for branched coverings of…

Let X be a nonsingular projective algebraic variety, and let S be a line bundle on X. Let A = (a_1,..., a_n) be a vector of integers. Consider a map f from a pointed curve (C,x_1,...,x_n) to X satisfying the following condition: the line…

Rectangular layouts, subdivisions of an outer rectangle into smaller rectangles, have many applications in visualizing spatial information, for instance in rectangular cartograms in which the rectangles represent geographic or political…

We develop a theory of residues for arithmetic surfaces, establish the reciprocity law around a point, and use the residue maps to explicitly construct the dualizing sheaf of the surface. These are generalisations of known results for…

In this paper, we investigate the possibility of constructing isomonodromic deformations of logarithmic connections on curves by using ramified covers. We give new examples and prove a classification result.